mm-4059
===
Subject: Even Functions?
How do I tell if a function is even?
I understand that a function is even if f(x) = f(-x), but how, for example,
could I tell if (x^3 - x)^4(x^2 + 1)^3 or (x^2 + 1)^3 is even or not?
===
Subject: Re: Even Functions?
>I understand that a function is even if f(x) = f(-x), but how, for
example,
>could I tell if (x^3 - x)^4(x^2 + 1)^3 or (x^2 + 1)^3 is even or not?
Substitute -x in for x, and try to simplify to the original
equation.
===
Subject: Re: Even Functions?
> How do I tell if a function is even?
> I understand that a function is even if f(x) = f(-x), but how, for
> example, could I tell if (x^3 - x)^4(x^2 + 1)^3 or (x^2 + 1)^3 is even or
> not?
Replace x in the expression by -x and then move the minus signs around 
until
you either get back to the original expression or you figure out that this
is impossible to do.
Also you can use properties of even and odd functions such as, (1) a 
product
of two even functions or two odd functions is even and a product of an even
and an odd function is odd, (2) A sum of even or odd functions is even or
odd respectively and the sum of an even and an odd function is neither even
nor odd unless one of them is identically 0, (3) constant functions are
even, (4) the identity map (x) is odd.
Have a tolerable existence. Eli
===
Subject: Re: Even Functions?
Adjunct Assistant Professor at the University of Montana.
>How do I tell if a function is even?
>I understand that a function is even if f(x) = f(-x), but how, for
example,
>could I tell if (x^3 - x)^4(x^2 + 1)^3 or (x^2 + 1)^3 is even or not?
Check to see if f(-x) is the same as f(x).
In the second case, f(x) = (x^2+1)^3, we have
f(-x) = ((-x)^2 + 1)^3 = (x^2+1)^3 = f(x) for all x, because
(-x)^2=x^2.
So f(x) is even.
In the former case, you have
g(x) = (x^3-x)^4 (x^2+1)^3.
g(-x) = ( (-x)^3 - (-x))^4 ( (-x)^2 + 1)^3
= (-x^3 + x)^4 (x^2+1)^3
= (-(x^3-x))^4 (x^2+1)^3
= (x^3-x)^4 (x^2+1)^3 (because (-a)^4 = a^4)
= g(x)
so for all x, g(-x)=g(x), and therefore the function is even.
To show a function is not even (e.g., h(x) = (x^3-x)^3), then exhibit
two points, a and -a, such that h(a) is not equal to h(-a). In the
example h(x) = (x^3-x)^3, note that
h(2) = (8-2)^3 = 6^3
and
h(-2) = (-8+2)^3 = -6^3
so h(2) is not equal to h(-2), and therefore h is not even.
===
Subject: Re: Even Functions?
>How do I tell if a function is even?
>I understand that a function is even if f(x) = f(-x), but how, for
example,
>could I tell if (x^3 - x)^4(x^2 + 1)^3 or (x^2 + 1)^3 is even or not?
> Check to see if f(-x) is the same as f(x).
> In the second case, f(x) = (x^2+1)^3, we have
> f(-x) = ((-x)^2 + 1)^3 = (x^2+1)^3 = f(x) for all x, because
> (-x)^2=x^2.
> So f(x) is even.
> In the former case, you have
> g(x) = (x^3-x)^4 (x^2+1)^3.
> g(-x) = ( (-x)^3 - (-x))^4 ( (-x)^2 + 1)^3
> = (-x^3 + x)^4 (x^2+1)^3
How did you go from the above....
> = (-(x^3-x))^4 (x^2+1)^3
... to the above....? Where did the extra brackets come from and why did
+
x become - x?
> = (x^3-x)^4 (x^2+1)^3 (because (-a)^4 = a^4)
... then to the above...? I thought (-a)^3 = (-a)^3 so where did the
negative go?
> = g(x)
> so for all x, g(-x)=g(x), and therefore the function is even.
need some further clarification.
===
Subject: Re: Even Functions?
>How do I tell if a function is even?
I understand that a function is even if f(x) = f(-x), but how, for
> example,
>could I tell if (x^3 - x)^4(x^2 + 1)^3 or (x^2 + 1)^3 is even or not?
> Check to see if f(-x) is the same as f(x).
> In the second case, f(x) = (x^2+1)^3, we have
> f(-x) = ((-x)^2 + 1)^3 = (x^2+1)^3 = f(x) for all x, because
> (-x)^2=x^2.
> So f(x) is even.
> In the former case, you have
> g(x) = (x^3-x)^4 (x^2+1)^3.
> g(-x) = ( (-x)^3 - (-x))^4 ( (-x)^2 + 1)^3
> = (-x^3 + x)^4 (x^2+1)^3
> How did you go from the above....
> = (-(x^3-x))^4 (x^2+1)^3
> ... to the above....? Where did the extra brackets come from and why did
+
> x become - x?
-x^3 + 3 = -(x^3 - x)
He just used the distributive property. The minus sign out
front can be considered a multiplication by -1. He factored
out -1 from each term, which changes the sign of each.
Thus:
-(a+b) = -a - b
-(a-b) = -a - (-b) = -a + b
and -(x^3-x) = -x^3 - (-x) = -x^3 + x
It looks like you need to review some elementary algebra.
> = (x^3-x)^4 (x^2+1)^3 (because (-a)^4 = a^4)
> ... then to the above...? I thought (-a)^3 = (-a)^3 so where did the
> negative go?
Elementary algebra again. You had:
[-(x^3 + 3)]^4 = (-1)^4 * (x^3+3)^4
and (-1)^4 = 1
Here the elementary fact is:
(ab)^m = a^m * b^m
> = g(x)
> so for all x, g(-x)=g(x), and therefore the function is even.
> need some further clarification.
Before tackling this kind of thing, you need to be so
comfortable with the elementary stuff that you can do it
in your sleep. Review material on simplifying complicated
algebraic expressions.
- R
===
Subject: Re: Even Functions?
> Before tackling this kind of thing, you need to be so
> comfortable with the elementary stuff that you can do it
> in your sleep. Review material on simplifying complicated
> algebraic expressions.
off.
===
Subject: Re: Mean of a random variable
>:>Is it possible that for a continuous random variable the following
holds:
>:>E[x]=integral_0^infty{1-F(x)} where F(x)=c.d.f.
>: More than just possible. Use integration by parts. It should be true
for
>: any distribution (continuous or not) supported on the nonnegative reals,
>: such that (1-F(x)) x -> 0 as x -> +infinity.
That condition is necessary but not sufficient for the
finiteness of the integral. The integral is infinite if and
only if the expectation does not exist. If the product
does not converge to 0, there exist c_n with c_n >= 2 c_{n-1}
and also (1-F(c_n))c_n >= h > 0. Then (1-F(x)) >= h/c_n on the
interval (c_{n-1}, c_n), so its integral on that interval is at
least h/2.
That it is not sufficient, take F(x) = 1 - e/[(e+x)ln(e+x)].
Then the indefinite integral of (1-F(x)) is ln(ln(e+x)), which
diverges.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
===
Subject: Re: moded out (was: algebra index problem.....
> which elements of this quotient need to be moded out to get
>> Is that the usual spelling, moded?
> Don't know. It's really more slang than actual English anyway,
> (we mod out by...), and I think I've always used the present tense
> in any written papers I've ever submitted. I guess it should be
mod-ed
> or something...
Below are counts of papers using tenses of {factor, mod, quotient} out.
xy out | -s -ding -ing -ded -ed | Total
--------+------------------------+-----
factor | 40 139 67 | 246
mod | 17 30 2 15 0 | 64
quotient| 6 15 2 | 23
So it seems authors greatly favor the double-d spelling,
i.e. modding out (30) vs. moding out (2)
modded out (15) vs. moded out (0)
Interestingly, most all of the matches occur in reviews
on physics or closely related fields, perhaps reflecting
an innate bias towards an active vs. passive viewpoint.
Such active views amount to < 12% of the 2854 reviews
with passive terms quotient group or factor group.
-Bill Dubuque
===
Subject: Re: moded out (was: algebra index problem.....
> which elements of this quotient need to be moded out to get
> Is that the usual spelling, moded?
>> Don't know. It's really more slang than actual English anyway,
>> (we mod out by...), and I think I've always used the present tense
>> in any written papers I've ever submitted. I guess it should be
mod-ed
>> or something...
> Below are counts of papers using tenses of {factor, mod, quotient}
out.
> xy out | -s -ding -ing -ded -ed | Total
> --------+------------------------+-----
> factor | 40 139 67 | 246
> mod | 17 30 2 15 0 | 64
> quotient| 6 15 2 | 23
> So it seems authors greatly favor the double-d spelling,
> i.e. modding out (30) vs. moding out (2)
> modded out (15) vs. moded out (0)
> Interestingly, most all of the matches occur in reviews
> on physics or closely related fields, perhaps reflecting
> an innate bias towards an active vs. passive viewpoint.
> Such active views amount to < 12% of the 2854 reviews
> with passive terms quotient group or factor group.
It is standard in English to double the letter when appending
a suffix to indicate that the short vowel sound is being retained
e.g. bated vs batted. But there are exceptions -- happened for one.
In this case, the only acceptable spelling is modded/modding.
--
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Needless to say, I had the last laugh.
Partridge, _Bouncing Back_ (14 times)
===
Subject: Re: moded out (was: algebra index problem.....
> Below are counts of papers using tenses of {factor, mod, quotient}
out.
Here's another strange question.
In England do they say factorize out ??
--
http://www.math.ohio-state.edu/~edgar/
===
Subject: Re: moded out (was: algebra index problem.....
>> Below are counts of papers using tenses of {factor, mod, quotient}
>> out.
> Here's another strange question.
> In England do they say factorize out ??
I don't recall hearing that. Is that what they say in N. America?
--
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Needless to say, I had the last laugh.
Partridge, _Bouncing Back_ (14 times)
===
Subject: Re: moded out (was: algebra index problem.....
> It is standard in English to double the letter when appending
> a suffix to indicate that the short vowel sound is being retained
> e.g. bated vs batted. But there are exceptions -- happened for one.
> In this case, the only acceptable spelling is modded/modding.
Another unusual exception: busing, bussing (they don't mean the same
thing!) Twenty years ago there were (perhaps mythological) newspaper
headlines about forced bussing for schoolchildren.
--
http://www.math.ohio-state.edu/~edgar/
===
Subject: Re: moded out (was: algebra index problem.....
...
> It is standard in English to double the letter when appending
> a suffix to indicate that the short vowel sound is being retained
> e.g. bated vs batted. But there are exceptions -- happened for one.
> In this case, the only acceptable spelling is modded/modding.
Isn't the exception (just like a similar exception in Dutch) that it is
(perhaps sometimes) not doubled if the syllable has no stress? In Dutch
the no-double rule comes in play when the last syllable of the base
word has an (unstressed) schwa.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland,
+31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
===
Subject: Re: Conditional Expectaion Question
> [...]
> Robert/Stephen,
> haven't gotten it yet, though.
> Robert, the steps in your approach above look simple and direct. The
> hard part would seem to be showing that E[XY|X] = XE[Y|X]. At least
> this is what I'm having a hard time showing.
> I can see intuitively that the composite RV XY will turn into a
> simple constant times the RV Y if X is given. (A note on notation:
> I think the notation should really read E[XY|x], where X is the
> random variable (i.e., the *function* mapping the elements in the
> sample space to the real numbers) and x is a real number in the
> range of X. However, I can't express it mathematically. Can you
> help me there?
I assume that you are taking an applied stochastic
processes/probability models course, so I will avoid appealing to the
measure theoretic arguments here. (The measure theoretic approach to
conditional expectation is quite delicate and sophisticated.)
First note that E[X|Y] *is* correct notation: E[X|Y] is a random
variable (which depends on Y). You are probably more comfortable
with the notation
E[X| Y=y] (which presents some technical difficulties when Y is
continuous - you are conditioning on an event of probability 0).
Think of this as a function f(y), so that E[X|Y]= f(Y), a random
variable (a function of Y). Does that work for you?
As I have pointed out previously, it is a general property that
E[g(X)Y | X] = g(X) E[Y|X]. Your intuition is correct: When you are
given X, X acts like a constant. Does the following argument
convince you?
E[g(X)Y | X=x] = E[g(x)Y| X=x] = g(x)E[Y| X=x]
Now replace the scalar x with the random variable X. Or, if we let
f(x) = E[g(X)Y | X=x] = g(x)E[Y| X=x], then
E[g(X)Y | X] = f(X) = g(X) E[Y|X].
Stephen J. Herschkorn
===
Subject: Re: help with problem
> can somone help me out with this econ problem... I would appreciate it:
> assume an industry with two firms facin an inverse market demand of
> P=100-Q. The product is homogeneous, and each firm has a cost function of
> 600+10q+0.25q^2
> Assume firms agree to equally share the market.
Try sci.econ
--
Will Twentyman
email: wtwentyman at copper dot net
===
Subject: Erdos and Selfridge paper
I've been looking at the paper by Erdos and Selfridge titled The
Product of Consecutive Integers Is Never a Power and, like every other
math paper, it has been cleaned up and made incomprehensible to the
non-mathematician (me). So I'm going to need some clarification.
They define two theorems, the first stating The product of two or
more consecutive positive integers is never a power and the second
one stating Let k, l, n be integers k>=3, l>=2 and n+k>=p^k, where
p^k is the least prime satisfying p^k>=k. Then there is a prime p>=k
for which alpha sub p is not congruent to 0 (mod l), alpha sub p is
the power of p dividing (n+1)...(n+k).
As an example, suppose k=5, n =23, giving the sequence 24, 25, 26, 27,
28. In this case, would the least prime be 2 since 2^5 = 32? And what
would alpha sub p be in this example?
On the next page, they state a theorem of Sylvester and Schur that
there is always a prime greater than k which divides (n+1)...(n+k),
since n>k. Such a prime divides only one of the k factors, so
n+k>>=(K+1)^l, whence n>k^l.
In the example I gave above, k=5, n=23 and n+k>=(k+1)^l is true only
if l=1.
Is this a correct interpretation?
===
Subject: Re: Erdos and Selfridge paper
> I've been looking at the paper by Erdos and Selfridge titled The
> Product of Consecutive Integers Is Never a Power and, like every other
> math paper, it has been cleaned up and made incomprehensible to the
> non-mathematician (me). So I'm going to need some clarification.
> They define two theorems, the first stating The product of two or
> more consecutive positive integers is never a power and the second
> one stating Let k, l, n be integers k>=3, l>=2 and n+k>=p^k, where
> p^k is the least prime satisfying p^k>=k. Then there is a prime p>=k
> for which alpha sub p is not congruent to 0 (mod l), alpha sub p is
> the power of p dividing (n+1)...(n+k).
> As an example, suppose k=5, n =23, giving the sequence 24, 25, 26, 27,
> 28. In this case, would the least prime be 2 since 2^5 = 32? And what
> would alpha sub p be in this example?
The phrase, p^k is the least prime..., makes no sense, as p^k
isn't a prime (unless k = 1). Did you get the wording right? Or
did it perhaps say p is the least prime...?
Now no matter what k is, 2 is the least prime p satisfying
p^k greater than or equal to k, so if you've quoted it correctly,
p is always 2. That seems pretty silly. Can you check the paper
again and see whether you've got it right?
Also, if k = 5, and n = 23, and p = 2, then the condition
n + k greater than or equal to p^k is not met.
> On the next page, they state a theorem of Sylvester and Schur that
> there is always a prime greater than k which divides (n+1)...(n+k),
> since n>k. Such a prime divides only one of the k factors, so
> n+k>>=(K+1)^l, whence n>k^l.
What does >>= mean?
--
===
Subject: Re: Erdos and Selfridge paper
> They define two theorems, the first stating The product of two or
> more consecutive positive integers is never a power and the second
> one stating Let k, l, n be integers k>=3, l>=2 and n+k>=p^k, where
> p^k is the least prime satisfying p^k>=k. Then there is a prime p>=k
> for which alpha sub p is not congruent to 0 (mod l), alpha sub p is
> the power of p dividing (n+1)...(n+k).
The phrase, p^k is the least prime..., makes no sense, as p^k
> isn't a prime (unless k = 1). Did you get the wording right? Or
> did it perhaps say p is the least prime...?
> Now no matter what k is, 2 is the least prime p satisfying
> p^k greater than or equal to k, so if you've quoted it correctly,
> p is always 2. That seems pretty silly. Can you check the paper
> again and see whether you've got it right?
I'm looking at a Xerox copy of the paper as it appears in Illinois J.
Math, 1975, and that's exactly what it says. I'm thinking this might
be a typo and he actually means p is the least prime satisfying p^k>=
k. Wouldn't p^k ALWAYS be greater than k for any p>=2 and for any k>1?
> Also, if k = 5, and n = 23, and p = 2, then the condition
> n + k greater than or equal to p^k is not met.
That is certainly true, which makes their paper even more confusing.
> On the next page, they state a theorem of Sylvester and Schur that
> there is always a prime greater than k which divides (n+1)...(n+k),
> since n>k. Such a prime divides only one of the k factors, so
> n+k>>=(K+1)^l, whence n>k^l.
> What does >>= mean?
It means I made a typo. Delete one of the > signs.
I don't know if I mentioned the title of this paper, namely The
Product of Consecutive Integers Is Never a Power. I've been looking
for a proof of this theorem for a long time. Now that I've found it, I
don't understand it. (I'm not a mathematician, but I've had a
long-time interest in number theory.)
===
Subject: Re: EVIL is real (was: Re: Simple principle in core error proof)
: Now I'm informing all of you that the people arguing against me are
: EVIL, yes they are real, live EVIL people as mathematics is that
: important, so it's important enough for Evil itself to send minions
: like them.
Evil may be real, but that doesn't change the fact that
math is abstract. PEople who point out mistakes in
a chain of abstract reasoning do not become evil just because
the person making the mistakes is a good person or means well.
And even if the people pointing out the mistakes ARE evil,
that doesn't mean they're WRONG.
--
---
It's difficult ... you need to be united to have any
strength, but internal issues have to be addressed.
--- E. Ray Lewis, on liberalism in America
===
Subject: Roots of equation
If I have an equation x^4 - x^3 - 8x^2 + 12x and I know that (x - 2) is a
root of the equation, how do I work out the other factor?
Another example:
e.g. x^2 - 6x^2 - 8x + 24
= (x - 2)(x^3 + 2x^2 - 2x -12)
How do I get the (x^3 + 2x^2 - 2x -12) part from the knowing that 2 is a
root? Is there a technique for finding this equation?
===
Subject: Re: Roots of equation
>If I have an equation x^4 - x^3 - 8x^2 + 12x and I know that (x - 2) is a
>root of the equation, how do I work out the other factor?
>Another example:
>e.g. x^2 - 6x^2 - 8x + 24
>= (x - 2)(x^3 + 2x^2 - 2x -12)
>How do I get the (x^3 + 2x^2 - 2x -12) part from the knowing that 2 is a
>root? Is there a technique for finding this equation?
Here is a french poem explaining how to do do this. My (French)
father-in-law
once told me that this enabled him to solve problems of this type in
about 1/4 the time of everyone else, much to the mystification of his
teacher.
Division d'un polyn.99me par (x-a)
LE premier terme du quotient
A pour coefficient
le premier terme DU dividende.
UN terme quelconque du quotient
A pour coefficient
le coefficient du terme PR.83C.83DENT MULTIPLI.83 par a
AUQUEL on ajoute ALG.83BRAIQUEMENT
le coefficient du terme correspondant DU dividende.
Derek Holt.
===
Subject: Re: Roots of equation
>If I have an equation x^4 - x^3 - 8x^2 + 12x and I know that (x - 2) is a
>root of the equation, how do I work out the other factor?
You do a polynomial long division, which is exactly the same as for
numbers, see http://www.karlscalculus.org/notes.html#plongdiv
You should also immediately recognize 'x' as another factor.
>Another example:
>e.g. x^2 - 6x^2 - 8x + 24
>= (x - 2)(x^3 + 2x^2 - 2x -12)
>How do I get the (x^3 + 2x^2 - 2x -12) part from the knowing that 2 is a
>root? Is there a technique for finding this equation?
Same thing here, polynomial long division of (I assume) x^4 - 6x^2 -
8x + 24 divided by (x-2) = (x^3 + 2x^2 - 2x -12). You divide by (x-2)
because you know a root is x=2 which means x-2=0.
===
Subject: Re: Roots of equation
> If I have an equation x^4 - x^3 - 8x^2 + 12x and I know that (x - 2) is a
> root of the equation, how do I work out the other factor?
long division
> Another example:
> e.g. x^2 - 6x^2 - 8x + 24
You mean x^4 - 6x^2 - 8x + 24 ?
> = (x - 2)(x^3 + 2x^2 - 2x -12)
> How do I get the (x^3 + 2x^2 - 2x -12) part from the knowing that 2 is a
> root? Is there a technique for finding this equation?
long division
--
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Needless to say, I had the last laugh.
Partridge, _Bouncing Back_ (14 times)
===
Subject: Re: Roots of equation
> If I have an equation x^4 - x^3 - 8x^2 + 12x and I know that (x - 2) is
a
> root of the equation, how do I work out the other factor?
> long division
> Another example:
> e.g. x^2 - 6x^2 - 8x + 24
> You mean x^4 - 6x^2 - 8x + 24 ?
Yep I did.
> = (x - 2)(x^3 + 2x^2 - 2x -12)
> How do I get the (x^3 + 2x^2 - 2x -12) part from the knowing that 2 is
a
> root? Is there a technique for finding this equation?
> long division
===
Subject: Re: JSH: Simple math facts
P(m) = (5 a_1 + 7)(5 a_2 + 7)(5 a_3 + 7).
[...]
Therefore,
P(m)/(49) = (5 a_1/7 + 1)(5 a_2/7 + 1)(5 a_3 + 7)
follows from the *constant* terms.
It looks to me like it follows from simple division.
Ok, so P(m)/49 is that expression. Now what? What's your point?
V.
>>(5 a_1/7 + 1)(5 a_2/7 + 1)(5 a_3 + 7) =
>> 300125 m^3 - 18375 m^2 + 360 m + 22
>>where readers can see that the constant term is 22, which is coprime
>>to 7.
>> And.....? Why is this important?
>>1 as their constant term, while the third of the a's is 3 when m=0,
>>which gives the last factor as 22 as required.
>> I have no idea why you think this is significant. I'm not talking about
>> whether or not anyone agrees or disagrees, I'm just wondering why your
>> statement matters. So a_1(m) = 3, a_2(m) = a_3(m) = 0 when m = 0. So
>> what?
>The constant terms are independent of m, right? So any changes to
>them must occur without regard to the value of m.
>Here's a simpler example to illustrate the principle.
>Q(m) = (7m + 7)(7m + 7)(5m + 22)
>and notice that the constant term for Q(m) is 7(7)(22), and that Q(m)
>has 49 as a factor. But dividing by 49 gives
>Q(m)/49 = (m+1)(m+1)(5m + 22)
>and the constant term is now 22.
No kidding. You didn't answer my question. So the constant terms are
independent of m, so what? Why does this *MATTER*? Has someone claimed
that they do? Has someone claimed that they don't? What does this
have to do with your fundamental issue of the algebraic integers not being
complete?
In a well written proof I can look at statements and tell what they *mean*.
Not what they say (that's obvious) but why they are there in the proof and
how they lead towards the solution. I accept that the constant term goes
from 49*22 to 22 when dividing by 49, but I'm really not sure what this 
shows.
===
Subject: Re: JSH: Simple math facts
P(m) = (5 a_1 + 7)(5 a_2 + 7)(5 a_3 + 7).
[...]
Therefore,
P(m)/(49) = (5 a_1/7 + 1)(5 a_2/7 + 1)(5 a_3 + 7)
follows from the *constant* terms.
It looks to me like it follows from simple division.
Ok, so P(m)/49 is that expression. Now what? What's your point?
V.
>>(5 a_1/7 + 1)(5 a_2/7 + 1)(5 a_3 + 7) =
>> 300125 m^3 - 18375 m^2 + 360 m + 22
>>where readers can see that the constant term is 22, which is coprime
>>to 7.
>> And.....? Why is this important?
>>1 as their constant term, while the third of the a's is 3 when m=0,
>>which gives the last factor as 22 as required.
>> I have no idea why you think this is significant. I'm not talking
about
>> whether or not anyone agrees or disagrees, I'm just wondering why your
>> statement matters. So a_1(m) = 3, a_2(m) = a_3(m) = 0 when m = 0. So
>> what?
>The constant terms are independent of m, right? So any changes to
>them must occur without regard to the value of m.
>Here's a simpler example to illustrate the principle.
>Q(m) = (7m + 7)(7m + 7)(5m + 22)
>and notice that the constant term for Q(m) is 7(7)(22), and that Q(m)
>has 49 as a factor. But dividing by 49 gives
>Q(m)/49 = (m+1)(m+1)(5m + 22)
>and the constant term is now 22.
> No kidding. You didn't answer my question. So the constant terms are
> independent of m, so what? Why does this *MATTER*? Has someone claimed
> that they do? Has someone claimed that they don't? What does this
> have to do with your fundamental issue of the algebraic integers not
being
> complete?
What does it matter?
Well it means that
P(m)/49 factors as (5 a_1/7 + 1)(5 a_2/7 + 1)(5 a_3 + 7).
However, 5a_1/7 and 5a_2/7 are not algebraic integers for all m.
The point is that dividing by 49 is not an activity that is dependent
on m's value, so you have that one factorization, which gives the
correct constant terms of 1, 1, and 22.
> In a well written proof I can look at statements and tell what they
*mean*.
> Not what they say (that's obvious) but why they are there in the proof
and
> how they lead towards the solution. I accept that the constant term goes
> from 49*22 to 22 when dividing by 49, but I'm really not sure what this
shows.
>
Well you posters keep doing your best to *ignore* posts where I step
out the proof, and instead spend a LOT of effort apparently trying to
convince people that I'm wrong, without bothering to consider the
mathematical argument that I present step-by-step, which is telling.
You're playing a social game, dedicated to trying to hide the truth,
while I keep saying, hey, I can step it out, step-by-step, talk about
*each* and every aspect of the proof, and give context.
My take on it all is that mathematicians are, besides being
intellectually weak, running away from a truth they don't want to
accept.
But you know that you need to try and block others from accepting that
truth, or they'll force you to stop running.
So you keep posting in reply to me.
You have to keep posting in reply to me, because of the social game.
James Harris
===
Subject: Continuum Hypothesis
Where can I found a G.9adel's proof of the CH (hopefully the original
translated into English)?
I say proof because he didn't prove CH but rather proved that it
couldn't
dis/proved.
===
Subject: Re: Continuum Hypothesis
> Where can I found a G.9adel's proof of the CH (hopefully the
original
> translated into English)?
> I say proof because he didn't prove CH but rather proved that it
couldn't
> dis/proved.
He showed it cot be disproved. Only later the other case was done
by Cohen.
I believe you can find both cases in:
P. J. Cohen, Set Theory and the Continuum Hypothesis. New York: W. A.
Benjamin, 1966.
and if not, G.9adel's own book is in English:
K. G.9adel, The Consistency of the Continuum-Hypothesis. Princeton, NJ:
Princeton University Press, 1940.
--
http://www.math.ohio-state.edu/~edgar/
===
Subject: Re: Transcendental numbers
> I know that rational and irrational numbers are everywhere dense in
> the real number continuum, but what about transcendental numbers? Do
> intervals exist in the real number continuum that contain no
> transcendental numbers? Has this problem even been solved and is there
> a proof? (Maybe this belongs in another math group?)
> There are more transcententals in any real interval than rational
> or even algebraic numbers. Transcendentals are , if anything, more
> dense, since there are uncontably many in any real interval whereas
> there are only countably many algebraics (including the rationals).
By what mechanism can you count the algebraics?
===
Subject: Re: Transcendental numbers
I know that rational and irrational numbers are everywhere dense in
> the real number continuum, but what about transcendental numbers? Do
> intervals exist in the real number continuum that contain no
> transcendental numbers? Has this problem even been solved and is
there
> a proof? (Maybe this belongs in another math group?)
There are more transcententals in any real interval than rational
> or even algebraic numbers. Transcendentals are , if anything, more
> dense, since there are uncontably many in any real interval whereas
> there are only countably many algebraics (including the rationals).
> By what mechanism can you count the algebraics?
How many polynomials (with rational coefficients) of degree one are
there? They are of the form a_0 + a_1*x. There are countably many
possibilities for the constant term a_0, and countably many
possibilities for a_1, the coefficient of x. Countable times countable
is countable, so there are countably many degree 1 polys. Each has 1
root, so there are countably many numbers that are roots of degree 1
polys.
How many of degree two? Same logic applied to a_0 + a_1*x + a_2*x^2.
Countable times countable times countable is countable, so there are
countably many polys. Each poly has two roots, so that's countably many
possible roots.
Dot dot dot . . . there are countably many reals that are roots of polys
of degree 1, of degree 2, . . ., of degree n, . . .
Adding them all up, we get a countable sum of countable numbers, which
is countable.
===
Subject: Re: Transcendental numbers
I know that rational and irrational numbers are everywhere dense in
> the real number continuum, but what about transcendental numbers?
Do
> intervals exist in the real number continuum that contain no
> transcendental numbers? Has this problem even been solved and is
there
> a proof? (Maybe this belongs in another math group?)
There are more transcententals in any real interval than rational
> or even algebraic numbers. Transcendentals are , if anything, more
> dense, since there are uncontably many in any real interval whereas
> there are only countably many algebraics (including the rationals).
> By what mechanism can you count the algebraics?
> How many polynomials (with rational coefficients) of degree one are
> there? They are of the form a_0 + a_1*x. There are countably many
> possibilities for the constant term a_0, and countably many
> possibilities for a_1, the coefficient of x. Countable times countable
> is countable, so there are countably many degree 1 polys. Each has 1
> root, so there are countably many numbers that are roots of degree 1
> polys.
> How many of degree two? Same logic applied to a_0 + a_1*x + a_2*x^2.
> Countable times countable times countable is countable, so there are
> countably many polys. Each poly has two roots, so that's countably many
> possible roots.
> Dot dot dot . . . there are countably many reals that are roots of polys
> of degree 1, of degree 2, . . ., of degree n, . . .
> Adding them all up, we get a countable sum of countable numbers, which
> is countable.
One tiny thing you left that makes a world of difference: a polynomial must
be of finite degree. Otherwise you would be claiming the R is countable.
===
Subject: Re: Transcendental numbers
I know that rational and irrational numbers are everywhere dense
in
> the real number continuum, but what about transcendental numbers?
Do
> intervals exist in the real number continuum that contain no
> transcendental numbers? Has this problem even been solved and is
> there
> a proof? (Maybe this belongs in another math group?)
There are more transcententals in any real interval than
rational
> or even algebraic numbers. Transcendentals are , if anything,
more
> dense, since there are uncontably many in any real interval
whereas
> there are only countably many algebraics (including the rationals).
By what mechanism can you count the algebraics?
> How many polynomials (with rational coefficients) of degree one are
> there? They are of the form a_0 + a_1*x. There are countably many
> possibilities for the constant term a_0, and countably many
> possibilities for a_1, the coefficient of x. Countable times countable
> is countable, so there are countably many degree 1 polys. Each has 1
> root, so there are countably many numbers that are roots of degree 1
> polys.
> How many of degree two? Same logic applied to a_0 + a_1*x + a_2*x^2.
> Countable times countable times countable is countable, so there are
> countably many polys. Each poly has two roots, so that's countably
many
> possible roots.
> Dot dot dot . . . there are countably many reals that are roots of
polys
> of degree 1, of degree 2, . . ., of degree n, . . .
> Adding them all up, we get a countable sum of countable numbers, which
> is countable.
> One tiny thing you left that makes a world of difference: a polynomial
must
> be of finite degree. Otherwise you would be claiming the R is countable.
Well, there are infinitely many orders of finite-ordered polynomials.
Then there are infinitely many coefficients.
Then, what you are looking at there is N x N x N x ....
There are those and then some.
It's been discussed here that that's uncountable. That means here
that there may be a bijection between N x N x N x ... x N x ... and R.
Do you say the algebraics are countable? There exists a one-to-one
function from them to the Cartesian product N and itself infinitely
many times. The Cartesian product of N and itself infinitely many
times is uncountable, just ask Ullrich or Virgil.
What the hell, you might say.
Consider the polynomials, in particular the polynomial with integer
coefficients.
a_0
That's a constant, or a_0 x^0. There is one for each integer,
Z(-oo,oo).
Then let's consider another coefficient. Let's only worry about the
positive integers, Z+.
a_1 x^1 + a_0 x^0.
Then we have the Cartesian product Z+ x Z+ for each possible value of
a_1 and a_0, representing a subset of the polynomials of order 1 with
integer coefficients.
1 x^1 + 1 x^0
1 x^1 + 2 x^0
1 x^1 + 3 x^0
1 x^1 + ...
2 x^1 + 1 x^0
2 x^1 + ...
...
Keep in mind that any polynomial a_1 x_1 + a_0 x^0 has roots that are
roots of (a_1 x_1 + a_0 x^0) *r for real r, eg for coefficients
(a_1, a_2)=(1, 3) that polynomial has the same roots as for (2, 6),
(3, 9), (4, 12), etc.
Anyways, to represent a polynomial with two positive integer
coefficients we have the Cartesian product of Z+ x Z+.
Then, go on to the third coefficient, etcetera. You might immediately
notice that that set of polynomials can be represented by Z+ x Z+ x Z+
..., one coordinate for each coefficient.
The polynomial has finite rank, or order, degree, and its rank can
range from zero to infinity. That's very similar to an integer, an
integer is finite, but there are infinitely many of them. The
polynomials rank is an integer.
So what we get then to represent only all polynomials with positive
integer coefficients is the Cartesian product Z+ x Z+ x Z+ x ...,
which has been claimed to be uncountable.
What's up with that?
Ross
===
Subject: Re: Transcendental numbers
> I know that rational and irrational numbers are everywhere dense
in
> the real number continuum, but what about transcendental
numbers?
> Do
> intervals exist in the real number continuum that contain no
> transcendental numbers? Has this problem even been solved and
is
> there
> a proof? (Maybe this belongs in another math group?)
There are more transcententals in any real interval than
rational
> or even algebraic numbers. Transcendentals are , if anything,
more
> dense, since there are uncontably many in any real interval
whereas
> there are only countably many algebraics (including the
rationals).
By what mechanism can you count the algebraics?
How many polynomials (with rational coefficients) of degree one are
> there? They are of the form a_0 + a_1*x. There are countably many
> possibilities for the constant term a_0, and countably many
> possibilities for a_1, the coefficient of x. Countable times
countable
> is countable, so there are countably many degree 1 polys. Each has 1
> root, so there are countably many numbers that are roots of degree 1
> polys.
How many of degree two? Same logic applied to a_0 + a_1*x + a_2*x^2.
> Countable times countable times countable is countable, so there are
> countably many polys. Each poly has two roots, so that's countably
many
> possible roots.
Dot dot dot . . . there are countably many reals that are roots of
polys
> of degree 1, of degree 2, . . ., of degree n, . . .
Adding them all up, we get a countable sum of countable numbers,
which
> is countable.
> One tiny thing you left that makes a world of difference: a polynomial
must
> be of finite degree. Otherwise you would be claiming the R is
countable.
> Well, there are infinitely many orders of finite-ordered polynomials.
Makes no sense.
> Then there are infinitely many coefficients.
> Then, what you are looking at there is N x N x N x ....
NxNxN . . . is not the polynomials, it's the ring of formal power
series. The polynomials are N+N+N+... where '+' means direct sum. In
an infinite direct sum of rings, all but finitely many terms of any
element are zero. That's what makes polynomials polynomials. Otherwise
they'd be power series.
> There are those and then some.
> It's been discussed here that that's uncountable. That means here
> that there may be a bijection between N x N x N x ... x N x ... and R.
Well yes there is, but that has nothing to do with algebraic numbers or
polynomials.
> Do you say the algebraics are countable?
Yes.
There exists a one-to-one
> function from them to the Cartesian product N and itself infinitely
> many times.
No, that's not true. The direct sum of countably many copies of N is
countable. The direct product is not.
The Cartesian product of N and itself infinitely many
> times is uncountable, just ask Ullrich or Virgil.
I agree. But the Cartesian product of countably many copies of N gives
you the formal power series, not polynomials.
> What the hell, you might say.
Yeah, you got me there.
> Consider the polynomials, in particular the polynomial with integer
> coefficients.
> a_0
> That's a constant, or a_0 x^0. There is one for each integer,
> Z(-oo,oo).
> Then let's consider another coefficient. Let's only worry about the
> positive integers, Z+.
> a_1 x^1 + a_0 x^0.
> Then we have the Cartesian product Z+ x Z+ for each possible value of
> a_1 and a_0, representing a subset of the polynomials of order 1 with
> integer coefficients.
> 1 x^1 + 1 x^0
> 1 x^1 + 2 x^0
> 1 x^1 + 3 x^0
> 1 x^1 + ...
> 2 x^1 + 1 x^0
> 2 x^1 + ...
> ...
> Keep in mind that any polynomial a_1 x_1 + a_0 x^0 has roots that are
> roots of (a_1 x_1 + a_0 x^0) *r for real r, eg for coefficients
> (a_1, a_2)=(1, 3) that polynomial has the same roots as for (2, 6),
> (3, 9), (4, 12), etc.
> Anyways, to represent a polynomial with two positive integer
> coefficients we have the Cartesian product of Z+ x Z+.
> Then, go on to the third coefficient, etcetera. You might immediately
> notice that that set of polynomials can be represented by Z+ x Z+ x Z+
> ..., one coordinate for each coefficient.
> The polynomial has finite rank, or order, degree, and its rank can
> range from zero to infinity. That's very similar to an integer, an
> integer is finite, but there are infinitely many of them. The
> polynomials rank is an integer.
> So what we get then to represent only all polynomials with positive
> integer coefficients is the Cartesian product Z+ x Z+ x Z+ x ...,
> which has been claimed to be uncountable.
> What's up with that?
You are confused about the distinction between a direct product and a
direct sum. In a direct sum, all but finitely terms are zero. So for
example in the countable direct sum of N, (1,1,1,1,0,0,0,0,0,0,0...) is
an element, but (1,1,1,1,1...) is not.
===
Subject: Re: Transcendental numbers
I know that rational and irrational numbers are everywhere dense
in
> the real number continuum, but what about transcendental numbers?
Do
> intervals exist in the real number continuum that contain no
> transcendental numbers? Has this problem even been solved and is
> there
> a proof? (Maybe this belongs in another math group?)
There are more transcententals in any real interval than
rational
> or even algebraic numbers. Transcendentals are , if anything,
more
> dense, since there are uncontably many in any real interval
whereas
> there are only countably many algebraics (including the rationals).
By what mechanism can you count the algebraics?
> How many polynomials (with rational coefficients) of degree one are
> there? They are of the form a_0 + a_1*x. There are countably many
> possibilities for the constant term a_0, and countably many
> possibilities for a_1, the coefficient of x. Countable times countable
> is countable, so there are countably many degree 1 polys. Each has 1
> root, so there are countably many numbers that are roots of degree 1
> polys.
> How many of degree two? Same logic applied to a_0 + a_1*x + a_2*x^2.
> Countable times countable times countable is countable, so there are
> countably many polys. Each poly has two roots, so that's countably
many
> possible roots.
> Dot dot dot . . . there are countably many reals that are roots of
polys
> of degree 1, of degree 2, . . ., of degree n, . . .
> Adding them all up, we get a countable sum of countable numbers, which
> is countable.
> One tiny thing you left that makes a world of difference: a polynomial
must
> be of finite degree. Otherwise you would be claiming the R is countable.
There is no such thing as an infinite degree polynomial. You're
thinking of formal power series.
===
Subject: Re: Transcendental numbers
> I know that rational and irrational numbers are everywhere dense in
> the real number continuum, but what about transcendental numbers? Do
> intervals exist in the real number continuum that contain no
> transcendental numbers? Has this problem even been solved and is
there
> a proof? (Maybe this belongs in another math group?)
> There are more transcententals in any real interval than rational
> or even algebraic numbers. Transcendentals are , if anything, more
> dense, since there are uncontably many in any real interval whereas
> there are only countably many algebraics (including the rationals).
> By what mechanism can you count the algebraics?
By counting their polynomials. Any (rational) polynomial has a finite
number of a_i and a countable number of choices for each a_i, so
(N_0)^n=N_0.
>
===
Subject: Re: Help rearranging equations
> I was wondering if any charitable person might give me some pointers
> on rearranging the following equations.
> (1) -Tsin(u)sin(v) = ML(u''cos(u)sin(v) + v''sin(u)cos(v) -
> u'^2sin(u)sin(v) - v'^2sin(u)sin(v) + 2u'v'cos(u)cos(v))
> (2) Tcos(u) - MG = ML(u''sin(u) + u'^2cos(u))
> (3) -Tsin(u)cos(v) = ML(u''cos(u)cos(v) - v''sin(u)sin(v) -
> u'^2sin(u)cos(v) - v'^2sin(u)cos(v) - 2u'v'cos(u)sin(v))
> I have got this far with my problem, but my mathematical juices have
> run dry.
> T, M, L and G are constants, however T is unknown so I would like to
> get rid of it. Similarly I expect M to disappear at some point in the
> rearrangement.
Multiply equation (1) by cos(u) and equation (2) by (sin(u) sin(v))
then add equations (left side to left side and right side to right
side) to get an equation without T in it.
Similarly, multiply equation (1) by cos(v) and equation (3) by
-sin(v) and add equations to get a second equation without T in it.
This system of two (new) equations does not contain T, but, together
with any one of the original equations, is a system or equations
equivalent to the original system of equations.
A similar, but more complicated, method applied to the two new
equations will give a single without M in it, since all the
equations are linear (at least as equations in T and M).
===
Subject: Math dependency logic
One of the more odd things that can happen when you deal with a
discoverer is that you find that things you thought were simple,
suddenly seem complicated and iffy. So I'm now facing a problem where
people are doubting algebra, which leads to the fun question of, just
what is the logic here?
The issue has to do with a factor like x+2 and how you know that 2 is
constant.
If the logic is expanded upon, my hope is that many of you will
realize what is happening in my core error proof, and quit doubting,
if you are doubting, as if you're not, and understand it, then that's
another problem entirely.
Ok, so how do you know that with even a polynomial factor, like x+2,
that 2 is *constant* and not related to x?
What's the mathematical logic?
I've talked about setting x=0, which would reveal the constant factor
which you can look at, and I think that for some of you, the ability
to *physically* see constants in polynomial factors, has left you
without ever knowing the *why* behind how it works.
How about this?
There are an infinity of number and letter combinations, of which x+2
is just one of that infinity. If you set x=2 though, you just have 2,
so how do you know from whence it came?
I mean, with just 2, well, it's just 2, so there's no reference back
to x, or y, or any other of that infinity of possibilities.
The answer is that 2 is just a number that has no other information
except itself.
Logically, you can say that 2 is *independent* of any particular
variable, even if it's associated with it, like in an expression like
x+2.
Now, as 0 clears out variables set to 0, you can show independent
terms by setting a particular value to 0, as that reveals everything
that can be associated with an infinity of other things.
It's like how it could be y+2, or z+2, or alpha + 2, as seeing just 2,
doesn't tell you anything about an association.
Possibly the problem for some of you is that you *remember* the
previous association. That is, you know that you had x+2, then you
set x=0, so in your mind you see a phantom x that holds the
association.
