mm-
Subject: Sets of functions
Im studying set theory on my own as a hobby. Ive just read
about sets
of functions, however I am having difculty solving the
following exercise
problem,
Let A be a non-empty set, and let x be an element (not
necessarily in
A).
(i) Show that there is a bijective map from F(A, {x}) to {x}.
(ii) Show that there is a bijective map from F({x},A) to A.
That is the 2nd exercise for the chapter on sets of
functions, and so I
assume that it should be quite simple to complete.
I reasoned, perhaps erroneously, the following for part (i),
If a function f is bijective, then it has a unique inverse,
which will
be denoted as g, that satises:
(1) f o g = 1_{x}.
(2) g o f = 1_F(A, {s}).
Let y in {x}. Then (f o g)(y) = f(g(y)) = y. Since there is
only a
single element in {x}, y = x. Thus, f(g(x)) = x. We see that
f is the
constant map, and since there is but a single element in {x},
it is also
surjective. Therefore, f(y) = x for all y in F(A, {x}). Since
f is
surjective, and has but a single element in its codomain, in
order for it
to
also be injective, and hence bijective, there must only be a
single element
in F(A, {x}).
Is that the tricky part? That is, to show that there is but a
single
element in F(A, {x}). Any element in F(A, {x}) will be a
function from A to
{x}. Since each element in A must be mapped to an element in
{x}, and since
there is but the single x to map to, there will be but a
single function
from A to {x}, and thus a single element of F(A, {x}). I
might be wrong,
but
that is how I reason it. The function f is then seen to be a
bijective map
from a single element in F(A, {x}) to a single element in {x}.
Is the above correct reasoning, and if so, how would I prove
this
formally?
Dont just read it; ght it! Ask your own questions, look for
your own
examples, discover your own proofs. Is the hypothesis
necessary? Is the
converse true? What happens in the classical special case?
What about the
degenerate cases? Where does the proof use the hypothesis?
--- Paul Halmos (1916 - )
addam@rogers.com
===
Subject: Re: Sets of functions
> Let A be a non-empty set, and let x be an element (not
necessarily in
> A).
> (i) Show that there is a bijective map from F(A, {x}) to
{x}.
> (ii) Show that there is a bijective map from F({x},A) to A.
I assume F(x,y) is your (the books?) notation for the set of
functions with domain x and range contained in y. This
notation is
Your proof (which I omitted) is, as usual, too complicated.
(The as
usual is meant not as a dig, but as constructive criticism.)
When A
is not empty, the only function in {x}^A is the constant
function;
that is, A is a singleton. When A is empty, {x}^A = {0}
(where 0
denotes the empty set}, again a singleton. There is a clear
bijection
between singletons.
When A is not empty, the only functions in A^{x} are the
constant
functions; thus, the bijection maps a function to the unique
element in
its image. When A is empty, so is A^{x}, and the empty set is
a
bijection from the empty set to itself.
-Stephen J. Herschkorn
===
Subject: Re: Sets of functions
> Your proof (which I omitted) is, as usual, too complicated.
(The as
> usual is meant not as a dig, but as constructive
criticism.) When A
> is not empty, the only function in {x}^A is the constant
function;
> that is, A is a singleton. When A is empty, {x}^A = {0}
(where 0
> denotes the empty set}, again a singleton. There is a clear
bijection
> between singletons.
I tend to be critical of myself, which leads me to ruminate
too much.
Comprehending ideas is easier for me, at least at this point,
than writing
a
formal proof of the ideas. In other words, I can usually
understand the
exercises, but have difculty in completing them using
mathematical
notation. The difculty for me stems from lack of sufcient
condence in
my knowledge, which manifests itself in my repeatedly
questioning myself.
This all results in my spending for more time than necessary
on each
exercise problem. I try not to complicate things, but always
to no avail.
> When A is not empty, the only functions in A^{x} are the
constant
> functions; thus, the bijection maps a function to the
unique element in
> its image. When A is empty, so is A^{x}, and the empty set
is a
> bijection from the empty set to itself.