That's ok, but it doesn't have a *mathematical* reality because your
memory is irrelevant.
The reality is that as far as the math is concerned 2 is a number that
can be by itself or associated with x or an infinity of other things,
and the math isn't going to pick or choose based on what YOU remember.
It handles all possibilities at once.
And with *just* a number, it sees independence.
That's why setting a variable to 0 is such a useful and powerful tool,
as it reveals infinite possibilities by removing a particular
association.
My argument works on that principle, as by setting x or m, depending
on what I'm calling the variable, I find that I have 7, 7 and 22 as
*constant* terms for factors of a polynomial.
I also know that polynomial has a factor that is constant as that
factor is 49.
When I divide the polynomial by 49 I have constant terms of 1, 1, and
22, which tells me something.
Now those numbers don't care about x or m. They don't *know* about x
or m, but you may remember them, so you think your memory has some
effect, but the math sees *infinite* possibility, while you may fixate
on an association you remember.
In the realm of infinite possibility, it's not possible for 7, 7, and
22 to go to 1, 1, and 22 based on the value of x, where they check it
first to decide how they'll behave, because they're just NUMBERS, and
they don't have enough data associated with them to be making those
kinds of decisions.
It's like, if human beings on earth constrain 7, 7 and 22 so that they
have to worry about the value of x and m, then, wow, we've affected
all reality in all dimensions and all possibilities, just with our
MEMORY of there being an x or m associated in some interesting
expression.
But, of course, your thoughts don't constrain those numbers as they
keep operating quite well throughout Totality, despite what you may
believe, or remember.
Just remember that when you're considering the issue of constants in a
math argument.
James Harris
===
Subject: Re: Math dependency logic
> The issue has to do with a factor like x+2 and how you know that 2 is
> constant.
And does 2 + 2 = 5, for very large values of 2?
===
Subject: Re: Math dependency logic
>One of the more odd things that can happen when you deal with a
>discoverer is that you find that things you thought were simple,
>suddenly seem complicated and iffy. So I'm now facing a problem where
>people are doubting
me, <snipwhich leads to the fun question of, just
>what is the logic here?
Excelent question. :)
Jim
===
Subject: Re: Math dependency logic
> One of the more odd things that can happen when you deal with a
> discoverer is that you find that things you thought were simple,
> suddenly seem complicated and iffy. So I'm now facing a problem where
> people are doubting algebra, which leads to the fun question of, just
> what is the logic here?
> The issue has to do with a factor like x+2 and how you know that 2 is
> constant.
Nope, the issue has to do with constant terms of non-polynomials.
What is the constant term of sqrt(1 + x) + sqrt(1 - x) + 1?
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland,
+31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
===
Subject: Re: Math dependency logic
Adjunct Assistant Professor at the University of Montana.
> One of the more odd things that can happen when you deal with a
> discoverer is that you find that things you thought were simple,
> suddenly seem complicated and iffy. So I'm now facing a problem where
> people are doubting algebra, which leads to the fun question of, just
> what is the logic here?
The issue has to do with a factor like x+2 and how you know that 2 is
> constant.
>Nope, the issue has to do with constant terms of non-polynomials.
>What is the constant term of sqrt(1 + x) + sqrt(1 - x) + 1?
I think it has two things really: one is something James let slip
recently: he thinks that if a function is 0 at x, then it has a
factor of x somewhere. This is in analogy to a polynomial, of course,
where if P(x)=0, then there exists a polynomial Q(x) such that
P(x)=x*Q(x). He realizes this is not the case for general functions,
but he figures there must be some y, factor of x, such that
f(x)=y*q(x).
His second error is thinking that the constant term constains
everything that does not change as x changes. Your example has
f(x) = sqrt(1+x) + sqrt(1-x) + 1; he wants to write it
f(x) = (f(x)-f(0)) + f(0)
and call f(0) the constant term and f(x)-f(0) the nonconstant
term. In polynomials, of course, if we think of P(x) as a bunch of
summands (the monomials), then P(x)-P(0) consists of all summands
which vary as x varies, and P(0) of all summands which do not vary as
x varies. James seems to think the same in general, even though what
he does already contradicts it.
In your example, for instance, f(0) = sqrt(1)+sqrt(1)+1 = 3, so
f(x) = [ sqrt(1+x)+sqrt(1-x)+1-3] + 3
= [sqrt(1+x)+sqrt(1-x)-2] + 3
with 3 the constant term and sqrt(1+x)+sqrt(1-x)-2 the nonconstant
term. Notably (or trivially, for the rest of us), there is a summand
in the nonconstant term which does NOT vary as x varies.
James has the same thing: his third term, 5a_3(x)+7 has a_3(0)=3, so
the constant term is 22, which means
g_3(x) = (5a_3(x)-15) + 22,
and there is a term which does not vary in the nonconstant term.
Nonetheless, he seems to be claiming that if
g_1(x) = 5a_1(x) + 7, then since a_1(0)=0, that means that a_1(x) has
a factor of x somewhere; so he probably thinks that all summands of
a_1(x) will vary as x varies, and so that when you divide by w_1(x)
(which is 7 at x=0), it must be that g_1(x) splits as the constant
term 1, and the NON CONSTANT TERM 5a_1(x)/w_1(x). And thus, that
7/w_1(x) is constant.
Which is of course a mistake, as you amply expanded elsewhere.
Why do you take so much trouble to expose such a reasoner as
Mr. Smith? I answer as a deceased friend of mine used to answer
on like occasions - A man's capacity is no measure of his power
to do mischief. Mr. Smith has untiring energy, which does
something; self-evident honesty of conviction, which does more;
and a long purse, which does most of all. He has made at least
ten publications, full of figures few readers can criticize. A great
many people are staggered to this extent, that they imagine there
must be the indefinite something in the mysterious all this.
They are brought to the point of suspicion that the mathematicians
ought not to treat all this with such undisguised contempt,
at least.
-- A Budget of Paradoxes, Vol. 2 p. 129 by Augustus de Morgan
Arturo Magidin
magidin@math.berkeley.edu
===
Subject: Re: Math dependency logic
> One of the more odd things that can happen when you deal with a
> discoverer is that you find that things you thought were simple,
> suddenly seem complicated and iffy. So I'm now facing a problem
where
> people are doubting algebra, which leads to the fun question of, just
> what is the logic here?
The issue has to do with a factor like x+2 and how you know that 2 is
> constant.
>Nope, the issue has to do with constant terms of non-polynomials.
>What is the constant term of sqrt(1 + x) + sqrt(1 - x) + 1?
> I think it has two things really: one is something James let slip
> recently: he thinks that if a function is 0 at x, then it has a
> factor of x somewhere. This is in analogy to a polynomial, of course,
> where if P(x)=0, then there exists a polynomial Q(x) such that
> P(x)=x*Q(x). He realizes this is not the case for general functions,
> but he figures there must be some y, factor of x, such that
> f(x)=y*q(x).
> His second error is thinking that the constant term constains
> everything that does not change as x changes. Your example has
> f(x) = sqrt(1+x) + sqrt(1-x) + 1; he wants to write it
> f(x) = (f(x)-f(0)) + f(0)
> and call f(0) the constant term and f(x)-f(0) the nonconstant
> term. In polynomials, of course, if we think of P(x) as a bunch of
> summands (the monomials), then P(x)-P(0) consists of all summands
> which vary as x varies, and P(0) of all summands which do not vary as
> x varies. James seems to think the same in general, even though what
> he does already contradicts it.
> In your example, for instance, f(0) = sqrt(1)+sqrt(1)+1 = 3, so
> f(x) = [ sqrt(1+x)+sqrt(1-x)+1-3] + 3
> = [sqrt(1+x)+sqrt(1-x)-2] + 3
> with 3 the constant term and sqrt(1+x)+sqrt(1-x)-2 the nonconstant
> term. Notably (or trivially, for the rest of us), there is a summand
> in the nonconstant term which does NOT vary as x varies.
> James has the same thing: his third term, 5a_3(x)+7 has a_3(0)=3, so
> the constant term is 22, which means
> g_3(x) = (5a_3(x)-15) + 22,
> and there is a term which does not vary in the nonconstant term.
> Nonetheless, he seems to be claiming that if
> g_1(x) = 5a_1(x) + 7, then since a_1(0)=0, that means that a_1(x) has
> a factor of x somewhere; so he probably thinks that all summands of
> a_1(x) will vary as x varies, and so that when you divide by w_1(x)
> (which is 7 at x=0), it must be that g_1(x) splits as the constant
> term 1, and the NON CONSTANT TERM 5a_1(x)/w_1(x). And thus, that
> 7/w_1(x) is constant.
> Which is of course a mistake, as you amply expanded elsewhere.
I got scared there. I thought math was going to crumble at the seams and
fall into the hands of JSH and his Core Errorian (not an attack on Koreans)
agents, but Arturo has saved us.
> Why do you take so much trouble to expose such a reasoner as
> Mr. Smith? I answer as a deceased friend of mine used to answer
> on like occasions - A man's capacity is no measure of his power
> to do mischief. Mr. Smith has untiring energy, which does
> something; self-evident honesty of conviction, which does more;
> and a long purse, which does most of all. He has made at least
> ten publications, full of figures few readers can criticize. A great
> many people are staggered to this extent, that they imagine there
> must be the indefinite something in the mysterious all this.
> They are brought to the point of suspicion that the mathematicians
> ought not to treat all this with such undisguised contempt,
> at least.
> -- A Budget of Paradoxes, Vol. 2 p. 129 by Augustus de Morgan
> Arturo Magidin
> magidin@math.berkeley.edu
===
Subject: Re: Math dependency logic
very good explanation;
will James Harris pursue it?
> In your example, for instance, f(0) = sqrt(1)+sqrt(1)+1 = 3, so
> f(x) = [ sqrt(1+x)+sqrt(1-x)+1-3] + 3
> = [sqrt(1+x)+sqrt(1-x)-2] + 3
> with 3 the constant term and sqrt(1+x)+sqrt(1-x)-2 the
nonconstant
> term. Notably (or trivially, for the rest of us), there is a summand
> in the nonconstant term which does NOT vary as x varies.
> James has the same thing: his third term, 5a_3(x)+7 has a_3(0)=3, so
> the constant term is 22, which means
> g_3(x) = (5a_3(x)-15) + 22,
> and there is a term which does not vary in the nonconstant term.
> Nonetheless, he seems to be claiming that if
> g_1(x) = 5a_1(x) + 7, then since a_1(0)=0, that means that a_1(x) has
> a factor of x somewhere; so he probably thinks that all summands
of
> a_1(x) will vary as x varies, and so that when you divide by w_1(x)
> (which is 7 at x=0), it must be that g_1(x) splits as the constant
> term 1, and the NON CONSTANT TERM 5a_1(x)/w_1(x). And thus, that
> 7/w_1(x) is constant.
--les ducs d'Enron!
===
Subject: Re: Math dependency logic
> One of the more odd things that can happen when you deal with a
> discoverer is that you find that things you thought were simple,
> suddenly seem complicated and iffy. So I'm now facing a problem
where
> people are doubting algebra, which leads to the fun question of,
just
> what is the logic here?
 The issue has to do with a factor like x+2 and how you know that 2
is
> constant.
Nope, the issue has to do with constant terms of non-polynomials.
>What is the constant term of sqrt(1 + x) + sqrt(1 - x) + 1?
> I think it has two things really: one is something James let slip
> recently: he thinks that if a function is 0 at x, then it has a
> factor of x somewhere. This is in analogy to a polynomial, of course,
> where if P(x)=0, then there exists a polynomial Q(x) such that
> P(x)=x*Q(x). He realizes this is not the case for general functions,
> but he figures there must be some y, factor of x, such that
> f(x)=y*q(x).
There is a large amount of deja vu here. Years ago James argued that
x^2 + y^2 could be factored in linear terms.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland,
+31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
===
Subject: Re: Math dependency logic
> I think it has two things really: one is something James let slip
> recently: he thinks that if a function is 0 at x, then it has a
> factor of x somewhere. This is in analogy to a polynomial, of course,
> where if P(x)=0, then there exists a polynomial Q(x) such that
> P(x)=x*Q(x). He realizes this is not the case for general functions,
> but he figures there must be some y, factor of x, such that
> f(x)=y*q(x).
Doesn't this work for all analytic functions?
Have a tolerable existence. Eli
===
Subject: Re: Math dependency logic
> I think it has two things really: one is something James let slip
> recently: he thinks that if a function is 0 at x, then it has a
> factor of x somewhere. This is in analogy to a polynomial, of
course,
> where if P(x)=0, then there exists a polynomial Q(x) such that
> P(x)=x*Q(x). He realizes this is not the case for general functions,
> but he figures there must be some y, factor of x, such that
> f(x)=y*q(x).
> Doesn't this work for all analytic functions?
Perhaps so. But the functions he uses are not analytic. They involve
roots (cube and square roots in this case).
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland,
+31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
===
Subject: Re: Math dependency logic
> One of the more odd things that can happen when you deal with a
> discoverer is that you find that things you thought were simple,
> suddenly seem complicated and iffy. So I'm now facing a problem where
> people are doubting algebra, which leads to the fun question of, just
> what is the logic here?
More nonsequiters than usual today.
> The issue has to do with a factor like x+2 and how you know that 2 is
> constant.
Today is Monday, so 2 is constant.
> If the logic is expanded upon, my hope is that many of you will
> realize what is happening in my core error proof, and quit doubting,
> if you are doubting, as if you're not, and understand it, then that's
> another problem entirely.
> Ok, so how do you know that with even a polynomial factor, like x+2,
> that 2 is *constant* and not related to x?
Tomorrow is Tuesday, 2 will still be constant.
> What's the mathematical logic?
Constants are constant.
> I've talked about setting x=0, which would reveal the constant factor
> which you can look at, and I think that for some of you, the ability
> to *physically* see constants in polynomial factors, has left you
> without ever knowing the *why* behind how it works.
> How about this?
> There are an infinity of number and letter combinations, of which x+2
> is just one of that infinity. If you set x=2 though, you just have 2,
> so how do you know from whence it came?
If you set x = 2 in the expression x+2, you get 4. Don't you?
> I mean, with just 2, well, it's just 2, so there's no reference back
> to x, or y, or any other of that infinity of possibilities.
> The answer is that 2 is just a number that has no other information
> except itself.
2 is 2, yes.
> Logically, you can say that 2 is *independent* of any particular
> variable, even if it's associated with it, like in an expression like
> x+2.
> Now, as 0 clears out variables set to 0, you can show independent
> terms by setting a particular value to 0, as that reveals everything
> that can be associated with an infinity of other things.
You are really off the deep end today. I mean, even though your
mathematical reasoning is wrong, it is usually interesting and capable
of being either true or false. This latest stuff makes no sense at all.
> It's like how it could be y+2, or z+2, or alpha + 2, as seeing just 2,
> doesn't tell you anything about an association.
> Possibly the problem for some of you is that you *remember* the
> previous association. That is, you know that you had x+2, then you
> set x=0, so in your mind you see a phantom x that holds the
> association.
Oh I see where this is going. All along you have clearly not understood
the distinction among polynomial expressions, polynomial functions, and
polynomial expressions evaluated at a particular value. I believe you
may yourself be dimly starting to understand what it is you are confused
about.
===
Subject: Re: Math dependency logic
James, you are becoming less and less coherent. If this error is so CORE
to
mathematics, can't you just give a few simple quadratics with integral
coefficients between -100 and 100 to prove your point?
> One of the more odd things that can happen when you deal with a
> discoverer is that you find that things you thought were simple,
> suddenly seem complicated and iffy. So I'm now facing a problem where
> people are doubting algebra, which leads to the fun question of, just
> what is the logic here?
> The issue has to do with a factor like x+2 and how you know that 2 is
> constant.
> If the logic is expanded upon, my hope is that many of you will
> realize what is happening in my core error proof, and quit doubting,
> if you are doubting, as if you're not, and understand it, then that's
> another problem entirely.
> Ok, so how do you know that with even a polynomial factor, like x+2,
> that 2 is *constant* and not related to x?
> What's the mathematical logic?
> I've talked about setting x=0, which would reveal the constant factor
> which you can look at, and I think that for some of you, the ability
> to *physically* see constants in polynomial factors, has left you
> without ever knowing the *why* behind how it works.
> How about this?
> There are an infinity of number and letter combinations, of which x+2
> is just one of that infinity. If you set x=2 though, you just have 2,
> so how do you know from whence it came?
> I mean, with just 2, well, it's just 2, so there's no reference back
> to x, or y, or any other of that infinity of possibilities.
> The answer is that 2 is just a number that has no other information
> except itself.
> Logically, you can say that 2 is *independent* of any particular
> variable, even if it's associated with it, like in an expression like
> x+2.
> Now, as 0 clears out variables set to 0, you can show independent
> terms by setting a particular value to 0, as that reveals everything
> that can be associated with an infinity of other things.
> It's like how it could be y+2, or z+2, or alpha + 2, as seeing just 2,
> doesn't tell you anything about an association.
> Possibly the problem for some of you is that you *remember* the
> previous association. That is, you know that you had x+2, then you
> set x=0, so in your mind you see a phantom x that holds the
> association.
> That's ok, but it doesn't have a *mathematical* reality because your
> memory is irrelevant.
> The reality is that as far as the math is concerned 2 is a number that
> can be by itself or associated with x or an infinity of other things,
> and the math isn't going to pick or choose based on what YOU remember.
> It handles all possibilities at once.
> And with *just* a number, it sees independence.
> That's why setting a variable to 0 is such a useful and powerful tool,
> as it reveals infinite possibilities by removing a particular
> association.
> My argument works on that principle, as by setting x or m, depending
> on what I'm calling the variable, I find that I have 7, 7 and 22 as
> *constant* terms for factors of a polynomial.
> I also know that polynomial has a factor that is constant as that
> factor is 49.
> When I divide the polynomial by 49 I have constant terms of 1, 1, and
> 22, which tells me something.
> Now those numbers don't care about x or m. They don't *know* about x
> or m, but you may remember them, so you think your memory has some
> effect, but the math sees *infinite* possibility, while you may fixate
> on an association you remember.
> In the realm of infinite possibility, it's not possible for 7, 7, and
> 22 to go to 1, 1, and 22 based on the value of x, where they check it
> first to decide how they'll behave, because they're just NUMBERS, and
> they don't have enough data associated with them to be making those
> kinds of decisions.
> It's like, if human beings on earth constrain 7, 7 and 22 so that they
> have to worry about the value of x and m, then, wow, we've affected
> all reality in all dimensions and all possibilities, just with our
> MEMORY of there being an x or m associated in some interesting
> expression.
> But, of course, your thoughts don't constrain those numbers as they
> keep operating quite well throughout Totality, despite what you may
> believe, or remember.
> Just remember that when you're considering the issue of constants in a
> math argument.
> James Harris
===
Subject: Integral
How do I integrate this?
f(x) = sin(x)/x
===
Subject: Re: Integral
> How do I integrate this?
> f(x) = sin(x)/x
I haven't tried it, but can't you just take sin(x) * (1/x) and use
integration by parts.
Lurch
===
Subject: Re: Integral
> How do I integrate this?
> f(x) = sin(x)/x
You could write
sin(x)/x = 1- x^2/3! + x^4/5! - ... [using the expansion of sin(x)] and
integrate it. You can't really do better than that.
===
Subject: Re: Integral
You can't.
> How do I integrate this?
> f(x) = sin(x)/x
===
Subject: Re: Integral
> You can't.
You can, you just don't know a name for it.
I hate it when people say you can't integrate something, just because
the
result is beyond the reach of elementary functions.
===
Subject: Re: Integral
> You can't.
> You can, you just don't know a name for it.
I certainly can't, and I don't think you can either.
(This is semantics)
> I hate it when people say you can't integrate something, just because
the
> result is beyond the reach of elementary functions.
===
Subject: Re: Integral
> You can't.
> You can, you just don't know a name for it.
> I certainly can't, and I don't think you can either.
> (This is semantics)
Saying one cot integrate that function is equivalent to not being able
to
integrate that function.
So you would dare to say that sin(x)/x is not integrable? Wrong. And even
if
it is semantics, it still gives me the creeps when someone says something
like that.
===
Subject: Re: Integral
>>You can't.
> You can, you just don't know a name for it.
It's called a Sine Integral :
Si(z)= int_0^z sin(x)/x dx
We may add :
lim_{x->oo} Si(x)= pi/2
Si(z)= sum_{n=0}^oo (-1)^n*z^(2n+1)/((2n+1)*(2n+1)!)
Si(z)= (E1(i*z)-E1(-i*z))/(2*i)+pi/2
with E1(z) the exponential integral
For further information see
http://functions.wolfram.com/GammaBetaErf/SinIntegral/
Raymond
> I hate it when people say you can't integrate something, just because
the
> result is beyond the reach of elementary functions.
===
Subject: Re: Integral
>You can't.
>> You can, you just don't know a name for it.
> It's called a Sine Integral :
> Si(z)= int_0^z sin(x)/x dx
Give it a name and it's solved, yup. It doesn't really address the
OP's question though, does it. He obviously wants to know how to work
out the integral. He has probably found that the methods he has
learned don't seem to work and wants to know if there is a clever
method he hasn't figured out yet. And the answer for him is no, there
isn't any way to work it.
Of course, giving the antiderivative a name and using that for the
answer has its uses, somewhat like in the medical profession when some
mysterious disease shows up. They may not know what causes it, how it
spreads, how to treat it, or anything else about it, but they can give
it a name. Our tests indicate that you have di-flukus. Feel better
now?
--Lynn
===
Subject: Re: Integral
> You can, you just don't know a name for it.
>> It's called a Sine Integral :
>> Si(z)= int_0^z sin(x)/x dx
>Give it a name and it's solved, yup. It doesn't really address the
>OP's question though, does it. He obviously wants to know how to work
>out the integral. He has probably found that the methods he has
>learned don't seem to work and wants to know if there is a clever
>method he hasn't figured out yet. And the answer for him is no, there
>isn't any way to work it.
>Of course, giving the antiderivative a name and using that for the
>answer has its uses, somewhat like in the medical profession when some
>mysterious disease shows up. They may not know what causes it, how it
>spreads, how to treat it, or anything else about it, but they can give
>it a name. Our tests indicate that you have di-flukus. Feel better
>now?
But once you have the name, you can look it up and see what is known
about it. And for functions such as Si, there is in fact a lot of
information that can be found in standard reference works
or in computer algebra systems such as Maple or Mathematica.
Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2
===
Subject: Re: Integral
>>You can't.
>You can, you just don't know a name for it.
>> It's called a Sine Integral :
>> Si(z)= int_0^z sin(x)/x dx
> Give it a name and it's solved, yup. It doesn't really address the
> OP's question though, does it. He obviously wants to know how to work
> out the integral. He has probably found that the methods he has
> learned don't seem to work and wants to know if there is a clever
> method he hasn't figured out yet. And the answer for him is no, there
> isn't any way to work it.
> Of course, giving the antiderivative a name and using that for the
> answer has its uses, somewhat like in the medical profession when some
> mysterious disease shows up. They may not know what causes it, how it
> spreads, how to treat it, or anything else about it, but they can give
> it a name. Our tests indicate that you have di-flukus. Feel better
> now?
> --Lynn
Of course I only gave it a name ;-)
(hint 1: nothing snipped?? hint 2:the name (and the link) indicates
that no closed form using only a finite number of 'elementary functions'
is known (this may be proved but I'll stop here...)).
R.
===
Subject: Re: Rational function
My thoughts exactly!
> How about the guy with the old chestnut comment...
> I suppose you mean Bob Kolker. But he might not be reading _this_
thread;
> after all, that comment was made by him in a different thread.
> You mean he does something other than read sci.math? Like he has a life?
> I am having trouble finding the equation of a rational function
where
> y^x = x^y and goes through (2,4) (4,2) (2.48832, 2.985984)
> (2.985984,2.48832) (2.25,3.375) (3.375,2.25) (2.44140625,3.0517578)
> (3.0517578, 2.44140625). The
> numbers are rounded off ofcourse, but they all are true for y^x =
x^y.
> Perhaps you're oyed that nobody has answered your question yet. But
> we're not compelled to answer questions, and your particular question,
> taken at face value, doesn't seem interesting. Sorry. OTOH, if you
could
> show us _why_ we should be interested in your question, then you would
> probably get some useful responses.
> Meanyheads. You don't have anything useful to do. Just pull the answer
out
> of your overgrown brains sitting on your spindly useless bodies and tell
me
> the answer.
> Una Grajjit
===
Subject: Re: Rational function
> I am having trouble finding the equation of a rational function where
y^x
> x^y and goes through (2,4) (4,2) (2.48832, 2.985984) (2.985984,2.48832)
> (2.25,3.375) (3.375,2.25) (2.44140625,3.0517578)
(3.0517578,2.44140625).
> The
> numbers are rounded off ofcourse, but they all are true for y^x = x^y.
Any
See, for example:
http://mathworld.wolfram.com/LagrangePolynomial.html
===
Subject: Re: Rational function
I certainly didn't mean to get off the subject. I like your excuse David,
but again I think it's because you don't know an answer. You seem to have
answered many other un-interesting questions as you put it, on the
forum.
You and Mr. Old Chestnut seem to be alike. If you don't have an answer,
please feel free not to reply. :) (I don't want to get off of the subject
too much)
> How about the guy with the old chestnut comment...
> I am having trouble finding the equation of a rational function where
y^x
> x^y and goes through (2,4) (4,2) (2.48832, 2.985984) (2.985984,2.48832)
> (2.25,3.375) (3.375,2.25) (2.44140625,3.0517578)
(3.0517578,2.44140625).
> The
> numbers are rounded off ofcourse, but they all are true for y^x = x^y.
Any
===
Subject: Re: Rational function
> I certainly didn't mean to get off the subject. I like your excuse David,
> but again I think it's because you don't know an answer. You seem to have
> answered many other un-interesting questions as you put it, on the
forum.
Interesting, like beauty, is in the eye of the beholder.
> You and Mr. Old Chestnut seem to be alike. If you don't have an answer,
> please feel free not to reply. :) (I don't want to get off of the subject
> too much)
They both know the answers. I think nobody realized that you don't have a
clue.
x^y = y^x implicitly defines y as a function of x. This function is not a
rational function (surprise!). Any rational function will only approximate
the function.
The study of approximating functions is interpolation. It is well-studied
and polynomials or even on interpolating polynomials, and you probably
want -linear. I think all calculus books still at least mention LaGrange
interpolation, but you're probably better off to look at a numerical
analysis book. Cubic splines might work very nicely. Another place to
look
might be graduation theory.
The choice of interpolation methods is almost always made on
non-mathematical grounds. What are you willing to give up in order to get
the data in the form you like?
Jon Miller
===
Subject: Re: Rational function
The reason I think it is a rational function is that y = 8/x comes close.
What is it with you people and rude comments. I'm not offended, but I think
it's imature, and I'm probably younger than most of you.
> I certainly didn't mean to get off the subject. I like your excuse
David,
> but again I think it's because you don't know an answer. You seem to
have
> answered many other un-interesting questions as you put it, on the
> forum.
> Interesting, like beauty, is in the eye of the beholder.
> You and Mr. Old Chestnut seem to be alike. If you don't have an answer,
> please feel free not to reply. :) (I don't want to get off of the
subject
> too much)
> They both know the answers. I think nobody realized that you don't have
a
> clue.
> x^y = y^x implicitly defines y as a function of x. This function is not
a
> rational function (surprise!). Any rational function will only
approximate
> the function.
> The study of approximating functions is interpolation. It is well-studied
interpolation
> and polynomials or even on interpolating polynomials, and you probably
> want -linear. I think all calculus books still at least mention LaGrange
> interpolation, but you're probably better off to look at a numerical
> analysis book. Cubic splines might work very nicely. Another place to
look
> might be graduation theory.
> The choice of interpolation methods is almost always made on
> non-mathematical grounds. What are you willing to give up in order to
get
> the data in the form you like?
> Jon Miller
===
Subject: bug in the faq section on CH
permission for an emailed response.
The discussion of Freiling's Axiom of Symmetry, in the excerpt from
Bill Allen, seems to have a typo. The complete bit is:
Let A be the set of functions mapping Real Numbers into countable
sets of Real Numbers. Given a function f in A , and some arbitrary
real numbers x and y , we see that x is in f(y) with probability 0,
i.e. x is not in f(y) with probability 1. Similarly, y is not in
f(x) with probability 1. Let AX be the axiom which states
``for every f in A , there exist x and y such that x is not in f(y)
and y is not in f(x)
The intuitive justification for AX is that we can find the x and y
by choosing them at random.
In ZFC, AX = not CH. proof: If CH holds, then well-order R as r_0,
r_1, .... , r_x, ... with x < aleph_1 . Define f(r_x) as { r_y : y
>= x } . Then f is a function which witnesses the falsity of AX.
If CH fails, then let f be some member of A . Let Y be a subset of R
of cardinality aleph_1 . Then Y is a proper subset. Let X be the
union of all the sets f(y) with y in Y , together with Y . Then, as
X is an aleph_1 union of countable sets, together with a single
aleph_1 size set Y , the cardinality of X is also aleph_1 , so X is
not all of R . Let a be in R X , so that a is not in f(y) for any y
in Y . Since f(a) is countable, there has to be some b in Y such
that b is not in f(a) . Thus we have shown that there must exist a
and b such that a is not in f(b) and b is not in f(a) . So AX holds.
I focus on the fourth paragraph, in the proof that CH -> ~AX.
We have:
f(r_x) := { r_y : y >= x}
Surely that should be
f(r_x) := { r_y : y <= x}
After all, given the first definition, the value of f would always be
uncountable!
Thomas
===
Subject: Proof for (x+y)^n = ...
I have to prove that for all n from |N and for arbitrary x,y
from |R the following is true:
(x+y)^n = sum(comb(n,k)*x^k*y^(n-k), k, 0, n)
(comb(n,k) - combination n above k)
( sum([..]) - comb(n,0)*x^0*y^(n-0)+ ... + comb(n,n)*x^n*y^(n-n) )
This is what I have done:
###
Proof through complete induction toward n:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
1.) n = 0 => (x+y)^0 = sum(comb(0,k)*x^k*y^(0-k), k, 0, 0) = 1
2.) Let us suppose that the sentence is right for n. Then we have
to prove it for n+1.
3.)
(x+y)^(n+1) = (x+y)(x+y)^n = 2.) = (x+y)sum(comb(n,k)*x^k*y^(n-k), k, 0,
n)
= x*sum(comb(n,k)*x^k*y^(n-k), k, 0, n)+y*sum(comb(n,k)*x^k*y^(n-k), k, 0,
n)
= sum(comb(n,k)*x^(k+1)*y^(n-k), k, 0, n)+sum(comb(n,k)*x^k*y^(n-k+1), k, 
0,
n)
###
And what do I have to do now? Can you give me a hint?
Please, I beg you! :-)
Karl.
===
Subject: Re: Proof for (x+y)^n = ...
> I have to prove that for all n from |N and for arbitrary x,y
> from |R the following is true:
> (x+y)^n = sum(comb(n,k)*x^k*y^(n-k), k, 0, n)
> (comb(n,k) - combination n above k)
> ( sum([..]) - comb(n,0)*x^0*y^(n-0)+ ... + comb(n,n)*x^n*y^(n-n)
)
> This is what I have done:
> ###
> Proof through complete induction toward n:
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> 1.) n = 0 => (x+y)^0 = sum(comb(0,k)*x^k*y^(0-k), k, 0, 0) = 1
> 2.) Let us suppose that the sentence is right for n. Then we have
> to prove it for n+1.
> 3.)
> (x+y)^(n+1) = (x+y)(x+y)^n = 2.) = (x+y)sum(comb(n,k)*x^k*y^(n-k), k,
0, n)
> = x*sum(comb(n,k)*x^k*y^(n-k), k, 0, n)+y*sum(comb(n,k)*x^k*y^(n-k), k, 
0,
n)
> = sum(comb(n,k)*x^(k+1)*y^(n-k), k, 0, n)+sum(comb(n,k)*x^k*y^(n-k+1), k,
0, n)
> ###
> And what do I have to do now? Can you give me a hint?
Hints:
1) Collect terms with equal powers in 'x' and 'y'.
2) To do #1, it may be useful to change the index, i.e.,
summing f(k) for k=1 to 6 is the same as summing
f(k+1) for k=0 to 5.
3) You may need to first prove a combinatorial identity. This
identity will be the obvious one that you need once you collect
terms.
4) Following Polya, if there is a problem you can't solve, there
is a simpler problem you can't solve. Write out the above steps
*explicitly* for cases of small n (n=1,2,3,4).
5) Look up Pascal's triangle.
Best wishes,
Mike
> Please, I beg you! :-)
No, no, none of that. A simple cash deposit in my Swiss bank account
will be quite sufficient :-).
Best wishes,
Mike
===
Subject: can anyone help me solve this problem?
How many ways are there to distribute B non-distinct Bones between D
distinct dogs?
if you know the answer to this, could you let me know how you came up with
it?
===
Subject: Re: can anyone help me solve this problem?
Adjunct Assistant Professor at the University of Montana.
>How many ways are there to distribute B non-distinct Bones between D
distinct dogs?
Number the dogs, 1,...,D.
Since the bones are indistinguishable, just choose B dogs, and give
them bones.
If you do not allow giving more than one bone to a dog, you are just
asking about the number of ways to choose a subset of size B out of
{1,...,D}, i.e., D choose B.
If you allow to give more than one bone to a dog, you have what are
called combinations with repetitions. It's the same problem as
counting how many different throws of B dice, each with D faces, there
are; the solution then is (B+D-1) choose B.
===
Subject: Re: can anyone help me solve this problem?
> How many ways are there to distribute B non-distinct Bones between D
> distinct dogs?
> if you know the answer to this, could you let me know how you came up
> with it?
Sounds like you want each bone to pick a dog. Or mathematically,
you want functions from the set of bones into the set of dogs--each
dog then gets the pre-image of this function.
Have you tried doing this explicitly for a small number of dogs
and bones? If I had one bone and 10 dogs, what could I do? If
I had two bones and ten dogs what could I do? Remember the
joke about the mathematician:
A mathematician is given an empty kettle and asked to boil
some water, so he (yes, he, no woman would be silly enough
to do what this mathematician is about to do) ... so he
fills the kettle with water, lights the stove, etc.
A while later he is given a kettle filled with water and
asked to boil some water. The mathematician spills out
the water, then presents the empty kettle and state
I have now reduced this to the previously solved problem.
So, if I have two bones, how can I reduce that to the previously
solved problem.
Best wishes,
Mike
===
Subject: Leibniz & Newton
Can anyone help me with this question? Why is Newton more widely accepted
as the man who developed calculus, instead of Leibniz?
Kavon
kavon@mathisradical.com
===
Subject: Re: Leibniz & Newton
In <U2inb.4216$Px2.3669@newsread4.news.pas.earthlink.net>, on
at 11:41 PM, Kavon Rueter <kavon@mathisradical.com> said:
>Can anyone help me with this question? Why is Newton more widely
>accepted as the man who developed calculus, instead of Leibniz?
And why isn't proper credit given to earlier work by, e.g.,
Archimedes, Fermat?
FWIW, our current notation stems from both Liebniz and Newton.
Physicist are more prone to use Newton's x dot notation, but both
mathematicians and physicists use both when appropriate. The notation
used for partial derivatives also stems from Liebniz's notation.
--
Shmuel (Seymour J.) Metz, SysProg and JOAT
Unsolicited bulk E-mail will be subject to legal action. I reserve
the right to publicly post or ridicule any abusive E-mail.
Reply to domain Patriot dot net user shmuel+news to contact me. Do
not reply to spamtrap@library.lspace.org
===
Subject: Re: Leibniz & Newton
> Can anyone help me with this question? Why is Newton more widely
accepted
> as the man who developed calculus, instead of Leibniz?
Who invented calculus?
In England, they say Newton; on the Contenant, they say Leibniz.
In former centuries, this was a heated dispute!
> Kavon
> kavon@mathisradical.com
===
Subject: Re: Leibniz & Newton
Hi A N Niel.
Didn't the Bernoulli's get involved in the dispute and take sides?
===
Subject: Re: Leibniz & Newton
> Can anyone help me with this question? Why is Newton more widely
accepted
> as the man who developed calculus, instead of Leibniz?
It's Leibniz's dy/dx notation that survives, rather than Newton's dot
notation for derivatives. Perhaps Newton gets more credit because his
mathematical discoveries in general were much more extensive than
Leibniz's, and because Newton used his calculus to solve the problem of
gravitation.
===
Subject: Re: Leibniz & Newton
>> Can anyone help me with this question? Why is Newton more widely
>> accepted as the man who developed calculus, instead of Leibniz?
> It's Leibniz's dy/dx notation that survives, rather than Newton's dot
> notation for derivatives. Perhaps Newton gets more credit because his
> mathematical discoveries in general were much more extensive than
> Leibniz's, and because Newton used his calculus to solve the problem of
> gravitation.
Actually, there is evidence that Newton created calculus before Leibnitz
even though Leibnitz published first. I read this in a book on math
history that I can't cite right now. However, this was not established
until a long while after fact and the author's opinion is that the real
reason that Newton get's more of the credit is because England had more
power in the international community at the time than Germany had.
Have a tolerable existence. Eli
===
Subject: Re: Leibniz & Newton
: Actually, there is evidence that Newton created calculus before Leibnitz
: even though Leibnitz published first. I read this in a book on math
: history that I can't cite right now. However, this was not established
: until a long while after fact and the author's opinion is that the real
: reason that Newton get's more of the credit is because England had more
: power in the international community at the time than Germany had.
I have read that the Brittish Acience Academy was set to solve the dispute
on who invented calculus first, and the Brittish Academy was at that time
led by Newton...
===
Subject: Re: Leibniz & Newton
Mikko,
I know at the time Germany followed with Leibniz. The mathematicians were
divided, often taking sides. Today, the dispute is all but forgotten.
Well,
until I had to go and post this original message, huh!!
Kavon
> : Actually, there is evidence that Newton created calculus before
Leibnitz
> : even though Leibnitz published first. I read this in a book on math
> : history that I can't cite right now. However, this was not established
> : until a long while after fact and the author's opinion is that the real
> : reason that Newton get's more of the credit is because England had more
> : power in the international community at the time than Germany had.
> I have read that the Brittish Acience Academy was set to solve the
dispute
> on who invented calculus first, and the Brittish Academy was at that time
> led by Newton...
===
Subject: Re: Leibniz & Newton
plague) and developed calculus at his farm, while Leibnitz was developing
his calculus at the same time, only doing so in Germany. The thought has
made me wonder, about English speaking peoples preferring Newton's over
Leibniz's. I wonder if Germans consider Leibniz the authority??
Kavon
===
===
Subject: Strange Automorphism Group
Let R denote the field of real numbers. Then let R+ denote the
additive group of the reals. Then my question concerns Aut(R+). In ZF,
it can be proved that this group contains a subgroup isomorphic to R*,
the multiplicative group of the reals. On the other hand, in ZFC, this
group is huge and nonabelian and isomorphic to a huge |R|-dimensional
general linear group.
Is there a model or axiomatic extension of set theory in which the
subgroup isomorphic to R* is all that is in Aut(R+)? Does ZF +
Determinacy work?
---- David
===
Subject: Re: Strange Automorphism Group
>Let R denote the field of real numbers. Then let R+ denote the
>additive group of the reals. Then my question concerns Aut(R+). In ZF,
>it can be proved that this group contains a subgroup isomorphic to R*,
>the multiplicative group of the reals. On the other hand, in ZFC, this
>group is huge and nonabelian and isomorphic to a huge |R|-dimensional
>general linear group.
>Is there a model or axiomatic extension of set theory in which the
>subgroup isomorphic to R* is all that is in Aut(R+)? Does ZF +
>Determinacy work?
An automorphism of R+ is an additive function on R. It's well-known
that all measurable additive functions on R are of the form x -> cx.
So any model of ZF in which all functions are measurable will do.
Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2
===
Subject: Math dependency logic REVISED
One of the more odd things that can happen when you deal with a
discoverer is that you find that things you thought were simple,
suddenly seem complicated and iffy. So I'm now facing a problem where
people are doubting algebra, which leads to the fun question of, just
what is the logic here?
The issue has to do with a factor like x+2 and how you know that 2 is
constant.
If the logic is expanded upon, my hope is that many of you will
realize what is happening in my core error proof, and quit doubting,
if you are doubting, as if you're not, and understand it, then that's
another problem entirely.
Ok, so how do you know that with even a polynomial factor, like x+2,
that 2 is *constant* and not related to x?
What's the mathematical logic?
I've talked about setting x=0, which would reveal the constant factor
which you can look at, and I think that for some of you, the ability
to *physically* see constants in polynomial factors, has left you
without ever knowing the *why* behind how it works.
How about this?
There are an infinity of number and letter combinations, of which x+2
is just one of that infinity. If you set x=0 though, you just have 2,
so how do you know from whence it came?
I mean, with just 2, well, it's just 2, so there's no reference back
to x, or y, or any other of that infinity of possibilities.
The answer is that 2 is just a number that has no other information
except itself.
Logically, you can say that 2 is *independent* of any particular
variable, even if it's associated with it, like in an expression like
x+2.
Now, as 0 clears out variables set to 0, you can show independent
terms by setting a particular value to 0, as that reveals everything
that can be associated with an infinity of other things.
It's like how it could be y+2, or z+2, or alpha + 2, as seeing just 2,
doesn't tell you anything about an association.
Possibly the problem for some of you is that you *remember* the
previous association. That is, you know that you had x+2, then you
set x=0, so in your mind you see a phantom x that holds the
association.
That's ok, but it doesn't have a *mathematical* reality because your
memory is irrelevant.
The reality is that as far as the math is concerned 2 is a number that
can be by itself or associated with x or an infinity of other things,
and the math isn't going to pick or choose based on what YOU remember.
It handles all possibilities at once.
And with *just* a number, it sees independence.
That's why setting a variable to 0 is such a useful and powerful tool,
as it reveals infinite possibilities by removing a particular
association.
My argument works on that principle, as by setting x or m, depending
on what I'm calling the variable, I find that I have 7, 7 and 22 as
*constant* terms for factors of a polynomial.
I also know that polynomial has a factor that is constant as that
factor is 49.
When I divide the polynomial by 49 I have constant terms of 1, 1, and
22, which tells me something.
Now those numbers don't care about x or m. They don't *know* about x
or m, but you may remember them, so you think your memory has some
effect, but the math sees *infinite* possibility, while you may fixate
on an association you remember.
In the realm of infinite possibility, it's not possible for 7, 7, and
22 to go to 1, 1, and 22 based on the value of x, where they check it
first to decide how they'll behave, because they're just NUMBERS, and
they don't have enough data associated with them to be making those
kinds of decisions.
It's like, if human beings on earth constrain 7, 7 and 22 so that they
have to worry about the value of x and m, then, wow, we've affected
all reality in all dimensions and all possibilities, just with our
MEMORY of there being an x or m associated in some interesting
expression.
But, of course, your thoughts don't constrain those numbers as they
keep operating quite well throughout Totality, despite what you may
believe, or remember.
Just remember that when you're considering the issue of constants in a
math argument.
James Harris
===
Subject: Re: Math dependency logic REVISED
> One of the more odd things that can happen when you deal with a
> discoverer is that you find that things you thought were simple,
> suddenly seem complicated and iffy.
No, actually, a person who's a discover in math, makes what sense out of
complicated things, and lays them on a firm foundation, so there is no
iffiness. It's when you don't know what you're doing that what is
simple
seems complicated.
MB
===
Subject: Re: Math dependency logic REVISED
> One of the more odd things that can happen when you deal with a
> discoverer is that you find that things you thought were simple,
> suddenly seem complicated and iffy. So I'm now facing a problem where
> people are doubting algebra, which leads to the fun question of, just
> what is the logic here?
No one is doubting algebra. We're just certain that you aren't using
it properly.
--
Wayne Brown (HPCC #1104) | When your tail's in a crack, you improvise
fwbrown@bellsouth.net | if you're good enough. Otherwise you give
| your pelt to the trapper.
e^(i*pi) = -1 -- Euler | -- John Myers Myers,
Silverlock
===
Subject: Re: Math dependency logic REVISED
> One of the more odd things that can happen when you deal with a
> discoverer is that you find that things you thought were simple,
> suddenly seem complicated and iffy. So I'm now facing a problem where
> people are doubting algebra, which leads to the fun question of, just
> what is the logic here?
The logic? Let's see:
A person who proudly declares he is uneducated in mathematics
does some algebra. He comes up with a result. People with
training in mathematics universally disagree with the
result. Therefore we conclude that it is ______ they are doubting.
(a) the person's ability to do algebra
(b) algebra itself
(c) life, the universe, and everything
(d) other
- R
===
Subject: Re: Math dependency logic REVISED
, which leads to the fun question of, just what is the logic here?
Apparently, the question has and still escapes you and it has been over
seven years!
Megalomaniac, go see a shrink so you can receive various psychotropic
drugs!
===
Subject: Re: Math dependency logic REVISED
Please, take a math class. Learn some math before you revolutionize
mathematics, it would be more useful (and necessary) than you probably
think. Look at some real proofs, for example. Work some stuff out that is
simpler than, say, fermat's last theorem.
Even at with my humble mathematical background, you're 'musings' are
clearly
the work of someone who has not been introduced properly to mathematics.
All your proofs seem to be a sort of juggling of equations at (or about) a
high school level. You might have a great intuition which would be a
terrible thing to waste, which is what you are doing right now.
Justin Van Winkle
===
Subject: Re: Math dependency logic REVISED
I made. They were made under the assumption that James Harris was about
15.
This is apparently incorrect.
James, give it up. Your math isn't coherent. It's nonsense. Utter
nonsense. It is entertaining to read the arguments though. (The arguments
between you and the other posters to the group. Reading your mathematical
'arguments' is painful, at best.)
Justin Van Winkle
> ?
> Please, take a math class. Learn some math before you revolutionize
> mathematics, it would be more useful (and necessary) than you probably
> think. Look at some real proofs, for example. Work some stuff out that
is
> simpler than, say, fermat's last theorem.
> Even at with my humble mathematical background, you're 'musings' are
clearly
> the work of someone who has not been introduced properly to mathematics.
> All your proofs seem to be a sort of juggling of equations at (or about)
a
> high school level. You might have a great intuition which would be a
> terrible thing to waste, which is what you are doing right now.
> Justin Van Winkle
===
Subject: Re: Math dependency logic REVISED
> I made. They were made under the assumption that James Harris was about
15.
> This is apparently incorrect.
> James, give it up. Your math isn't coherent. It's nonsense. Utter
> nonsense. It is entertaining to read the arguments though. (The
arguments
> between you and the other posters to the group. Reading your
mathematical
> 'arguments' is painful, at best.)
> Justin Van Winkle
And now readers should notice the psych out game.
Usenet is easy, if you don't like a poster, don't read them.
However, math society is STUCK. If it completely ignores me, then I
can explain without hecklers distracting or lying, and people might
see how simple my argument is, and realize that mathematicians are
engaging in an amazing fraud.
If they reply to me with mathematics, either they have to admit I'm
right, or obfuscate. But I SIMPLIFY, as I've been doing lately, which
eventually puts them in a box. Math IS wonderful in that way.
So some of them just switch to insulting posts meant to convince other
readers that I must be wrong because people SAY I'm wrong, which is
kind of interesting.
Math society has gone rogue. Given a very simple and basic proof of a
problem in the discipline, members of math society are choosing a
fantasy world, where their discipline is perfect.
It'd be like if Einstein introduced the general theory of relativity,
and physicists spent a lot of time calling him a crank, refused to
acknowledge experimental results verifying his theories, and spent a
lot of effort trying to make sure that the rest of the world, never
knew who he was.
Mathematicians are basically behaving like sorry excuses for
intellectuals.
James Harris
===
Subject: Re: Math dependency logic REVISED
readers -- and just who are these ghostly entities?
have you gotten recruits from the Sokal School of Numbertheory,
or what?
anyway, you don't think that Einstein made any mistakes
in his math?... how about his hypotheses?
and what about Ienstien?
> And now readers should notice the psych out game.
--Dec.2000 'WAND' Chairman Paul O'Neill, reelected to Board. Newsish?
http://www.rand.org/publications/randreview/issues/rr.12.00/
http://members.tripod.com/~american_almanac
===
Subject: Re: Math dependency logic REVISED
comments
> I made. They were made under the assumption that James Harris was
about
15.
> This is apparently incorrect.
> James, give it up. Your math isn't coherent. It's nonsense. Utter
> nonsense. It is entertaining to read the arguments though. (The
arguments
> between you and the other posters to the group. Reading your
mathematical
> 'arguments' is painful, at best.)
> Justin Van Winkle
> And now readers should notice the psych out game.
> Usenet is easy, if you don't like a poster, don't read them.
> However, math society is STUCK. If it completely ignores me, then I
> can explain without hecklers distracting or lying, and people might
> see how simple my argument is, and realize that mathematicians are
> engaging in an amazing fraud.
> If they reply to me with mathematics, either they have to admit I'm
> right, or obfuscate. But I SIMPLIFY, as I've been doing lately, which
> eventually puts them in a box. Math IS wonderful in that way.
> So some of them just switch to insulting posts meant to convince other
> readers that I must be wrong because people SAY I'm wrong, which is
> kind of interesting.
> Math society has gone rogue. Given a very simple and basic proof of a
> problem in the discipline, members of math society are choosing a
> fantasy world, where their discipline is perfect.
> It'd be like if Einstein introduced the general theory of relativity,
> and physicists spent a lot of time calling him a crank, refused to
> acknowledge experimental results verifying his theories, and spent a
> lot of effort trying to make sure that the rest of the world, never
> knew who he was.
> Mathematicians are basically behaving like sorry excuses for
> intellectuals.
> James Harris
But see, most everyone here has formal training in mathematics. I could
argue with you all day long about a physics idea (since you have a physics
degree), but if you disagree with me, does that entitle me to call you a
liar? Why or why not?
David Moran
===
Subject: Re: Math dependency logic REVISED
Do you just have a lot of time on your hand (and no life), or do you have a
*machine* write this for you?
> One of the more odd things that can happen when you deal with a
> discoverer is that you find that things you thought were simple,
> suddenly seem complicated and iffy. So I'm now facing a problem where
> people are doubting algebra, which leads to the fun question of, just
> what is the logic here?
> The issue has to do with a factor like x+2 and how you know that 2 is
> constant.
> If the logic is expanded upon, my hope is that many of you will
> realize what is happening in my core error proof, and quit doubting,
> if you are doubting, as if you're not, and understand it, then that's
> another problem entirely.
> Ok, so how do you know that with even a polynomial factor, like x+2,
> that 2 is *constant* and not related to x?
> What's the mathematical logic?
> I've talked about setting x=0, which would reveal the constant factor
> which you can look at, and I think that for some of you, the ability
> to *physically* see constants in polynomial factors, has left you
> without ever knowing the *why* behind how it works.
> How about this?
> There are an infinity of number and letter combinations, of which x+2
> is just one of that infinity. If you set x=0 though, you just have 2,
> so how do you know from whence it came?
> I mean, with just 2, well, it's just 2, so there's no reference back
> to x, or y, or any other of that infinity of possibilities.
> The answer is that 2 is just a number that has no other information
> except itself.
> Logically, you can say that 2 is *independent* of any particular
> variable, even if it's associated with it, like in an expression like
> x+2.
> Now, as 0 clears out variables set to 0, you can show independent
> terms by setting a particular value to 0, as that reveals everything
> that can be associated with an infinity of other things.
> It's like how it could be y+2, or z+2, or alpha + 2, as seeing just 2,
> doesn't tell you anything about an association.
> Possibly the problem for some of you is that you *remember* the
> previous association. That is, you know that you had x+2, then you
> set x=0, so in your mind you see a phantom x that holds the
> association.
> That's ok, but it doesn't have a *mathematical* reality because your
> memory is irrelevant.
> The reality is that as far as the math is concerned 2 is a number that
> can be by itself or associated with x or an infinity of other things,
> and the math isn't going to pick or choose based on what YOU remember.
> It handles all possibilities at once.
> And with *just* a number, it sees independence.
> That's why setting a variable to 0 is such a useful and powerful tool,
> as it reveals infinite possibilities by removing a particular
> association.
> My argument works on that principle, as by setting x or m, depending
> on what I'm calling the variable, I find that I have 7, 7 and 22 as
> *constant* terms for factors of a polynomial.
> I also know that polynomial has a factor that is constant as that
> factor is 49.
> When I divide the polynomial by 49 I have constant terms of 1, 1, and
> 22, which tells me something.
> Now those numbers don't care about x or m. They don't *know* about x
> or m, but you may remember them, so you think your memory has some
> effect, but the math sees *infinite* possibility, while you may fixate
> on an association you remember.
> In the realm of infinite possibility, it's not possible for 7, 7, and
> 22 to go to 1, 1, and 22 based on the value of x, where they check it
> first to decide how they'll behave, because they're just NUMBERS, and
> they don't have enough data associated with them to be making those
> kinds of decisions.
> It's like, if human beings on earth constrain 7, 7 and 22 so that they
> have to worry about the value of x and m, then, wow, we've affected
> all reality in all dimensions and all possibilities, just with our
> MEMORY of there being an x or m associated in some interesting
> expression.
> But, of course, your thoughts don't constrain those numbers as they
> keep operating quite well throughout Totality, despite what you may
> believe, or remember.
> Just remember that when you're considering the issue of constants in a
> math argument.
> James Harris
===
Subject: Re: Math dependency logic REVISED
> One of the more odd things that can happen when you deal with a
> discoverer is that you find that things you thought were simple,
> suddenly seem complicated and iffy. So I'm now facing a problem where
> people are doubting algebra, which leads to the fun question of, just
> what is the logic here?
> The issue has to do with a factor like x+2 and how you know that 2 is
> constant.
James, revising this post is not going to help. What on earth do you
mean how do you know 2 is constant? Do you mean that sometimes it's 3?
Technical folk sometimes make a joke like 2+1 = 4, for suitable values
of 2. But it's a joke, not a philosophical argument.
What are you talking about?
===
Subject: Re: Math dependency logic REVISED
> One of the more odd things that can happen when you deal with a
> discoverer is that you find that things you thought were simple,
> suddenly seem complicated and iffy. So I'm now facing a problem where
> people are doubting algebra, which leads to the fun question of, just
> what is the logic here?
The issue has to do with a factor like x+2 and how you know that 2 is
> constant.
James, revising this post is not going to help. What on earth do you
> mean how do you know 2 is constant? Do you mean that sometimes it's 3?
> Technical folk sometimes make a joke like 2+1 = 4, for suitable values
> of 2. But it's a joke, not a philosophical argument.
> What are you talking about?
Mathematicians have been fighting me on the issue of constant terms
being constant. It's crazy, it's wacky, and I find it infuriating, so
I set up a stage for context for readers on the other newsgroups.
Notice the replies I got, and now pay attention carefully to the
mathematics these people are fighting.
Notice how I'll be strongly emphasizing constant terms all the way
down.
P(x) = 14706125 x^3 - 900375 x^2 + 17640 x + 1078
which has a constant term that is 1078.
Well P(x) can also be written out as
P(x)= 7^2(2401 x^3 - 147 x^2 + 3x) (5^3) - 3(-1 + 49 x )(5)(7^2) + 7^3
so I can factor to get
P(x) = (5 a_1 + 7)(5 a_2 + 7)(5 a_3 + 7)
where the a's are roots of
a^3 + 3(-1 + 49x)a^2 - 49(2401 x^3 - 147 x^2 + 3x).
Notice it *appears* that the constant terms for the three factors are
all 7, which can't be right, as the constant term of P(x) is 1078, so
setting x=0, reveals
P(0) = (5(0) + 7)(5(0) + 7)(5(3) + 7) = 7(7)(22)
as the cubic defining the a's with x=0 is
a^3 - 3a^2, which has roots, 0, 0 and 3, and I've picked a_1 and a_2
for 0, so that leaves a_3 with a value of 3 when x=0.
So let a_3 = b_3 + 3, where I keep indices matched. Then I have
P(x) = (5 a_1 + 7)(5 a_2 + 7)(5 b_3 + 5(3) + 7)
P(x) = (5 a_1 + 7)(5 a_2 + 7)(5 b_3 + 22)
and now my constant terms work out correctly.
But P(x) has 49 as a factor as every term in
P(x) = 14706125 x^3 - 900375 x^2 + 17640 x + 1078
has 49 as a factor, so I can divide by 49, and dividing 1078 by 49
gives me 22, as the new constant term.
Well that means that
P(x)/49 = (5 a_1/7 + 1)(5 a_2/7 + 1)(5 b_3 + 22)
is the only way that the constant terms keep matching.
And if you let mathematicians debate that conclusion or cast doubt on
it, while calling me names and acting like I'm the one who's crazy,
then you piss on the intellectual basis for civilization itself.
Why let mathematicians get away with it? What's in it for you?
Why let them trample on civilization, as if honesty and integrity in a
discipline don't mean anything if enough people in that discipline
don't like the truth?
What's wrong with you people?
Don't ANY of you believe in anything?
James Harris
===
Subject: Re: Math dependency logic REVISED
In sci.physics, James Harris
<jstevh@msn.com> One of the more odd things that can happen when you deal 
with
a
>> discoverer is that you find that things you thought were simple,
>> suddenly seem complicated and iffy. So I'm now facing a problem where
>> people are doubting algebra, which leads to the fun question of, just
>> what is the logic here?
>> The issue has to do with a factor like x+2 and how you know that 2 is
>> constant.
>> James, revising this post is not going to help. What on earth do you
>> mean how do you know 2 is constant? Do you mean that sometimes it's
3?
>> Technical folk sometimes make a joke like 2+1 = 4, for suitable values
>> of 2. But it's a joke, not a philosophical argument.
>> What are you talking about?
> Mathematicians have been fighting me on the issue of constant terms
> being constant. It's crazy, it's wacky, and I find it infuriating, so
> I set up a stage for context for readers on the other newsgroups.
> Notice the replies I got, and now pay attention carefully to the
> mathematics these people are fighting.
> Notice how I'll be strongly emphasizing constant terms all the way
> down.
> P(x) = 14706125 x^3 - 900375 x^2 + 17640 x + 1078
> which has a constant term that is 1078.
> Well P(x) can also be written out as
> P(x)= 7^2(2401 x^3 - 147 x^2 + 3x) (5^3) - 3(-1 + 49 x )(5)(7^2) + 7^3
> so I can factor to get
> P(x) = (5 a_1 + 7)(5 a_2 + 7)(5 a_3 + 7)
> where the a's are roots of
> a^3 + 3(-1 + 49x)a^2 - 49(2401 x^3 - 147 x^2 + 3x).
Why is x still in this cubic? Are we expected to solve
for a as a function of x, while (before? after?) solving
for x in the original equation?
[rest snipped]
--
#191, ewill3@earthlink.net
It's still legal to go .sigless.
===
Subject: Re: Math dependency logic REVISED
> Mathematicians have been fighting me on the issue of constant terms
> being constant.
Step 1. Misrepresent the opposition.
[snip other steps, since 1st step is false.]
--
A man with integrity identifies, acknowledges and corrects his errors. One
without it ignores, denies or defends them.
--
Democracy: The triumph of popularity over principle.
--
http://www.crbond.com
===
Subject: Re: Math dependency logic REVISED
>> What's wrong with you people?
> Don't ANY of you believe in anything?
I believe I'll have another beer.
===
Subject: Re: Math dependency logic REVISED
>> What's wrong with you people?
> Don't ANY of you believe in anything?
> I believe I'll have another beer.
I'm *tired* of the games. Mathematicians are running and there are
posters trying to help them run, but I'm giving notice, I'll keep
putting the information out there.
Notice how I'll be strongly emphasizing constant terms all the way
down.
P(x) = 14706125 x^3 - 900375 x^2 + 17640 x + 1078
which has a constant term that is 1078.
Well P(x) can also be written out as
P(x)= 7^2(2401 x^3 - 147 x^2 + 3x) (5^3) - 3(-1 + 49 x )(5)(7^2) + 7^3
so I can factor to get
P(x) = (5 a_1 + 7)(5 a_2 + 7)(5 a_3 + 7)
where the a's are roots of
a^3 + 3(-1 + 49x)a^2 - 49(2401 x^3 - 147 x^2 + 3x).
Notice it *appears* that the constant terms for the three factors are
all 7, which can't be right, as the constant term of P(x) is 1078, so
setting x=0, reveals
P(0) = (5(0) + 7)(5(0) + 7)(5(3) + 7) = 7(7)(22)
as the cubic defining the a's with x=0 is
a^3 - 3a^2, which has roots, 0, 0 and 3, and I've picked a_1 and a_2
for 0, so that leaves a_3 with a value of 3 when x=0.
So let a_3 = b_3 + 3, where I keep indices matched. Then I have
P(x) = (5 a_1 + 7)(5 a_2 + 7)(5 b_3 + 5(3) + 7)
P(x) = (5 a_1 + 7)(5 a_2 + 7)(5 b_3 + 22)
and now my constant terms work out correctly.
But P(x) has 49 as a factor as every term in
P(x) = 14706125 x^3 - 900375 x^2 + 17640 x + 1078
has 49 as a factor, so I can divide by 49, and dividing 1078 by 49
gives me 22, as the new constant term.
Well that means that
P(x)/49 = (5 a_1/7 + 1)(5 a_2/7 + 1)(5 b_3 + 22)
is the only way that the constant terms keep matching.
And if you let mathematicians debate that conclusion or cast doubt on
it, while calling me names and acting like I'm the one who's crazy,
then you piss on the intellectual basis for civilization itself.
Why let mathematicians get away with it? What's in it for you?
Why let them trample on civilization, as if honesty and integrity in a
discipline don't mean anything if enough people in that discipline
don't like the truth?
What's wrong with you people?
Don't ANY of you believe in anything?
James Harris
===
Subject: Re: Math dependency logic REVISED
One of the interesting things I've noticed about mathematics is that the
truth or falsity of a mathematical statement is not affected by the
number of times it is repeated.
Gib
===
Subject: Re: Math dependency logic REVISED
>One of the interesting things I've noticed about mathematics is that the
>truth or falsity of a mathematical statement is not affected by the
>number of times it is repeated.
You can say that again.
>Gib
**
===
Subject: Re: Math dependency logic REVISED
[.snip.]
>Notice how I'll be strongly emphasizing constant terms all the way
>down.
>P(x) = 14706125 x^3 - 900375 x^2 + 17640 x + 1078
>which has a constant term that is 1078.
>Well P(x) can also be written out as
>P(x)= 7^2(2401 x^3 - 147 x^2 + 3x) (5^3) - 3(-1 + 49 x )(5)(7^2) + 7^3
>so I can factor to get
>P(x) = (5 a_1 + 7)(5 a_2 + 7)(5 a_3 + 7)
>where the a's are roots of
>a^3 + 3(-1 + 49x)a^2 - 49(2401 x^3 - 147 x^2 + 3x).
>Notice it *appears* that the constant terms for the three factors are
>all 7, which can't be right, as the constant term of P(x) is 1078, so
>setting x=0, reveals
>P(0) = (5(0) + 7)(5(0) + 7)(5(3) + 7) = 7(7)(22)
>as the cubic defining the a's with x=0 is
>a^3 - 3a^2, which has roots, 0, 0 and 3, and I've picked a_1 and a_2
>for 0, so that leaves a_3 with a value of 3 when x=0.
>So let a_3 = b_3 + 3, where I keep indices matched. Then I have
>P(x) = (5 a_1 + 7)(5 a_2 + 7)(5 b_3 + 5(3) + 7)
>P(x) = (5 a_1 + 7)(5 a_2 + 7)(5 b_3 + 22)
>and now my constant terms work out correctly.
>But P(x) has 49 as a factor as every term in
>P(x) = 14706125 x^3 - 900375 x^2 + 17640 x + 1078
>has 49 as a factor, so I can divide by 49, and dividing 1078 by 49
>gives me 22, as the new constant term.
>Well that means that
>P(x)/49 = (5 a_1/7 + 1)(5 a_2/7 + 1)(5 b_3 + 22)
>is the only way that the constant terms keep matching.
No. Here's another way:
P(x)/49 = [ (5a_1(x)/w_1(x) + (7/w_1(x)) -1) + 1 ]
* [ (5a_2(x)/w_2(x) + (7/w_2(x)) -1) + 1 ]
* [ ( ( (5b_3(x)+22)/w_3(x) ) -22 ) + 22 ]
where w_1(x) is the common factor of a_1(x) and 7 (which happens to
equal 7 at x=0); w_2(x) is the common factor of a_2(x) and 7 (which
happens to equal 7 at x=0); and w_3(x) is the common factor of a_3(x)
and 7 (which happens to equal 1 at x=0).
So long as w_1(x)*w_2(x)*w_3(x) = 49, the equality is true, the
constant terms still match.
You are ASSUMING that 7/w_1(x) = 1 for all values of x. But that is
what you want to PROVE. So you are engaging in a circular argument.
Remember: your definitions are:
the constant term of f(x) is f(0); and we write f(x) as
f(x) = g(x) + f(0), where g(x) = f(x)-f(0).
That is, all you are doing is adding and subtracting f(0) in your
expression, just as I did above.
In order to conclude that
(5a_1(x)/w_1(x) + (7/w_1(x)) -1) = 5a_1(x)/7
you must be assuming that w_1(x) = 7 for all x. But that is your
claimed CONCLUSION, so you cot assume it.
To conclude that
(5a_2(x)/w_2(x) + (7/w_2(x)) -1) = 5a_2(x)/7
for all x, you must be assuming that w_2(x)=7 for all x, but that is
your claimed CONCLUSION, so you cot assume it.
To conclude that
(5b_3(x)+22)/w_3(x) ) -22 = 5b_3(x)+22
you must be assuming that w_3(x) = 1 for all x; but that is your
claimed CONCLUSION, so you cot assume it.
Why do you take so much trouble to expose such a reasoner as
Mr. Smith? I answer as a deceased friend of mine used to answer
on like occasions - A man's capacity is no measure of his power
to do mischief. Mr. Smith has untiring energy, which does
something; self-evident honesty of conviction, which does more;
and a long purse, which does most of all. He has made at least
ten publications, full of figures few readers can criticize. A great
many people are staggered to this extent, that they imagine there
must be the indefinite something in the mysterious all this.
They are brought to the point of suspicion that the mathematicians
ought not to treat all this with such undisguised contempt,
at least.
-- A Budget of Paradoxes, Vol. 2 p. 129 by Augustus de Morgan
Arturo Magidin
magidin@math.berkeley.edu
===
Subject: Re: Math dependency logic REVISED
> The issue has to do with a factor like x+2 and how you know that 2 is
> constant.
2 = 1 + 1 for nearly all values of 1.
Has anyone ever told you that you are in idiot and a mathematical
incompetent?
Bob Kolker
===
Subject: Re: Math dependency logic REVISED [JSH, needless to say]
> The issue has to do with a factor like x+2 and how you know that 2 is
> constant.
> 2 = 1 + 1 for nearly all values of 1.
> Has anyone ever told you that you are in idiot and a mathematical
> incompetent?
You must me new to sci.math, BK :) Hundreds have told him.
LH
===
Subject: Re: Math dependency logic REVISED
> One of the more odd things that can happen when you deal with a
> discoverer is that you find that things you thought were simple,
> suddenly seem complicated and iffy.
http://b5.sdvc.uwyo.edu/bab5/snds/argcstpd.wav
http://w0rli.home.att.net/youare.swf
http://www.mazepath.com/uncleal/sunshine.jpg
Harris, did you ever wonder why dog turds weathered white through the
1960s but don't do that any more? Uncle Al knows.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
Quis custodiet ipsos custodes? The Net!
===
Subject: Re: Math dependency logic REVISED
> Harris, did you ever wonder why dog turds weathered white through the
> 1960s but don't do that any more? Uncle Al knows.
I'm intrigued. Why is it?
BTW, are there any mammals for which your URL is not toxic?
Gib
===
Subject: Re: Math dependency logic REVISED
permission for an emailed response.
> Ok, so how do you know that with even a polynomial factor, like x+2,
> that 2 is *constant* and not related to x?
It doesn't matter whether it is constant or not. The exact same
identities apply.
Thomas
===
Subject: Tunze
I No speak inglisch, sorry
________________________________________________4
2.0| |
1,9 | |
1.8 | |
1,7 | |
1,6 | |
1,5| |
1,4| |
1,3| | sqrt 2
1,2| | /
1,1|__!__|__|__|__|__|__|__|__!_1^2_|__|__|__|__|__|__|__|__|
1,0| /|
0;9| / |
0,8| / |
0,7| / |
0,6|____________ 0,5 |
0,5| | |
0,4| | |
0,3| 0,5*0,5= | |
0,2| 0,25 | |
0,1|__|__|__|__|__|__|__|__|__|__1__|__|__|__|__|__|__|__|__|2
0*0 0,1 0.5
0*0=0
0*0,1=0,1 lineare.
0,1 della Tunze, is linea, 0,1*0,1 is quadrato =0,1^2
0,10 della Tunze is linea, 0,10*0,10 =0,10^2=100*(0,1^2)=1^2.
0,10 *0 = 0,10 Lineare!!
0,10*0,1=0,10*(0,1^2) quindi area.
--
Sorrentino, libero Ricercatore
Web: http://digilander.libero.it/socratis
===
Subject: Integral of e^x^2 dx ?
I am an undergrad college student and I ran across a problem that intrigued
me. What is the integral of e^x^2 dx ? I asked a few teachers and searched
the internet for a little while, but to no avail. Does anyone out there 
have
any idea how to solve this one? Possibly prove it too? I'm killing myself
not being able to figure it out even after a week of thought!!!
Kris
===
Subject: Re: Integral of e^x^2 dx ?
could be expressed as some form of error function
> I am an undergrad college student and I ran across a problem that
intrigued me. What is the integral of e^x^2 dx ? I asked a few teachers
and searched the internet for a little while, but to no avail. Does anyone
out there have any idea how to solve this one? Possibly prove it too? I'm
killing myself not being able to figure it out even after a week of
thought!!!
> Kris
===
Subject: Re: Integral of e^x^2 dx ?
> I am an undergrad college student and I ran across a problem that
intrigued me. What is the integral of e^x^2 dx ? I asked a few teachers
and searched the internet for a little while, but to no avail. Does anyone
out there have any idea how to solve this one? Possibly prove it too? I'm
killing myself not being able to figure it out even after a week of
thought!!!
> Kris
One could also numerically integrate it. Such as using Simpson's rule, or
the trapezoidal rule.
Lurch
===
Subject: Re: Integral of e^x^2 dx ?
> I am an undergrad college student and I ran across a problem that
intrigued
> me. What is the integral of e^x^2 dx ? I asked a few teachers and
searched
> the internet for a little while, but to no avail. Does anyone out there
have
> any idea how to solve this one? Possibly prove it too? I'm killing
myself
> not being able to figure it out even after a week of thought!!!
> Kris
The integral of e^(x^2) is not an elementary function.
===
Subject: Re: Integral of e^x^2 dx ?
> I am an undergrad college student and I ran across a problem that
> intrigued me. What is the integral of e^x^2 dx ? I asked a few teachers
> and searched the internet for a little while, but to no avail. Does
> anyone out there have any idea how to solve this one? Possibly prove it
> too? I'm killing myself not being able to figure it out even after a
week
> of thought!!!
> Kris
For the indefinite integral, there is no elementary expression. It can be
expressed as an integral or an infinite power series but that's about it.
I've never seen a proof of this but that's what I'm told anyway.
For the improper, definite integral over the entire real line (i.e.
int(e^x^2,x=-infinity..infinity) ), the answer is of course infinite.
However, if you add in a little negative sign to make
int(e^(-x^2),x=-infinity..infinity) the answer is, incredibly, sqrt(pi).
The proof of this is one of my favorite proofs. You'll probably see it if
you take vector calculus.
Have a tolerable existence. Eli
===
Subject: Re: Integral of e^x^2 dx ?
> I am an undergrad college student and I ran across a problem that
intrigued me. What is the integral of e^x^2 dx ? I asked a few teachers
and searched the internet for a little while, but to no avail. Does anyone
out there have any idea how to solve this one? Possibly prove it too? I'm
killing myself not being able to figure it out even after a week of
thought!!!
> Kris
Try looking at the Power Series for e^x.
David Moran
===
Subject: Re: Kent William Rathwell - March 13th 1971
>R A T H W E L L
>18 1 20 8 23 5 12 12 = 99
> In the afternoon I went to Starbucks on the corner of 22nd Street and
2nd
>Ave. and met Kent, he is from Ontario and in town for business, he is
>seeking out the purchase of farm land for foreign clients. Based upon
Kent's
<<<snipped a lot of psycho crap from Shawn pedophile-boy Kabatoff>
The following (courtesy of Waxy.org) is sort of an unofficial FAQ
explaining the psychotic nonsense posted to Usenet by Shawn Daryl
Kabatoff AKA Dar, AKA Probababbilities. And now AKA marcia and
me.
WARNING: Read below before even thinking about responding to this
twit.
http://www.waxy.org/archive/2002/05/21/dar_kaba.shtml#000643
Usenet has the tendency to provide a public forum for those who would
normally be scribbling in a closet. For example, take Daryl Shawn
Kabatoff. For the last few years, he's methodically gathered
statistics from various sources, ranging from local newspaper
obituary pages to the food court of the Saskatoon Midtown Plaza mall.
With all the raw data he's collected, he's attempting to prove daily
that our full names are in mathematical harmony with our birthdays.
His rants normally focus on a single individual he's met or read
about, starting with calculations related to their birthdate and full
names, blending in whatever other personal information about their
family members, spouses, birthplace, and career he's been able to
zealotry, and personal torment. I've never seen anything like it.
With all the prime numbers, Fibonacci sequences and biblical
references, it's like reading the notebooks of Maximillian Cohen and
John Nash combined. Unsurprisingly, several posts unfold to reveal a
history of painful mental illness. If you have some time, take a look.
I've detailed his posting history and a several sample posts below.
Usenet Posting History:
January 27, 1999 to July 5, 2000 as Catsco@home.com
December 9, 2000 to May 4, 2001 as s.kabatoff@sk.sympatico.ca
Oct 30, 2001 to Oct 31, 2001 as kabatoff@the.link.ca
January 20, 2002 to April 17, 2002 as s_kabatoff@hotmail.com (original
posts have been
removed from Google Groups archive)
April 26, 2002 to Present as dar_kabatoff@hotmail.com
Selected Posts:
Tessa Lynne Smith
Dastageer Sakhizai and Helen Smith
Brett David Maki
Andrew Meredith Cotton
Kathryn Lee Hipperson
Amanda Dawn Newton
Mona Marie Etcheverry
Tony Peter Nuspl
Lisa Charlene McMillan
Grant Allyn Wood
Comments
scarier still is that saskatoon is my hometown, though not my current
residence. and every single place he's mentioned in his posts (most
notably nervous harold's and the roastary) were either places i've
been (as it's a small city of 200K) or hangouts, ie. the two places
mentioned. chances are i could email some friends back home and find
out if they know of him, they (my friends that is) being of the
broadway-centred slacker ilk. myself, too, until i got out of there.
eh, anyways. thought it odd to see all this. midtown mall. i ate my
meals there, whilst waiting several days in line for star wars episode
one, at the theatre across the street.
posted by raad on May 22, 2002 06:20 PM
Fascinating. It's like he's trying to take chaos and bind it into
whatever rules he can find, religious, logical and otherwise. Numbers
and math have a reliable pattern, something that can always be proven
to true or false. People and religion do not. It reminds me of Darren
Aronofsky's movie Pi. It's the story of an paraniod genius who is
trying to find a pattern in Pi. A group that takes interest in his
work is convinced that the existence of Pi, a number whose existence
can be proven but no quantified, is proof of the existence of God.
Kabatoff's hunt for patterns in something as random as name selection
is a way to reconcile his deeply logical thought process with his
conflicting religious views.
Exactly. I probably shouldn't have, but I e-mailed Daryl yesterday,
asking him if he'd be willing to create a numerological analysis for
me. I also asked him if he had seen either Pi or A Beautiful Mind, and
what he thought of them. If he replies, I'll be sure to post it.
I baked many pumpkin pies for Shawn (he likes pumpkin pies). I rubbed
pumpkin pie all over my breasts for him, and my breasts turned orange.
I am a pumpkin for Shawn.
posted by Trisha Blondie on July 24, 2002 10:41 PM
Um, that's swell. So, you're in love with him?
Shawn once went to a funeral for a Jehovah Witness that shot himself
and the lemon tarts were very bad, they were not only sour but were
rubbery as well. Shawn said that the guy was some kind of Jehovah
Witness prophet, he saw in advance that the lemon tarts at his funeral
were to be very very bad, and so he shot himself. Shawn said that he
never ate pumpkin pie at a funeral but would like to some day. Shawn
likes pumpkin pie and so I have been practicing to make very good
pumpkin pies.
posted by Trisha Blondie on July 25, 2002 02:49 PM
Shawn said that the lemon tarts were sour, bitter and rubbery.
I don't think this guy takes notes. I think he has Total Recall, and
it has driven him insane...
Oh... I almost forgot... I didnt spend thousands of dollars a day
tormenting Daryl... We got a deal on tormenting that fiscal year, it
only came to about 37cents a day....
Mr. Kabatoff attempts to portray himself as a victim, but in fact he
is a violent predatory pedophile who is well known to his local law
enforcement. In his post to multiple newsgroups with the subject
Collecting Mail For The Coming Anti-Christ, he encourages mothers to
send him photos of their naked daughters. Mr Kabatoff explains, I
personally did not want photographs being mailed to (the coming
Ant-Christ) that were of underage children unless the parent was
signing consent. He is bed from virtually all the shopping malls
in his community because he stalks young people and sexually harasses
them. He has an extensive arrest record which includes sexual
molestation charges. He's been hospitalized in mental institutions
about his contact with young girls in many posts. Search newsgroup
archives for posts by him containing the word nubile. As part of his
harrassment, he provides personal details in a public forum, such as
the real names of real children, in these and other posts. About one
wanted her and her sister dead.
He not only curses children and prays for their death in his posts, he
also enjoys attending the funerals of young people: And so, since
nubile sweeties are found in greatest abundance at the funerals of
high school students, then it is the funerals of high school students
that make the very very best funerals, especially if there is food...
I stuff my face (and my pockets) with all the good food and look at
all the pretty nubile sweeties and have the time of my life..
r=&ie=UTF-8&scoring=d&selm=LfXN8.63042%24R53.25142039%40twister.socal.rr.
com&rnum=1
Many of his posts are sent to alt.teens.advice. However, he liberally
spams, floods and crossposts his off-topic threatening and offensive
missives to countless newsgroups. Some people HAVE problems and some
folks ARE problems. Don't dismiss Mr. Kabatoff as a harmless nut. When
he sends these posts to any newgroup, please help by reporting him to
I knew of him when I was attending the University of Saskatchewan.
He'd hang out in the Arts computer lab and all you'd see is screens of
numbers racing by on his laptop. I have an original copy of his
Collecting Mail for the Coming Anti-Christ pamphlet, and have seen
him be hauled away by campus security on more than one occasion. My
friends and I refer to him as Crazy Number Man.
I've been posting to (and about) Shawn for over two years with big
gaps in between. He has seen Pi and didn't like it and didn't think it
resembled him at all. (Wrong, it fits him to a tee) He doesn't have
total recall and has stated that he travels with a lap top to notate
items. Also, he uses cut n' paste a lot if you read all the way
through his ramblings. He is anti-social as shown by his angry
statements towards those who, by his own admission, have been kind
(but not kind enough) to him. Still, he's intelligent and seems to be
able to take a joke on occassion. That's where I came in.
ALOHA
Reply to group
(Unsolicited e-mail is deleted from the server unread
if it comes from anyone not already in my addressbook.
I'll never even see it)
===
Subject: Re: Darwin Henry Seed - March 2nd 1960
>S E E D
>19 5 5 4 = 33
> Shortly after midnite today I found the obituary of a Mormon kid
(Braeden
>John Vermeeren) in the Calgary Herald, I was working on those stats during
>the night and posted them on the usenet, then later in the day I met
Darwin,
<<<snipped a lot of psycho crap from Shawn pedophile-boy Kabatoff>
The following (courtesy of Waxy.org) is sort of an unofficial FAQ
explaining the psychotic nonsense posted to Usenet by Shawn Daryl
Kabatoff AKA Dar, AKA Probababbilities. And now AKA marcia and
me.
WARNING: Read below before even thinking about responding to this
twit.
http://www.waxy.org/archive/2002/05/21/dar_kaba.shtml#000643
Usenet has the tendency to provide a public forum for those who would
normally be scribbling in a closet. For example, take Daryl Shawn
Kabatoff. For the last few years, he's methodically gathered
statistics from various sources, ranging from local newspaper
obituary pages to the food court of the Saskatoon Midtown Plaza mall.
With all the raw data he's collected, he's attempting to prove daily
that our full names are in mathematical harmony with our birthdays.
His rants normally focus on a single individual he's met or read
about, starting with calculations related to their birthdate and full
names, blending in whatever other personal information about their
family members, spouses, birthplace, and career he's been able to
zealotry, and personal torment. I've never seen anything like it.
With all the prime numbers, Fibonacci sequences and biblical
references, it's like reading the notebooks of Maximillian Cohen and
John Nash combined. Unsurprisingly, several posts unfold to reveal a
history of painful mental illness. If you have some time, take a look.
I've detailed his posting history and a several sample posts below.
Usenet Posting History:
January 27, 1999 to July 5, 2000 as Catsco@home.com
December 9, 2000 to May 4, 2001 as s.kabatoff@sk.sympatico.ca
Oct 30, 2001 to Oct 31, 2001 as kabatoff@the.link.ca
January 20, 2002 to April 17, 2002 as s_kabatoff@hotmail.com (original
posts have been
removed from Google Groups archive)
April 26, 2002 to Present as dar_kabatoff@hotmail.com
Selected Posts:
Tessa Lynne Smith
Dastageer Sakhizai and Helen Smith
Brett David Maki
Andrew Meredith Cotton
Kathryn Lee Hipperson
Amanda Dawn Newton
Mona Marie Etcheverry
Tony Peter Nuspl
Lisa Charlene McMillan
Grant Allyn Wood
Comments
scarier still is that saskatoon is my hometown, though not my current
residence. and every single place he's mentioned in his posts (most
notably nervous harold's and the roastary) were either places i've
been (as it's a small city of 200K) or hangouts, ie. the two places
mentioned. chances are i could email some friends back home and find
out if they know of him, they (my friends that is) being of the
broadway-centred slacker ilk. myself, too, until i got out of there.
eh, anyways. thought it odd to see all this. midtown mall. i ate my
meals there, whilst waiting several days in line for star wars episode
one, at the theatre across the street.
posted by raad on May 22, 2002 06:20 PM
Fascinating. It's like he's trying to take chaos and bind it into
whatever rules he can find, religious, logical and otherwise. Numbers
and math have a reliable pattern, something that can always be proven
to true or false. People and religion do not. It reminds me of Darren
Aronofsky's movie Pi. It's the story of an paraniod genius who is
trying to find a pattern in Pi. A group that takes interest in his
work is convinced that the existence of Pi, a number whose existence
can be proven but no quantified, is proof of the existence of God.
Kabatoff's hunt for patterns in something as random as name selection
is a way to reconcile his deeply logical thought process with his
conflicting religious views.
Exactly. I probably shouldn't have, but I e-mailed Daryl yesterday,
asking him if he'd be willing to create a numerological analysis for
me. I also asked him if he had seen either Pi or A Beautiful Mind, and
what he thought of them. If he replies, I'll be sure to post it.
I baked many pumpkin pies for Shawn (he likes pumpkin pies). I rubbed
pumpkin pie all over my breasts for him, and my breasts turned orange.
I am a pumpkin for Shawn.
posted by Trisha Blondie on July 24, 2002 10:41 PM
Um, that's swell. So, you're in love with him?
Shawn once went to a funeral for a Jehovah Witness that shot himself
and the lemon tarts were very bad, they were not only sour but were
rubbery as well. Shawn said that the guy was some kind of Jehovah
Witness prophet, he saw in advance that the lemon tarts at his funeral
were to be very very bad, and so he shot himself. Shawn said that he
never ate pumpkin pie at a funeral but would like to some day. Shawn
likes pumpkin pie and so I have been practicing to make very good
pumpkin pies.
posted by Trisha Blondie on July 25, 2002 02:49 PM
Shawn said that the lemon tarts were sour, bitter and rubbery.
I don't think this guy takes notes. I think he has Total Recall, and
it has driven him insane...
Oh... I almost forgot... I didnt spend thousands of dollars a day
tormenting Daryl... We got a deal on tormenting that fiscal year, it
only came to about 37cents a day....
Mr. Kabatoff attempts to portray himself as a victim, but in fact he
is a violent predatory pedophile who is well known to his local law
enforcement. In his post to multiple newsgroups with the subject
Collecting Mail For The Coming Anti-Christ, he encourages mothers to
send him photos of their naked daughters. Mr Kabatoff explains, I
personally did not want photographs being mailed to (the coming
Ant-Christ) that were of underage children unless the parent was
signing consent. He is bed from virtually all the shopping malls
in his community because he stalks young people and sexually harasses
them. He has an extensive arrest record which includes sexual
molestation charges. He's been hospitalized in mental institutions
about his contact with young girls in many posts. Search newsgroup
archives for posts by him containing the word nubile. As part of his
harrassment, he provides personal details in a public forum, such as
the real names of real children, in these and other posts. About one
wanted her and her sister dead.
He not only curses children and prays for their death in his posts, he
also enjoys attending the funerals of young people: And so, since
nubile sweeties are found in greatest abundance at the funerals of
high school students, then it is the funerals of high school students
that make the very very best funerals, especially if there is food...
I stuff my face (and my pockets) with all the good food and look at
all the pretty nubile sweeties and have the time of my life..
r=&ie=UTF-8&scoring=d&selm=LfXN8.63042%24R53.25142039%40twister.socal.rr.
com&rnum=1
Many of his posts are sent to alt.teens.advice. However, he liberally
spams, floods and crossposts his off-topic threatening and offensive
missives to countless newsgroups. Some people HAVE problems and some
folks ARE problems. Don't dismiss Mr. Kabatoff as a harmless nut. When
he sends these posts to any newgroup, please help by reporting him to
I knew of him when I was attending the University of Saskatchewan.
He'd hang out in the Arts computer lab and all you'd see is screens of
numbers racing by on his laptop. I have an original copy of his
Collecting Mail for the Coming Anti-Christ pamphlet, and have seen
him be hauled away by campus security on more than one occasion. My
friends and I refer to him as Crazy Number Man.