The term singleton is unfamiliar to me. Would accept, as a
proof to
the exercise, what you in your reply? Or was that only for my
benet and
not how you would formally present your answer?
===
Subject: A Ring of n x n matrices with entries in R is
Noetherian if R is
Noetherian
Does anyone know where I might nd a proof of this? I thought
that it
might proceed by induction on n. I was trying to embed the
ring of n-1 x
n-1 matrices inside the ring of n x n matrices, and then
hoping to take
quotients and get something which was Noetherian , perhaps a
direct sum
of copies of R. However I couldnt get this to work since I
couldnt get
the ring of n-1 x n-1 matrices to sit inside as an ideal. Is
it possible
to do this? Or am I on the wrong track?
===
Subject: Re: A Ring of n x n matrices with entries in R is
Noetherian if R
is Noetherian
> Does anyone know where I might nd a proof of this? I
thought that it
> might proceed by induction on n. I was trying to embed the
ring of n-1 x
> n-1 matrices inside the ring of n x n matrices, and then
hoping to take
> quotients and get something which was Noetherian , perhaps
a direct sum
> of copies of R. However I couldnt get this to work since I
couldnt get
> the ring of n-1 x n-1 matrices to sit inside as an ideal.
Is it possible
> to do this? Or am I on the wrong track?
Blimey .... you are making hard work for yourself. :-(
M_n(R) is isomorphic as an R-module to R^{n^2}. As R is
Noetherian,
R^{n^2} and so M_n(R) is Noetherian as a left R-module. Thus
M_n(R)
is Noetherian as a left M_n(R)-module.
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Lacan, Jacques, 79, 91-92; mistakes his penis for a square
root, 88-9
Francis Wheen, _How Mumbo-Jumbo Conquered the World_
===
Subject: Re: Power of 2 with all even digits?
> In order for 2^n to have all even digits, 2^(n-1) has to
have all its
> digits less than 5. Im not sure if this happens.
A quick check turns up 1, 2, 3, 6 and 11 as values of n
satisfying the
condition. No others within the range of powers of 2 that I
can rattle off
by heart.
Paul Townsend
I put it down there, and when I went back to it, there it was
GONE!
Interchange the alphabetic elements to reply
===
Subject: Re: Power of 2 with all even digits?
> In order for 2^n to have all even digits,
> 2^(n-1) has to have all its digits less than 5.
> A quick check turns up 1, 2, 3, 6 and 11 as values
> of n satisfying the condition.
Correct. Compare with the quick hack of HP two days
ago, which got a new column with a fancy function
ff(n) = Number of digits > 4
in the decimal expansion of 2^n
Smallest mis- # digits
n 2^n sing digit larger 4
-------------------------------------
0 1 0 0
1 2 0 0
2 4 0 0
3 8 0 1
4 16 0 1
5 32 0 0
6 64 0 1
7 128 0 1
8 256 0 2
9 512 0 1
10 1024 3 0
11 2048 1 1
12 4096 1 2
13 8192 0 2
14 16384 0 2
15 32768 0 3
16 65536 0 4
17 131072 4 1
18 262144 0 1
19 524288 0 3
20 1048576 2 4
21 2097152 3 3
22 4194304 2 1
23 8388608 1 5
24 16777216 0 5
25 33554432 0 2
26 67108864 2 5
27 134217728 0 3
28 268435456 0 5
29 536870912 4 5
30 1073741824 5 3
31 2147483648 0 4
32 4294967296 0 6
33 8589934592 0 7
34 17179869184 0 7
35 34359738368 0 6
36 68719476736 0 8
37 137438953472 0 5
38 274877906944 1 7
39 549755813888 0 9
40 1099511627776 3 8
41 2199023255552 4 6
42 4398046511104 2 4
43 8796093022208 1 6
44 17592186044416 3 6
45 35184372088832 6 6
46 70368744177664 2 8
47 140737488355328 6 7
48 281474976710656 3 9
49 562949953421312 0 6
50 1125899906842624 3 8
51 2251799813685248 0 9
52 4503599627370496 1 9
53 9007199254740992 3 8
54 18014398509481984 2 8
55 36028797018963968 4 11
56 72057594037927936 1 10
57 144115188075855872 3 10
58 288230376151711744 9 7
59 576460752303423488 1 8
60 1152921504606846976 3 10
61 2305843009213693952 7 7
62 4611686018427387904 5 9
63 9223372036854775808 1 10
64 18446744073709551616 2 10
65 36893488147419103232 5 7
66 73786976294838206464 1 12
67 147573952589676412928 0 13
68 295146905179352825856 - 13
69 590295810358705651712 4 12
71 2361183241434822606848 5 7
72 4722366482869645213696 0 12
73 9444732965739290427392 1 10
74 18889465931478580854784 2 15
75 37778931862957161709568 4 16
76 75557863725914323419136 0 12
77 151115727451828646838272 0 12
78 302231454903657293676544 8 10
79 604462909807314587353088 - 12
80 1208925819614629174706176 3 13
81 2417851639229258349412352 0 10
Here is sequence a(n) = rst m with ff(m)=n:
0,3,8,15,16,23,32,33,36,39,56,55,66,67,...