I've been posting to (and about) Shawn for over two years with big
gaps in between. He has seen Pi and didn't like it and didn't think it
resembled him at all. (Wrong, it fits him to a tee) He doesn't have
total recall and has stated that he travels with a lap top to notate
items. Also, he uses cut n' paste a lot if you read all the way
through his ramblings. He is anti-social as shown by his angry
statements towards those who, by his own admission, have been kind
(but not kind enough) to him. Still, he's intelligent and seems to be
able to take a joke on occassion. That's where I came in.
ALOHA
Reply to group
(Unsolicited e-mail is deleted from the server unread
if it comes from anyone not already in my addressbook.
I'll never even see it)
===
Subject: Re: Erin Marie Sorenson - August 5th 1985
>Friday April 12th 2002 102/263 16490
>S O R E N S O N
>19 15 18 5 14 19 15 14 = 119
> Oh dear. Nubile sweety Erin Sorenson lost control of her little Honda
>Civic on April 10th and swerved into the path of a big Buick Lesabre. The
>supposed accident occurred on Catron Boulevard, Erin's little Civic was
<<<snipped a lot of psycho crap from Shawn pedophile-boy Kabatoff>
The following (courtesy of Waxy.org) is sort of an unofficial FAQ
explaining the psychotic nonsense posted to Usenet by Shawn Daryl
Kabatoff AKA Dar, AKA Probababbilities. And now AKA marcia and
me.
WARNING: Read below before even thinking about responding to this
twit.
http://www.waxy.org/archive/2002/05/21/dar_kaba.shtml#000643
Usenet has the tendency to provide a public forum for those who would
normally be scribbling in a closet. For example, take Daryl Shawn
Kabatoff. For the last few years, he's methodically gathered
statistics from various sources, ranging from local newspaper
obituary pages to the food court of the Saskatoon Midtown Plaza mall.
With all the raw data he's collected, he's attempting to prove daily
that our full names are in mathematical harmony with our birthdays.
His rants normally focus on a single individual he's met or read
about, starting with calculations related to their birthdate and full
names, blending in whatever other personal information about their
family members, spouses, birthplace, and career he's been able to
zealotry, and personal torment. I've never seen anything like it.
With all the prime numbers, Fibonacci sequences and biblical
references, it's like reading the notebooks of Maximillian Cohen and
John Nash combined. Unsurprisingly, several posts unfold to reveal a
history of painful mental illness. If you have some time, take a look.
I've detailed his posting history and a several sample posts below.
Usenet Posting History:
January 27, 1999 to July 5, 2000 as Catsco@home.com
December 9, 2000 to May 4, 2001 as s.kabatoff@sk.sympatico.ca
Oct 30, 2001 to Oct 31, 2001 as kabatoff@the.link.ca
January 20, 2002 to April 17, 2002 as s_kabatoff@hotmail.com (original
posts have been
removed from Google Groups archive)
April 26, 2002 to Present as dar_kabatoff@hotmail.com
Selected Posts:
Tessa Lynne Smith
Dastageer Sakhizai and Helen Smith
Brett David Maki
Andrew Meredith Cotton
Kathryn Lee Hipperson
Amanda Dawn Newton
Mona Marie Etcheverry
Tony Peter Nuspl
Lisa Charlene McMillan
Grant Allyn Wood
Comments
scarier still is that saskatoon is my hometown, though not my current
residence. and every single place he's mentioned in his posts (most
notably nervous harold's and the roastary) were either places i've
been (as it's a small city of 200K) or hangouts, ie. the two places
mentioned. chances are i could email some friends back home and find
out if they know of him, they (my friends that is) being of the
broadway-centred slacker ilk. myself, too, until i got out of there.
eh, anyways. thought it odd to see all this. midtown mall. i ate my
meals there, whilst waiting several days in line for star wars episode
one, at the theatre across the street.
posted by raad on May 22, 2002 06:20 PM
Fascinating. It's like he's trying to take chaos and bind it into
whatever rules he can find, religious, logical and otherwise. Numbers
and math have a reliable pattern, something that can always be proven
to true or false. People and religion do not. It reminds me of Darren
Aronofsky's movie Pi. It's the story of an paraniod genius who is
trying to find a pattern in Pi. A group that takes interest in his
work is convinced that the existence of Pi, a number whose existence
can be proven but no quantified, is proof of the existence of God.
Kabatoff's hunt for patterns in something as random as name selection
is a way to reconcile his deeply logical thought process with his
conflicting religious views.
Exactly. I probably shouldn't have, but I e-mailed Daryl yesterday,
asking him if he'd be willing to create a numerological analysis for
me. I also asked him if he had seen either Pi or A Beautiful Mind, and
what he thought of them. If he replies, I'll be sure to post it.
I baked many pumpkin pies for Shawn (he likes pumpkin pies). I rubbed
pumpkin pie all over my breasts for him, and my breasts turned orange.
I am a pumpkin for Shawn.
posted by Trisha Blondie on July 24, 2002 10:41 PM
Um, that's swell. So, you're in love with him?
Shawn once went to a funeral for a Jehovah Witness that shot himself
and the lemon tarts were very bad, they were not only sour but were
rubbery as well. Shawn said that the guy was some kind of Jehovah
Witness prophet, he saw in advance that the lemon tarts at his funeral
were to be very very bad, and so he shot himself. Shawn said that he
never ate pumpkin pie at a funeral but would like to some day. Shawn
likes pumpkin pie and so I have been practicing to make very good
pumpkin pies.
posted by Trisha Blondie on July 25, 2002 02:49 PM
Shawn said that the lemon tarts were sour, bitter and rubbery.
I don't think this guy takes notes. I think he has Total Recall, and
it has driven him insane...
Oh... I almost forgot... I didnt spend thousands of dollars a day
tormenting Daryl... We got a deal on tormenting that fiscal year, it
only came to about 37cents a day....
Mr. Kabatoff attempts to portray himself as a victim, but in fact he
is a violent predatory pedophile who is well known to his local law
enforcement. In his post to multiple newsgroups with the subject
Collecting Mail For The Coming Anti-Christ, he encourages mothers to
send him photos of their naked daughters. Mr Kabatoff explains, I
personally did not want photographs being mailed to (the coming
Ant-Christ) that were of underage children unless the parent was
signing consent. He is bed from virtually all the shopping malls
in his community because he stalks young people and sexually harasses
them. He has an extensive arrest record which includes sexual
molestation charges. He's been hospitalized in mental institutions
about his contact with young girls in many posts. Search newsgroup
archives for posts by him containing the word nubile. As part of his
harrassment, he provides personal details in a public forum, such as
the real names of real children, in these and other posts. About one
wanted her and her sister dead.
He not only curses children and prays for their death in his posts, he
also enjoys attending the funerals of young people: And so, since
nubile sweeties are found in greatest abundance at the funerals of
high school students, then it is the funerals of high school students
that make the very very best funerals, especially if there is food...
I stuff my face (and my pockets) with all the good food and look at
all the pretty nubile sweeties and have the time of my life..
r=&ie=UTF-8&scoring=d&selm=LfXN8.63042%24R53.25142039%40twister.socal.rr.
com&rnum=1
Many of his posts are sent to alt.teens.advice. However, he liberally
spams, floods and crossposts his off-topic threatening and offensive
missives to countless newsgroups. Some people HAVE problems and some
folks ARE problems. Don't dismiss Mr. Kabatoff as a harmless nut. When
he sends these posts to any newgroup, please help by reporting him to
I knew of him when I was attending the University of Saskatchewan.
He'd hang out in the Arts computer lab and all you'd see is screens of
numbers racing by on his laptop. I have an original copy of his
Collecting Mail for the Coming Anti-Christ pamphlet, and have seen
him be hauled away by campus security on more than one occasion. My
friends and I refer to him as Crazy Number Man.
I've been posting to (and about) Shawn for over two years with big
gaps in between. He has seen Pi and didn't like it and didn't think it
resembled him at all. (Wrong, it fits him to a tee) He doesn't have
total recall and has stated that he travels with a lap top to notate
items. Also, he uses cut n' paste a lot if you read all the way
through his ramblings. He is anti-social as shown by his angry
statements towards those who, by his own admission, have been kind
(but not kind enough) to him. Still, he's intelligent and seems to be
able to take a joke on occassion. That's where I came in.
ALOHA
Reply to group
(Unsolicited e-mail is deleted from the server unread
if it comes from anyone not already in my addressbook.
I'll never even see it)
===
Subject: Re: Erin Marie Sorenson - August 5th 1985
[snips]
> The central mathematical puzzles are absurd. The math major chick
> sweats and grunts to figure out if numbers ending in 5 and even
> numbers, for instance, are prime. (Prime numbers being those divisible
> only by themselves and one, for those not keeping track of such things
> since high school.) Uh...duh, they're not. Anything ending in 5 is
> divisible by 5, and no even number can be prime.
Thus, neither 5 nor 2 are prime. Hmm. Not sure many math geeks would
agree. :)
===
Subject: Re: Braeden John Vermeeren - November 9th 2001
>V E R M E E R E N
>22 5 18 13 5 5 18 5 14 = 105
<<<snipped a lot of psycho crap from Shawn pedophile-boy Kabatoff>
The following (courtesy of Waxy.org) is sort of an unofficial FAQ
explaining the psychotic nonsense posted to Usenet by Shawn Daryl
Kabatoff AKA Dar, AKA Probababbilities. And now AKA marcia and
me.
WARNING: Read below before even thinking about responding to this
twit.
http://www.waxy.org/archive/2002/05/21/dar_kaba.shtml#000643
Usenet has the tendency to provide a public forum for those who would
normally be scribbling in a closet. For example, take Daryl Shawn
Kabatoff. For the last few years, he's methodically gathered
statistics from various sources, ranging from local newspaper
obituary pages to the food court of the Saskatoon Midtown Plaza mall.
With all the raw data he's collected, he's attempting to prove daily
that our full names are in mathematical harmony with our birthdays.
His rants normally focus on a single individual he's met or read
about, starting with calculations related to their birthdate and full
names, blending in whatever other personal information about their
family members, spouses, birthplace, and career he's been able to
zealotry, and personal torment. I've never seen anything like it.
With all the prime numbers, Fibonacci sequences and biblical
references, it's like reading the notebooks of Maximillian Cohen and
John Nash combined. Unsurprisingly, several posts unfold to reveal a
history of painful mental illness. If you have some time, take a look.
I've detailed his posting history and a several sample posts below.
Usenet Posting History:
January 27, 1999 to July 5, 2000 as Catsco@home.com
December 9, 2000 to May 4, 2001 as s.kabatoff@sk.sympatico.ca
Oct 30, 2001 to Oct 31, 2001 as kabatoff@the.link.ca
January 20, 2002 to April 17, 2002 as s_kabatoff@hotmail.com (original
posts have been
removed from Google Groups archive)
April 26, 2002 to Present as dar_kabatoff@hotmail.com
Selected Posts:
Tessa Lynne Smith
Dastageer Sakhizai and Helen Smith
Brett David Maki
Andrew Meredith Cotton
Kathryn Lee Hipperson
Amanda Dawn Newton
Mona Marie Etcheverry
Tony Peter Nuspl
Lisa Charlene McMillan
Grant Allyn Wood
Comments
scarier still is that saskatoon is my hometown, though not my current
residence. and every single place he's mentioned in his posts (most
notably nervous harold's and the roastary) were either places i've
been (as it's a small city of 200K) or hangouts, ie. the two places
mentioned. chances are i could email some friends back home and find
out if they know of him, they (my friends that is) being of the
broadway-centred slacker ilk. myself, too, until i got out of there.
eh, anyways. thought it odd to see all this. midtown mall. i ate my
meals there, whilst waiting several days in line for star wars episode
one, at the theatre across the street.
posted by raad on May 22, 2002 06:20 PM
Fascinating. It's like he's trying to take chaos and bind it into
whatever rules he can find, religious, logical and otherwise. Numbers
and math have a reliable pattern, something that can always be proven
to true or false. People and religion do not. It reminds me of Darren
Aronofsky's movie Pi. It's the story of an paraniod genius who is
trying to find a pattern in Pi. A group that takes interest in his
work is convinced that the existence of Pi, a number whose existence
can be proven but no quantified, is proof of the existence of God.
Kabatoff's hunt for patterns in something as random as name selection
is a way to reconcile his deeply logical thought process with his
conflicting religious views.
Exactly. I probably shouldn't have, but I e-mailed Daryl yesterday,
asking him if he'd be willing to create a numerological analysis for
me. I also asked him if he had seen either Pi or A Beautiful Mind, and
what he thought of them. If he replies, I'll be sure to post it.
I baked many pumpkin pies for Shawn (he likes pumpkin pies). I rubbed
pumpkin pie all over my breasts for him, and my breasts turned orange.
I am a pumpkin for Shawn.
posted by Trisha Blondie on July 24, 2002 10:41 PM
Um, that's swell. So, you're in love with him?
Shawn once went to a funeral for a Jehovah Witness that shot himself
and the lemon tarts were very bad, they were not only sour but were
rubbery as well. Shawn said that the guy was some kind of Jehovah
Witness prophet, he saw in advance that the lemon tarts at his funeral
were to be very very bad, and so he shot himself. Shawn said that he
never ate pumpkin pie at a funeral but would like to some day. Shawn
likes pumpkin pie and so I have been practicing to make very good
pumpkin pies.
posted by Trisha Blondie on July 25, 2002 02:49 PM
Shawn said that the lemon tarts were sour, bitter and rubbery.
I don't think this guy takes notes. I think he has Total Recall, and
it has driven him insane...
Oh... I almost forgot... I didnt spend thousands of dollars a day
tormenting Daryl... We got a deal on tormenting that fiscal year, it
only came to about 37cents a day....
Mr. Kabatoff attempts to portray himself as a victim, but in fact he
is a violent predatory pedophile who is well known to his local law
enforcement. In his post to multiple newsgroups with the subject
Collecting Mail For The Coming Anti-Christ, he encourages mothers to
send him photos of their naked daughters. Mr Kabatoff explains, I
personally did not want photographs being mailed to (the coming
Ant-Christ) that were of underage children unless the parent was
signing consent. He is bed from virtually all the shopping malls
in his community because he stalks young people and sexually harasses
them. He has an extensive arrest record which includes sexual
molestation charges. He's been hospitalized in mental institutions
about his contact with young girls in many posts. Search newsgroup
archives for posts by him containing the word nubile. As part of his
harrassment, he provides personal details in a public forum, such as
the real names of real children, in these and other posts. About one
wanted her and her sister dead.
He not only curses children and prays for their death in his posts, he
also enjoys attending the funerals of young people: And so, since
nubile sweeties are found in greatest abundance at the funerals of
high school students, then it is the funerals of high school students
that make the very very best funerals, especially if there is food...
I stuff my face (and my pockets) with all the good food and look at
all the pretty nubile sweeties and have the time of my life..
r=&ie=UTF-8&scoring=d&selm=LfXN8.63042%24R53.25142039%40twister.socal.rr.
com&rnum=1
Many of his posts are sent to alt.teens.advice. However, he liberally
spams, floods and crossposts his off-topic threatening and offensive
missives to countless newsgroups. Some people HAVE problems and some
folks ARE problems. Don't dismiss Mr. Kabatoff as a harmless nut. When
he sends these posts to any newgroup, please help by reporting him to
I knew of him when I was attending the University of Saskatchewan.
He'd hang out in the Arts computer lab and all you'd see is screens of
numbers racing by on his laptop. I have an original copy of his
Collecting Mail for the Coming Anti-Christ pamphlet, and have seen
him be hauled away by campus security on more than one occasion. My
friends and I refer to him as Crazy Number Man.
I've been posting to (and about) Shawn for over two years with big
gaps in between. He has seen Pi and didn't like it and didn't think it
resembled him at all. (Wrong, it fits him to a tee) He doesn't have
total recall and has stated that he travels with a lap top to notate
items. Also, he uses cut n' paste a lot if you read all the way
through his ramblings. He is anti-social as shown by his angry
statements towards those who, by his own admission, have been kind
(but not kind enough) to him. Still, he's intelligent and seems to be
able to take a joke on occassion. That's where I came in.
ALOHA
Reply to group
(Unsolicited e-mail is deleted from the server unread
if it comes from anyone not already in my addressbook.
I'll never even see it)
===
Subject: Re: Braeden John Vermeeren - November 9th 2001
Yes, Thomas, we know by this time. Why do you not read before you post:
> WARNING: Read below before even thinking about responding to this
> twit.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland,
+31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
===
Subject: Re: Carl Richard Koopang - April 22nd 1972
>Saturday August 24th 2002 236/129 16624
> Oh dear. Rick gets his obituary published in North Dakota's Grande
Forks
>Herald, he died as a result of an automotive accident.
<<<snipped a lot of psycho crap from Shawn pedophile-boy Kabatoff>
The following (courtesy of Waxy.org) is sort of an unofficial FAQ
explaining the psychotic nonsense posted to Usenet by Shawn Daryl
Kabatoff AKA Dar, AKA Probababbilities. And now AKA marcia and
me.
WARNING: Read below before even thinking about responding to this
twit.
http://www.waxy.org/archive/2002/05/21/dar_kaba.shtml#000643
Usenet has the tendency to provide a public forum for those who would
normally be scribbling in a closet. For example, take Daryl Shawn
Kabatoff. For the last few years, he's methodically gathered
statistics from various sources, ranging from local newspaper
obituary pages to the food court of the Saskatoon Midtown Plaza mall.
With all the raw data he's collected, he's attempting to prove daily
that our full names are in mathematical harmony with our birthdays.
His rants normally focus on a single individual he's met or read
about, starting with calculations related to their birthdate and full
names, blending in whatever other personal information about their
family members, spouses, birthplace, and career he's been able to
zealotry, and personal torment. I've never seen anything like it.
With all the prime numbers, Fibonacci sequences and biblical
references, it's like reading the notebooks of Maximillian Cohen and
John Nash combined. Unsurprisingly, several posts unfold to reveal a
history of painful mental illness. If you have some time, take a look.
I've detailed his posting history and a several sample posts below.
Usenet Posting History:
January 27, 1999 to July 5, 2000 as Catsco@home.com
December 9, 2000 to May 4, 2001 as s.kabatoff@sk.sympatico.ca
Oct 30, 2001 to Oct 31, 2001 as kabatoff@the.link.ca
January 20, 2002 to April 17, 2002 as s_kabatoff@hotmail.com (original
posts have been
removed from Google Groups archive)
April 26, 2002 to Present as dar_kabatoff@hotmail.com
Selected Posts:
Tessa Lynne Smith
Dastageer Sakhizai and Helen Smith
Brett David Maki
Andrew Meredith Cotton
Kathryn Lee Hipperson
Amanda Dawn Newton
Mona Marie Etcheverry
Tony Peter Nuspl
Lisa Charlene McMillan
Grant Allyn Wood
Comments
scarier still is that saskatoon is my hometown, though not my current
residence. and every single place he's mentioned in his posts (most
notably nervous harold's and the roastary) were either places i've
been (as it's a small city of 200K) or hangouts, ie. the two places
mentioned. chances are i could email some friends back home and find
out if they know of him, they (my friends that is) being of the
broadway-centred slacker ilk. myself, too, until i got out of there.
eh, anyways. thought it odd to see all this. midtown mall. i ate my
meals there, whilst waiting several days in line for star wars episode
one, at the theatre across the street.
posted by raad on May 22, 2002 06:20 PM
Fascinating. It's like he's trying to take chaos and bind it into
whatever rules he can find, religious, logical and otherwise. Numbers
and math have a reliable pattern, something that can always be proven
to true or false. People and religion do not. It reminds me of Darren
Aronofsky's movie Pi. It's the story of an paraniod genius who is
trying to find a pattern in Pi. A group that takes interest in his
work is convinced that the existence of Pi, a number whose existence
can be proven but no quantified, is proof of the existence of God.
Kabatoff's hunt for patterns in something as random as name selection
is a way to reconcile his deeply logical thought process with his
conflicting religious views.
Exactly. I probably shouldn't have, but I e-mailed Daryl yesterday,
asking him if he'd be willing to create a numerological analysis for
me. I also asked him if he had seen either Pi or A Beautiful Mind, and
what he thought of them. If he replies, I'll be sure to post it.
I baked many pumpkin pies for Shawn (he likes pumpkin pies). I rubbed
pumpkin pie all over my breasts for him, and my breasts turned orange.
I am a pumpkin for Shawn.
posted by Trisha Blondie on July 24, 2002 10:41 PM
Um, that's swell. So, you're in love with him?
Shawn once went to a funeral for a Jehovah Witness that shot himself
and the lemon tarts were very bad, they were not only sour but were
rubbery as well. Shawn said that the guy was some kind of Jehovah
Witness prophet, he saw in advance that the lemon tarts at his funeral
were to be very very bad, and so he shot himself. Shawn said that he
never ate pumpkin pie at a funeral but would like to some day. Shawn
likes pumpkin pie and so I have been practicing to make very good
pumpkin pies.
posted by Trisha Blondie on July 25, 2002 02:49 PM
Shawn said that the lemon tarts were sour, bitter and rubbery.
I don't think this guy takes notes. I think he has Total Recall, and
it has driven him insane...
Oh... I almost forgot... I didnt spend thousands of dollars a day
tormenting Daryl... We got a deal on tormenting that fiscal year, it
only came to about 37cents a day....
Mr. Kabatoff attempts to portray himself as a victim, but in fact he
is a violent predatory pedophile who is well known to his local law
enforcement. In his post to multiple newsgroups with the subject
Collecting Mail For The Coming Anti-Christ, he encourages mothers to
send him photos of their naked daughters. Mr Kabatoff explains, I
personally did not want photographs being mailed to (the coming
Ant-Christ) that were of underage children unless the parent was
signing consent. He is bed from virtually all the shopping malls
in his community because he stalks young people and sexually harasses
them. He has an extensive arrest record which includes sexual
molestation charges. He's been hospitalized in mental institutions
about his contact with young girls in many posts. Search newsgroup
archives for posts by him containing the word nubile. As part of his
harrassment, he provides personal details in a public forum, such as
the real names of real children, in these and other posts. About one
wanted her and her sister dead.
He not only curses children and prays for their death in his posts, he
also enjoys attending the funerals of young people: And so, since
nubile sweeties are found in greatest abundance at the funerals of
high school students, then it is the funerals of high school students
that make the very very best funerals, especially if there is food...
I stuff my face (and my pockets) with all the good food and look at
all the pretty nubile sweeties and have the time of my life..
r=&ie=UTF-8&scoring=d&selm=LfXN8.63042%24R53.25142039%40twister.socal.rr.
com&rnum=1
Many of his posts are sent to alt.teens.advice. However, he liberally
spams, floods and crossposts his off-topic threatening and offensive
missives to countless newsgroups. Some people HAVE problems and some
folks ARE problems. Don't dismiss Mr. Kabatoff as a harmless nut. When
he sends these posts to any newgroup, please help by reporting him to
I knew of him when I was attending the University of Saskatchewan.
He'd hang out in the Arts computer lab and all you'd see is screens of
numbers racing by on his laptop. I have an original copy of his
Collecting Mail for the Coming Anti-Christ pamphlet, and have seen
him be hauled away by campus security on more than one occasion. My
friends and I refer to him as Crazy Number Man.
I've been posting to (and about) Shawn for over two years with big
gaps in between. He has seen Pi and didn't like it and didn't think it
resembled him at all. (Wrong, it fits him to a tee) He doesn't have
total recall and has stated that he travels with a lap top to notate
items. Also, he uses cut n' paste a lot if you read all the way
through his ramblings. He is anti-social as shown by his angry
statements towards those who, by his own admission, have been kind
(but not kind enough) to him. Still, he's intelligent and seems to be
able to take a joke on occassion. That's where I came in.
ALOHA
Reply to group
(Unsolicited e-mail is deleted from the server unread
if it comes from anyone not already in my addressbook.
I'll never even see it)
===
Subject: Re: Angel Cadwell - August 16th 2002
>Friday August 23 2002 235/130 16623
>C A D W E L L
>3 1 4 23 5 12 12 = 60
> Oh dear. I see in South Dakota's Rapid City Journal that Monique
Cadwell
>lost her child when she gave birth on August 16th. Mom and kid have first
>names adding together for 133 (Numbers 16), pretty as the kid was born on
<<<snipped a lot of psycho crap from Shawn pedophile-boy Kabatoff>
The following (courtesy of Waxy.org) is sort of an unofficial FAQ
explaining the psychotic nonsense posted to Usenet by Shawn Daryl
Kabatoff AKA Dar, AKA Probababbilities. And now AKA marcia and
me.
WARNING: Read below before even thinking about responding to this
twit.
http://www.waxy.org/archive/2002/05/21/dar_kaba.shtml#000643
Usenet has the tendency to provide a public forum for those who would
normally be scribbling in a closet. For example, take Daryl Shawn
Kabatoff. For the last few years, he's methodically gathered
statistics from various sources, ranging from local newspaper
obituary pages to the food court of the Saskatoon Midtown Plaza mall.
With all the raw data he's collected, he's attempting to prove daily
that our full names are in mathematical harmony with our birthdays.
His rants normally focus on a single individual he's met or read
about, starting with calculations related to their birthdate and full
names, blending in whatever other personal information about their
family members, spouses, birthplace, and career he's been able to
zealotry, and personal torment. I've never seen anything like it.
With all the prime numbers, Fibonacci sequences and biblical
references, it's like reading the notebooks of Maximillian Cohen and
John Nash combined. Unsurprisingly, several posts unfold to reveal a
history of painful mental illness. If you have some time, take a look.
I've detailed his posting history and a several sample posts below.
Usenet Posting History:
January 27, 1999 to July 5, 2000 as Catsco@home.com
December 9, 2000 to May 4, 2001 as s.kabatoff@sk.sympatico.ca
Oct 30, 2001 to Oct 31, 2001 as kabatoff@the.link.ca
January 20, 2002 to April 17, 2002 as s_kabatoff@hotmail.com (original
posts have been
removed from Google Groups archive)
April 26, 2002 to Present as dar_kabatoff@hotmail.com
Selected Posts:
Tessa Lynne Smith
Dastageer Sakhizai and Helen Smith
Brett David Maki
Andrew Meredith Cotton
Kathryn Lee Hipperson
Amanda Dawn Newton
Mona Marie Etcheverry
Tony Peter Nuspl
Lisa Charlene McMillan
Grant Allyn Wood
Comments
scarier still is that saskatoon is my hometown, though not my current
residence. and every single place he's mentioned in his posts (most
notably nervous harold's and the roastary) were either places i've
been (as it's a small city of 200K) or hangouts, ie. the two places
mentioned. chances are i could email some friends back home and find
out if they know of him, they (my friends that is) being of the
broadway-centred slacker ilk. myself, too, until i got out of there.
eh, anyways. thought it odd to see all this. midtown mall. i ate my
meals there, whilst waiting several days in line for star wars episode
one, at the theatre across the street.
posted by raad on May 22, 2002 06:20 PM
Fascinating. It's like he's trying to take chaos and bind it into
whatever rules he can find, religious, logical and otherwise. Numbers
and math have a reliable pattern, something that can always be proven
to true or false. People and religion do not. It reminds me of Darren
Aronofsky's movie Pi. It's the story of an paraniod genius who is
trying to find a pattern in Pi. A group that takes interest in his
work is convinced that the existence of Pi, a number whose existence
can be proven but no quantified, is proof of the existence of God.
Kabatoff's hunt for patterns in something as random as name selection
is a way to reconcile his deeply logical thought process with his
conflicting religious views.
Exactly. I probably shouldn't have, but I e-mailed Daryl yesterday,
asking him if he'd be willing to create a numerological analysis for
me. I also asked him if he had seen either Pi or A Beautiful Mind, and
what he thought of them. If he replies, I'll be sure to post it.
I baked many pumpkin pies for Shawn (he likes pumpkin pies). I rubbed
pumpkin pie all over my breasts for him, and my breasts turned orange.
I am a pumpkin for Shawn.
posted by Trisha Blondie on July 24, 2002 10:41 PM
Um, that's swell. So, you're in love with him?
Shawn once went to a funeral for a Jehovah Witness that shot himself
and the lemon tarts were very bad, they were not only sour but were
rubbery as well. Shawn said that the guy was some kind of Jehovah
Witness prophet, he saw in advance that the lemon tarts at his funeral
were to be very very bad, and so he shot himself. Shawn said that he
never ate pumpkin pie at a funeral but would like to some day. Shawn
likes pumpkin pie and so I have been practicing to make very good
pumpkin pies.
posted by Trisha Blondie on July 25, 2002 02:49 PM
Shawn said that the lemon tarts were sour, bitter and rubbery.
I don't think this guy takes notes. I think he has Total Recall, and
it has driven him insane...
Oh... I almost forgot... I didnt spend thousands of dollars a day
tormenting Daryl... We got a deal on tormenting that fiscal year, it
only came to about 37cents a day....
Mr. Kabatoff attempts to portray himself as a victim, but in fact he
is a violent predatory pedophile who is well known to his local law
enforcement. In his post to multiple newsgroups with the subject
Collecting Mail For The Coming Anti-Christ, he encourages mothers to
send him photos of their naked daughters. Mr Kabatoff explains, I
personally did not want photographs being mailed to (the coming
Ant-Christ) that were of underage children unless the parent was
signing consent. He is bed from virtually all the shopping malls
in his community because he stalks young people and sexually harasses
them. He has an extensive arrest record which includes sexual
molestation charges. He's been hospitalized in mental institutions
about his contact with young girls in many posts. Search newsgroup
archives for posts by him containing the word nubile. As part of his
harrassment, he provides personal details in a public forum, such as
the real names of real children, in these and other posts. About one
wanted her and her sister dead.
He not only curses children and prays for their death in his posts, he
also enjoys attending the funerals of young people: And so, since
nubile sweeties are found in greatest abundance at the funerals of
high school students, then it is the funerals of high school students
that make the very very best funerals, especially if there is food...
I stuff my face (and my pockets) with all the good food and look at
all the pretty nubile sweeties and have the time of my life..
r=&ie=UTF-8&scoring=d&selm=LfXN8.63042%24R53.25142039%40twister.socal.rr.
com&rnum=1
Many of his posts are sent to alt.teens.advice. However, he liberally
spams, floods and crossposts his off-topic threatening and offensive
missives to countless newsgroups. Some people HAVE problems and some
folks ARE problems. Don't dismiss Mr. Kabatoff as a harmless nut. When
he sends these posts to any newgroup, please help by reporting him to
I knew of him when I was attending the University of Saskatchewan.
He'd hang out in the Arts computer lab and all you'd see is screens of
numbers racing by on his laptop. I have an original copy of his
Collecting Mail for the Coming Anti-Christ pamphlet, and have seen
him be hauled away by campus security on more than one occasion. My
friends and I refer to him as Crazy Number Man.
I've been posting to (and about) Shawn for over two years with big
gaps in between. He has seen Pi and didn't like it and didn't think it
resembled him at all. (Wrong, it fits him to a tee) He doesn't have
total recall and has stated that he travels with a lap top to notate
items. Also, he uses cut n' paste a lot if you read all the way
through his ramblings. He is anti-social as shown by his angry
statements towards those who, by his own admission, have been kind
(but not kind enough) to him. Still, he's intelligent and seems to be
able to take a joke on occassion. That's where I came in.
ALOHA
Reply to group
(Unsolicited e-mail is deleted from the server unread
if it comes from anyone not already in my addressbook.
I'll never even see it)
===
Subject: Re: Adam Bruce Millikan - August 15th 1982
>Monday June 10th 2002 161/204 16549
>M I L L I K A N
>13 9 12 12 9 11 1 14 = 81
<<<snipped a lot of psycho crap from Shawn pedophile-boy Kabatoff>
The following (courtesy of Waxy.org) is sort of an unofficial FAQ
explaining the psychotic nonsense posted to Usenet by Shawn Daryl
Kabatoff AKA Dar, AKA Probababbilities. And now AKA marcia and
me.
WARNING: Read below before even thinking about responding to this
twit.
http://www.waxy.org/archive/2002/05/21/dar_kaba.shtml#000643
Usenet has the tendency to provide a public forum for those who would
normally be scribbling in a closet. For example, take Daryl Shawn
Kabatoff. For the last few years, he's methodically gathered
statistics from various sources, ranging from local newspaper
obituary pages to the food court of the Saskatoon Midtown Plaza mall.
With all the raw data he's collected, he's attempting to prove daily
that our full names are in mathematical harmony with our birthdays.
His rants normally focus on a single individual he's met or read
about, starting with calculations related to their birthdate and full
names, blending in whatever other personal information about their
family members, spouses, birthplace, and career he's been able to
zealotry, and personal torment. I've never seen anything like it.
With all the prime numbers, Fibonacci sequences and biblical
references, it's like reading the notebooks of Maximillian Cohen and
John Nash combined. Unsurprisingly, several posts unfold to reveal a
history of painful mental illness. If you have some time, take a look.
I've detailed his posting history and a several sample posts below.
Usenet Posting History:
January 27, 1999 to July 5, 2000 as Catsco@home.com
December 9, 2000 to May 4, 2001 as s.kabatoff@sk.sympatico.ca
Oct 30, 2001 to Oct 31, 2001 as kabatoff@the.link.ca
January 20, 2002 to April 17, 2002 as s_kabatoff@hotmail.com (original
posts have been
removed from Google Groups archive)
April 26, 2002 to Present as dar_kabatoff@hotmail.com
Selected Posts:
Tessa Lynne Smith
Dastageer Sakhizai and Helen Smith
Brett David Maki
Andrew Meredith Cotton
Kathryn Lee Hipperson
Amanda Dawn Newton
Mona Marie Etcheverry
Tony Peter Nuspl
Lisa Charlene McMillan
Grant Allyn Wood
Comments
scarier still is that saskatoon is my hometown, though not my current
residence. and every single place he's mentioned in his posts (most
notably nervous harold's and the roastary) were either places i've
been (as it's a small city of 200K) or hangouts, ie. the two places
mentioned. chances are i could email some friends back home and find
out if they know of him, they (my friends that is) being of the
broadway-centred slacker ilk. myself, too, until i got out of there.
eh, anyways. thought it odd to see all this. midtown mall. i ate my
meals there, whilst waiting several days in line for star wars episode
one, at the theatre across the street.
posted by raad on May 22, 2002 06:20 PM
Fascinating. It's like he's trying to take chaos and bind it into
whatever rules he can find, religious, logical and otherwise. Numbers
and math have a reliable pattern, something that can always be proven
to true or false. People and religion do not. It reminds me of Darren
Aronofsky's movie Pi. It's the story of an paraniod genius who is
trying to find a pattern in Pi. A group that takes interest in his
work is convinced that the existence of Pi, a number whose existence
can be proven but no quantified, is proof of the existence of God.
Kabatoff's hunt for patterns in something as random as name selection
is a way to reconcile his deeply logical thought process with his
conflicting religious views.
Exactly. I probably shouldn't have, but I e-mailed Daryl yesterday,
asking him if he'd be willing to create a numerological analysis for
me. I also asked him if he had seen either Pi or A Beautiful Mind, and
what he thought of them. If he replies, I'll be sure to post it.
I baked many pumpkin pies for Shawn (he likes pumpkin pies). I rubbed
pumpkin pie all over my breasts for him, and my breasts turned orange.
I am a pumpkin for Shawn.
posted by Trisha Blondie on July 24, 2002 10:41 PM
Um, that's swell. So, you're in love with him?
Shawn once went to a funeral for a Jehovah Witness that shot himself
and the lemon tarts were very bad, they were not only sour but were
rubbery as well. Shawn said that the guy was some kind of Jehovah
Witness prophet, he saw in advance that the lemon tarts at his funeral
were to be very very bad, and so he shot himself. Shawn said that he
never ate pumpkin pie at a funeral but would like to some day. Shawn
likes pumpkin pie and so I have been practicing to make very good
pumpkin pies.
posted by Trisha Blondie on July 25, 2002 02:49 PM
Shawn said that the lemon tarts were sour, bitter and rubbery.
I don't think this guy takes notes. I think he has Total Recall, and
it has driven him insane...
Oh... I almost forgot... I didnt spend thousands of dollars a day
tormenting Daryl... We got a deal on tormenting that fiscal year, it
only came to about 37cents a day....
Mr. Kabatoff attempts to portray himself as a victim, but in fact he
is a violent predatory pedophile who is well known to his local law
enforcement. In his post to multiple newsgroups with the subject
Collecting Mail For The Coming Anti-Christ, he encourages mothers to
send him photos of their naked daughters. Mr Kabatoff explains, I
personally did not want photographs being mailed to (the coming
Ant-Christ) that were of underage children unless the parent was
signing consent. He is bed from virtually all the shopping malls
in his community because he stalks young people and sexually harasses
them. He has an extensive arrest record which includes sexual
molestation charges. He's been hospitalized in mental institutions
about his contact with young girls in many posts. Search newsgroup
archives for posts by him containing the word nubile. As part of his
harrassment, he provides personal details in a public forum, such as
the real names of real children, in these and other posts. About one
wanted her and her sister dead.
He not only curses children and prays for their death in his posts, he
also enjoys attending the funerals of young people: And so, since
nubile sweeties are found in greatest abundance at the funerals of
high school students, then it is the funerals of high school students
that make the very very best funerals, especially if there is food...
I stuff my face (and my pockets) with all the good food and look at
all the pretty nubile sweeties and have the time of my life..
r=&ie=UTF-8&scoring=d&selm=LfXN8.63042%24R53.25142039%40twister.socal.rr.
com&rnum=1
Many of his posts are sent to alt.teens.advice. However, he liberally
spams, floods and crossposts his off-topic threatening and offensive
missives to countless newsgroups. Some people HAVE problems and some
folks ARE problems. Don't dismiss Mr. Kabatoff as a harmless nut. When
he sends these posts to any newgroup, please help by reporting him to
I knew of him when I was attending the University of Saskatchewan.
He'd hang out in the Arts computer lab and all you'd see is screens of
numbers racing by on his laptop. I have an original copy of his
Collecting Mail for the Coming Anti-Christ pamphlet, and have seen
him be hauled away by campus security on more than one occasion. My
friends and I refer to him as Crazy Number Man.
I've been posting to (and about) Shawn for over two years with big
gaps in between. He has seen Pi and didn't like it and didn't think it
resembled him at all. (Wrong, it fits him to a tee) He doesn't have
total recall and has stated that he travels with a lap top to notate
items. Also, he uses cut n' paste a lot if you read all the way
through his ramblings. He is anti-social as shown by his angry
statements towards those who, by his own admission, have been kind
(but not kind enough) to him. Still, he's intelligent and seems to be
able to take a joke on occassion. That's where I came in.
ALOHA
Reply to group
(Unsolicited e-mail is deleted from the server unread
if it comes from anyone not already in my addressbook.
I'll never even see it)
===
Subject: Re: Fundamental Reason for High Achievements of Jews
>>Hey, pot, (as in illegal substance or pot [quite applicable for
>>this troll], your are becoming quite old. The Protocols of the Elders
> of
>>Zion was shown to be a Czarist Secret Police forgery a very long time
>>ago. You keep flailing a deceased equine. Go somewhere else, troll.
>>FK
>>... snip insupportable myths ...
>As can be seen, fkasner uses most of the standard
>boilerplate tactics of the people who instigate conflict and war
>for power and profit.
>>Considering you're a racist bastard, that's the least anyone should do to
> you.
> As can be seen,
> the Bolsheviks and their fellow travelers,
> use the standard, time-proven, boilerplate tactic
> of cluttering messages with all kinds of irrational,
> boilerplate, phrases and references,
> and trying to make the messenger the issue,
> in order to obscure messages critical of their activity.
> Although this tactic works on ignorant people,
> who don't have access to information,
> rational, intelligent folks have access to the facts,
> and they understand that
> what affects humanity, is many orders of magnitude
> more important than any insignificant messenger.
> What I am, and what I believe, is of little consequence to mankind,
> but the instigation of conflict and war for power and riches,
> is mankind's most serious problem, and needs to be addressed.
> And as can be seen by Lloyd Parker's statement:
> that's the least anyone should do to you.
> character and real assassination are,
> and have always been, the major weapons
> used by evil, greedy, immoral people
> to silence and intimidate their critics.
> The issue of great importance to mankind,
> is not me or what I believe.
> It is not these petty defenders of
> the people who instigate conflict and war.
> It is the instigation of conflict and war for power and riches.
> Blacks, Rednecks and Latinos should not
> allow themselves to be manipulated into killing
> folks they would otherwise get along with just fine,
> and into being killed, so that a tiny group of
> greedy, immoral people profit from it.
> The same people who instigated the class wars of the 1900's
> are instigating the religious wars of the 2000's.
> Don't fall for it.
> Fool you once, shame on the Bolsheviks.
> Fool you twice, shame on you.
> --
> Tom Potter http://tompotter.us
Oooh, a real boo-boo on your part. Lack of consistency. YOu refer to a
small group of people pulling off all this stuff. However a small group
(especially the Jews who are not a very rich group at all) could not
marshall the financial resources to accomplish what you claim. You have
tripped over your own verbal turds.
FK
===
Subject: Re: Fundamental Reason for High Achievements of Jews
>Hey, pot, (as in illegal substance or pot [quite applicable for
>this troll], your are becoming quite old. The Protocols of the Elders
:)
Bruce
-----------------------------------------------------------------------
It was so much easier to blame it on Them. It was bleakly depressing to
think that They were Us. If it was Them, then nothing was
anyones fault.
If it was Us, what did that make Me ? After all, Im one of
Us. I must be.
Ive certainly never thought of myself as one of Them. No-one
ever thinks
of themselves as one of Them. Were always one of Us.
Its Them that do
the bad things. <=> Terry Pratchett. Jingo.
===
Subject: Re: Fundamental Reason for High Achievements of Jews
>>
Hey, pot, (as in illegal substance or pot [quite applicable for
>this troll], your are becoming quite old. The Protocols of the
Elders
It usually helps (though it probably won't in this case) if you
identify the group you are reading. As far as I can tell, there aren't
any alt.psychic regulars contributing to this thread.
===
Subject: Re: Fundamental Reason for High Achievements of Jews
Hey, pot, (as in illegal substance or pot [quite applicable
for
>>this troll], your are becoming quite old. The Protocols of the
Elders
>It usually helps (though it probably won't in this case) if you
>identify the group you are reading. As far as I can tell, there aren't
>any alt.psychic regulars contributing to this thread.
The theory was that it didn't matter and any replies would be ...
automagically redirected away from the group :).
As an aside, I don't think this thread is relevant to a single group
.. not now anyway :)
Bruce
-----------------------------------------------------------------------
It was so much easier to blame it on Them. It was bleakly depressing to
think that They were Us. If it was Them, then nothing was
anyones fault.
If it was Us, what did that make Me ? After all, Im one of
Us. I must be.
Ive certainly never thought of myself as one of Them. No-one
ever thinks
of themselves as one of Them. Were always one of Us.
Its Them that do
the bad things. <=> Terry Pratchett. Jingo.
===
Subject: Re: Fundamental Reason for High Achievements of Jews
>
Hey, pot, (as in illegal substance or pot [quite applicable for
>this troll], your are becoming quite old. The Protocols of the
Elders
> It usually helps (though it probably won't in this case) if you
> identify the group you are reading. As far as I can tell, there aren't
> any alt.psychic regulars contributing to this thread.
Actually, Bob, I'm with you on this. It has absolutely nothing to do
with chemistry at all. It should be expunged. I promise from now on not
to respond to that ass.
FK
===
Subject: Re: Fundamental Reason for High Achievements of Jews
... snip ...
>>But this very small number of people with only
>>very limited financial resources are asserted by you as having the
>>ability to delude incredibly large numbers of people in developing a
>>master plan of world domination. Rather incredible on the face of it.
>>But then again you are an incredulous type. I'm still waiting for a
>>shred of documentary evidence that such a world conspiracy (save your
>>demented unsupported claims and save the well demythologized Protocols
>>of the Elders of Zion forgery) exists in any mer. This old myth of
>>the war lovers was at one time hurled toward the munitions makers after
>>the horrors of WWI. Many refused to react to the rearming of Germany as
>>WWII appeared on the horizon by once again making that tired old claim
>>that the munitions makers were once again fostering a war. However that
>>turned out not to be true as Hitler was as surprised as were his enemies
>>when he marched toward total rearmament without much response from the
>>WWI former enemies of Germany. What we really need now if for you to
>>intervene at this point and present us with a list of the major arms
>>manufacturers of the world who can be demonstrated (not claimed but
>>documented) to be controlled by Jews. You can't because the Jews didn't
>>control anywhere enough resources in save a few scattered places in
>>Europe. The French Rothschilds were a major banking company but not big
>>enough to even begin to bring this off by themselves. Nor were a few
>>modest sized investment banking companies in New York City. That's it,
>>dummy, zippo financial strength. The major part of the world locked in
>>terrible depression and deflation. Financial resources to a very minor
>>group of people who had little political power in any country in the
>>world too small to even do a good job of supporting the most financially
>> desperate numbers of their co-religionists. And yet, as your depraved
>>rantings keep insisting, they are the major financial agents behind the
>>production of wars in the modern era. The whole of Russian Jews living
>>in the nascent Soviet Union would have never been able to raise a
>>sufficient amount of money to bribe their way through the Communist
>>Party to power. The small number of deluded idealists who thought almost
>>anything was better than Czarist oppression went along with the CP and
>>it eventually, in the person of Joseph Stalin, killed them all.
> After all this parroting of the standard, Bolshevik boilerplate
> obfuscations,
> fkasner states that Joseph Stalin, killed them all.
> As can be seen by the fact that over a million Bolsheviks
> migrated to Israel and New York, from where they are
> instigating their class wars, and today's arrest of Khodorkovsky,
> it is obvious that the native Russians are still fighting to
> regain control of their nation from the greedy, immoral criminals
> who raped, and continue to rape, Russia.
> And of course, Stalin, who had a Jewish wife,
> and who appointed Jews to most of the key power
> positions in Russia, killed a few of the more aggressive
> contenders, regardless of their race or religion.
> Like most leaders, when he got power,
> he protected his ass.
>>Where
>>were they to influence the acts leading up to WWII. In the grave!
> All you have to do,
> is to look at the Spainsh Civil War,
> the assassinations by the Bolsheviks
> of leaders in various nations, and the speeches
> by the politicians and leaders during those times,
> to see that the Bolsheviks were aggressively
> trying to instigate conflict and war, and to
> buy and intimidate leaders in all major nations.
>>As for
>>the wars today, as you call them religious wars - a totally
>>inappropriate appellation , They are no more religious for the secular
>>society (largely totally devoid of religious activity) that is Israel
>>than is this usenet newsgroup.
>>That having been dealt with and your total failure to document the
>>astounding claims you keep making there is only one remaining comment to
>>make. YOU ARE TOTALLY OF TOPIC for this newsgroup. Plonk.
>>FK
> Considering that I have posted information about events that
> can be verified with very little research, and that
> fkasner has posted personal attacks,
> all of which are completely undocumented lies,
> it is obvious who the liar and propagandist is.
> --
> Tom Potter http://tompotter.us
Wonderfully amusing that your claim that the Jews who migrated to Israel
from the USSR are Bolsheviks. That alone is sufficient to to mark you as
a demented fool of the first order. What you claim as verifiable claims
on your part shows further your mendacity. Where are the documents that
support such claims. Not a one proffered by you. I note further that you
cot bring yourself to address the historical facts I presented (not
claims or opinions) Your claims are specious and not verifiable. And
until such time as you find enough intellectual capacity as to even
present the documents of some purported historians we shall see you for
what you are. An agent provocateur. Perhaps the most amazingly self
contradictory claim on your part is to see the Jews of the world as
having the wealth and power to bring about the nonsense you produce. I
suppose next we will see you claiming that the Jews were responsible for
the assassination of the Arch Duke that started WWI. Or the bombing of
Pearl Harbor was instigated by Jews. Why don't you throw in that canard
that FDR purposely disarmed Pearl Harbor to entice the attack and that
the Jews made him do it. You are hopelessly naive, stupid, bigoted, and
clueless. Yes that is a character attack. You richly deserve it. Your
claims are transparently insupportable. Facts, stupid. Facts, not
opinions. You claim your opinions are facts. But any person with a mot
more intelligence than you can see otherwise.
Hopeless troll!
FK
===
Subject: Re: Fundamental Reason for High Achievements of Jews
> ... snip ...
>>But this very small number of people with only
>>very limited financial resources are asserted by you as having the
>>ability to delude incredibly large numbers of people in developing a
>>master plan of world domination. Rather incredible on the face of it.
>>But then again you are an incredulous type. I'm still waiting for a
>>shred of documentary evidence that such a world conspiracy (save your
>>demented unsupported claims and save the well demythologized Protocols
>>of the Elders of Zion forgery) exists in any mer. This old myth of
>>the war lovers was at one time hurled toward the munitions makers after
>>the horrors of WWI. Many refused to react to the rearming of Germany as
>>WWII appeared on the horizon by once again making that tired old claim
>>that the munitions makers were once again fostering a war. However that
>>turned out not to be true as Hitler was as surprised as were his
enemies
>>when he marched toward total rearmament without much response from the
>>WWI former enemies of Germany. What we really need now if for you to
>>intervene at this point and present us with a list of the major arms
>>manufacturers of the world who can be demonstrated (not claimed but
>>documented) to be controlled by Jews. You can't because the Jews didn't
>>control anywhere enough resources in save a few scattered places in
>>Europe. The French Rothschilds were a major banking company but not big
>>enough to even begin to bring this off by themselves. Nor were a few
>>modest sized investment banking companies in New York City. That's it,
>>dummy, zippo financial strength. The major part of the world locked in
>>terrible depression and deflation. Financial resources to a very minor
>>group of people who had little political power in any country in the
>>world too small to even do a good job of supporting the most
financially
>> desperate numbers of their co-religionists. And yet, as your depraved
>>rantings keep insisting, they are the major financial agents behind the
>>production of wars in the modern era. The whole of Russian Jews living
>>in the nascent Soviet Union would have never been able to raise a
>>sufficient amount of money to bribe their way through the Communist
>>Party to power. The small number of deluded idealists who thought
almost
>>anything was better than Czarist oppression went along with the CP and
>>it eventually, in the person of Joseph Stalin, killed them all.
> After all this parroting of the standard, Bolshevik boilerplate
> obfuscations,
> fkasner states that Joseph Stalin, killed them all.
> As can be seen by the fact that over a million Bolsheviks
> migrated to Israel and New York, from where they are
> instigating their class wars, and today's arrest of Khodorkovsky,
> it is obvious that the native Russians are still fighting to
> regain control of their nation from the greedy, immoral criminals
> who raped, and continue to rape, Russia.
> And of course, Stalin, who had a Jewish wife,
> and who appointed Jews to most of the key power
> positions in Russia, killed a few of the more aggressive
> contenders, regardless of their race or religion.
> Like most leaders, when he got power,
> he protected his ass.
>>Where
>>were they to influence the acts leading up to WWII. In the grave!
> All you have to do,
> is to look at the Spainsh Civil War,
> the assassinations by the Bolsheviks
> of leaders in various nations, and the speeches
> by the politicians and leaders during those times,
> to see that the Bolsheviks were aggressively
> trying to instigate conflict and war, and to
> buy and intimidate leaders in all major nations.
>>As for
>>the wars today, as you call them religious wars - a totally
>>inappropriate appellation , They are no more religious for the secular
>>society (largely totally devoid of religious activity) that is Israel
>>than is this usenet newsgroup.
>>That having been dealt with and your total failure to document the
>>astounding claims you keep making there is only one remaining comment
to
>>make. YOU ARE TOTALLY OF TOPIC for this newsgroup. Plonk.
>>FK
> Considering that I have posted information about events that
> can be verified with very little research, and that
> fkasner has posted personal attacks,
> all of which are completely undocumented lies,
> it is obvious who the liar and propagandist is.
> --
> Tom Potter http://tompotter.us
> Wonderfully amusing that your claim that the Jews who migrated to Israel
> from the USSR are Bolsheviks.
A war-for-profit instigator by any other name,
would be a war-for-profit instigator.
I trust that fkasner will explain to us
why over one million Russian Jews migrated to Israel,
and thousands to New York,
after the native Russians began to regain control of their nation?
Of course, it was because the Russian were/are anti-Semitic,
and NOT because the Bolsheviks had raped Russia,
and destroyed its' viability,
and that their standard of living had slipped below
that of their free world brothers,
and that as the Native Russians were regaining control of their nation,
it was becoming even harder for them to enjoy a high life style.
Yeah!
That's the ticket!
It was because the Russians are anti-Semitic!
Like the Germans, the Muslims, the French, the Italians,
most Americans, Asians, etc., the Russians are anti-Semitic!
Yeah!
That's the ticket!
--
Tom Potter http://tompotter.us
===
Subject: Re: Fundamental Reason for High Achievements of Jews
>>... snip ...
>>But this very small number of people with only
>>very limited financial resources are asserted by you as having the
>>ability to delude incredibly large numbers of people in developing a
>>master plan of world domination. Rather incredible on the face of it.
>>But then again you are an incredulous type. I'm still waiting for a
>>shred of documentary evidence that such a world conspiracy (save your
>>demented unsupported claims and save the well demythologized Protocols
>>of the Elders of Zion forgery) exists in any mer. This old myth of
>>the war lovers was at one time hurled toward the munitions makers after
>>the horrors of WWI. Many refused to react to the rearming of Germany as
>>WWII appeared on the horizon by once again making that tired old claim
>>that the munitions makers were once again fostering a war. However that
>>turned out not to be true as Hitler was as surprised as were his
enemies
>>when he marched toward total rearmament without much response from the
>>WWI former enemies of Germany. What we really need now if for you to
>>intervene at this point and present us with a list of the major arms
>>manufacturers of the world who can be demonstrated (not claimed but
>>documented) to be controlled by Jews. You can't because the Jews didn't
>>control anywhere enough resources in save a few scattered places in
>>Europe. The French Rothschilds were a major banking company but not big
>>enough to even begin to bring this off by themselves. Nor were a few
>>modest sized investment banking companies in New York City. That's it,
>>dummy, zippo financial strength. The major part of the world locked in
>>terrible depression and deflation. Financial resources to a very minor
>>group of people who had little political power in any country in the
>>world too small to even do a good job of supporting the most
financially
>> desperate numbers of their co-religionists. And yet, as your depraved
>>rantings keep insisting, they are the major financial agents behind the
>>production of wars in the modern era. The whole of Russian Jews living
>>in the nascent Soviet Union would have never been able to raise a
>>sufficient amount of money to bribe their way through the Communist
>>Party to power. The small number of deluded idealists who thought
almost
>>anything was better than Czarist oppression went along with the CP and
>>it eventually, in the person of Joseph Stalin, killed them all.
>After all this parroting of the standard, Bolshevik boilerplate
>obfuscations,
>fkasner states that Joseph Stalin, killed them all.
...snip stuff that never responded to my historical factual efforts ...
>Considering that I have posted information about events that
>can be verified with very little research, and that
>fkasner has posted personal attacks,
>all of which are completely undocumented lies,
>it is obvious who the liar and propagandist is.
>--
>Tom Potter http://tompotter.us
>>Wonderfully amusing that your claim that the Jews who migrated to Israel
>>from the USSR are Bolsheviks.
> A war-for-profit instigator by any other name,
> would be a war-for-profit instigator.
> I trust that fkasner will explain to us
> why over one million Russian Jews migrated to Israel,
> and thousands to New York,
> after the native Russians began to regain control of their nation?
> Of course, it was because the Russian were/are anti-Semitic,
> and NOT because the Bolsheviks had raped Russia,
> and destroyed its' viability,
> and that their standard of living had slipped below
> that of their free world brothers,
> and that as the Native Russians were regaining control of their nation,
> it was becoming even harder for them to enjoy a high life style.
> Yeah!
> That's the ticket!
> It was because the Russians are anti-Semitic!
> Like the Germans, the Muslims, the French, the Italians,
> most Americans, Asians, etc., the Russians are anti-Semitic!
> Yeah!
> That's the ticket!
> --
> Tom Potter http://tompotter.us
I have already supplied you with historical facts that you do not
address whereas you keep insisting that I have to do the investigations
that demonstrate the things you claim to be true. Please note that the
Jews who left the Soviet Union when it collapsed dis so because they
finally were able to leave the Soviet Union. Prior to that they were
generally not allowed to leave. Very few got out before the USSR
listening? Or are you just dreaming about other specious claims that you
say are obvious truths but you refuse to deal with in detail or produce
documentary proof.
Note also that few Russians who were Jews were permitted to join the
Communist Party. How then can you insist on calling them Bolsheviks. In
fact that term is applicable to those members of the Communist Party who
continued to favor revolution rather than deal with the Kerensky led new
Duma and its socialist flavored attempt at a constitutional monarchy.
But then again you probably never heard of Kerensky. Whereas I and
several hundred others heard him speak at the University of Chicago and
the Communists were dumbfounded and were silent during the question
period. It seems he was an element of history they couldn't fabricate
quickly enough. Similar to you. Your similarity to the Communists is
quite striking. If we merely substitute the word Capitalist for your
use of the word Jew we see the way you have absorbed their political
and thought processes in toto. You have revealed yourself thoroughly,
Comrade.
FK
===
Subject: Re: space elevator
I don't think it is restricted to one orbit, it can come from all
directions. Also even if it came from certain directions more often then if
shaped to handle that an unlucky strike could severely damage it.
> also consider what sort of debris your cable is up against. In LEO it
> will be mostly man made and in an equatorial orbit, thus shaping your
> cable would seem to make sense.
>> I am having a discussion with some people about the optimum
>> shape for a space elevator cable to survive impacts, perhaps someone
>> may be able to help with it.
>> Basically it breaks down into two alternatives, a hollow
>> cylinder or a flat strip or an arc shape in between. Say for example
>> you have a flat strip that of course is very long to get to orbit
>> and for example is 10 centimetres wide and 1 centimetre deep. These
>> numbers are arbitrary, there may be an equation that changes the
>> result according to different values. Now the flat strip is the
>> most dangerous because space debris travelling at speed could cut
>> through the 10 cm width and cut the whole cable. The opposite
>> alternative is to bend that strip into a hollow cylinder. Now a
>> grazing impact is less dangerous but other impacts would create
>> twice the damage by making two holes, an entry hole and an exit
>> hole. There are other curves in between to consider, for example a
>> half
>> circle, quarter circle, parabola, etc. Which would be the safest?
>> There are two aspects to safety. A flat strip might survive some
>> impacts best of all but an impact from the side would destroy it
>> completely. A cylinder might be the optimum for all kinds of impacts
>> if the worst impact scenario is safer than the other arcs but it is
>> most likely to suffer a double hole from an entry hole and an exit
>> hole. So there is an average safety, which shape is the safest
>> overall. Then there is also the worst case scenario as to which
>> shape is the least likely to suffer a catastrophic failure?
>> This can be further complicated by using a mesh as the cable
>> wall. This mesh would have large holes in it so that if debris hit
>> one part it would be less likely to make a large hole. Assume though
>> the same material with the same sized holes in it is used for all
>> cross section shapes. I believe the hollow cylinder is safest
>> overall, someone else believes
>> an arc, probably 1/4 of a circle is safest. What is the safest shape?
===
Subject: Re: space elevator
> I don't think it is restricted to one orbit, it can come from all
> directions. Also even if it came from certain directions more often then
if
> shaped to handle that an unlucky strike could severely damage it.
> also consider what sort of debris your cable is up against. In LEO it
> will be mostly man made and in an equatorial orbit, thus shaping your
> cable would seem to make sense.
How about good ole earth cable? lowest overall cross section to tension.
Ahh I get
it, least probability of catastrophic failure VS least probability of
damage.
Surely a simulation would arrive at the answer, 1/4 of an arc is vulnerable
to
critical angle of attack, semicircle is vulnerable to 2 holes, so around 
1/3
of an arc.
3 cables would be the best design with spacers, that way at most 2 are
knocked
out by a small projectile.
O
o
o
o
O o
o
o o O
composite design
===
Subject: Re: space elevator
>> I don't think it is restricted to one orbit, it can come from all
>> directions. Also even if it came from certain directions more often
>> then if shaped to handle that an unlucky strike could severely
>> damage it.
> also consider what sort of debris your cable is up against. In LEO
> it will be mostly man made and in an equatorial orbit, thus shaping
> your cable would seem to make sense.
> How about good ole earth cable? lowest overall cross section to
> tension. Ahh I get it, least probability of catastrophic failure VS
> least probability of damage.
> Surely a simulation would arrive at the answer, 1/4 of an arc is
> vulnerable to critical angle of attack, semicircle is vulnerable to 2
> holes, so around 1/3 of an arc.
> 3 cables would be the best design with spacers, that way at most 2
> are knocked
> out by a small projectile.
> o
> o
> o
> O o
> o
> o o O
> composite design
>
So you think may be 1/3 of an arc would be optimial? The way I see it
the answer is fairly critical. Assuming when they build it for weight
reasons it will be as light as possible relative to the debris so the risk
of catastrophic damage will be high. Then they would build in safety
margins
but these would be as low as possible so as not to add on too much weight.
After that point that may decide to make it thicker to carry more
weight
in which case they may be free to consider other shapes. For example an arc
is easier for a cable car to grip on than a hollow cylinder.
Separate cables with spacers becomes similar to a mesh where the fibres
are arranged vertically and horizontally with large holes in between to
localise the damage from debris.
===
Subject: Re: space elevator
> I am having a discussion with some people about the optimum shape for a
> space elevator cable to survive impacts, perhaps someone may be able to
help
> with it.
> Basically it breaks down into two alternatives, a hollow cylinder or
a
> flat strip or an arc shape in between. Say for example you have a flat
strip
> that of course is very long to get to orbit and for example is 10
> centimetres wide and 1 centimetre deep. These numbers are arbitrary,
there
> may be an equation that changes the result according to different values.
It may be helpful to post some links _about_ the SE. For context.
ISR's SE page
http://www.isr.us/SEHome.asp
The Space Elevator Final report to NIAC
The NIAC Phase I Report: The technical result of the initial 6 month study
for NASA.
http://www.isr.us/Downloads/niac_pdf/contents.html
See especially
Chapter 2: Cable Design and Production
Chapter 10: Challenges
===
Subject: Re: space elevator
They don't seem to mention much about the shape though. The slightly curved
strip they show would seem to be highly vulnerable from certain angles.
That's why I was wondering if a symmetrical shape like a cylinder is best.
>> I am having a discussion with some people about the optimum shape
>> for a space elevator cable to survive impacts, perhaps someone may
>> be able to help with it.
>> Basically it breaks down into two alternatives, a hollow
>> cylinder or a flat strip or an arc shape in between. Say for example
>> you have a flat strip that of course is very long to get to orbit
>> and for example is 10 centimetres wide and 1 centimetre deep. These
>> numbers are arbitrary, there may be an equation that changes the
>> result according to different values.
> It may be helpful to post some links _about_ the SE. For context.
> ISR's SE page
> http://www.isr.us/SEHome.asp
> The Space Elevator Final report to NIAC
> The NIAC Phase I Report: The technical result of the initial 6 month
> study for NASA. http://www.isr.us/Downloads/niac_pdf/contents.html
> See especially
> Chapter 2: Cable Design and Production
> Chapter 10: Challenges
===
Subject: Re: space elevator
> They don't seem to mention much about the shape though. The slightly
curved
> strip they show would seem to be highly vulnerable from certain angles.
> That's why I was wondering if a symmetrical shape like a cylinder is
best.
I think they're trying to avoid the problem of micrometeors that come in
nearly parallel to the flat face of the ribbon, thereby slicing it in
half. Making it curved ensures that no meteor travelling in a straight
line can do more than a small amount of damage to the ribbon.
Of course, making it a cylinder would be better, but more expensive than
it needs to be.
===
Subject: Re: space elevator
Is a cylinder the safest shape for this though? I thought it would be
though others were saying an arc would be safest. Compare say the same
amount of material and weight, like a flat strip either rolled into a
cylinder or various kinds of arcs. You can compare say half cylinders 1/4
cylinders, etc. the smaller the arc as it approaches a flat strip this is
equivalent to a piece of a circle with a larger diameter. So generally I
would have though that the cylinder would be safest as it has the smallest
diameter hence any grazing impact would remove the least amount of
material.
On the other hand as you approach a cylinder you have more chance of a
double hole, an entry hole on one side of the cylinder and an exit hole on
the other.
So it may be that there is an optimum between these two risk factors.
The flat strip and arcs however have a higher potential for disaster
because
the worst grazing impact can cause mch larger damage than on a cylinder. So
my opinion was that the cylinder was the safest overall. If the debris was
concentrated more in a general direction perhaps an ellipse.
>> They don't seem to mention much about the shape though. The slightly
>> curved strip they show would seem to be highly vulnerable from
>> certain angles. That's why I was wondering if a symmetrical shape
>> like a cylinder is best.
> I think they're trying to avoid the problem of micrometeors that come
> in nearly parallel to the flat face of the ribbon, thereby slicing it
> in half. Making it curved ensures that no meteor travelling in a
> straight line can do more than a small amount of damage to the ribbon.
> Of course, making it a cylinder would be better, but more expensive
> than it needs to be.
===
Subject: Re: space elevator
> I am having a discussion with some people about the optimum shape for
a
> space elevator cable to survive impacts, perhaps someone may be able to
help
> with it.
> Basically it breaks down into two alternatives, a hollow cylinder or
a
> flat strip or an arc shape in between. Say for example you have a flat
strip
> that of course is very long to get to orbit and for example is 10
> centimetres wide and 1 centimetre deep. These numbers are arbitrary,
there
> may be an equation that changes the result according to different values.
> Now the flat strip is the most dangerous because space debris
travelling
> at speed could cut through the 10 cm width and cut the whole cable.
> The opposite alternative is to bend that strip into a hollow
cylinder.
> Now a grazing impact is less dangerous but other impacts would create
twice
> the damage by making two holes, an entry hole and an exit hole.
> There are other curves in between to consider, for example a half
> circle, quarter circle, parabola, etc. Which would be the safest?
The double helix, I think. DNA is a long string, and it has to be
strong and safe and have structural integrity in the nucleus of the cell.
I saw a paper on the most 'optimal design for a column against buckling'
by Stephen Cox and Michael Overton, in which they stated that the
optimal column's cross sectional area would vanish at 1/4 and 3/4 of the
length. There is another paper on this called
The shape of the tallest column. at
http://citeseer.nj.nec.com/360447.html
I am not a mathematician, but an electrical engineer, so I can't quite
grasp the whole picture. I was wondering if anyone would give me some
background on this, the attempt by Lagrange to tacke this problem for
example.
> There are two aspects to safety. A flat strip might survive some
impacts
> best of all but an impact from the side would destroy it completely. A
> cylinder might be the optimum for all kinds of impacts if the worst
impact
> scenario is safer than the other arcs but it is most likely to suffer a
> double hole from an entry hole and an exit hole.
> So there is an average safety, which shape is the safest overall.
Then
> there is also the worst case scenario as to which shape is the least
likely
> to suffer a catastrophic failure?
> This can be further complicated by using a mesh as the cable wall.
This
> mesh would have large holes in it so that if debris hit one part it would
be
> less likely to make a large hole. Assume though the same material with
the
> same sized holes in it is used for all cross section shapes.
> I believe the hollow cylinder is safest overall, someone else
believes
> an arc, probably 1/4 of a circle is safest. What is the safest shape?
===
Subject: Re: space elevator
So you think the double helix would be the strongest shape for impacts from
all directions?
>> I am having a discussion with some people about the optimum
>> shape for a space elevator cable to survive impacts, perhaps someone
>> may be able to help with it.
>> Basically it breaks down into two alternatives, a hollow
>> cylinder or a flat strip or an arc shape in between. Say for example
>> you have a flat strip that of course is very long to get to orbit
>> and for example is 10 centimetres wide and 1 centimetre deep. These
>> numbers are arbitrary, there may be an equation that changes the
>> result according to different values. Now the flat strip is the
>> most dangerous because space debris travelling
>> at speed could cut through the 10 cm width and cut the whole cable.
>> The opposite alternative is to bend that strip into a hollow
>> cylinder. Now a grazing impact is less dangerous but other impacts
>> would create twice the damage by making two holes, an entry hole and
>> an exit hole. There are other curves in between to consider, for
>> example a half
>> circle, quarter circle, parabola, etc. Which would be the safest?
> The double helix, I think. DNA is a long string, and it has to be
> strong and safe and have structural integrity in the nucleus of the
> cell.
> I saw a paper on the most 'optimal design for a column against
> buckling' by Stephen Cox and Michael Overton, in which they stated
> that the optimal column's cross sectional area would vanish at 1/4
> and 3/4 of the length. There is another paper on this called
> The shape of the tallest column. at
> http://citeseer.nj.nec.com/360447.html
> I am not a mathematician, but an electrical engineer, so I can't quite
> grasp the whole picture. I was wondering if anyone would give me some
> background on this, the attempt by Lagrange to tacke this problem for
> example.
>> There are two aspects to safety. A flat strip might survive some
>> impacts best of all but an impact from the side would destroy it
>> completely. A cylinder might be the optimum for all kinds of impacts
>> if the worst impact scenario is safer than the other arcs but it is
>> most likely to suffer a double hole from an entry hole and an exit
>> hole. So there is an average safety, which shape is the safest
>> overall. Then there is also the worst case scenario as to which
>> shape is the least likely to suffer a catastrophic failure?
>> This can be further complicated by using a mesh as the cable
>> wall. This mesh would have large holes in it so that if debris hit
>> one part it would be less likely to make a large hole. Assume though
>> the same material with the same sized holes in it is used for all
>> cross section shapes. I believe the hollow cylinder is safest
>> overall, someone else believes
>> an arc, probably 1/4 of a circle is safest. What is the safest shape?
===
Subject: Re: space elevator
> So you think the double helix would be the strongest shape for impacts
from
> all directions?
I think possibly. If it is in tension (a la a rope), the twin strands
will be held in place the lateral 'rungs' of the ladder. A meteor
crashing into it will probably not break the rope, but destroy a few
rungs and that section of the double helix would be reduced to 2
parallel twisted ropes. Overall, the tension in the double helix would
be reduced a little.
I don't know what the technical term for this is, but it's like marring
a lens. The overall contrast diminishes, but there are no total breaks
in the image.
> I am having a discussion with some people about the optimum
>shape for a space elevator cable to survive impacts, perhaps someone
>may be able to help with it.
> Basically it breaks down into two alternatives, a hollow
>cylinder or a flat strip or an arc shape in between. Say for example
>you have a flat strip that of course is very long to get to orbit
>and for example is 10 centimetres wide and 1 centimetre deep. These
>numbers are arbitrary, there may be an equation that changes the
> result according to different values. Now the flat strip is the
>most dangerous because space debris travelling
>at speed could cut through the 10 cm width and cut the whole cable.
> The opposite alternative is to bend that strip into a hollow
>cylinder. Now a grazing impact is less dangerous but other impacts
>would create twice the damage by making two holes, an entry hole and
> an exit hole. There are other curves in between to consider, for
>example a half
>circle, quarter circle, parabola, etc. Which would be the safest?
>>The double helix, I think. DNA is a long string, and it has to be
>>strong and safe and have structural integrity in the nucleus of the
>>cell.
>>I saw a paper on the most 'optimal design for a column against
>>buckling' by Stephen Cox and Michael Overton, in which they stated
>>that the optimal column's cross sectional area would vanish at 1/4
>>and 3/4 of the length. There is another paper on this called
>>The shape of the tallest column. at
>>http://citeseer.nj.nec.com/360447.html
>>I am not a mathematician, but an electrical engineer, so I can't quite
>>grasp the whole picture. I was wondering if anyone would give me some
>>background on this, the attempt by Lagrange to tacke this problem for
>>example.
> There are two aspects to safety. A flat strip might survive some
>impacts best of all but an impact from the side would destroy it
>completely. A cylinder might be the optimum for all kinds of impacts
>if the worst impact scenario is safer than the other arcs but it is
>most likely to suffer a double hole from an entry hole and an exit
> hole. So there is an average safety, which shape is the safest
>overall. Then there is also the worst case scenario as to which
>shape is the least likely to suffer a catastrophic failure?
> This can be further complicated by using a mesh as the cable
>wall. This mesh would have large holes in it so that if debris hit
>one part it would be less likely to make a large hole. Assume though
>the same material with the same sized holes in it is used for all
> cross section shapes. I believe the hollow cylinder is safest
>overall, someone else believes
>an arc, probably 1/4 of a circle is safest. What is the safest shape?
===
Subject: Re: space elevator
If you put a helix under load wouldn't there be a tendency for it to unwind
and rotate? Another aspect too is that once a strand is broken then that
whole strand below it becomes a dead weight. As these accumulate then there
would be a certain probability these might occur in one section and break
the whole cable.
>> So you think the double helix would be the strongest shape for
>> impacts from all directions?
> I think possibly. If it is in tension (a la a rope), the twin strands
> will be held in place the lateral 'rungs' of the ladder. A meteor
> crashing into it will probably not break the rope, but destroy a few
> rungs and that section of the double helix would be reduced to 2
> parallel twisted ropes. Overall, the tension in the double helix
> would be reduced a little.
> I don't know what the technical term for this is, but it's like
> marring a lens. The overall contrast diminishes, but there are no
> total breaks in the image.
>> I am having a discussion with some people about the optimum
>> shape for a space elevator cable to survive impacts, perhaps
>> someone may be able to help with it.
>> Basically it breaks down into two alternatives, a hollow
>> cylinder or a flat strip or an arc shape in between. Say for
>> example you have a flat strip that of course is very long to get
>> to orbit and for example is 10 centimetres wide and 1 centimetre
>> deep. These numbers are arbitrary, there may be an equation that
>> changes the result according to different values. Now the flat
>> strip is the most dangerous because space debris travelling
>> at speed could cut through the 10 cm width and cut the whole
>> cable. The opposite alternative is to bend that strip into a
>> hollow cylinder. Now a grazing impact is less dangerous but other
>> impacts would create twice the damage by making two holes, an
>> entry hole and an exit hole. There are other curves in between
>> to consider, for example a half
>> circle, quarter circle, parabola, etc. Which would be the safest?
> The double helix, I think. DNA is a long string, and it has to be
> strong and safe and have structural integrity in the nucleus of the
> cell.
> I saw a paper on the most 'optimal design for a column against
> buckling' by Stephen Cox and Michael Overton, in which they stated
> that the optimal column's cross sectional area would vanish at 1/4
> and 3/4 of the length. There is another paper on this called
> The shape of the tallest column. at
> http://citeseer.nj.nec.com/360447.html
> I am not a mathematician, but an electrical engineer, so I can't
> quite grasp the whole picture. I was wondering if anyone would
> give me some background on this, the attempt by Lagrange to tacke
> this problem for example.
>> There are two aspects to safety. A flat strip might survive some
>> impacts best of all but an impact from the side would destroy it
>> completely. A cylinder might be the optimum for all kinds of
>> impacts if the worst impact scenario is safer than the other arcs
>> but it is most likely to suffer a double hole from an entry hole
>> and an exit hole. So there is an average safety, which shape is
>> the safest overall. Then there is also the worst case scenario as
>> to which shape is the least likely to suffer a catastrophic
>> failure? This can be further complicated by using a mesh as the
>> cable
>> wall. This mesh would have large holes in it so that if debris hit
>> one part it would be less likely to make a large hole. Assume
>> though the same material with the same sized holes in it is used
>> for all cross section shapes. I believe the hollow cylinder is
>> safest overall, someone else believes
>> an arc, probably 1/4 of a circle is safest. What is the safest
>> shape?
===
Subject: Re: space elevator
> If you put a helix under load wouldn't there be a tendency for it to
unwind
> and rotate? Another aspect too is that once a strand is broken then that
Quite the opposite. If you removed the load, then the helix would
unwind. It's a tensegrity structure (Buckminster fullers term). His
tensegrity columns.
> whole strand below it becomes a dead weight. As these accumulate then
there
> would be a certain probability these might occur in one section and break
> the whole cable.
If one strand breaks, then the whole thing will unwind quickly with
devastating results.
Hasan
>So you think the double helix would be the strongest shape for
>impacts from all directions?
>>I think possibly. If it is in tension (a la a rope), the twin strands
>>will be held in place the lateral 'rungs' of the ladder. A meteor
>>crashing into it will probably not break the rope, but destroy a few
>>rungs and that section of the double helix would be reduced to 2
>>parallel twisted ropes. Overall, the tension in the double helix
>>would be reduced a little.
>>I don't know what the technical term for this is, but it's like
>>marring a lens. The overall contrast diminishes, but there are no
>>total breaks in the image.
> I am having a discussion with some people about the optimum
>shape for a space elevator cable to survive impacts, perhaps
>someone may be able to help with it.
> Basically it breaks down into two alternatives, a hollow
>cylinder or a flat strip or an arc shape in between. Say for
>example you have a flat strip that of course is very long to get
>to orbit and for example is 10 centimetres wide and 1 centimetre
>deep. These numbers are arbitrary, there may be an equation that
> changes the result according to different values. Now the flat
>strip is the most dangerous because space debris travelling
>at speed could cut through the 10 cm width and cut the whole
> cable. The opposite alternative is to bend that strip into a
>hollow cylinder. Now a grazing impact is less dangerous but other
>impacts would create twice the damage by making two holes, an
> entry hole and an exit hole. There are other curves in between
>to consider, for example a half
>circle, quarter circle, parabola, etc. Which would be the safest?
>>The double helix, I think. DNA is a long string, and it has to be
>>strong and safe and have structural integrity in the nucleus of the
>>cell.
>>I saw a paper on the most 'optimal design for a column against
>>buckling' by Stephen Cox and Michael Overton, in which they stated
>>that the optimal column's cross sectional area would vanish at 1/4
>>and 3/4 of the length. There is another paper on this called
>>The shape of the tallest column. at
>>http://citeseer.nj.nec.com/360447.html
>>I am not a mathematician, but an electrical engineer, so I can't
>>quite grasp the whole picture. I was wondering if anyone would
>>give me some background on this, the attempt by Lagrange to tacke
>>this problem for example.
> There are two aspects to safety. A flat strip might survive some
>impacts best of all but an impact from the side would destroy it
>completely. A cylinder might be the optimum for all kinds of
>impacts if the worst impact scenario is safer than the other arcs
>but it is most likely to suffer a double hole from an entry hole
> and an exit hole. So there is an average safety, which shape is
>the safest overall. Then there is also the worst case scenario as
>to which shape is the least likely to suffer a catastrophic
> failure? This can be further complicated by using a mesh as the
>cable
>wall. This mesh would have large holes in it so that if debris hit
>one part it would be less likely to make a large hole. Assume
>though the same material with the same sized holes in it is used
> for all cross section shapes. I believe the hollow cylinder is
>safest overall, someone else believes
>an arc, probably 1/4 of a circle is safest. What is the safest
>shape?
===
Subject: Re: space elevator
Maybe also a hollow cylinder with sides like a geodesic dome. Would you be
interested in mentioning some of this to our group? We talk on a Yahoo
forum
on Space Elevators. You can join on the link below:
http://groups.yahoo.com/group/space-elevator/
>> If you put a helix under load wouldn't there be a tendency for it to
>> unwind and rotate? Another aspect too is that once a strand is
>> broken then that
> Quite the opposite. If you removed the load, then the helix would
> unwind. It's a tensegrity structure (Buckminster fullers term). His
> tensegrity columns.
>> whole strand below it becomes a dead weight. As these accumulate
>> then there would be a certain probability these might occur in one
>> section and break the whole cable.
> If one strand breaks, then the whole thing will unwind quickly with
> devastating results.
> Hasan
>> So you think the double helix would be the strongest shape for
>> impacts from all directions?
> I think possibly. If it is in tension (a la a rope), the twin
> strands will be held in place the lateral 'rungs' of the ladder. A
> meteor crashing into it will probably not break the rope, but
> destroy a few rungs and that section of the double helix would be
> reduced to 2 parallel twisted ropes. Overall, the tension in the
> double helix would be reduced a little.
> I don't know what the technical term for this is, but it's like
> marring a lens. The overall contrast diminishes, but there are no
> total breaks in the image.
> I am having a discussion with some people about the optimum
>> shape for a space elevator cable to survive impacts, perhaps
>> someone may be able to help with it.
>> Basically it breaks down into two alternatives, a hollow
>> cylinder or a flat strip or an arc shape in between. Say for
>> example you have a flat strip that of course is very long to get
>> to orbit and for example is 10 centimetres wide and 1 centimetre
>> deep. These numbers are arbitrary, there may be an equation that
>> changes the result according to different values. Now the flat
>> strip is the most dangerous because space debris travelling
>> at speed could cut through the 10 cm width and cut the whole
>> cable. The opposite alternative is to bend that strip into a
>> hollow cylinder. Now a grazing impact is less dangerous but other
>> impacts would create twice the damage by making two holes, an
>> entry hole and an exit hole. There are other curves in between
>> to consider, for example a half
>> circle, quarter circle, parabola, etc. Which would be the safest?
The double helix, I think. DNA is a long string, and it has to be
> strong and safe and have structural integrity in the nucleus of
> the cell.
> I saw a paper on the most 'optimal design for a column against
> buckling' by Stephen Cox and Michael Overton, in which they stated
> that the optimal column's cross sectional area would vanish at 1/4
> and 3/4 of the length. There is another paper on this called
> The shape of the tallest column. at
> http://citeseer.nj.nec.com/360447.html
> I am not a mathematician, but an electrical engineer, so I can't
> quite grasp the whole picture. I was wondering if anyone would
> give me some background on this, the attempt by Lagrange to tacke
> this problem for example.
> There are two aspects to safety. A flat strip might survive
>> some impacts best of all but an impact from the side would
>> destroy it completely. A cylinder might be the optimum for all
>> kinds of impacts if the worst impact scenario is safer than the
>> other arcs but it is most likely to suffer a double hole from an
>> entry hole and an exit hole. So there is an average safety,
>> which shape is the safest overall. Then there is also the worst
>> case scenario as to which shape is the least likely to suffer a
>> catastrophic failure? This can be further complicated by using
>> a mesh as the cable
>> wall. This mesh would have large holes in it so that if debris
>> hit one part it would be less likely to make a large hole. Assume
>> though the same material with the same sized holes in it is used
>> for all cross section shapes. I believe the hollow cylinder is
>> safest overall, someone else believes
>> an arc, probably 1/4 of a circle is safest. What is the safest
>> shape?
===
Subject: Re: space elevator
> Maybe also a hollow cylinder with sides like a geodesic dome. Would you
be
> interested in mentioning some of this to our group? We talk on a Yahoo
forum
> on Space Elevators. You can join on the link below:
> http://groups.yahoo.com/group/space-elevator/
Sure, I'd love to.
Hasan
>If you put a helix under load wouldn't there be a tendency for it to
>unwind and rotate? Another aspect too is that once a strand is
>broken then that
>>Quite the opposite. If you removed the load, then the helix would
>>unwind. It's a tensegrity structure (Buckminster fullers term). His
>>tensegrity columns.
>whole strand below it becomes a dead weight. As these accumulate
>then there would be a certain probability these might occur in one
>section and break the whole cable.
>>If one strand breaks, then the whole thing will unwind quickly with
>>devastating results.
>>Hasan
>So you think the double helix would be the strongest shape for
>impacts from all directions?
>>I think possibly. If it is in tension (a la a rope), the twin
>>strands will be held in place the lateral 'rungs' of the ladder. A
>>meteor crashing into it will probably not break the rope, but
>>destroy a few rungs and that section of the double helix would be
>>reduced to 2 parallel twisted ropes. Overall, the tension in the
>>double helix would be reduced a little.
>>I don't know what the technical term for this is, but it's like
>>marring a lens. The overall contrast diminishes, but there are no
>>total breaks in the image.
 I am having a discussion with some people about the optimum
>shape for a space elevator cable to survive impacts, perhaps
>someone may be able to help with it.
> Basically it breaks down into two alternatives, a hollow
>cylinder or a flat strip or an arc shape in between. Say for
>example you have a flat strip that of course is very long to get
>to orbit and for example is 10 centimetres wide and 1 centimetre
>deep. These numbers are arbitrary, there may be an equation that
> changes the result according to different values. Now the flat
>strip is the most dangerous because space debris travelling
>at speed could cut through the 10 cm width and cut the whole
> cable. The opposite alternative is to bend that strip into a
>hollow cylinder. Now a grazing impact is less dangerous but other
>impacts would create twice the damage by making two holes, an
> entry hole and an exit hole. There are other curves in between
>to consider, for example a half
>circle, quarter circle, parabola, etc. Which would be the safest?
>>The double helix, I think. DNA is a long string, and it has to be
>>strong and safe and have structural integrity in the nucleus of
>>the cell.
>>I saw a paper on the most 'optimal design for a column against
>>buckling' by Stephen Cox and Michael Overton, in which they stated
>>that the optimal column's cross sectional area would vanish at 1/4
>>and 3/4 of the length. There is another paper on this called
>>The shape of the tallest column. at
>>http://citeseer.nj.nec.com/360447.html
>>I am not a mathematician, but an electrical engineer, so I can't
>>quite grasp the whole picture. I was wondering if anyone would
>>give me some background on this, the attempt by Lagrange to tacke
>>this problem for example.
> There are two aspects to safety. A flat strip might survive
>some impacts best of all but an impact from the side would
>destroy it completely. A cylinder might be the optimum for all
>kinds of impacts if the worst impact scenario is safer than the
>other arcs but it is most likely to suffer a double hole from an
> entry hole and an exit hole. So there is an average safety,
>which shape is the safest overall. Then there is also the worst
>case scenario as to which shape is the least likely to suffer a
> catastrophic failure? This can be further complicated by using
>a mesh as the cable
>wall. This mesh would have large holes in it so that if debris
>hit one part it would be less likely to make a large hole. Assume
>though the same material with the same sized holes in it is used
> for all cross section shapes. I believe the hollow cylinder is
>safest overall, someone else believes
>an arc, probably 1/4 of a circle is safest. What is the safest
>shape?
===
Subject: Sometimes-implied sequence(s)
Here is one of those unsophisticated, but weird (to me), curiosities.
Let {a(k)} be a sequence of reals such that:
a(0) = x,
for k = each positive integer,
a(k) = sum{j=0 to k} binomial(k,j) a(j) y^j,
where y is complex.
Now, I am guessing (I could have erred anywhere below):
IF |y| is not 1,
then there is only one value for each a(k),
a(k) = x/(1-y)^k.
(Just take sum from 0 to {k-1}, then divide by (1 -y^k) to get a(k)
explicitly.)
*But* we can get other {a(k)}'s for other y's.
For example, if y = -1 and x = 0, there are many sequences equal to
{a(k)}, only one of which is
a(0) = a(1) = 0,
a(k) = 1 +1/2 +1/3 +...+1/(k-1),
the (k-1)th harmonic number.
Yet, we do *not* necessarily have 0/0 = x/(1-y)^k for every k.
So, I am guessing (correctly?) that,
if y = exp(i pi 2 r), for r = rational, then
a(k) = x/(1-y)^k for every k < the denominator of the reduced r.