(Still not in the OEIS)
Rainer Rosenthal, r.rosenthal@web.de
_
(_) Given A, P and a circle. Find B, C on the
A P circle with P on BC and area(ABC)=maximum.
(Ingmar Rubin in de.sci.mathematik)
===
Subject: Hey, lying little tommie: why are you continuing to
run from
this?
In one age, called the Second Age by some,
(an Age yet to come, an Age long past)
in message
<8e6c2276f9a79c8b9326909a1e590114@news.teranews.com>:
>> So, have you nally done that research on the moon landing
you lied
>> about doing right before you ran away this last time?
>You have yet to refute the Urls that I posted.
>> Wrong answer: from message
>> 0f0752206adafc7e8ef86d9b5de218d1@news.teranews.com:
>>
>> Lying little tommie, embarrassed by zir penchant for
swallowing whole
>> crackpot conspiracy theories, has run away from the
following thread
>> in yet another lame attempt to pretend zie did not get zir
head handed
>> to him (reinforcing once again the advice that zie has
been given time
>> and again: research *rst*, think about it realistically,
*then*
>> post)
>>
>> In one age, called the Second Age by some,
>> (an Age yet to come, an Age long past)
>> in message <10d6ajmcld0e4bf@corp.supernews.com>:
>>
>Facts that make Steve run..Walz thinks we went to the moon.
>> is there *no* subject on which you are afraid to
demonstrate your
>> ignorance, lying little tommie?
>(1) How did Apollo get through the Van Allen Belt Steve?
>Radiation is a big problem when it comes to space travel and
the Earths
>magnetic eld concentrates this radiation into the Van Allen
belts that
>surround the Earth.
>> What, exactly, are those concentrations? Veriable
citation to a
>> reliable authority only, please.
>No matter what, the Apollo crafts had to go through
>these belts and there was no way the Apollo crafts could
afford to take
>all the weight of lead shielding with them..
>> Given thick the VA belts are, and the amount of time the
spacecraft
>> spent actually exposed to them, how much shielding of what
sort would
>> be required? Again, show your work.
>They could not have survived travelling through the Van
Allen Belt
without
>suffering from radiation sickness, or death, without a 6
feet thick
solid
>lead shield.
>> How did you come up with this gure?
>Nasa claims that we were in the belts for about an hour give
or take a few
>minutes.
They do? Where?
>Calculate the radiation absorption factor with that of the
>shielding that was used..
No, your claim, *you* do the math -- but I will check it
after, the
depth of your ignorance and willingness to lie being well
known.
>What about the Starsh Prime test?
What about it? Or are you about to try to argue that this was
an
attempt to blast a hole thru the belts?
>mmmmmm, care
>to deny that created even more radioisotopes?
Care to explain what relevancy this has to the Van Allen
belts? Are
you under the impression that the VAB are composed of
radioisotopes?
>I dont buy into this Half-Life radioactive decay either.