But for k >= this denominator, the sequence can take on many values.
Leroy Quet
===
Subject: Applying to Grad school (GRE verbal?)
I don't know how many can comment, but I am applying to Math grad school
and
was wondering how important the general GRE test is when applying to the
top
math schools. In particular, the Verbal section. I am an American
student,
and this section still troubles me...The rest of my application is very
good. I expect to get in the low to mid 500's on the verbal...(800 quant
and 4-5 on the writing section out of 6).
John
===
Subject: Re: Applying to Grad school (GRE verbal?)
Arturo's assessment is pretty accurate, with the caveat that he's only
talking about tests. But to be honest, if you're applying to the top
math schools, none of these tests is very important, except maybe as
a warning sign if you do too poorly. The most important parts of your
application, IMHO, are the range of classes that you've taken, the
grades you received, the letters you get from your professors, and any
other indication of research potential and willingness to work hard
that you can show. (For the last, I'm talking about things like summer
programs, UTRA's, honors thesis, etc.)
Good luck with your apps.
JSH
> I don't know how many can comment, but I am applying to Math grad school
and
> was wondering how important the general GRE test is when applying to the
top
> math schools. In particular, the Verbal section. I am an American
student,
> and this section still troubles me...The rest of my application is very
> good. I expect to get in the low to mid 500's on the verbal...(800 quant
> and 4-5 on the writing section out of 6).
> John
===
Subject: Re: Applying to Grad school (GRE verbal?)
Adjunct Assistant Professor at the University of Montana.
>I don't know how many can comment, but I am applying to Math grad school
and
>was wondering how important the general GRE test is when applying to the
top
>math schools.
The most important is the Math Subject Test; second most important is
the analytic part of the general GRE, then the quantitative; and
finally the verbal.
===
Subject: Re: Applying to Grad school (GRE verbal?)
>I don't know how many can comment, but I am applying to Math grad school
and
>was wondering how important the general GRE test is when applying to the
top
>math schools.
> The most important is the Math Subject Test; second most important is
> the analytic part of the general GRE, then the quantitative; and
> finally the verbal.
> Arturo Magidin
> magidin@math.berkeley.edu
Do you mean the analytical writing section which recently replaced the
analytic section?
In other words, is the analyitical writing section considered more
important than the quantitative section?
By the way, I don't think the math subject test actually tests very
many of the skills which are most useful in grad school. A half baked
understanding of the concepts combined with good memorization can
yield a good grade.
In particular, the test does not measure the ability to write proofs.
I think, therefore, it is unfortunate that it is taken so seriously.
===
Subject: Re: Applying to Grad school (GRE verbal?)
Adjunct Assistant Professor at the University of Montana.
>>I don't know how many can comment, but I am applying to Math grad school
and
>>was wondering how important the general GRE test is when applying to the
top
>>math schools.
>> The most important is the Math Subject Test; second most important is
>> the analytic part of the general GRE, then the quantitative; and
>> finally the verbal.
>> Arturo Magidin
>> magidin@math.berkeley.edu
>Do you mean the analytical writing section which recently replaced the
>analytic section?
I did not know there was a change. When I took the GRE (over 11 years
ago), one section was verbal (synonyms, analogies, etc); one was
quantitative; and the last one, called the analytical part, included
logic problems, reading comprehension, and so on. All the Departments
I looked at encouraged you to take the Math Subject Test (when they
did not ->require<- it), and specified that they were interested in
high scores in the analytical section of the general test. Since the
quantitative section involved some basic mathematics as well, they
were also important.
The point was that a very large part of the analytical section
involved logical thinking and abstraction, which are far more
important for an advanced degree in mathematics than is being able to
quickly multiply two large numbers.
>In other words, is the analyitical writing section considered more
>important than the quantitative section?
I don't know if the new section would be considered more
important. And the description at the GRE site is no help to me in
deciding.
I would suggest the OP drop a note to a few schools and ask them point
blank which sections of the general GRE they consider most important,
and whether they encourage, require, or ignore, the subject test.
>By the way, I don't think the math subject test actually tests very
>many of the skills which are most useful in grad school.
No, it does not. But it tests many of the skills which are basic and
that you need to have down for grad school. You can't do well in grad
school if you cot remember how to find the rel. max. of a
polynomial, even if you don't need to understand the analysis behind
it.
> A half baked
>understanding of the concepts combined with good memorization can
>yield a good grade.
Basically, the math subject test covers the material that you should
have down cold. If you understand them, then you should be able to
use them easily and quickly. If you cot use these basic concepts
quickly and easily, then you are certainly not ready for grad
school. That is, being able to obtain a good grade in the subject test
is certainly necessary, though not sufficient.
>In particular, the test does not measure the ability to write proofs.
It is extremely hard to teach how to write proofs, and in my
experience, even when I went to grad school I would say that at least
half of 1st year grad students did not have a good grasp of how to
write a proof. They either learned by example and trial and error, or
they failed miserably at grad school (usually, by failing the
Prelim).
>I think, therefore, it is unfortunate that it is taken so seriously.
Basically, I suspect it is like Churchill once said of democracy: It
is the best possible system, except for all other systems that have
been tried from time to time. The math GRE subject test is certainly
not an ideal tool to decide who has a good chance of success in
graduate school in mathematics, and it is severely flawed, but it
seems to be the best available tool (short of letting everyone in for
a semester and then kicking out the non-promising ones).
In reality, I suspect that what is given the MOST weight in the final
decision is not the GRE test, but rather the coursework taken and the
letters of recommendation. Particularly the latter. As I recall from
my own application experience, the GRE test was more a filter than a
decision maker: in order for your application to be considered, you
should normally score at least this much on each part; and then it was
ignored in favor of letters of rec. and so on.
===
Subject: Re: limitations on mutual anti-correlation? determinant
apparently p must be greater than -1/(N-1) because the determinant
of the highly symmetric matrix is
det = (1-p)^(N-1) (1 + (N-1)p). So
det > 0 if, and only if, p > 1/(N-1).
Now, what is the simplest way to prove that my formula for det is correct?
===
Subject: Re: limitations on mutual anti-correlation? determinant
>apparently p must be greater than -1/(N-1) because the determinant
>of the highly symmetric matrix is
>det = (1-p)^(N-1) (1 + (N-1)p). So
>det > 0 if, and only if, p > 1/(N-1).
>Now, what is the simplest way to prove that my formula for det is correct?
Take v to be the (column) vector of dimension n with all the
components equal 1/sqrt(n) (that's just for normalization. Then the
matrix
P(v) = vv^T
(i.e. v multiplied by the transpose of v) is the projection operator
on the 1-dim subspace sped by v and you can immediately check that
all the components of P(v) are the same, = 1/n. So, the matrix which
has all the components equal p is just n*p*P(v). Finally, the matrix
C you're interested in, the one which has 1s on the diagonal and all
other components equal p is given by
C = (1-p)*I + n*p*P(v)
where I is the identity matrix, of course.
OK, that was setting the stage, now we can wrap it up. Given any
vector u from the n-1 dimensional subspace normal to v we've
Cu = (1-p)u
Thus 1-p is an eigenvalue of C, with an (n-1) degeneracy. As for v
itself, we've
Cv = (1-p+np)v = (1 + (n-1)p)v
So 1 - (n-1)p is the remaining eigenvalue (no degeneracy). Now, the
determinant is just the product of all the eigenvalues, i.e.
det = (1 - (n-1)p)*(1-p)^n
Mati Meron | When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same
===
Subject: Re: limitations on mutual anti-correlation? determinant
>>apparently p must be greater than -1/(N-1) because the determinant
>>of the highly symmetric matrix is
>>det = (1-p)^(N-1) (1 + (N-1)p). So
>>det > 0 if, and only if, p > 1/(N-1).
>>Now, what is the simplest way to prove that my formula for det is
correct?
>Take v to be the (column) vector of dimension n with all the
>components equal 1/sqrt(n) (that's just for normalization. Then the
>matrix
> P(v) = vv^T
>(i.e. v multiplied by the transpose of v) is the projection operator
>on the 1-dim subspace sped by v and you can immediately check that
>all the components of P(v) are the same, = 1/n. So, the matrix which
>has all the components equal p is just n*p*P(v). Finally, the matrix
>C you're interested in, the one which has 1s on the diagonal and all
>other components equal p is given by
> C = (1-p)*I + n*p*P(v)
>where I is the identity matrix, of course.
>OK, that was setting the stage, now we can wrap it up. Given any
>vector u from the n-1 dimensional subspace normal to v we've
> Cu = (1-p)u
>Thus 1-p is an eigenvalue of C, with an (n-1) degeneracy. As for v
>itself, we've
> Cv = (1-p+np)v = (1 + (n-1)p)v
>So 1 - (n-1)p is the remaining eigenvalue (no degeneracy). Now, the
>determinant is just the product of all the eigenvalues, i.e.
> det = (1 - (n-1)p)*(1-p)^n
oops, sorry, typo in the last line, it is
det = (1 + (n-1)p)*(1-p)^n
Mati Meron | When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same
===
Subject: Re: limitations on mutual anti-correlation?
> :> It may help your intuition to think of the correlation
> :> as the cosine of the angle between vectors. Now the
> :> question can be put this way: is it possible to arrange
> :> three vectors in space so that the angle between any
> :> pair of vectors is greater than 90 degrees?
> : If you are asking if it is possible to arrange three vectors in
> : 3-space such that the angle between any pair is greater than 90
> : degrees, the answer is yes: put them all in the same plane, and let
> : the angles be 120/120/120.
> I wasn't asking anything.
I see. You were rephrasing a question, and you object to my preamble
to rephrasing your rephrasing as just possibly implying in the mind of
an unbiased observer that you were personally asking the question?
Your objection has an Alice-in-Wonderland quality to it:
Mad Hatter: If I were to ask you if you were to like some tea ...
March Hare: The answer is I don't want any tea ...
Mad Hatter: I wasn't asking you anything.
Perhaps we can clean this up now, anyway. The answer to the first
part of the OP's question was yes, whereas the specific example
given was impossible. Since we are being so punctilious, I'm
surprised prior posters were so fast and loose with the correlation
matrix vs. the variance-covariance matrix.
===
Subject: Re: limitations on mutual anti-correlation?
:
:> :> It may help your intuition to think of the correlation
:> :> as the cosine of the angle between vectors. Now the
:> :> question can be put this way: is it possible to arrange
:> :> three vectors in space so that the angle between any
:> :> pair of vectors is greater than 90 degrees?
:>
:> : If you are asking if it is possible to arrange three vectors in
:> : 3-space such that the angle between any pair is greater than 90
:> : degrees, the answer is yes: put them all in the same plane, and let
:> : the angles be 120/120/120.
:> I wasn't asking anything.
: I see. You were rephrasing a question, and you object to my preamble
: to rephrasing your rephrasing as just possibly implying in the mind of
: an unbiased observer that you were personally asking the question?
I think my response came across snippier than intended. Sorry.
Mike
===
Subject: Re: can anyone help me solve this problem?
===
>Subject: can anyone help me solve this problem?
>How many ways are there to distribute B non-distinct Bones between D
distinct
>dogs?
>if you know the answer to this, could you let me know how you came up with
it?
consider the case of 3 bones and 2 dogs:
I can represent the two dogs with one stick | in this way.
if the bone is on the left side of the stick it
belongs to dog1. If the bone is on the right side of
the stick it belongs to dog2. E.G.
BB| 2 bones for dog1 none for dog2
B|B 1 bone for each
|BB 2 bones for dog2 none for dog1
I have (D-1) sticks and B bones, so there are
(B+D-1)! different permutations of sticks and bones...
but B! of them are the same... and (D-1)! of them
are the same...
so the answer is that there are
((B+D-1)!) / ((B!)((D-1)!))
Different ways to distribute B identical bones to D distinct dogs.
Hopefully I've not made any mistakes... but if you want to
see a solution from a more offical source you should check out
the book:
Thermodynamics and an Introduction to Thermostatistics, 2nd Edition
by Herbert B. Callen
Chapter 15.2 (The Einstein model of a crystalline solid)
adam
===
Subject: Re: can anyone help me solve this problem?
===
>Subject: can anyone help me solve this problem?
>How many ways are there to distribute B non-distinct Bones between D
distinct
>dogs?
>if you know the answer to this, could you let me know how you came up
with it?
> consider the case of 3 bones and 2 dogs:
> I can represent the two dogs with one stick | in this way.
> if the bone is on the left side of the stick it
> belongs to dog1. If the bone is on the right side of
> the stick it belongs to dog2. E.G.
> BB| 2 bones for dog1 none for dog2
> B|B 1 bone for each
> |BB 2 bones for dog2 none for dog1
> I have (D-1) sticks and B bones, so there are
> (B+D-1)! different permutations of sticks and bones...
> but B! of them are the same... and (D-1)! of them
> are the same...
> so the answer is that there are
> ((B+D-1)!) / ((B!)((D-1)!))
> Different ways to distribute B identical bones to D distinct dogs.
> Hopefully I've not made any mistakes... but if you want to
> see a solution from a more offical source you should check out
> the book:
> Thermodynamics and an Introduction to Thermostatistics, 2nd Edition
> by Herbert B. Callen
> Chapter 15.2 (The Einstein model of a crystalline solid)
> adam
bone, but could never get that last step to coalesce the answer into
B+D-1 choose B format. I was even solving it using the dividing
lines, and found out in the process that b bones into d dogs gives the
same answer as d-1 bones into b+1 dogs. Given the above solution - it
makes sense.
cheers
c
===
Subject: Re: Leibniz & Newton
===
>Subject: Re: Leibniz & Newton
>> Can anyone help me with this question? Why is Newton more widely
accepted
>> as the man who developed calculus, instead of Leibniz?
>It's Leibniz's dy/dx notation that survives, rather than Newton's dot
>notation for derivatives.
We physicists use the dot notation all the time to signify a
dirivative w.r.t time
Also, the dy/dx notation is a little misleading in that it makes you
think Fraction!
adam
===
Subject: Re: Leibniz & Newton
Hi Adam,
May I ask, then, in your opinion, is Newton's calculus more effective than
Leibniz's? I realize he has won the debate over the years, as we are
taught
in school that he is the founder of the calculus. However, I am
interested to know how your personally feel about it, being a physicist.
Kavon
P.S. I agree, dy/dx instantly has me thinking of a fraction. However, my
math skills are surely limited compared to yours.
===
>Subject: Re: Leibniz & Newton
>> Can anyone help me with this question? Why is Newton more widely
accepted
>> as the man who developed calculus, instead of Leibniz?
>It's Leibniz's dy/dx notation that survives, rather than Newton's dot
>notation for derivatives.
> We physicists use the dot notation all the time to signify a
> dirivative w.r.t time
> Also, the dy/dx notation is a little misleading in that it makes you
> think Fraction!
> adam
===
Subject: Re: Leibniz & Newton
> I realize he has won the debate over the years, as we are taught
> in school that he is the founder of the calculus.
I was a bit surprised to read this. I looked in a few American
calculus texts on my shelf, and found Newton & Leibniz with equal
billing for this.
--
http://www.math.ohio-state.edu/~edgar/
===
Subject: Re: Leibniz & Newton
Hi GO.A. Edgar,
That would be in more recent times. During the 70s & 80s I recall Newton's
image on most Calculus texts.
It could have been a biased publisher, though.
Kavon
> I realize he has won the debate over the years, as we are taught
> in school that he is the founder of the calculus.
> I was a bit surprised to read this. I looked in a few American
> calculus texts on my shelf, and found Newton & Leibniz with equal
> billing for this.
> --
> G. A. Edgar
http://www.math.ohio-state.edu/~edgar/
===
Subject: Re: Leibniz & Newton
>Hi Adam,
>May I ask, then, in your opinion, is Newton's calculus more effective than
>Leibniz's? I realize he has won the debate over the years, as we are
taught
>in school that he is the founder of the calculus. However, I am
>interested to know how your personally feel about it, being a physicist.
I was not aware that Newton got more credit than Leibniz these days. I
thought almost everybody agrees now that, no matter which of them was first
in time, they made their discoveries independently, and so they should be
given joint credit.
But the answer to your question about notation is a definite no. Leibniz's
notation was far superior to Newton's. After Newton, British mathematics
went
into decline, whereas German and continental mathematics prospered. The
superior notation of Leibniz and the unwillingness of the Brits to adopt it
(because of their oyance about the priority dispute) is thought to be
a significant factor in developments over the following couple of
centuries.
Derek Holt.
===
Subject: Re: Leibniz & Newton
Derek,
I certainly can agree. Not only were there disputes across borders, even
in
one's own family, such as the Bernoulli's. So many were not even realized
until recent times, for the work they have done to further the development
of mathematics & the sciences.
Kavon
>Hi Adam,
>May I ask, then, in your opinion, is Newton's calculus more effective
than
>Leibniz's? I realize he has won the debate over the years, as we are
taught
>in school that he is the founder of the calculus. However, I am
>interested to know how your personally feel about it, being a physicist.
> I was not aware that Newton got more credit than Leibniz these days. I
> thought almost everybody agrees now that, no matter which of them was
first
> in time, they made their discoveries independently, and so they should be
> given joint credit.
> But the answer to your question about notation is a definite no.
Leibniz's
> notation was far superior to Newton's. After Newton, British mathematics
went
> into decline, whereas German and continental mathematics prospered. The
> superior notation of Leibniz and the unwillingness of the Brits to adopt
it
> (because of their oyance about the priority dispute) is thought to be
> a significant factor in developments over the following couple of
centuries.
> Derek Holt.
===
Subject: Re: Leibniz & Newton
> But the answer to your question about notation is a definite no.
Leibniz's
> notation was far superior to Newton's. After Newton, British mathematics
> went into decline, whereas German and continental mathematics prospered.
> The superior notation of Leibniz and the unwillingness of the Brits to
> adopt it (because of their oyance about the priority dispute) is
> thought to be a significant factor in developments over the following
> couple of centuries.
Geniuses are so stupid.
Have a tolerable existence. Eli
===
Subject: Re: Leibniz & Newton
permission for an emailed response.
Today, THREE WINOS from DETROIT sold me a framed photo of TAB HUNTER
before his MAKEOVER!
> May I ask, then, in your opinion, is Newton's calculus more effective
than
> Leibniz's? I realize he has won the debate over the years, as we are
taught
> in school that he is the founder of the calculus.
They are identical. They developed the same system, in all essential
parts. In areas where they happen to differ in inessential things,
modern usage prefers neither.
> P.S. I agree, dy/dx instantly has me thinking of a fraction. However, my
> math skills are surely limited compared to yours.
Alas, the problem is that dy/dx is misleading. The d notation is
h, but deceptive. For an excellent treatment of how this can lead
physics astray, I suggest looking at Sussman and Wisdom Structure and
Interpretation of Classical Mechanics, which studiously avoids such
things and sticks to a pure functional notation. In the process, they
uncovered mistakes and errors not previously noted.
Thomas
===
Subject: Re: Leibniz & Newton
Thomas,
Since dy/dx is a very common usage, especially in the lower physics
classes,
one does become used to it. I wish functional notation were more common in
Mechanics. I will certainly seek it out.
Kavon
===
Subject: Re: why 1 + 1 equals 2?
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id h9QF5As29689;
Check out peano's axioms and axiomatic construction of addition and natural
numbers
Padmasambhava
===
Subject: Re: simple vector equation
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id h9QF59429658;
123456789 123456789 123456789 123456789 123456789 123456789 123456789 12
> So, just today I have realized the significance of this mental
> stack depth thing clearly enough to give it that name. Of course,
> I had an intuition about it for years, which I was why I intuitively
> preferred syntaxes that reduce the stack depth. So, what else can
> be done along these lines in an ideal computer language? I guess
> it is just a matter of defining more prefix, postfix, and infix
> operators.
>> Have you tried Forth?
> No, I have not. I will look into it. Does it allow you to define
> new infix operators and set their precedence, associativity,
> commutativity, and distributive properties?
Another language that is a nice compromise between the extremes
of Lisp and Forth is PostScript. Like Forth, all operators are
postfix, but there are braces and brackets for grouping which
makes it a lot easier to read than Forth. It also uses linked
data structures which can be manipulated as in Lisp.
http://www.cs.wisc.edu/~ghost/
As far as defining your own syntax, there is the archaic string
manipulation language Snobol and its modern variant Icon:
http://www.snobol4.com/
http://unicon.sourceforge.net/
The following PostScript program draws a Penrose tiling variation.
The file is called snail.ps because the tiles resemble snails.
/xd {exch def} def
/t 1 5 sqrt 1 add 2 div div def
/tri1 {
/cy xd /cx xd /by xd /bx xd /ay xd /ax xd
lev 0 le {
bx by moveto
cx t mul bx add t mul cy t mul by add t mul lineto
ax t mul cx add t mul bx t mul add t mul cx t mul add t mul
ay t mul cy add t mul by t mul add t mul cy t mul add t mul
lineto cx cy lineto stroke
}{
/hy ay t mul cy add t mul def
/hx ax t mul cx add t mul def
/lev lev 2 sub def
bx by ax ay hx hy
bx by cx cy hx hy
tri1
/lev lev 1 add def
tri2
/lev lev 1 add def
} ifelse
}def
/tri2 {
/fy xd /fx xd /ey xd /ex xd /dy xd /dx xd
lev 0 le {
dx dy moveto
dx t mul ex add t mul t mul dx add t mul
dy t mul ey add t mul t mul dy add t mul lineto
ex t mul fx add t mul dx t mul add t mul
ey t mul fy add t mul dy t mul add t mul lineto
fx fy lineto stroke
}{
/hy dy t mul ey add t mul def
/hx dx t mul ex add t mul def
/lev lev 2 sub def
dx dy hx hy fx fy
ex ey fx fy hx hy
tri4
/lev lev 1 add def
tri3
/lev lev 1 add def
} ifelse
}def
/tri3 {
/cy xd /cx xd /by xd /bx xd /ay xd /ax xd
lev 0 le {
bx by moveto
cx t mul bx add t mul cy t mul by add t mul lineto
ax t mul cx add t mul bx t mul add t mul cx t mul add t mul
ay t mul cy add t mul by t mul add t mul cy t mul add t mul
lineto
ax t mul cx add t mul ay t mul cy add t mul lineto
cx t mul ax add t mul cy t mul ay add t mul lineto
bx t mul ax add t mul ax t mul add t mul
by t mul ay add t mul ay t mul add t mul lineto
ax ay lineto stroke
}{
/hy ay t mul cy add t mul def
/hx ax t mul cx add t mul def
/lev lev 2 sub def
bx by ax ay hx hy
bx by cx cy hx hy
tri3
/lev lev 1 add def
tri4
/lev lev 1 add def
} ifelse
}def
/tri4 {
/fy xd /fx xd /ey xd /ex xd /dy xd /dx xd
lev 0 le {
ex ey moveto
dx t mul ex add t mul ex t mul add t mul
dy t mul ey add t mul ey t mul add t mul lineto
ex t mul fx add t mul ey t mul fy add t mul lineto
fx fy lineto stroke
}{
/hy dy t mul ey add t mul def
/hx dx t mul ex add t mul def
/lev lev 2 sub def
dx dy hx hy fx fy
ex ey fx fy hx hy
tri2
/lev lev 1 add def
tri1
/lev lev 1 add def
} ifelse
}def
/lev 14 def
.36 setlinewidth 1 setlinejoin 1 setlinecap
306 756 moveto 540 36 lineto 72 36 lineto closepath stroke
306 756 540 36 72 36 tri1
showpage
===
Subject: Probability question
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id h9QF5A329680;
In an experiment, two cards are drawn from a deck of well-shuffled
pack
find the probability for the event that
(a)the two cards have a sum of 3
(b)the two cards have a sum of 3 if one of the cards is an ace of
heart.
===
Subject: proper map
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id h9QF59K29646;
Hi
I have some simple questions about proper maps for topological spaces:
The definition of a map f: X -> Y being proper is that, any compact 
subspace
of
Y has its inverse image in X being compact.
I am just wondering: suppose g: X -> Y is a continuous map such that for
some
dense open subspace V of Y, the restriction of g to g^(-1) (V) -> V is
proper.
Then is it true that g itself must have been proper? Is it relevant here
that X
and Y be Hausdorff? And what if I did not assume that V is dense, i.e. V is
just
some open subspace?
I've tried to look up texts on topology, but few of them seem to mention
proper
maps...so any help would be greatly appreciated!
Jason
===
Subject: Re: proper map
>I have some simple questions about proper maps for topological spaces:
>The definition of a map f: X -> Y being proper is that, any compact
subspace of
>Y has its inverse image in X being compact.
>I am just wondering: suppose g: X -> Y is a continuous map such that for
some
>dense open subspace V of Y, the restriction of g to g^(-1) (V) -> V is
proper.
>Then is it true that g itself must have been proper? Is it relevant here
that X
>and Y be Hausdorff? And what if I did not assume that V is dense, i.e. V 
is
just
>some open subspace?
Consider X = [0,infinity) x (0,pi), mapped continuously to the union of
the open upper half plane and the origin by
g:(s,t) -> (s cos(t), s sin(t)).
Let V be the open upper half plane, so V is a dense open subspace in Y.
Of course X and Y are Hausdorff, and the restriction of g to
g^(-1)(V) = (0,infinity) x (0,pi) is a homeomorphism and therefore
proper. But g is not proper because the inverse image of the origin is
{0} x (0,pi) which is not compact.
Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2
===
Subject: Re: Mean of a random variable
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id h9QMsad25933;
A message received from Stephen J. Herschkorn
You asked
> Is it possible that for a continuous random variable the following
> holds: E[x]=integral_0^infty{1-F(x)} where F(x)=c.d.f.
This is true as long as the random variable is *nonnegative*, and the fact
holds true for *all* nonnegative random variables, not just continuous 
ones.
The proof (which is in most of Ross's books):
Let I(x) be the indicator variable for the event {X > x}. You may verify
that X = int(x=0..infty, I(x)) (draw the picture). Thus, EX =
E[int(x=0..infty, I(x))] = int(x=0..infty, EI(x)) (by Tonelli) =
int(x=0..infty, 1 - F(x)).
Thus, no need to appeal to change of variables, and no need for F(x)-> 1 as
x -> infty. (If the latter condition does not hold, X takes on the value
+infty with positive probability and the expectation is infinite.)
For general random variables, the formula is
EX = int(x=0..infty, 1-F(x)) - int(x= -infty..0, F(x)).
Stephen J. Herschkorn
herschko@rutcor.rutgers.edu
===
Subject: Re: reverse convolution??
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id h9QMsZL25923;
>Sorry to bother you.
>I get a confusing question.
>Given the convolution of the input vectors a and b, denoted as c,
>where
>c_{j}=sum_{k=0}{j} a_{k} b_{j-k},
>(1) Is it possible to get a and b?
>(2) If it is not possible to get the unique solution, is it possible
>to get any one of the possible solution?
>(3) If the length of a is equal to that of b, does that help to
>recover a and b from c?
It helps if the c_{j} are available up to
j = sum of max a index and max b index.
In that case the result is equivalent to multiplication of polynomials.
If you factor the polynomial sum( c_{j} x^j ), then you can try
different combinations of factors to make up the a and b polynomials.
===
Subject: Re: Probability question
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id h9QMsZP25913;
>In an experiment, two cards are drawn from a deck of well-shuffled
>pack
>find the probability for the event that
>(a)the two cards have a sum of 3
>(b)the two cards have a sum of 3 if one of the cards is an ace of
>heart.
There are C(52,2) = 1326 possible pairs of cards.
(a) The cards must be an Ace and a Deuce.
There are 4 choices of Aces and 4 choices of Deuces.
Hence, there are 4x4 = 16 pairs which contain an Ace and a Deuce.
The probability is: 16/1326 = 8/663
(b) If one card is the Ace of Hearts, the other card is a Deuce.
There are 4 choices for a Deuce among the other 51 cards.
The probability is: 4/51
===
Subject: Re: Mean of a random variable
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id h9QMsbT25949;
>>Is it possible that for a continuous random variable the following holds:
>>E[x]=integral_0^infty{1-F(x)} where F(x)=c.d.f.
>More than just possible. Use integration by parts. It should be true for
>any distribution (continuous or not) supported on the nonnegative reals,
>such that (1-F(x)) x -> 0 as x -> +infinity.
>Robert Israel israel@math.ubc.ca
>Department of Mathematics <a
href=http://www.math.ubc.ca/~israel>http://www.math.ubc.ca/~israel</aUniversity of British Columbia
>Vancouver, BC, Canada V6T 1Z2
However, is there a distribution function (supported on the nonnegative
reals, with finite mean and variance) where x(1-F(x))->0 as x->-infinity
doesn't hold? Isn't this always true?
===
Subject: math
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id h9QMsdh26001;
What is the first number that can be divided byt he frist three prime
numbers?
===
Subject: Re: math
> What is the first number that can be divided byt he frist three prime
> numbers?
The first three primes are 2, 3, and 5. The smallest number divisible
by all of them is 30.
===
Subject: Covering pairs with m-sets
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id h9RD6Ln13263;
Does anybody knows something (answer, references...) about the following
problem :
Let E be a finite set, with |E| = n, and m be a positive integer such that 
2
=< m =< n.
What is the minimum number f(m,n) of m-subsets of E which cover each pair 
of
element of E (That is, for every a,b in E, {a,b} is contained in at least 
one
of the m-subsets) ?
I'm also interseted in generalizations of this problem (for example, what 
if
we ask for cover the k-subsets instead of the 2-subsets?).
Pierre.
===
Subject: Re: Mean of a random variable
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id h9RD6Gr13245;
Dudi-
> Does this mean that x(1-F(x)) is 0 when x->infty (again, nonnegative
> random variable)? This was my original problem. I assume that:
Not necessarily: 1- F(x) can be any nonincreasing function, e.g., 1/x.
With this example, though, X has infinite expectation. I don't know: For
nonnegatve monotone G, does the convergence of int(0..infty,G) imply that
x G(x) -> 0 as x -> infty?
While I see where you are coming from, the following does not make much
sense.
> If we use integration by parts then:
> E(x)=[xF(x)]_0^infty-int_0_infty{F(x)}
the right-hand side is infty - infty
> and so x(1-F(x))=x-xF(x)=x-E(x)-
> int_0_infty{F(x)}=-E(x)+int_0_infty{1-F(x)}= -E(x)+E(x)=0 Is this
> true?
the second equality in this last quote (first line) makes no sense.
Better:
EX = lim int(x=0..a, x f(x)), where limit is as a -> infty Integrate by
parts: u = x, dv = f(x) dx du = dx, v = -[1-F(x)] int(x=0..a, x f(x)] =
-a[1-F(a)] + int(0..a, 1-F)
So maybe lim x[1-F(x)] *does* equal 0. In fact, it seems we have just
proven that. I may have seen my conjecture above (about monotone G) as a
homework problem somewhere, but I am away from my books as well as my
computer. Ask on sci.math. Feel free to post this response as well.
===
Subject: Re: Mean of a random variable
>So maybe lim x[1-F(x)] *does* equal 0. In fact, it seems we have just
proven that. I may have seen my conjecture above (about monotone G) as a
homework problem somewhere, but I am away from my books as well as my
computer. Ask on sci.math. Feel free to post this response as well.
Yes, I found it as an exercise in Goldberg, Methods of Real Analysis:
If G is monotone and int(0..infty, G) converges, then x G(x) -> 0
as x -> infty.
--
===
Subject: expectation value
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id h9RD62313206;
There are 3000 lucky draw tickets priced at $2 each. The
grand prize is a $500 color TV and there are five $200 black-and-white
TV's as consolation prizes. What is the expected value of a $2 ticket
in this draw?
===
Subject: Re: expectation value
> There are 3000 lucky draw tickets priced at $2 each. The
> grand prize is a $500 color TV and there are five $200 black-and-white
> TV's as consolation prizes. What is the expected value of a $2 ticket
> in this draw?
Have you set up a probability distribution yet? Do you know what the
formula is for expected value?
Showing what you've done so far will be far more productive.
--
Will Twentyman
email: wtwentyman at copper dot net
===
Subject: Re: expectation value
> There are 3000 lucky draw tickets priced at $2 each. The
> grand prize is a $500 color TV and there are five $200 black-and-white
> TV's as consolation prizes. What is the expected value of a $2 ticket
> in this draw?
Much less that $2. Think about it. They're raking in $6000 and paying
out $1500 for a gross gain of $4500. So 3000 suckers pony up $6000 for a
$1500 return which gives each of them a puny share for their $2
investment.
===
Subject: a request
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id h9RD6Vt13280;
Hello
I'm a math student .
I have a request:
it will be kind of you to send me the solution of this question as soon as
possible;
Lim(1+1/2+....+1/n - ln (n))
sincerely yours
mona
===
Subject: Re: a request
> Hello
> I'm a math student .
> I have a request:
> it will be kind of you to send me the solution of this question as soon 
as
possible;
> Lim(1+1/2+....+1/n - ln (n))
> sincerely yours
> mona
See
http://mathworld.wolfram.com/Euler-MascheroniConstant.html
Jose Carlos Santos
===
Subject: Re: nonlinear derivation equations
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id h9RD6DF13232;
> I have set of two equations on functions x(t) y(t)
> (derivstion on t):
> x' = a*y + b*x*y +c*x + d
> y' = a*y + b*x*y + d
> I will be very thankful for any help on solving it.
> It seems to be very regular, despite its nonlinear,
> but I have no idea how to solve it.
(1) y' = ay + bxy + d
(2) x' = ay + bxy + cx + d
(3) y = (x' - cx - d)(a + bx)^-1
(4) y' = (x'-cx-d)'(a+bx)^-1 + (x'-cx-d)(a+bx)^-1'
= (x-cx')(a+bx)^-1 - (x'-cx-d)(a+bx)^-2(bx')
= (a+bx)^-2[(x-cx')(a+bx) - (x'-cx-d)(bx')]
(a+bx)^-2[(x-cx')(a+bx) - (x'-cx-d)(bx')]
= a(x'-cx-d)(a+bx)^-1 + bx(x'-cx-d)(a+bx)^-1 + d
does not seem that simple to me.
is that a textbook problem?
> Dargen
===
Subject: Re: nonlinear derivation equations
===
Subject: Re: nonlinear derivation equations
>> I have set of two equations on functions x(t) y(t)
>> x' = a*y + b*x*y +c*x + d
>> y' = a*y + b*x*y + d
>(1) y' = ay + bxy + d
>(2) x' = ay + bxy + cx + d
>(3) y = (x' - cx - d)(a + bx)^-1
>(4) y' = (x'-cx-d)'(a+bx)^-1 + (x'-cx-d)(a+bx)^-1'
> = (x-cx')(a+bx)^-1 - (x'-cx-d)(a+bx)^-2(bx')
> = (a+bx)^-2[(x-cx')(a+bx) - (x'-cx-d)(bx')]
>(a+bx)^-2[(x-cx')(a+bx) - (x'-cx-d)(bx')]
> = a(x'-cx-d)(a+bx)^-1 + bx(x'-cx-d)(a+bx)^-1 + d
>does not seem that simple to me.
>> x' = a*y + b*x*y +c*x + d
>> y' = a*y + b*x*y + d
As suggested by others
> x' = y' + cx
> y' = (a + bx)y + d
from 2nd eq
(y' - d)/y = a + bx
(y' - d)/by - a/b = x
plugging into 1st eq
y/by - (y' - d)/byy = y' + c(y' - d)/by - ca/b
yy - y' + d = bcyyy' + bcy(y' - d) - cayy
yy - y' - bdyy'(y+1) + bcdy + cayy + d = 0
How about that, one line less mess.
BTW, dy isn't 'dy'. ;-)
----
===
Subject: science
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id h9RD6km13349;
><pre<Nm0k3.277$y4.54114@c01read05.service.talkway.com>...
>> simple quiestion....how do you convert yards into tons?
>Maybe yards to cm to grams to tons
>with geometrized units to convert cm to grams?
>Geometrized units means that
>c speed of light
>G Newton's gravitational constant
>k Bolzman's constant
>are considered one and dimensionless.
>Misner Thorne & Wheeler say that
>Mass of the sun is 1.989x10^33 g = 1.477x10^5 cm
>Chris
></pre>
===
Subject: Covering pairs with m-sets.
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id h9RHpdN32535;
Does anybody knows something (answer, references...) about the following
problem :
Let E be a finite set, with |E| = n, and let m be an integer such that 2 =<
m =< n.
What is the minimum number f(n,m) of m-subsets of E to cover each of the
pairs of elements of E ?
(That is : determine the minimum number of subsets of E, each of them
containing exactly m elements, such that for each a,b in E, there exists at
least one of these m-subsets, say F, such that {a,b} is contained in F)
I'm also interested with generalizations of this problem (for example : 
what
if we say about k-sets instead of pairs?)
Pierre.
(P.S. Sorry, if this post has already appeared, but I do not see it...)
===
Subject: Was: Convergence on a space with no topology
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id h9RHppt32577;
The messages in response to
Convergence on a space with no topology
got cluttered relatively fast. In my opinion,
it was getting hard for anyone reading the message for the
first time to follow. Therefore, I try to give the main points
of what was said some sort of chronological order.
Let X be a metric space (or just a topological one). Let
B* be any subset of P(X), the set of all subsets of X. Choose an
element A in B*. Then, without attempting to define a topology on B,
we just say A_n -> A in B* if for every a' in A there exists a
sequence (a'_n) in X which converges to a' in the metric
topology of X with a'_n in A_n for all n.
This is related to the Hausdorff metric on subsets of a metric space.
And for your limit you probably want the set of all a' such that
there is a sequence as written. In case your sets are all compact,
this will coincide with convergence in the Hausdorff metric,
as I recall.
>You have a problem here, because a limit is not unique, if A' is a
>subset of A, then A_n -> A implies A_n -> A'.
My response:
I hope I covered your concern in my first Re:, where the
following was added to the initial question:
... A_n subset A for all n should also be required (or something
similar like there exists an m such that for all n > m: A_n
subset A). That way two sequences A_n and B_n approaching A will
also approach each other...
Under
these conditions, it appears the limit is almost
unique, i.e., it is unique if the set A' subset A your are
refering to above is closed in the metric topology of X;
a little proof:
If A_n -> A and A_n -> A', then (by definition)
A_n subset A for all n and A_n subset A' for all n. If
A' is a proper subset of A, then there must exist an element
x which is in A but not in A'. Thus, there exists a sequence
(x_n) converging to x in the metric topology of X with
x_n in A_n for all n. Since A_n subset A' for all n,
x_n in A' for all n. Since A' is closed, x in A', a
contradiction.
...end of response, the first message then continues as:
Then we have (at least) a notion of convergence on a space
that is not directly equipped with a topology itself. Thus,
we may also speak of the continuity of functions from
B* to B* or from B* to any other (metric) spaces.
>You've given B a topology,
>thee subspace topology inherited from X.
My first message ends with the question...
To further demonstrate this, let C be any finite subset of X and
f_C: B* -> N (the natural numbers) the counting function, i.e.
f_C(A) gives how many elements of A coincide with C. Is f_C
continuous?
>You want something like lim f_C(A_n)=f_C(A), right? But for the
>limit is not unique, this doesn't actually make any sense.
This problem was already adressed above (uniqueness was
achieved by requiring A_n subset A for all n)
>You could make the limit unique by requiring A to be the maximal such
>set. But f_C wouldn't be continous. Take A_n to be {a_n} where none
>of the a_n is in C, but a:=lim a_n is in C. Then lim f_C(A_n)=0,
>because all f_C(A_n)=0, but F_C(A)=1.
>I don't really see the sense in this definition, is this just >abstract
playing-around or are you working on something?
Philipp
Regarding the subsequent posts on
Cauchy-sequences, too, on a space with no topology.
In retrospect, there was no need for me to define this
concept right from the outset in extremely general terms, i.e.
in terms of countable local bases on topological spaces. I think
it is much easier if we take (X, d) as a metric space whose
metric is induced by a norm || || (Why not just start with a normed
space?- because, in my opinion, the proof below would get overly
cluttered with norm signs if we did...)
Let (X, d) be a space whose metric is induced by a norm.
Call (A_n) subset B* subset P(x), the set of all subsets of X,
a *Cauchy sequence if (R = reals, N = natural numbers)
For all p > 0, p in R, exists q in N for all n,m > q for all
a in A_n exists b in A_m: d(a,b) < p.
Let us demonstrate that this monster definition actually
appears managable... by proving the following statement:
If (r_n) subset R is a Cauchy-sequence and and r_n !=0 for all n,
then (B(x ,r_n)) is a *Cauchy-sequence for all x in X, where
B is the open ball of radius r_n at x (we could presumably
just as easily take closed balls of radius r_n at x).
With no loss to generality, assume x = 0.
Proof (by contradiction):
If (B(x,r_n)) is not a *Cauchy-sequence, then
exists p > 0, p in R, for all q in N exists n,m > q exists
a in B(0, r_n) for all b in B(0,r_m): d(a,b) >= p.
Choose any such p as above. Since (r_n) is a Cauchy sequence, there
exists a q in N such that |r_n-r_m| < p for all n, m > q.
For this q, choose an a in B(0,r_n) and n,m > q with the property that
for all b in B(0,r_m): d(a,b) >= p.
Now define t_n in R as: t_n*r_n = r_m. Notice that r_m != r_n,
since then a would also be in B(0,r_m) and d(a,a)=0 < p,
contradicting d(a,b) >= p for all b in B(0,r_m).
It follows that t_n != 1. In addition, it follows that
t_n a in B(0,r_m), since
d(t_n a, 0) = t_n d(a, 0) < t_n r_n = r_m.
By our assumption, d(t_n a, a) >= p.
By the homogenity of our metric,
d(a, 0) >= p / |1-t_n| > |r_n - r_m| / |1- t_n | =
= |r_n - r_m| / (|r_n - r_m| / r_n) ) = r_n
where the last line comes from the property:
if t_n r_n = r_m, then |(1-t_n) r_n| = |r_n - r_m|
But d(a,0) >= r_n contradicts a in B(0,r_n), q.e.d.
(I apopolize for any mistakes in the above...)
C. Dement
C. Dement (not mathematition)
===
Subject: Re: Was: Convergence on a space with no topology
===
Subject: Was: Convergence on a space with no topology
>Convergence on a space with no topology got cluttered relatively
>fast. In my opinion, it was getting hard for anyone reading the
>message for the first time to follow. Therefore, I try to give the
>main points of what was said some sort of chronological order.
With all that feedback, you need present revision.
Skip the blah blah and just get to the punch line.
Are you reinventing the Hausdorff metric for sets?
Do you know what the Hausdorff metric for sets is?
>Let (X, d) be a space whose metric is induced by a norm.
>Call (A_n) subset B* subset P(x), the set of all subsets of X,
>a *Cauchy sequence if (R = reals, N = natural numbers)
>For all p > 0, p in R, exists q in N for all n,m > q for all
>a in A_n exists b in A_m: d(a,b) < p.
Toss B* out, it isn't being used nor is it defined.
>If (r_n) subset R is a Cauchy-sequence and and r_n !=0 for all n,
>then (B(x ,r_n)) is a *Cauchy-sequence for all x in X, where
>B is the open ball of radius r_n at x (we could presumably
>just as easily take closed balls of radius r_n at x)
That's r_n > 0 for all n > 0
Let the metric space be {0,1} subset Reals, x = 0 and
r_n = 1 + 1/n for even n, and r_n = 1 - 1/n for odd n.
Let p = 1/2. Pick any q in N. 2q, 2q+1 > q
1 in B(0, 1 + 1/2q) and B(0, 1 - 1/(2q+1)) = {0}.
So no b in B(0, 1 - 1/(2q+1)) with d(1,b) < 1/2.
Proposition is false.
-- Define C-seq as
for all eps > 0, some n in N with
for all j,k > n, a in A_j, b in A_k, d(a,b) < eqs
Theorem
0 < r_n -> 0 implies B(x,r_n) is C-sequence.
----
===
Subject: Re: MKC Set Theories
> at 10:45 PM, john_correy@yahoo.com (John) said:
>--Nevertheless not all collections satisfy Standard Extensionality.
>It is a commonplace that *clubs* don't, for different clubs may be
>identical in membership.
> A club is not a collection, or at least not a collection of members. A
> club has other attributes besides its membership.
> To put this into the context of set theory, if x and y are not
> identical then neither are (x,y) and (y,x). Does that violate
> extensionality?
I'm not clear on what you're asking.
Are you asking if ~(x=y) -> ~({x,y} = {y,x})?
Or are you asking if ~(x=y) -> [~({x,y}={x,y}) & ~({y,x} = {y,x})]?
Or, taking (x,y) as an abbreviation for {{x},{x,y}}, are you
asking if ~(x=y) -> ~({{x},{x,y}} = {{y},{y,x}})?
Or are you asking if ~(x=y) -> [~({{x},{x,y}} = {{x},{x,y}})
& ~({{y},{y,x}} = {{y},{y,x}})]?
(I'm working on a laptop & it's evening & kind of dark in here,
so I hope I haven't made any bracketing mistakes.)
--John
===
Subject: Re: MKC Set Theories
<3f98510e$10$fuzhry+tra$mr2ice@news.patriot.net>
at 08:10 PM, john_correy@yahoo.com (John) said:
>I'm not clear on what you're asking.
I'm asking why it's a problem that clubs violate extensionality. I'm
bringing in ordered pairs a s a reductio ad absurdum.
>Are you asking if ~(x=y) -> ~({x,y} = {y,x})?
>Or are you asking if ~(x=y) -> [~({x,y}={x,y}) & ~({y,x} =
>{y,x})]?
>Or, taking (x,y) as an abbreviation for {{x},{x,y}}, are you
>asking if ~(x=y) -> ~({{x},{x,y}} = {{y},{y,x}})?
>Or are you asking if ~(x=y) -> [~({{x},{x,y}} = {{x},{x,y}}) &
>~({{y},{y,x}} = {{y},{y,x}})]?
No. It was a rhetorical question, and I was asking whether
~AwAxAyAz {w,x}={y,z} -> (w,x)=(y,z)
That's an exact analogy to the club; the ordered pair (x,y) is not
uniquely determined by {x,y}. If I wanted to talk about clubs in a set
theory, I see no need to abandon extensionality, just as I don't need
to abandon it in order to have ordered pairs.
--
Shmuel (Seymour J.) Metz, SysProg and JOAT
Unsolicited bulk E-mail will be subject to legal action. I reserve
the right to publicly post or ridicule any abusive E-mail.
Reply to domain Patriot dot net user shmuel+news to contact me. Do
not reply to spamtrap@library.lspace.org
===
Subject: Re: MKC Set Theories
>> at 10:45 PM, john_correy@yahoo.com (John) said:
>>--Nevertheless not all collections satisfy Standard Extensionality.
>>It is a commonplace that *clubs* don't, for different clubs may be
>>identical in membership.
>> A club is not a collection, or at least not a collection of members. A
>> club has other attributes besides its membership.
>> To put this into the context of set theory, if x and y are not
>> identical then neither are (x,y) and (y,x). Does that violate
>> extensionality?
>I'm not clear on what you're asking.
He's asking whether the fact that (1,2) <> (2,1) violates
extensionality - those ordered pairs have the same
elements but they're not equal.
Hint: the answer is of course not.
Hint: It was a rhetorical question, meant to illustrate why the
fact that two different clubs can have the same members
is not a violation of extensionality either.
>Are you asking if ~(x=y) -> ~({x,y} = {y,x})?
>Or are you asking if ~(x=y) -> [~({x,y}={x,y}) & ~({y,x} = {y,x})]?
>Or, taking (x,y) as an abbreviation for {{x},{x,y}}, are you
>asking if ~(x=y) -> ~({{x},{x,y}} = {{y},{y,x}})?
>Or are you asking if ~(x=y) -> [~({{x},{x,y}} = {{x},{x,y}})
>& ~({{y},{y,x}} = {{y},{y,x}})]?
>(I'm working on a laptop & it's evening & kind of dark in here,
>so I hope I haven't made any bracketing mistakes.)
>--John
**
===
Subject: Re: Is Nature a Logical System?
Eli
> Any challenges to my reasoning are confirmations of its validity are
> enthusiastically anticipated.
> One of the most common flags for pseudoscience.
I'm not sure what this comment refers to, but I should correct the
typo:
Any challenges to my reasoning _or_ confirmations of its validity are
enthusiastically anticipated.
My conclusions are not science, they are reason. They are not science
because they do not discuss observed phenomena but instead discuss the
underlying rules of nature. As you said yourself:
It is important in physics to eliminate statements about
non-observable things as much as possible, but no statement that
claims to be a universal law of nature can avoid this completely.
> Observed by who or what? This is ill-defined.
I included a link to the entire paper my post was contained in.
Observation is defined in that paper as an interaction between an
observer and its environment where information about the environment
is relayed over a distance to the observer. Physics tells us that all
interactions are electromagnetic or gravitational.
> More initial conditions will be
> required beyond the ladybug simply being in the picture.
> The result of a measurement is depends on many factors. For example, the
> measurement method
I agree. That is why I chose an arbitrary set of initial conditions
for the example I was using. Its much easier to describe than every
detail of reality!
> If the generic rules underlying statement b produce a system of
> statements, is statement a also contained in a system of statements?
> What the hell is a system of statements?
Well, if I can use the rules I described to produce a statement about
the measurement of a ladybug, I can use the same rules to produce many
statements about many things. This set of statements and its rules are
what was meant by system of statements.
> 1. The logical rules can produce many statements
The system of rules used to measure the lady bug was also used to
> measure my laptop. The collection of all the statements produced by
> these rules can be considered all the true facts of that logical
> system.
> This system not nearly all of nature.
I completely agree. You snipped out what immediately followed:
2. We have many systems of measurement.
But there is more than just that one collection. A 12-inch ruler isn't
the only thing to measure with and distance isn't the only thing to
measure. We have many systems of measurement that produce many
collections of true facts. The set of all the collections of rules and
their results is what is meant by the set of all observed phenomena.
> According to G.9adel's Incompleteness Theorem this logical system can
> only contain all the true facts consistently with each other by
> creating a larger encompassing system.
> This is not true. Goedoel's incompleteness theorem dealt with axiomatic
> systems. Your system does not seem to be axiomatic.
That is the question I'm asking. Is the system is axiomatic (ie, a
logical system)?
conditions from which I can produce a statement. Is that not
axiomatic?
> It is also not clear that your system contains natural number arithmetic
in the usual sense.
Is this a requirement to be a logical system?
> can be produced from the initial conditions of the universe and the
> rules of the universe which we have attempted to describe with our
> laws of physics.
> Are you trying to refute quantum mechanics? Not that it can't be done but
> you'll need to do better than that.
Actually, no. If you read the paper it explains how the deterministic
continious system described above is capable of producing a subset of
statements that can be considered its own system. In this sub-system
the Principle of Uncertainity is demonstrated while the larger
encompassing system continues in its evolution.
It might sound un-thinkable but you should read the paper and let me
know what you think of my arguments.
Mike Helland
===
Subject: Re: Is Nature a Logical System?
> Is Nature a Logical System?
Error, missing operator or `;`
> Is; Nature; a; Logical; System;
Is
Nature
a
Logical
System
===
Subject: Re: Is Nature a Logical System?
Jon Briggs,
> Is Nature a Logical System?
> The answer is obviously that we don't know and that we can't know.
True, we cot know with perfect certainty, but we can still observe
that it does happen to have the properties of a logical system.
At this point, we can ask the question: Is Nature a Logical System?
While we cot perform an experiment that will tell us, it still may
be useful to discuss what the consequences of an answer would mean.
If the answer is no, the discussion probably ends right there. But if
the answer is yes, we are now allowed to make more statements about
it. Such as (from the original post):
<quote>Unless nature is presumed to be an exception to the
Incompleteness
Theorem, to contain all the statements of nature completely and
consistently the system of all observations would require additional
statements beyond what is observed. Because these new statements lie
beyond the set of all observations these statements cot be made
using the scientific method, and therefore, physics is concluded to be
unable to provide a final theory of nature.</quote You don't need to invoke 
an
incompleteness theorem to know that
> we have no complete and certain knowledge about the universe. That's
> a physical fact of life from the start.
If what you say is true, this fact must be demonstrated in a
mathematical model of the universe.
And if what I say is true then we can create a model of the universe
that produces this fact.
Mike Helland
===
Subject: Re: Is Nature a Logical System?
> Is Nature a Logical System?
> I think it is. The following explains my position and makes
> several insightful conclusions beginning with this premise.
> Any challenges to my reasoning [or] confirmations of its
> validity are enthusiastically anticipated.
[...]
> The above is section II from the following paper:
> http://www.techmocracy.net/science/time.htm
Is Nature Logical?
I think a better question would be, Is Logic Natural?
I would answer that Logic seems to be Natural, so far.
If it ever ceases to be, I suppose it will be up to
the survivors to decide how it will need to be reformed.
Jim Burns
===
Subject: Re: Is Nature a Logical System?
>> Is Nature a Logical System?
>> I think it is. The following explains my position and makes
>> several insightful conclusions beginning with this premise.
>> Any challenges to my reasoning [or] confirmations of its
>> validity are enthusiastically anticipated.
>[...]
>> The above is section II from the following paper:
>> http://www.techmocracy.net/science/time.htm
>Is Nature Logical?
>I think a better question would be, Is Logic Natural?
quoting from http://www.druidic.org/bennish/essays/status.htm
In his 1968 paper The Logic of Quantum Mechanics Hilary Putnam argues
for the thesis that logic is empirical. By this he means that the laws
of logic, like any other scientific laws, can be tested empirically
and modified if they do not fit with our experience.
(later in the essay)
A rather more serious objection was raised by Crispin Wright in his
paper Inventing Logical Necessity (1986). Wright argues that Quineas
theory of knowledge cot treat logical beliefs simply as another set
of beliefs clustered near the centre of our array. Logic is needed to
form the links between our beliefs, and as such they have an entirely
different role to specific beliefs about states of affairs
(Ithe cat
sits on the mata) or scientific theories (Icats tend to
fall from
mantelpieces to mats with a constant acceleration of 9/8ms-2a).
(the essay concludes:)
Quineas picture falls apart if we have no logic to provide
connections
between the beliefs in our array. Nevertheless, that is only an
argument for the need for some sort of logic for us to be able to
think coherently o it does not prove that the specific logical
beliefs
that we hold at any one time could not be changed.
Nevertheless, the thought is persuasive that logical statements are in
principle open to such verification within the sort of structure that
Quine has proposed.
John Bailey
http://home.rochester.rr.com/jbxroads/mailto.html
===
Subject: Re: Is Nature a Logical System?
>> Is Is Nature a Logical System? a mathematical question?
> Is Is Is Nature a Logical System? a mathematical question?
> a logical question?
>> Is Is Is Is Nature a Logical System? a mathematical question?
>> a logical question? a grammatically-correct question?
>Is Is Is Is Is Nature a Logical System? a mathematical
question?
>a logical question? a grammatically-correct question? a genuine
>question?
Yes.
Oh, sorry, was I supposed to say something different?
===
Subject: Re: Is Nature a Logical System?
> Is Is Nature a Logical System? a mathematical question?
>> Is Is Is Nature a Logical System? a mathematical question?
>> a logical question?
> Is Is Is Is Nature a Logical System? a mathematical question?
> a logical question? a grammatically-correct question?
>>Is Is Is Is Is Nature a Logical System? a mathematical
question?
>>a logical question? a grammatically-correct question? a genuine
>>question?
>Yes.
>Oh, sorry, was I supposed to say something different?
Well, in the interest of grammatical correctness you were supposed
to spell it grammatically correct instead of
grammatically-correct.
**
===
Subject: Re: Is Nature a Logical System?
>> Is Is Nature a Logical System? a mathematical question?
Is Is Is Nature a Logical System? a mathematical question?
> a logical question?
>> Is Is Is Is Nature a Logical System? a mathematical
question?
>> a logical question? a grammatically-correct question?
>Is Is Is Is Is Nature a Logical System? a mathematical
question?
>a logical question? a grammatically-correct question? a genuine
>question?
> Yes.
> Oh, sorry, was I supposed to say something different?
Ah, you spoiled it :-(
Dirk Vdm
===
Subject: Re: Is Nature a Logical System?
> <snip Is Is Nature a Logical System? a mathematical question?
>>Is Is Is Nature a Logical System? a mathematical question?
>>a logical question?
>Is Is Is Is Nature a Logical System? a mathematical question?
>a logical question? a grammatically-correct question?
Is Is '[...]' a grammatically-correct question a
_grammatically correct_ question?
**
===
Subject: Re: Is Nature a Logical System?
In sci.math, David C Ullrich
<ullrich@math.okstate.edu>
<qkcrpvkbftffmheq0s36mbi4pvmri9kdni@4ax.com>:
>> <snip> Is Is Nature a Logical System? a mathematical question?
>Is Is Is Nature a Logical System? a mathematical question?
>a logical question?
>>Is Is Is Is Nature a Logical System? a mathematical question?
>>a logical question? a grammatically-correct question?
> Is Is '[...]' a grammatically-correct question a
> _grammatically correct_ question?
> **
>
Is all this leading anywhere? My brain is beginning to hurt...
:-)
--
#191, ewill3@earthlink.net
It's still legal to go .sigless.
===
Subject: Re: Is Nature a Logical System?
> Is Nature a Logical System?
It seems pretty illogical to me.
> Any challenges to my reasoning are confirmations of its validity are
> enthusiastically anticipated.
One of the most common flags for pseudoscience.
> what is meant by the definition. If nature will be defined as the set
> of all observed phenomena, what is all observed phenomena supposed to
> mean?
Observed by who or what? This is ill-defined. How do you decide who or
what counts as an observer, what counts as an observation, and why is this
a reasonable decision?
> Statement b is a little tricker. More initial conditions will be
> required beyond the ladybug simply being in the picture. I need to
> define what an inch is and then produce a 12-inch ruler with 1/8
> marks along it. Once I have these, I then follow the simple procedure
> of placing the ladybug along the edge of the ruler, counting the
> number of marks covered by the ladybug, and multiplying that number by
> 1/8. When follow those steps I observed that the ladybug covered 2
> marks (similarly to the way I observed the lady bug to produce
> statement a) and the measurement resulted in 1/4. Which was the
> statement I needed to produce.
The result of a measurement is depends on many factors. For example, the
measurement method (in this case, the ruler, which only a 1/8 resolution),
the observer's judgement (the end of the ladybug will almost certainly fall
between two marks on the ruler and it is a matter of judgement which mark
to choose), and other unpredictable factors.
> If the generic rules underlying statement b produce a system of
> statements, is statement a also contained in a system of statements?
What the hell is a system of statements?
> 1. The logical rules can produce many statements
> The system of rules used to measure the lady bug was also used to
> measure my laptop. The collection of all the statements produced by
> these rules can be considered all the true facts of that logical
> system.
This system not nearly all of nature.
> According to G?del's Incompleteness Theorem this logical system can
> only contain all the true facts consistently with each other by
> creating a larger encompassing system.
This is not true. Goedoel's incompleteness theorem dealt with axiomatic
systems. Your system does not seem to be axiomatic. It is also not clear
that your system contains natural number arithmetic in the usual sense.
> 4. At basic levels, all systems are governed by the laws of physics
This is not true. Even physicists admit that the laws of physics do not
cover all situations, or even all situations that are obviously physical.
For example, none of the laws of physics say anything about what happens
inside the event horizon of a black hole.
> can be produced from the initial conditions of the universe and the
> rules of the universe which we have attempted to describe with our
> laws of physics.
Are you trying to refute quantum mechanics? Not that it can't be done but
you'll need to do better than that.
> But metaphysics and philosophy are not limited to making statements
> about what can be observed and might be capable of providing a
> consistent theory of nature. This consistent theory of nature can also
Nor is physics. It is important in physics to eliminate statements about
non-observable things as much as possible, but no statement that claims to
be a universal law of nature can avoid this completely
Have a tolerable existence. Eli
===
Subject: Re: Is Nature a Logical System?
> Robin Chapman,
>> Is Is Nature a Logical System? a mathematical question?
> If mathematics is:
> The study of the measurement, properties, and relationships of
> quantities and sets, using numbers and symbols.
> And if my question is:
> can nature (defined as the collection of statements we make about the
> universe using measurement and general observation) be considered a
> logical system that is governed by rules of mathematics such a the
> incompleteness theorem.
> Then I'm thinking that my question can most likely be answered by a
> mathematician.
> The answer is obviously that we don't know and that we can't know.
> If Nature is a logical system, we can't know. Because even if we
> stumble upon the correct formulation for it, we cot
> know if the next experiment we perform will produce a result that
> is inconsistent with that formulation.
> If Nature is not a logical system, we can't know. Because no
> matter what finite set of measurements we perform, there will always
> be a finite logical system (perhaps requiring extremely large numbers
> of ad hoc parameters and hidden variables) consistent with those
> measurements.
> You don't need to invoke an incompleteness theorem to know that
> we have no complete and certain knowledge about the universe. That's
> a physical fact of life from the start.
But no one, sob sob, bothered to reply in sci.physics, sob, sob.
;-)
Dirk Vdm
===
Subject: Re: Is Nature a Logical System?
Dirk Van de moortel
> But no one, sob sob, bothered to reply in sci.physics, sob, sob.
You're absolutely correct that I posted this here after no one replied
in the physics group. I have something I'd like to discuss with people
and I tried the topic here because the heavy use of mathematical
models and logical systems.
It seems to have generated some discussion (with some noise even) and
thats all I'm looking for.
Mike
===
Subject: Re: Is Nature a Logical System?
> It seems to have generated some discussion (with some noise even) and
> thats all I'm looking for.
The discussion, or the noise?
--
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Needless to say, I had the last laugh.
Partridge, _Bouncing Back_ (14 times)
===
Subject: Re: expectation value
===
>Subject: expectation value
>There are 3000 lucky draw tickets priced at $2 each. The
>grand prize is a $500 color TV and there are five $200 black-and-white
>TV's as consolation prizes. What is the expected value of a $2 ticket
>in this draw?
The answer is:
fifty three gazillion dollars.
Go write that on your homework... also, this problem is very
dated... there's not a black and white TV in the world that's
worth 200 dollars.
adam
===
Subject: Re: Boolean Algebra - Arithmetic Relationship
> Logic seems so central to our thinking, I want to say it's biological.
> But if that's true it is also subjective. Which I'm not sure I agree
> with.
Where do you stand?
> A Chomskian theory appeals.
> What's the consensus of the mathematical
> community?
> I don't know, I'm not a mathematician. Maybe there isn't a consensus.
I sense this objective vs. subjective nature of logic is still a hot
topic for debate.
I have the feeling that Modus Ponens (or A => B, A then B) emerges
from the causality of our temporal perceptions.
I think the Pavlovian Response is empircal evidence for this:
Ring a bell, Feed the Dog.
Ring a bell, Feed the Dog.
Ring a bell, Dog salivates
A, B
A, B
A, B (I've begun to assume A implies B)
A, Where's B?
Do you think this has merit? Are there other elements of logic
exhibited in very basic behavioral patterns?
===
Subject: Re: Boolean Algebra - Arithmetic Relationship
> Logic seems so central to our thinking, I want to say it's
biological.
> But if that's true it is also subjective. Which I'm not sure I
agree
> with.
Where do you stand?
> A Chomskian theory appeals.
> What's the consensus of the mathematical
> community?
> I don't know, I'm not a mathematician. Maybe there isn't a consensus.
> I sense this objective vs. subjective nature of logic is still a hot
> topic for debate.
> I have the feeling that Modus Ponens (or A => B, A then B) emerges
> from the causality of our temporal perceptions.
> I think the Pavlovian Response is empircal evidence for this:
> Ring a bell, Feed the Dog.
> Ring a bell, Feed the Dog.
> Ring a bell, Dog salivates
> A, B
> A, B
> A, B (I've begun to assume A implies B)
> A, Where's B?
> Do you think this has merit? Are there other elements of logic
> exhibited in very basic behavioral patterns?
Many years ago when I was a student of philosophy I read Popper writing
against this Pavlovian idea. The observation (made by the dog) of A is
followed by B does _not_ give rise to the hypothesis A causes B.
Can't remember why.
I would warn you against confusing A causes B with the logician's if
A then B. For the logician, if A then B is defined by the table
A B if A then B
t t t
t f f
f t t
f f t
where t means true and f means false. The ancient Greeks discussed
this and it was taken up again in the late nineteenth century.
--
G.C.
===
Subject: Re: Boolean Algebra - Arithmetic Relationship
> Many years ago when I was a student of philosophy I read Popper writing
> against this Pavlovian idea. The observation (made by the dog) of A is
> followed by B does _not_ give rise to the hypothesis A causes B.
> Can't remember why.
> I would warn you against confusing A causes B with the logician's
if
> A then B. For the logician, if A then B is defined by the table
> A B if A then B
> t t t
> t f f
> f t t
> f f t
> where t means true and f means false. The ancient Greeks
discussed
> this and it was taken up again in the late nineteenth century.
I agree that the Pavlovian response is an inference, whereas the
Logician's assertion that A implies B, is necessarily true by
definition.
But isn't this how we learn and develop logical models of our
environment? I don't think we could live without making inferences
such as these from experience.
Furthermore, isn't all reasoning basically based upon this idea of
inference?
SomeEquation => SomeOtherEquation
SomeTruth => SomeOtherTruth
Other than that, it appears variable subtitution is all that is
necessary.
Of course I may be terribly confused and misinformed, but this seems
to me to be the way things work.
I have a deep respect for the basic ideas of Karl Popper, Thomas Kuhn
and the Logical Positivists camp in general. I like to learn more
about his argument against Pavlovian inferences.
-Steve
===
Subject: Re: Leibniz & Newton
===
>Subject: Re: Leibniz & Newton
>Hi Adam,
>May I ask, then, in your opinion, is Newton's calculus more effective than
>Leibniz's? I realize he has won the debate over the years, as we are
taught
>in school that he is the founder of the calculus. However, I am
>interested to know how your personally feel about it, being a physicist.
>Kavon
>P.S. I agree, dy/dx instantly has me thinking of a fraction. However, my
>math skills are surely limited compared to yours.
Like Thomas said in his post, there is no difference between
Newton's calculus and Leibniz's calculus.
If someone is just starting to learn calculus then I think that
the notation of Leibniz is better to use. It's definitly more
intuitive because you can think fraction... which is not
always bad... in fact, if you have to think about what a
dirivative is, then you might a well think of it as a
fraction. Just don't take the analogy too far.
As for how I personally feel about the Newton/Leibniz debate...
I don't really have an opinion one way or the other. Maybe
Newton came up with it first, maybe Leibniz did, but no one
will ever know for sure. The best thing is probably just to
give them both equal credit.
adam
===
Subject: Re: Leibniz & Newton
Adam,
Kavon
===
>Subject: Re: Leibniz & Newton
>Hi Adam,
>May I ask, then, in your opinion, is Newton's calculus more effective
than
>Leibniz's? I realize he has won the debate over the years, as we are
taught
>in school that he is the founder of the calculus. However, I am
>interested to know how your personally feel about it, being a physicist.
>Kavon
>P.S. I agree, dy/dx instantly has me thinking of a fraction. However,
my
>math skills are surely limited compared to yours.
> Like Thomas said in his post, there is no difference between
> Newton's calculus and Leibniz's calculus.
> If someone is just starting to learn calculus then I think that
> the notation of Leibniz is better to use. It's definitly more
> intuitive because you can think fraction... which is not
> always bad... in fact, if you have to think about what a
> dirivative is, then you might a well think of it as a
> fraction. Just don't take the analogy too far.
> As for how I personally feel about the Newton/Leibniz debate...
> I don't really have an opinion one way or the other. Maybe
> Newton came up with it first, maybe Leibniz did, but no one
> will ever know for sure. The best thing is probably just to
> give them both equal credit.
> adam
===
Subject: WMD, Dark Energy, UFOs Conformal Group
See comment on Tony Smith's conformal gravitons below.
Message 1
Hi Jack,
Let me take a moment away from the TV, where we've been watching the
progress of the horrendous local fires and hoping they don't come any
closer to Pasadena, to comment on Robert Sheaffer's recent comment that
It is exceedingly unlikely that UFOs... are real entities, they are
mostly due to 'random errors' occurring in the human perceptual and
social-belief formation system. There is noise in every information
chel, and our society has agreed to describe a certain kind of that
noise as UFOs. While we may argue about their origin and purpose, it
has long since become abundantly clear that what we call UFOs are not
simply noise. Unless the thousands of internally consistent reports
by credible witnesses, including abductees, are some form of mass
hallucination, these phenomena clearly have an objective existence.
Moreover, as a student of comparative mythology and folklore, I can
firmly attest that the patterns reported by contemporary witnesses and
experiencers jibe remarkably well with pre-modern accounts of flying
shields, abductions to fairy-land by short creatures with big eyes
and pointed, elfin chins, missing-time episodes, and rides in flying
wheels a la Ezekiel's famous trip.
To ignore all this evidence, soft though it most of it may be
(although I strongly suspect that despite a half-century of
stonewalling, some members of the U.S. and other intelligence
communities-the CIA, MI6, the old KGB, etc.-have in their possession an
abundance of hard evidence garnered from Roswell, Kecksburg, and other
UFO crash sites), is to wallow in a state of denial so all-embracing
that it beggars the imagination. Or do debunkers like Sheaffer, Oberg,
Klass, and the rest have another, more devious agenda, that is, to
further the Government's long-standing policy of keeping the lid on by
systematically ridiculing those of us who suspect the truth about this
phenomenon, all the while being privy to above-top-secret knowledge that
would prove us right? One > wonders....
All best wishes &
Scott
C. SCOTT LITTLETON
President, Phi Beta Kappa Alumni in Southern California
Professor of Anthropology, Emeritus
Occidental College
Los Angeles, CA 90041
TEL (323) 255-5477
FAX (323) 982-0264
http://www.oxy.edu/~yokatta/home.htm
Any sufficiently advanced technology is
indistinguishable from magic
--Sir Arthur C. Clarke
I think we're property. . .
--Charles Fort
Again, the basic exotic physics of Chapter 9 of Sir Martin Rees's WMD
book Our Final Hour as well as how UFOs, if they are real, would have
to fly via metrically engineered weightless warp drive (local absence of
g-force) in my opinion is summarized in
http://qedcorp.com/APS/StarGate1.mov However, again I emphasize that
the physics there in no way depends on whether or not UFOs are real. If
they are not real now, if my physics is on the right path, they will be!
Message 2
===
Subject: Re: CHINA - Quantum Vacuum Reaction WMD research?
relatively close to the sorts of ideas I am playing with relevant to
Martin Rees's Chapter 9 in Our Final Hour. ...
Agent X from Russia commented:
.. I'm aware about existence in f. USSR of strategical scenarios of
psychotronic war games - in course of which were resolved problems of
minimization of collateral damage to civilian population, maximizing at
the same time efficiency of influencing of decision-making of national
leaders of target countries.
Dr. Sergeyev told me that similar data were in possession of our Western
colleagues; - with whom Russian military elite routinely shared most
p. 94-95 of '97 edition of his book), so as not to break mutual trust
which during Cold War years had been the principal basis of Global
Stability. (Of course, it wasn't necessary to carry across borders
carloads of technical papers - for intelligent enough people, comprising
intellectual elite, it was sufficient few words. Here can be drawn
parallels with first years of Atomic Era: sources of Soviet atomic
spies in USA - including such top scientists as Einstein, Oppenheimer,
Bohr & others - needed just to tell few words to such Soviet scientific
agents as Ya. Terletsky etc.)
See my comments on this in Pavel Sudoplatov's Special Tasks paperback
ed. with foreword by Robert Conquest of the Hoover Inst. Stanford.
Majority of competent Soviet (and post-Soviet) experts in this area
feel it to be morally permissible to use in cases of extreme necessity
surgical psychotronic strikes against selected human targets instead
of destructive & inefficient massive interventions like Vietnam,
Afghanistan & Iraq; - which bring much needless suffferings to innocent
civilians, lots of political problems, terrible financial expenses - and
almost no positive results. Regretfully, collapse of f. USSR stopped
development of selective varieties of psychotronic genome weapons
which might be precisely aimed at genome patterns of some chosen human
target - this was long before lists of death genes became freely
obtainable from Internet. As I've mentioned, in 1989 in Kiev - then an
important center of Soviet psychotronic research - there were performed
tests of non-selective torsionic weapons, capable to interfere with
some of biochemical reactions inside the cell; - whose influence could
not be shielded by any material screens. However, these - compact enough
to be installed on a satellite & requiring very little electric power -
devices couldn't function as an efficient weapon, as their effects took
too much time (perhaps, years) to manifest themselves (because of this
such weapons weren't used in Afghanistan & Chechnya). Soviet experts
guessed that in order to create really efficient swift weapon there must
be undertaken more thorough research, involving use of supercomputers
for precise calculation of resonance frequencies of vulnerable genes (in
fact, they believe that this is the main task of recently built in USA
for genetic research Blue Gene supercomputer with teraflop processing
speed).
My comments on above. I cot comment on the particulars of the above
allegations. We did have Gennady Shipov here from Moscow for extended
visits in 1999-2000 as part of the ISSO effort to try to figure out the
torsion physics. I did not make much progress until perhaps only a few
days ago because of a remark from Professor Thomas Angelides in London
about the structure of the Penrose Masseless Twistor Conformal Group
SU(2,2) or SU(4) depending on topological signature in 4 complex
dimensions.
Professor Angelides pointed out that 4 of the 5 extra elements of the
Lie Algebra of the Conformal Group are a kind of mirrored version of the
translation subgroup of the Poincare group. The Fifth Element is the
dilation group implicit in inflation where in the FRW metric
R(t) ~ e^Ht
H is the Hubble not the Hamiltonian. ;-)
Now in my toy model, the Dirac vacuum for the electron in globally flat
space-time is unstable to the BCS formation of a ODLRO BEC of virtual
electron-positron pairs due to virtual photon exchange near the edge of
the -mc^2 Fermi surface.
This results in the microscopic derivation of the Vacuum Coherence
Field, which in the large scale is the Inflation Field
Vacuum Coherence Field = (Higgs Amplitude Field)e^i(Goldstone Phase)
Since the Vacuum Coherence Field is a complex scalar field the ONLY
topological defects in 3D space must be 1D strings sweeping out a world
sheet as further explained in this thread by Saul-Paul Sirag. This is a
nice after thought.
This is a toy model. The rest of the lepto-quarks will have to be
considered later.
Note that Haisch, Puthoff, Rueda, Marshall, Cole et-al zero point energy
gravity program fails to ask the right questions because vacuum
coherence is entirely lacking in their model.
Utiyama in the 60's showed that local gauging of the classical Poincare
group of special relativity gave Einstein's curved space-time
geometrodynamic symmetric tensor field from the 5 energy-momentum
generators of the Lie algebra of the translation subgroup. Locally
gauging the 6 space-time rotations of the Lorentz subgroup of the
invariant light cones of null geodesics ds = 0 gave the torsion
antisymmetric tensor field years before Shipov rederived it in Moscow
probably without knowing of Utiyama's work in Japan.
It is common knowledge that the rest mass of elementary lepto-quarks and
the weak radioactive gauge force bosons required breaking down the 15
parameter Conformal Group to the 10 parameter Poincare group.
from the Higgs field in the standard U(1)xSU(2)xSU(3) with
Higgs-Goldstone BCS type phase transitions in the quantum vacuum.
In my theory
Einstein's Diff(4) symmetric geometrodynamic field comes from the
modulation or rippling of the coherent Goldstone phase of the Vacuum
Coherence Field.
Indeed, the 4 generators of the translation subgroup of the Poincare
group of special relativity are Pu ~ h/id/dx^u
The Sakharov metric elasticity field is simply (without holographic
t'Hooft-Sussking renormalization at first) (Lp^2/ih)Pu(Goldstone Phase).
Lp^2 = hG(Newton)/c^3 ~ 10^-66 cm^2
I need a second set of generators P'u from the Conformal Group operating
on the Higgs Field to get the unified Dark Energy/Matter w = -1 exotic
vacuum field
/zpf* = Lp*^2[1 - Lp*^3(Higgs Field)^2]
where if
Lp* = Lp^2/3(c/H*)^1/3
where H is the Hubble , which clearly needs a more a-temporal meaning in
terms of the constant total mass M of the Universe inside the expanding
Hubble horizon.
That is
GM/c^2 = c/H* independent of cosmic time t and the FRW scaling R(t) of
the dimensionless comoving r coordinate of the Hubble flow.
M = M(on mass shell real matter + radiation) + M(near EM fields) +
M(exotic vacuum fields)
M is a contingent WAP initial condition of the Level 1 parallel universe
M(exotic vacuum) = M(dark energy) + M(dark matter)
M(dark energy) ~ 0.73M
M(dark matter) ~ 0.23M
M(on mass shell real matter + radiation) + M(near EM fields) ~ 0.04M
Not to be confused with the LARGE-SCALE ONLY cosmic time-dependent
H(t) = R(t)^-1(dR(t)/dt)
Note that the time dependent densities scale as
R(t)^-3 for real matter with w ~ 0
R(t)^-4 for real EM radiation like the CMB with w = +1/3
and independent of R(t) for exotic vacuum with w = -1 from Einstein's
equivalence principle + Heisenberg's uncertainty principle
Where the equation of state of ALL STUFF REAL OR VIRTUAL is
w = pressure/(energy density)
The electron rest mass is
m ~ (e/c)^2/zpf*^1/2
from the strongly attractive dark matter vortex ring core of positive
zero point energy pressure where Higgs Field --> 0 like in a quantized
vortex string of a superfluid.
Indeed, /zpf =/= 0 comes from modulating or rippling the Higgs field.
That is, in the sense of a Taylor series expansion about the normal vacuum
(Higgs Field)^2Lp*^3 = 1 where Einstein's Cosmological Constant VANISHES
from pouring macro-quantum coherent oil on the random chaotic
micro-quantum zero point fluctuations of ALL quantum fields. This
stillness was the calm before the storm of the Big Bang reheating
post-inflation in this decoding of The Cipher of Genesis (Carlo Suares).
;-)
/zpf ~ Lp*^2(Pu'/ih)(Higgs Field)^2
that can be positive or negative giving Dark Energy or Dark Matter
respectively.
The Pu' are from the mirror translation subgroup of the Conformal Group.
Let PSI = Vacuum Coherence Field
(PSI),u = Higgs e^iGoldstone iGoldstone,u + Higgs,u e^iGoldstone
= e^iGoldstone [Higgs(Pu/ih)Goldstone + (Pu'/ih)Higgs]
= Translation Gradient Ripple + Mirrored Conformal Translation Gradient
Ripple
= Einstein Gravity Ripple + Exotic Vacuum (Dark Energy/Matter) Ripple
The quanta normal fluid noise of these ripples in the emergent More
is different (PW Anderson) vacuum superfluid signal are
Einstein's gravitons and Tony Smith's conformal gravitons.
===
Subject: Re: elliptic integral of first kind
>> --snip
> The above formula also implies, that your expression for e(r) will
> not be bounded for r->1. However, differentiating phi wrt r does
> not give [2] (btw, do you really call the potential differentiated
> wrt r the electric field? For me, the electric field is the gradient
> of the potential, so the electric field in this case should be
> the potential differentiated wrt r times the gradient of r.)
> What I get when [1] is differentiated wrt r is
>> 1/(pi*r^2) ((a^2+2*r^2)*E[z^2]-(2*a^2+r^2)*K[z^2]).
>> However, this expression is still unbounded as r->a.
> yes sorry. i forgot the gradient of r. however it is still unbounded
> which
>> is very disturbing. it should be bounded!
>> This may be a stupid question, but my physics knowledge is somewhat
>> limited. Why must the electric field be bounded?
> well to me - it would seem that anything where the force was becomming
> singular would imply that we were approaching a point like source
generating
> the electric field. but why would this make sense when we are dealing
with
> a *constant* distribution of charge. It seems reasonable that if you have
a
> finite amount of charge spread evently over the disc, then forces for
test
> charges in that domain should be finite as well. shouldnt they? check
my
> calculations:
> 1. start with poissons formula in axially symmetric cylindrical coords -
> with a source term of
> Laplacian(phi) = -sigma(r)*delta(z)*U(a-r)
> where U = heaviside step function. delta = dirac delta. sigma charge
> density. Solve using hankel transforms and then integrate the dual
bessel
> functions to get the elliptic integral - integrate again to get the
result.
> i should note that above you say my differentiation is incorrect. i fear
> that this comment was probably due to bad notation on my part. remember
> that z=a/r in the arguments of the elliptic funcitons. i probably should
> have made it s = a/r instead or something similar
> so we have
> phi = 2/(pi*r) * [ r^2*E(s^2) + (a^2-r^2)*K(s^2) ]
I had not too much time, but yesterday I did a quick
back-of-the-envelope calculation and obtained a result
which looks quite different. The main difference was,
that the arguments of the elliptic functions look
different. In fact, for a=1 I got expressions of the
form
E(-4 r/(1+r^2+z^2)) and K(-4 r/(1+r^2+z^2)).
Furthermore, I am now quite sure that the electric field
will get unbounded as you approach the edge of the disc.
I am not sure at all, that I did not miscalculate, but
I recommend that you go over your computations again.
HTH,
Michael.
--
&&&&&&&&&&&&&&&&#@#&&&&&&&&&&&&&&&&
Dr. Michael Ulm
FB Mathematik, Universitaet Rostock
michael.ulm@mathematik.uni-rostock.de
===
Subject: Re: Defining the multiplicative inverse of an element in a
polynomial ring.
Jaco
> If I have an element g(x) in R[x], where R[x] is a polynomial ring
> with coefficients from a finite field GF(2^m), how do I define the
> multiplicative inverse of g(x)? (The multiplicative identity would be
> e, the multiplicative identity of GF(2^m).)
> What I do not understand is how two polynomials with positive degree
> greater or equal to one can be multiplied to give e (which is a
> polynomial of degree 0 in R[x])?
> Your time, effort and suggestions will be greatly appreciated
> Jaco
===
Subject: Re: Defining the multiplicative inverse of an element in a
polynomial ring.
> If I have an element g(x) in R[x], where R[x] is a polynomial ring
> with coefficients from a finite field GF(2^m), how do I define the
> multiplicative inverse of g(x)? (The multiplicative identity would be
> e, the multiplicative identity of GF(2^m).)
> What I do not understand is how two polynomials with positive degree
> greater or equal to one can be multiplied to give e (which is a
> polynomial of degree 0 in R[x])?
Is it possible that you mean to be working, not in R[x], where
R = GF(2^m), but in R[x] / < f(x) >, where < f(x) > is the ideal
generated by some polynomial in R[x]? If so, then after you multiply
your two polynomials you get to reduce the product modulo f, making
it more likely you'll get a polynomial of degree zero.
--
===
Subject: Re: Defining the multiplicative inverse of an element in a
polynomial ring.
> What I do not understand is how two polynomials with positive degree
> greater or equal to one can be multiplied to give e (which is a
> polynomial of degree 0 in R[x])?
If the ring of coefficients has zero divisors, products of
polynomials can be very odd.
Let the ring be Z/9Z, and consider the product of 3 x^2 + 3 x + 3
with itself, for example.
===
Subject: Re: math
===
>Subject: math
>What is the first number that can be divided byt he frist three prime
>numbers?
Hi Luke,
Go through all the numbers from one to twenty and ask
Is this number divisable by 2 AND 3 AND 4?
If you find one that is, let us know.
adam
===
Subject: Re: math
===
>Subject: math
>What is the first number that can be divided byt he frist three prime
>numbers?
> Hi Luke,
> Go through all the numbers from one to twenty and ask
> Is this number divisable by 2 AND 3 AND 4?
> If you find one that is, let us know.
Seems like a little bit of attitude from one who thinks that 4 is prime!
> adam
===
Subject: Re: math
===
>>Subject: math
>>What is the first number that can be divided byt he frist three prime
>>numbers?
>Hi Luke,
>Go through all the numbers from one to twenty and ask
>Is this number divisable by 2 AND 3 AND 4?
>If you find one that is, let us know.
>adam
Whoops, I meant to say:
Go through all the numbers from one to thirty and ask
Is this number divisable by 2 AND 3 AND 5?
..and of course you could say zero since
0/2 = 0/3 = 0/5 = 0
adam
===
Subject: Nonlinear Warping based on translation, rotation, and shearing.
Suppose I have points X(x_0,...,x_n) and Y(y_0,...,y_n) with y_i and x_i
in R^3. I want to find an approximate nonlinear warping based only
on translation, rotation, and shearing that maps X->Y, what
is the best way of doing this? Can I produce a warping which
is optimal int he least squares sense?
===
Subject: Re: Nonlinear Warping based on translation, rotation, and
shearing.
>Suppose I have points X(x_0,...,x_n) and Y(y_0,...,y_n) with y_i and x_i
>in R^3. I want to find an approximate nonlinear warping based only
>on translation, rotation, and shearing that maps X->Y, what
>is the best way of doing this? Can I produce a warping which
>is optimal int he least squares sense?
I suppose you want a map F: R^3 -> R^3 such that F(x_i) = y_i for
i=0...n. But I'm not sure what you mean by based only on
translation, rotation, and shearing, as those are all linear maps.
I think what you want to do is write a general formula for your map
with various unknown parameters, and then the constraints F(x_i) = y_i
represent a set of equations in those parameters. The best situation
is where the map is linear in the parameters (even though it's nonlinear
in the x coordinates), in which case you have a good chance of being
able to solve for the parameters, if there are enough of them. Or you
can do the standard linear least-squares if you'd be satisfied with an
approximation rather than a perfect fit.
Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2
===
Subject: Re: Multiplying by Five
> A long time ago, I vaguely recall an elementary school teacher telling
> us some trick for quickly multiplying two numbers (2 digits, I believe)
> with one or both having 5 as the second digit. Anyone recall the trick?
> Numbers like 35*45 or maybe even 20*35.
The trick for multipling by 5 is multiply by 10 and divide by two.
That is add 0 to the end of the number and then divide by two.
===
Subject: Damped harmonic oscillation
Im searching for a function of either velocity or accelaration ( d(t) =
f(v)
or/and d(t) = f(a)), which expresses the damped oscillation d(t) caused by
varying velocity or accelaration.
I found this formula, which express a mass m in [kg] hanging in a spring k
in [N/m],
d(t) = C*[e^(-t/tau)]*cos(o*t - phi)
where:
d(t) = distance in [m] to the time t in [s],
C = distance different from neutral position in [m],
o = SQRT(kg/m), resonance frequency in [rad/s]
tau = time constant for damping oscillation
phi = initial phase
but it does only express oscillation beginning in t=0. I need a formula
which express d(t) to any time t, for the purpose of simulation in a
computer.
I'm amatuer and not very well in the english language, but I hope my
explanation is understandable.
Torben W. Hansen
Denmark
===
Subject: Re: Damped harmonic oscillation
> Im searching for a function of either velocity or accelaration ( d(t) =
f(v)
> or/and d(t) = f(a)), which expresses the damped oscillation d(t) caused
by
> varying velocity or accelaration.
> I found this formula, which express a mass m in [kg] hanging in a spring
k
> in [N/m],
> d(t) = C*[e^(-t/tau)]*cos(o*t - phi)
> where:
> d(t) = distance in [m] to the time t in [s],
> C = distance different from neutral position in [m],
> o = SQRT(kg/m), resonance frequency in [rad/s]
> tau = time constant for damping oscillation
> phi = initial phase
> but it does only express oscillation beginning in t=0. I need a formula
> which express d(t) to any time t, for the purpose of simulation in a
> computer.
> I'm amatuer and not very well in the english language, but I hope my
> explanation is understandable.
> Torben W. Hansen
> Denmark
Simply replace t with t-t0 ie
d(t)=C*[e^(-(t-t0)/tau)]*cos(o*(t-t0) - phi), t>=t0 and t0 is starting time
I hope this helps
Goran
===
Subject: Re: Damped harmonic oscillation
> Im searching for a function of either velocity or accelaration ( d(t) =
f(v)
> or/and d(t) = f(a)), which expresses the damped oscillation d(t) caused
by
> varying velocity or accelaration.
> I found this formula, which express a mass m in [kg] hanging in a spring
k
> in [N/m],
> d(t) = C*[e^(-t/tau)]*cos(o*t - phi)
to start in t0 you should take
d(t) = C*[e^(-(t-t0)/tau)]*cos(o*(t-t0) - phi)
hth (and I hope you wanted this simple solution)
klaus
> where:
> d(t) = distance in [m] to the time t in [s],
> C = distance different from neutral position in [m],
> o = SQRT(kg/m), resonance frequency in [rad/s]
> tau = time constant for damping oscillation
> phi = initial phase
> but it does only express oscillation beginning in t=0. I need a formula
> which express d(t) to any time t, for the purpose of simulation in a
> computer.
> I'm amatuer and not very well in the english language, but I hope my
> explanation is understandable.
> Torben W. Hansen
> Denmark
===
Subject: Re: Newbie: Find all nodes of a graph?
Hi!
Martin
> Hi!
> First, I am not a mathematician :-) I will thank you for any simple
> explanation you may want to give.
> I have a list of edges in a graph:
> EdgeID: nodeA -> nodeB.
> I have a given start node and want to get a list of all edges that are
> connected directly or indirectly to this node. I _don't_ need the
travelling
> salesman to find the shortest possible route, it's just that there may
be
> separate closed graphs in this edge cloud and I just need all the
edges in
> the special sub-graph the given node is in.
> Hope, I could make myself understandable.
> I will also appreciate any hint on literature understandable for a
> non-mathematician.
> Martin
> Have a look at:
> http://planetmath.org/encyclopedia/ConnectedGraph.html
> http://www.cs.sunysb.edu/~algorith/files/dfs-bfs.shtml
> Or any standard implementation of Depth First Search or Breadth First
> Search.
> Jack
===
===
> Subject:
> quantify Baseball to other sports; Optimal Strategy for
> Baseball
> Archimedes Plutonium <a_plutonium@dtgnet.com NOdtgEMAIL
> whole entire Universe is just one big atom where dots of
> the electron-dot-cloud are galaxies
> sci.logic, soc.history, sci.math
> A friend asked me to watch this years World Series to render my
> opinion.
> I sketchedly watched and here is my opinion, as I usually do not have
> time for such recreation.
> I watched only parts of game 2 & 3 where the Florida Marlins were
> being
> overpowered, and missed game 1. And from game 3 I decided it was a
> waste
> of time to watch games 4 or 5 in that the New York Yanks would
> probably
> overpower the Marlins and so only watched a few innings of pitching. I
> watched nearly the full game of 6.
> I had seen some clips of Baseball sluggers such as B. Bonds and S.
> Sosa
> (excuse me if name is incorrect spelling) from the sports section of
> the
> local TV news when getting the weather report so I have some awareness
> of the best hitters of Baseball.
> I am not interested in sports only to the extent in which my
> analytical
> mind can
> recast the sport as to Optimal Strategies.
> Baseball Optimal Strategy: after watching this last game of World
> Series
> which includes these threads.
> (1) The pitcher in Baseball, unlike many other sports, is the dominate
> feature of baseball when you consider that of 9 players, the pitcher
> has
> a say in every offensive action.
> (2) We can math quantify the dominance of Baseball pitcher with other
> sports such as Football. Where the quarterback has a big control of
> the
> offense but not as much of control of the overall game as the Baseball
> pitcher for defense. The quarterback if he ran every play would have
> as
> much control as the Baseball pitcher. But he does not and has a
> handoff
> to a running back or a receiver. So we can say mathwise that the
> Baseball pitcher has 100% control of defense Say-of-Action whereas in
> Football the quarterback at most has 25% to 33% Say-of-Action concept.
> Because in each offensive play in Football, the quarterback either
> runs
> himself or hands to a runningback or throws to a receiver. But in
> Baseball, every offensive play has a Say by the pitcher with his
> pitch.
> (3) So, unlike every other sport, the pitcher in Baseball is the
> dominate feature because the Say-of-Action is 100% the pitcher.
> So, the OS of Baseball in order to assemble a team that will win the
> World Series for that year, is key in having as many pitchers that are
> ace pitchers such as Beckett and Pavano of Marlins. Beckett pitching
> was
> superior to that of Pettite and Pavano to that of Clemens.
> would
> have the highest chances of reaching the World Series.
> By the way, I did not see the pitchers batting, so I guess the game of
> Baseball has made some progressive rule change where it is optional
> for
> the pitchers to go to bat; and in the old days I remember the pitcher
> was usually the 9th spot hitter and usually an easy out. I guess the
> new
> rule is that when the option is picked that the team rotates the 8
> hitters and leaves out the pitchers as hitters.
> Getting back to this idea that pitching is the key to baseball
> winning.
> What does it matter for a team to have great hitting such as a Bonds
> or
> Sosa if they choke on pitching in that the other team with average
> hitters but with great pitching. By the way, did Beckett pitch to
> Bonds
> Now suppose the Yankees had both Bonds and Sosa in their lineup.
> Facing
> had 3 pitchers of the quality of Beckett then I would guess that the
> Marlins would have still won the game.
> I did see clips of the Boston game versus the Yankees and the Boston
> ace
> pitcher of Martinez (forgive the spelling). So I am guessing that
> teams
> that have at least one or two good pitchers make it to the playoffs.
> Pitching is number one key.
> So, these concepts would then ask for a Baseball historian to look at
> the winning teams and to see whether every World Series champ had 2
> So, the above should guide all club owners who aspire to win the World
> Series that if your team has at least 2 excellent pitchers, is the
> basic
> prerequisite. And to concentrate the effort more in getting great
> pitching than in getting great batting.
> The batting of the Marlins was often frustrating and it seemed as
> though
> homeruns were a rarity for the Marlins so it goes to show that teams
> that focus on hitting are not really the Optimal Strategy thread.
> And finally a discussion of Pitching itself. I would hate to be a
> pitcher personally because throwing a ball at 95 mph for many hours
> has
> a toll on the arm and is a job that does not last too long. I think
> there is a Optimal-Strategy-Subset for pitching itself in baseball.
> The
> key is to get the batter out in fast quick time. That means it is no
> good to strike out a batter rather than to get him to fly out. If a
> pitcher is so good at devising a pitch that is popped up for a fly
> out,
> then that is better than going for 3 strikes because if you pitch a
> ball
> with a great spin on it such that the probability when hit popps up
> then
> conceivably 3 pitches for the inning can retire the side whereas
> strikeouts require at least 9 pitches. By the way is there any
> statistic
> where a pitcher retires a complete side with only 3 pitches in all???
> So, the pitcher that can devise a pitch that is prone to pop up is
> superior to the pitcher that relies on fastballs and strikes. I am
> guessing that some pitch has such a spin on it that the batter is
> likely
> to pop up or ground out.
> The perfect pitched Baseball game would have 9 innings and only 9 X 3
> 27
> pitches where all batters swung and hit the first pitch and popped out
> or grounded out. Not the game where the pitcher made 9 X 9 = 81
> pitches
> and all strikes and all strikeouts.
> Archimedes Plutonium, a_plutonium@hotmail.com
> whole entire Universe is just one big atom where dots
> of the electron-dot-cloud are galaxies
Now physics tells me that a 95mph pitch is added onto the hit vector
of a homerun hit. So, I wonder if all major league pitchers were to
begin slow pitching such as an underarm lob, whether batters such as
Bonds or Sosa are unable to hit a slow pitch as a homerun??
If so, then why in the world does not a club owner or manager ever
advise his pitchers to begin lobbing the ball at the plate as in
softball and here the aim is to force the batter to fly out or ground
out.
I think the entire game of baseball ought to be reexamined as to
whether pitching at high speeds is actually the best way to pitch.
I suspect no physicist or scientist has researched the Maximum
greatest pitch for our modern stadium distance to homeruns.
I would not be at all surprized if a slow underarm pitch with a spin
on the ball
renders the most popups.
hit pitches end up as foul balls. Going from that fact, then devise a
pitch that has the greatest likelihood of fouling and where a fielder
or the catcher or the infield can get to the ball and make the out.
I suspect that if a physicist closely and carefully examines the
physics of speed of pitch and a spin on the ball will render a flyout
most often. And that this speed is not a fast pitch but rather instead
a slow pitch.
Question: I just wonder if a Barry Bonds (excuse any misspelling) were
pitched the slowest strikes whether he can hit those as a homerun. It
is certain that he can hit fastballs as homeruns for the past seasons
proves that fact. If it is impossible for Bonds to hit a slow pitch
with a spin on it as a homerun, then it is obviously clear what the
future trend of baseball will be--- pitchers adopting slow pitching
with some wicked spins on the ball. And a gradual phase out of
fastball pitching.
Another physics to use on pitching is that when a ball is pitched high
and lofty such that it comes and falls down onto the homeplate and
when such a ball is hit
it is usually grounded and not airbound flight. I believe the physics
explanation for that is that the hitter's bat general hits the ball
not in the middle of the ball but the upper hemisphere of the ball is
struck by the bat causing the ball to head for the ground direction.
If that is the case, then a pitch that is slow and lofty and comes
falling down onto the homeplate as a strike pitch and if hit by the
batter would generally be a ground ball to an infielder and a easy out
at first or even a double play.
I do not know if the rules of Baseball make it such that a pitcher
must have a certain speed on the ball or whether the rules allow for a
softball pitcher to come into the sport and pitch the slowest pitches
possible.
I feel that no physicist has really involved himself thoroughly in the
sport of baseball and beginning to answer some of these questions that
I have raised. And if someone serious would get involved, I expect
many surprizes to issue forth from such a research. I believe the idea
of fast ball pitching is more of a faith than a science in that almost
everyone believes that fast ball pitching is superior to slow speed
pitching. But no-one has proven that belief. I am testing that belief
and saying it is faith and not science.
Prove: prove that fastball pitching is superior in getting hitters out
more than slow speed pitching. Additionally, spin on slow speed
pitching must be included
in the research.
As I said in my original post that a team that wants to win the World
Series must have 2 ace pitchers such as Beckett of the Florida Marlins
winning the Series because if the first ace pitched game 1, and the
second ace pitched game 2, then the first ace would come back and
pitch game 3 and the second ace game 4 and thus a done deal.
And I suspect anyone can go back in baseball history since so much of
it is filmed, that one can see that a team that won the series had 2
pitchers that were higher aces than the defeated team.
Now if Florida had used Beckett in game 1, Pavano in game 2 and
Beckett in game 3
4 games. But since ace pitchers are not perfect and since the hitters
of the Marlins are not perfect that it took 6 games to defeat the
Yankees. But the Yankees were totally inferior in pitching to the
Marlins and due to that inferiority it was prone to defeat.
The World Series in baseball is a tournament to uncover what team in
baseball has the 2 most best ace pitchers. It is not about hitting.
And that is the sick thing about movies on baseball for rarely do
movies spend any time on the pitcher. But all movies on baseball
should be concentrated on the pitcher.
So, if anyone right now wants to figure out what team will win the
is scout and look at the teams for which team has the Two Best Ace
pitchers. And if they do not get injured during the season, then those
2 ace pitchers should nail down the World Series for you.
Archimedes Plutonium
whole entire Universe is just one big atom where dots
of the electron-dot-cloud are galaxies
===
Whether a pitcher is hittable or not depends solely on whether the batter
can predict when the ball will cross the plate and where the ball will be
at
that moment.
Fastballs are difficult to hit because their inherent spread of velocities
(typically 80-100 MPH) make it difficult for the batter to know when to
swing -- the change up is a slow ball delivered with exactly the same
motion as a fastball and its velocity (typically 60-80 MPH) tempts the
batter to swing long before the ball reaches the plate.
Curve balls are difficult to hit because it's very difficult for the batter
to know how much the ball will curve -- i.e. how much below the point of
the
trajectory of a fastball of the same speed where it will cross the plate.
The most unhittable pitchers are (a) knuckleball pitchers and (b) the
so-called junk-ball pitchers. Knuckleball pitchers succeed because even
they don't know where the ball will cross the plate; the batter is even
more
perplexed. Junk-ball pitchers simply throw such a variety of curving and
swerving pitchers that the batter also can't predict what the next pitch
will be.
In general, it really doesn't matter what kind or speed of pitch is thrown
if the batter can predict when to swing to hit it.
Norm
===
===
> Subject:
> quantify Baseball to other sports; Optimal Strategy for
> Baseball
> I think the entire game of baseball ought to be reexamined as to
> whether pitching at high speeds is actually the best way to pitch.
> I suspect no physicist or scientist has researched the Maximum
> greatest pitch for our modern stadium distance to homeruns.
> I would not be at all surprized if a slow underarm pitch with a spin
> on the ball
> renders the most popups.
Archimedes might have a good point!
Ewell Blackwell was a blooper ball pitcher
who had a low earned run average,
and he appeared in several All Star games.
Ted Williams was the only person to hit
a home run off of one of his blooper balls.
--
Tom Potter http://tompotter.us
===
Subject: Delay differential equation
Hi !
I have a 2nd order DDE
y''(x) + ay'(x) + b(y(x) - y(x-a) = 0
with 2 bc's
y(0) = 1 and y(x) = 0 when x->Inf
I know y(x) for 0<x<a
so I can easily solve for each interval na<x<(n+1)a n=1,...
My problem is that to enforce the second bc I need the solution as
there is any shortcuts for getting the solution at x=Large without going
through all x<Large.
Stefan Nilsson
Marine ecology
G.9ateborg university
===
Subject: Re: Delay differential equation
>I have a 2nd order DDE
>y''(x) + ay'(x) + b(y(x) - y(x-a) = 0
I assume this should be
y''(x) + ay'(x) + b(y(x) - y(x-a)) = 0
but do you really want the two a's to be the same?
>with 2 bc's
>y(0) = 1 and y(x) = 0 when x->Inf
>I know y(x) for 0<x<a
So actually the boundary condition on the left is y(x) = (some known
function) for 0 <= x <a? This will then determine y(x) for all x,
as you know because you can solve for each interval in turn. And then
it's not a matter of enforcing the second bc, it's either true or
false.
But maybe you only know y(x) for 0<x<a up to some unknown parameter.
>so I can easily solve for each interval na<x<(n+1)a n=1,...
>My problem is that to enforce the second bc I need the solution as
>x->Inf , and I am looking for a analytic solution so I was wondering if
>there is any shortcuts for getting the solution at x=Large without going
>through all x<Large.
If you try y = exp(r t), you'll see that this is a solution iff
(r^2 + a r + b) exp(r a) - b = 0. One root of this is r = 0, and
there are probably infinitely many other roots (mostly complex).
To have y -> 0 as x -> infinity, you'll want to use a linear
combination of the solutions for roots with negative real part.
Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2
===
Subject: Re: An Ownership Puzzle
so what happened to Zeno Mr Gerl?
===
Subject: Mathematical library for C++
What is the most POPULAR C++ library for mathematical calculations
(ordinary differential equations, matrices, mathematical statistics,
partial differential equations, dynamic optimization)? Please indicate
one free library and one commercial library. I need to include this
information in my lecture.
===
Subject: Modular power series?
Consider a power series sum(i=1 to oo,a_i*x^i) mod p.
I think this can only make sense if for all i bigger
than a fixed value j, p|a_i and the tail vanishes
identically. a_i=i! comes to mind.
Now I was wondering if such a power series can be
defined and converges mod p AND as a normal series.
i! evidently is far too big, but I wonder if the
binomial coefficient (i*k over i) would work.
(If I thought correctly, 1. it grows like (k^k)^i
and the series can converge at least on an interval
and b) i|(ik k) for all k. Correct? If not - do you
have an alternative example?)
--
Hauke Reddm <:-EX8
Private email:fc3a501@math.uni-hamburg.de
For our chemistry workgroup,remove math from the address
For spamming, remove anything else
===
Subject: Re: Modular power series?
>Consider a power series sum(i=1 to oo,a_i*x^i) mod p.
>I think this can only make sense if for all i bigger
>than a fixed value j, p|a_i and the tail vanishes
>identically. a_i=i! comes to mind.
>Now I was wondering if such a power series can be
>defined and converges mod p AND as a normal series.
>i! evidently is far too big, but I wonder if the
>binomial coefficient (i*k over i) would work.
>(If I thought correctly, 1. it grows like (k^k)^i
>and the series can converge at least on an interval
>and b) i|(ik k) for all k. Correct? If not - do you
>have an alternative example?)
Try a_i = floor(ln(i))!.
Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2
===
Subject: Re: Explaining math definition problem
In sci.math, David Moran
<ktulwxwatcher@hotmail.com>
<bnh9c7$10i1bi$1@ID-206850.news.uni-berlin.de>:
>> I'm an independent researcher, which means that I use my *own*
>> funding, and my *own* direction to go out and see what knowledge I can
>> obtain. Some of my research has been in the area of mathematics.
>> Getting important research findings is one thing, and getting them
>> noticed, is another.
[JSH stuff snipped]
>> What's in it for you?
>> James Harris
> James,
> Again, the problem is not with the definition; It is with the subsets
of
> numbers. If I create a ring with all even integers [2,4,6...] and want to
> introduce 9 into the ring, I can't because 9 is odd. If the numbers you
are
> describing do not belong to the ring, then they must be in another ring.
I
> think you need to write an argument without all this crap about how
> mathematicians are evil and are hiding an error. That is beside the point
> and I don't think you're educated enough in mathematics to make that
call.
Pedant point: you can easily construct the set gen[2] union {9}
(I write gen[2] to indicate the set of all even numbers, for brevity).
This is of course not a closed set under addition, so it's
definitely not a ring.
If one attempts to construct (gen[2])[9], to deal with
this issue, one gets J. [*]
I should also note that Z[1/2], according to James, is also too
small, if I read his logic correctly (such as it is). Z[1/2],
according to James, should equal the set of all reals.
(Yes, this is preposterous. 1/3 is not in this set, let
alone an arbitrary real number such as pi or e or
Re(r_i) where r_i are the roots of the equation 3x^5+2x^3-12x+17=0,
whatever they are. :-) )
> David Moran
[*] there's probably a more standard notation for this somewhere. :-)
--
#191, ewill3@earthlink.net
It's still legal to go .sigless.
===
Subject: Re: Explaining math definition problem
In sci.math, James Harris
<jstevh@msn.com I'm an independent researcher, which means that I use my 
*own*
> funding, and my *own* direction to go out and see what knowledge I can
> obtain. Some of my research has been in the area of mathematics.
> Getting important research findings is one thing, and getting them
> noticed, is another.
> At least here on Usenet I can talk freely to people around the world.
But will anyone listen? :-)
> What I'd like to explain is my disturbing and to me fascinating
> finding of a problem with a math definition that's over a hundred
> years old. In looking over various replies to my previous posts on
> this subject, I've seen assertions that definitions can't cause
> problems, which is something that I can address quickly at the start.
> Over a hundred years ago, the great German mathematicians Karl Gauss
> played with numbers of the form a+bi, where 'a' and 'b' are integers.
> In his honor they were later called gaussian integers, though a number
> like 1+2i is not an integer. The gaussian up-front is important.
> Later mathematicians came up with other numbers they called algebraic
> integers, which include gaussian integers.
> They thought they'd found THE set, or superset you might call it,
> which includes all numbers with certain special properties of
> integrality.
> The most important property to point out is the ability to have
> primeness between numbers.
> For instance, with integers, 2 and 3 are coprime, that is, they don't
> share non-unit factors, that is, factors other than 1 or -1, with each
> other.
> Just be clear here, factors of 1, are called units or unit factors.
> But notice that with rationals, you have 2(3/2) = 3, so 2 and 3 *do*
> share a factor and are not coprime in that ring, which is typically
> called a field *because* every element except 0, has a multiplicative
> inverse.
> What Gauss had started considering, which other mathematicians
> extended, was the idea of sets of numbers where you kept interesting
> properties of the set of integers, like being able to say two numbers
> were coprime.
> What I've found is a problem with their set of algebraic integers, as
> unfortunately, despite what many mathematicians think, it's too small.
> That's it. The definition they use is too small to do what they think
> it does, which is include all these interesting numbers with special
> properties.
> But because they *think* it's big enough, mathematicians have an error
> in their discipline based on their false assumption, as they've come
> up with more arguments based on that assumption, which then aren't
> actually proven.
> It's like when the Greeks with their word atom thought they had the
> smallest thing, and later our civilization used it, and broke atoms
> apart, though part of the definition is that they are *indivisible*,
> as people can define things, and later *refine* their definitions.
> Now my research finding isn't hard to show quickly in broad strokes.
> On of my important analysis tools is a simple technique to factor
> polynomials into non-polynomial factors.
> For instance, with the polynomial
> P(x) = 14706125 x^3 - 900375 x^2 + 17640 x + 1078
The roots of this polynomial are, approximately:
r_1 = -0.02320596700418064467907344992
r_2 = 0.04221522840004950601300611271 - 0.03710343776564665666915421379*I
r_3 = 0.04221522840004950601300611271 + 0.03710343776564665666915421379*I
courtesy of GP/PARI.
This equation is divisible by 7^2, yielding
P(x) = 7^2 * (300125 * x^3 - 18375 * x^2 + 360 * x + 22)
.
> that technique gives you
> P(x)= 7^2(2401 x^3 - 147 x^2 + 3x) (5^3) - 3(-1 + 49 x )(5)(7^2) + 7^3
For some reason I cot verify this in GP/PARI:
7^2*(2401*x^3-147*x^2+3*x)*(5^3)-3*(-1+49*x)*(5)*(7^2)+7^3
-(14706125*x^3-900375*x^2+17640*x+1078)
= -35280 * x.
Were your claim correct I should get identically 0. I suspect a sign error
during equation transcription.
Fix.
> so I can factor to get
> P(x) = (5 a_1 + 7)(5 a_2 + 7)(5 a_3 + 7).
> where the a's are the roots of the cubic
> a^3 + 3(-1 + 49x)a^2 - 49(2401 x^3 - 147 x^2 + 3x).
Erm...what exactly are you doing? Did you mean that you could
factor P(x) into
P(x) = (5 * a_1 * x + 7) * (5 * a_2 * x + 7) * (5 * a_3 * x + 7) ?
We know we can factor P(x) = 14706125 * (x - r_1) * (x - r_2) * (x - r_3)
(as I've done above). It turns out 14706125 = 5^3 * 7^6, and
therefore we can write
P(x) = 5^3 * 7^3 * (5 * a_1 * x + 7) * (5 * a_2 * x + 7) * (5 * a_3 * x +
7)
where
a_i = -7 / (5 * r_i)
or
a_1 = 60.32931098056739402658477747
a_2 = -18.71011003573824246783784328 - 16.44452558021931061668416939*I
a_3 = -18.71011003573824246783784328 + 16.44452558021931061668416939*I
It turns out these a's empirically satisfy the equation
E(a) = 22*a^3 - 504*a^2 - 36015*a - 823543 = 0
and the gcd of the coefficients of this equation is 1.
I'd have to do some work to prove this precisely, though, as GP/PARI
in this case is doing the equivalent of a toy calculator's
division of 1/3 = 0.33333333 ; it's not giving me a nice
representation here but simply approximating it to the best of
its ability.
Unfortunately, it turns out the roots of this equation are in fact
b_1 = 60.32931098056739402658477746
b_2 = -18.71011003573824246783784328 + 16.44452558021931061668416939*I
b_3 = -18.71011003573824246783784328 - 16.44452558021931061668416939*I
and b_1 - a_1 = -1.21169034 E-26, which is a very tiny
error, but not identically 0. So I can't construe this
as a mathematically iron-clad proof. (Basically, the last
digit is a 6 instead of a 7.) Even if b_1 = a_1 to 53 bits
of precision I couldn't construe it as such.
But I can check the equation by deriving it using a
different method. It's worth noting that, if we assume
r_i are the roots of P(x) = 0, (we have already computed
approximations to r_i above, but let's pretend that we
haven't) where
P(x) = 14706125 x^3 - 900375 x^2 + 17640 x + 1078
then 1/r_i are the roots of Q(x) = 0, where
Q(x) = x^3 * P(1/x) = 1078 x^3 + 17640 x^2 - 900375 x + 14706125
and we can manufacture an equation with roots a_i = -7/(5*r_i), with
this technique; if we set R(x) = 0, where
R(x) = x^3 * P(-7/(5*x)) = 1078*x^3 - 24696*x^2 - 1764735*x - 40353607
Changing independent variables and dividing by 49, we get
R(a)/49 = 22 * a^3 - 504 * a^2 - 36015 * a - 823543
which turns out to be equal to E(a) above. So GP/PARI wasn't
too far off after all.
> Now despite the complexity, you can rely on *simple* ideas still, by
> noticing that setting x=0, pulls out constant terms, as
> P(0) = (5(0) + 7)(5(0) + 7)(5(3) + 7) = 7(7)(22)
> as the cubic defining the a's with x=0 is
> a^3 - 3a^2, which has roots, 0, 0 and 3.
Well, now you've completely lost *me*, for starters; are you solving
P(x) = 0 or deriving a cubic in a using x as a parameter instead
of a variable to be solved for?
Ow, my brain hurts.
However, you are correct in that P(0) = 7^2 * 22. These factors
must be accounted for in some fashion -- although since the
roots of P(x) = 0 aren't algebraic integers it's a bit like
asking for the factors of 6 (2 and 3) to be accounted for in the
equation
35 y^2 + 11y - 6 = 0
In short, such a statement doesn't appear all that meaningful.
> You may not realize it, but what you just saw is revolutionary, both
> in the special techniques, and most importantly with the consequences
> that quickly follow.
> That's because P(x) has another special feature as
> P(x) = 49(300125 x^3 - 18375 x^2 + 360 x + 22)
> where that 49 is just begging to be divided off, which gives, of
> course,
> P(x)/49 = 300125 x^3 - 18375 x^2 + 360 x + 22.
This equation is correct, fortunately for you. ;-)
> But remember, my three factors with the a's from before had *constant*
> terms of 7, 7 and 22, so dividing by 49 must give constant terms of 1,
> 1, and 22, which is the result that is so earth shattering.
The roots of the equation E(a) = 0 aren't algebraic integers anyway.
> Here the principle is like if you have
> S(x) = 7x^2 + 14x + 7 = (7x+7)(x+1)
> in that setting x=0 gives you *constant* terms within the expression,
> which you can conveniently, also look at to see how it works.
> S(0) = (7(0) + 7)(0 + 1) = 7(1).
> The point is that the 7 is constant, so x's value means nothing to it.
> So from before with
> P(0) = (5(0) + 7)(5(0) + 7)(5(3) + 7) = 7(7)(22)
> I know that dividing through by 49, it must go like
> P(0)/49 = (5(0)/7 + 1)(5(0)/7 + 1)(5(3) + 7) = 1(1)(22)
> and as the constant terms are *independent* of the value of x, it MUST
> be that in general
> P(x)/49 = (5a_1/7 + 1)(5a_2/7 + 1)(5a_3 + 7).
Your logic appears flawed, as is easily shown by example. Consider
the equation
F(x) = x^3 - 49 = 0.
This equation must have 3 algebraic integer roots. One can factor it
F(x) = 49 * (7 * d_1 * x - 1) * (7 * d_2 * x - 1) * (d_3 * x - 1)
where I've arbitrarily selected two d's to be divided by 7 in
the final representation, and used -1 for simplicity; as one
can easily see,
d_1 = 1/(7 * c_1)
d_2 = 1/(7 * c_2)
d_3 = 1/c_3
for some permutation of the c's.
What can I conclude? Not much.
It turns out c_1 = 7^(2/3) so clearly it's not divisible by 7.
c_2 = 7^(2/3) * exp(2 * pi * i / 3) and
c_3 = 7^(2/3) * exp(4 * pi * i / 3).
None of these are divisible by 7, in the sense that c_i / 7
yields an algebraic integer. (exp(i * theta) is a unit
in the ring of algebraic integers, for any theta = 2 *
pi * m / n, m, n > 0.) Therefore, at most one of the d's
is an algebraic integer, and since d_3 = 7^(-2/3) * exp(2 * pi *i * n /3)
where n is 0, 1, or 2 (ah yes, this is a hand-picked equation!),
d_3 is not an algebraic integer (it satisfies the equation
49 y^3 - 1). The other two aren't, either.
> The problem now though is that conclusion can be used to show that
> unequivocally beyond any reasonable doubt the definition of algebraic
> numbers is TOO SMALL, as at times 5a_1/7 and 5a_2/7 are not included.
> You see, they get left out, which is a problem because from the
> *assumption* of mathematicians, they should be included, if the ring
> of algebraic integers is the ring that mathematicians thought it was.
And what is the set of algebraic integers, then?
It's clearly not a field:
7 is in the set (x - 7 = 0)
2 is in the set (x - 2 = 0)
7/2 is not in the set (2x - 7 = 0 is not monic in its highest non-zero x
power).
> Some of you may find yourselves fearful of using your own mathematical
> understanding, if you realize I'm right, and then realize that
> mathematicians are disputing the result, especially if you see posters
> tossing out far more complicated math in reply to my post, but
> remember, math isn't magic.
> Logic rules mathematics, so look for what makes sense. And remember
> that you can't assume that posters are on your side. I don't want you
> to assume that I'm on your side either.
> You see, I don't need you to assume anything, as what I need you to do
> is check.
> While some mathematicians may erroneously believe now that it's in
> their interest to hide the problem I've revealed, that mistake in
> thinking does not help the rest of the world. After all, what good
> does it do everyone else for mathematicians to hide their definition
> problem?
> What's in it for you?
Understanding. So far, you've not extended mine. :-) You'll need
to fix a number of glaring logic errors, to start.
> James Harris
--
#191, ewill3@earthlink.net
It's still legal to go .sigless.
===
Subject: Re: Explaining math definition problem
he either can't, or won't, or doesn't get the question, or
the definitions behind the question, or all or part
of the trivium (logic, grammar, rhetoric ... well,
he seems to have some elements of rhetoric, down-cold .-)
> Can you write down a1, a2, a3 explicitly for your polynomial
> as others have done (not another polynomial, YOUR polynomial)
> and show they have the behavior you want them to have?
--les ducs d'Enron!
===
Subject: Re: Explaining math definition problem
have you considered a career in acting?... I mean,
about half of the time you fail to follow-up
on questions to your own postings, immediately, but
that applies to virtually all of your originations,
eventually, in the ten-year programme
to prove ... some thing -- what is it that you're trying to prove?
incidentally,
the book taht I quoted on rings made at least one mistake,
in saying that Fermat proved the case of FLT for n=3,
wehn he actually used infinite descent for n=4,
which apparently did not comply to his more-general proof. so,
the question is, do all cases fall to your peculiar method, or
did you find a counterexample in Object Ring Theory?
that's the 64-centivo question for me, and if
it's answered, maybe something will be in it
for me, two!
> What I'd like to explain is a disturbing and fascinating finding of a
> problem with a math definition that's over a hundred years old.
> But notice that with rationals, you have 2(3/2) = 3, so 2 and 3 do
> share a non-unit factor and are not coprime in that ring, which is
> typically called a field because every element except 0, has a
> multiplicative inverse.
> That's it. The definition they use is too small to do what they think
> it does, which is include all these interesting numbers with special
> properties.
> What's in it for you?
--les ducs d'Enron!
===
Subject: Re: Explaining math definition problem
another error that it made was:
said that Cusa made an erroneous proof
that the circle was incomeasurable with teh tetragon
(skware).
> the book taht I quoted on rings made at least one mistake,
> in saying that Fermat proved the case of FLT for n=3,
> wehn he actually used infinite descent for n=4,
> which apparently did not comply to his more-general proof. so,
> the question is, do all cases fall to your peculiar method, or
> did you find a counterexample in Object Ring Theory?
--les ducs d'Enron!
===
Subject: Re: Explaining math definition problem
> I'm an independent researcher, which means that I use my *own*
> funding, and my *own* direction to go out and see what knowledge I can
> obtain. Some of my research has been in the area of mathematics.
[mostly non-math SNIPPED]
> On of my important analysis tools is a simple technique to factor
> polynomials into non-polynomial factors.
> For instance, with the polynomial
> P(x) = 14706125 x^3 - 900375 x^2 + 17640 x + 1078
> that technique gives you
> [1] P(x)= 7^2(2401 x^3 - 147 x^2 + 3x) (5^3) - 3(-1 + 49 x )(5)(7^2) +
7^3
I really think this was clearer when you were writing it as
[2] P(m) = f^2*((m^3*f^4 - 3*m^2*f^2 + 3*m)*x^3 - 3*(-1 + m*f^2)*x*u^2 +
u^3*f).
Your expression [1] is obtained from [2] by the following substitions:
u = 1
f = 7
x = 5
m = x
It is clear that in your factorization of [1], you want to treat
5 not as a number, but as a polynomial variable. Therefore
it was clearer when you had x, as in [2], rather than 5.
> so I can factor to get
> P(x) = (5 a_1 + 7)(5 a_2 + 7)(5 a_3 + 7).
That is, P(x) = (a1*y + 7)*(a2*y + 7)*(a3*y + 7),
where y is the polynomial variable for which you
have substituted 5.
> where the a's are the roots of the cubic
> a^3 + 3(-1 + 49x)a^2 - 49(2401 x^3 - 147 x^2 + 3x).
It is worth noting that the roots are all algebraic
integers since this polynomial is monic.
> Now despite the complexity, you can rely on *simple* ideas still, by
> noticing that setting x=0, pulls out constant terms, as
> P(0) = (5(0) + 7)(5(0) + 7)(5(3) + 7) = 7(7)(22)
> as the cubic defining the a's with x=0 is
> a^3 - 3a^2, which has roots, 0, 0 and 3.
OK so far.
> You may not realize it, but what you just saw is revolutionary, both
> in the special techniques, and most importantly with the consequences
> that quickly follow.
> That's because P(x) has another special feature as
> P(x) = 49(300125 x^3 - 18375 x^2 + 360 x + 22)
> where that 49 is just begging to be divided off, which gives, of
> course,
> P(x)/49 = 300125 x^3 - 18375 x^2 + 360 x + 22.
Also OK.
> But remember, my three factors with the a's from before had *constant*
> terms of 7, 7 and 22, so dividing by 49 must give constant terms of 1,
> 1, and 22, which is the result that is so earth shattering.
All you are saying is that P(0)/49 = 1*1*22. Why is that earth-
shattering ?
> Here the principle is like if you have
> S(x) = 7x^2 + 14x + 7 = (7x+7)(x+1)
> in that setting x=0 gives you *constant* terms within the expression,
> which you can conveniently, also look at to see how it works.
> S(0) = (7(0) + 7)(0 + 1) = 7(1).
> The point is that the 7 is constant, so x's value means nothing to it.
What you have done in this little example is not parallel to
what you have done with P(x). You are not factoring P(x)
into linear terms involving x: that is, your factors for
P(x) are terms g1, g2, and g3, where, for example,
g1 = 5*a1 + 7
where it is a1 which is a function of x. Moreover, a1 is
not a *polynomial* function of x.
You have made this point yourself many, many times before:
you have often said very proudly that you were factoring P(m)
(as you were calling it previously) into NONPOLYNOMIAL factors.
You were right, in the sense that the coefficients ai were
functions of m, but not polynomial functions.
This is important because when you try to draw the
parallel with S(x), you ARE factoring it into linear
factors involving x.
It looks like the old shell game. It looks like you
are pulling the old switcheroo on the variable of factorization.
To maintain the parallel between S(x) and P(x), you should
not be using x: you should be using 5 !
> So from before with
> P(0) = (5(0) + 7)(5(0) + 7)(5(3) + 7) = 7(7)(22)
> I know that dividing through by 49, it must go like
> P(0)/49 = (5(0)/7 + 1)(5(0)/7 + 1)(5(3) + 7) = 1(1)(22)
> and as the constant terms are *independent* of the value of x, it MUST
> be that in general
> P(x)/49 = (5a_1/7 + 1)(5a_2/7 + 1)(5a_3 + 7).
No - first of all, a_1, a_2, and a_3 are dependent
on x. Secondly, in order for P(x) to factor in the
form you have given, the number 49 is split up in
ways that ALSO depend on x. In symbols, you would
have
49 = f1(x)*f2(x)*f3(x),
where a1(x)/f1(x), a2(x)/f2(x), a3(x)/f3(x) and
7/f1(x), 7/f2(x), and 7/f3(x) are ALL algebraic
integers.
When x = 0, f1(0) = f2(0) = 7, and f3(0) = 1.
This works just fine, because a1(0) = a2(0) = 0.
But for other values of x, there is no reason to
think that f1(x) = f2(x) = 7 and f3(x) = 1. They
are just three algebraic integer divisors of 49.
Their values are dependent on x, and they do in
fact have the values you expect when x = 0.
*
* The following section is the important stuff in this post.
*
Now: you may say, yes, but if I consider
[3] g1(x) = 5*a1 + 7,
the constant term is 7. Moreover, the constant
term of g1(x)/7 is 1. This is true no matter
what x is. I always get the same constant term.
It has the value 7 INDEPENDENT of x.
Of course that is true. But so what? If f1
is an algebraic integer factor of both 7 and a1,
then g1(x)/f1(x) = 5*a1(x)/f1(x) + 7/f1(x). To which
you say, AHA! NOW you are saying that the constant
term is 7/f1(x) !!! Right?
To which I say: not at all. *By your own definition*,
the constant term of g1(x)/f1(x) is g1(0)/f1(0).
Recalling that f1(0) = 7, I have
g1(0)/f1(0) = 5*a1(0)/f1(0) + 7/f1(0)
= 5*a1(0)/7 + 7/7 = 5*0 + 1 = 1.
of g1 is:
g1(0) = f1(0)*(5*a1(0)/7 + 7/7) = 7,
just as in [3] above. No problem at all!
Here is *my* conjecture about where your thinking
goes wrong. You are using constant term in two
different ways. It goes back to the expression
h1(x) = g1(x)/f1(x) = 5*a1(x)/f1(x) + 7/f1(x).
You are accustomed to thinking that the terms there
on the end comprise the constant term, and has the same value
for all x. THAT IS NOT TRUE. The constant term of h1(x)
is nothing but 7/f1(0). Realizing that f1(x) can be a nonconstant
function of x whose values are algebraic integer divisors
of 7 for all values of x does NOT lead to any contradiction or problem.
Put it another way: 7^2 is factored differently
into 3 pieces depending on the value of x. Those
three pieces are algebraic integers. You appear to be
assuming that that part on the end, 7/f1(x), is the constant
term of the function h1(x). IT ISN'T. The constant term as
you have consistently and correctly used it is h1(0). Since,
however, because of its placement, you are thinking
of 7/f1(x) as the constant term, you think it must be *constant*.
That is, it must have the same value for all x. THAT IS
NOT TRUE. The constant term of h1(x) is nothing but 7/f1(0).
Realizing that f1(x) can be a nonconstant function
of x whose values are algebraic integer divisors
of 7 for all values of x does NOT lead to any
contradiction or problem.
Put it another way: 7^2 is factored differently
into 3 pieces depending on the value of x. Those
three pieces are algebraic integers. Assuming that
they are not always equal to the values that they
have when x = 0 does not lead to any contradiction
of the independence of the constant term.
Put yet another way: the constant term in g1
is not 7/f1(x) *unless* you assume f1(x) is itself
constant, and thus always equal to f1(0). But that
is assuming what you want to prove!
The constant term in g1(x) is 7/f1(0). That is
*all* it is, and there is no way to show that it is
7/f1(x) for other values of x. Whether this is where your
thinking has gone off the track, I don't know for sure,
though it seems consistent with many things you have said.
Arturo has a related theory, possibly even the same theory,
about what you are thinking. But it's all academic. The various
counterexamples that we have produced show that your
thinking goes wrong SOMEWHERE. You are whistling past
graveyard when you persist in your belief that there is
some error in core mathematics, or that there is a
problem with the definition of algebraic integers.
The far simpler (and correct) explanation is that your argument is
wrong. We know exactly *where* it is wrong, but only
you can reveal what you are actually thinking. And
so far you have not completely done that. Until you do,
we will not be able to resolve to your own satisfaction what
your mistake is. But we know enough, I would say, to satisfy
everyone else.
> The problem now though is that conclusion can be used to show that
> unequivocally beyond any reasonable doubt the definition of algebraic
> numbers is TOO SMALL, as at times 5a_1/7 and 5a_2/7 are not included.
Face up to what you are saying. You are claiming above to
have an airtight argument that a1 has 7 as a factor, which of
course means a1/7 is an algebraic integer. Now you say you
can conclude that 5*a1/7 is not an algebraic integer. That is
not a definition problem. That is an out-and-out CONTRADICTION.
Face up to it! Bite the bullet! And a contradiction like this can
only mean one of two things:
1. Mathematics is inconsistent, or
2. You have an error in your reasoning.
We have pointed this out to you over and over again. We
have pointed out exactly where your error is: it is in
saying that because a1(0) is divisible by 7, that the
same must be true for a1(x) when x is not zero. You refuse
to listen. You just keep repeating your mantra about
the constant terms of P(x) and its factors being
*independent* of x, as if that leads to any conclusion.
Get this through your incredibly thick head: the fact
that the constant terms, when x = 0, satisfy certain
divisibility criteria tells you NOTHING about what
happens when x is nonzero. Nor is factorization of
overly simplistic REDUCIBLE quadratic polynomials a reliable guide
to what happens with IRREDUCIBLE polynomials. Algebraic
integers, as you yourself have pointed out, are really
different from ordinary integers: they cot be factored
into little indivisible atoms called 'primes'; they are
*infinitely divisible* and they can factor in ways that
are quite strange, compared to factorization of integers.
Nora B.
> You see, they get left out, which is a problem because from the
> *assumption* of mathematicians, they should be included, if the ring
> of algebraic integers is the ring that mathematicians thought it was.
> Some of you may find yourselves fearful of using your own mathematical
> understanding, if you realize I'm right, and then realize that
> mathematicians are disputing the result, especially if you see posters
> tossing out far more complicated math in reply to my post, but
> remember, math isn't magic.
> Logic rules mathematics, so look for what makes sense. And remember
> that you can't assume that posters are on your side. I don't want you
> to assume that I'm on your side either.
> You see, I don't need you to assume anything, as what I need you to do
> is check.
> While some mathematicians may erroneously believe now that it's in
> their interest to hide the problem I've revealed, that mistake in
> thinking does not help the rest of the world. After all, what good
> does it do everyone else for mathematicians to hide their definition
> problem?
> What's in it for you?
> James Harris