What, specically, about the well documented and proven
phenomena
known as radioactive decay, or the measurement thereof known
as half
life do you not buy into, and on what basis?
>(2) Where are the stars?
>Why are there no stars in the sky in the photographs taken
from the
lunar
>surface?
>> Pretend for a moment you are an astronaut on the surface
of the Moon.
>> You want to take a picture of your fellow space traveler.
The Sun is
>> low off the horizon, since all the lunar landings were
done at local
>> morning. How do you set your camera? The lunar landscape
is brightly
>> lit by the Sun, of course, and your friend is wearing a
white
>> spacesuit also brilliantly lit by the Sun. To take a
picture of a
>> bright object with a bright background, you need to set
the exposure
>> time to be fast, and close down the aperture setting too;
thats like
>> the pupil in your eye constricting to let less light in
when you walk
>> outside on a sunny day.
>> So the picture you take is set for bright objects. Stars
are faint
>> objects! In the fast exposure, they simply do not have
time to
>> register on the lm. It has nothing to do with the sky
being black or
>> the lack of air, its just a matter of exposure time. If
you were to
>> go outside here on Earth on the darkest night imaginable
and take a
>> picture with the *exact same camera settings the
astronauts used*, you
>> wont see any stars!
>Stars would have been seen.......END OF STORY.
One usually ends a statement of faith with an Amen, lying
little
tommie.
On what basis do you make this declaration -- have you even
tried
taking a picture under the conditions which applied?
>> from http://www.badastronomy.com/bad/tv/foxapollo.html,
emphasis
>> theirs.
>> In fact, this site discusses the television show lying
little tommie
>> appears to accept as truth.
>Much more evidence that it was a hoax than some tv show.
Not that you have been able to demonstrate.
>That show did make
>a few good points. America and Russia were in a major
space-race. Russia
>had just launched Sputnik etc..Hmmmmm, we couldnt even get
a satalite in
>space yet we manged to put a man on moon.
No, Sputnik launched on October 4, 1957. The rst American
satellite, Explorer I, was launched on Jan. 31, 1958. Mercury
put a
man in space three years later (the count of known American
satellites
by that point including Vanguard (58) Pioneer 4 (59 -- rst
craft
to break free of Earths gravity) and Pioneer 5 and the rst
OSCAR,
designed and launched by a non-governmental American
association of
ham radio operators. Get that? *Amateurs* put a satellite up.
Successful American manned space ights prior to Apollo
included 10
Gemini ights between 1965 and 1966. The Apollo projects rst
launch was December, 1968, more than a decade after Sputnik,
and a
less than nine years after the mandate was given by Kennedy.
Really, lying little tommie: educate yourself at least a
*little* on
these subjects before continuing to make yourself look
foolish.
>> Research *rst*, think about it a bit, *then* post, lying
little
>> tommie...
>(3) The video shows Neil Armstrong climbing down the ladder
and stepping
>onto the surface. If he was supposed to be the rst man on
the Moon,
who
>took the video?
>> Because, of course, there is no such thing as a remotely
controlled
>> camera...
>Must be some camera...Imagine a camra that will survive
radiation..I guess
>they dont make em like that anymore..
Not so hard to imagine when one knows what one is talking
about. This
*does* exclude you, however. The Pioneers and Vanguards are
not the
only satellites to include cameras by the time of the Apollo
launches.
>(4) They didnt have the computer technology in those days
to get to
the
>Moon and back. Recentley China said: The technology to get
to the moon
>could come within the next ten years.
>> China did, huh? On what basis did they make this claim,
assuming
>> youre not just lying about it?
>As you can see.......In about 3/5 years they may have the
technology to
get
>a probe to the moon..
>http://embassy-denmark.fmprc.gov.cn/eng/57118.html
>They guess that within 10-years or so, it could be possible
to get a man
on
>the moon.
Still no citation for your quote. And guess what: itll be
even
longer before Liechtenstein puts a man on the moon -- guess
that means
that these Chinese claims are wrong, too.
They dont have cable TV most places in West Texas -- guess
*that*
technology doesnt exist either.
>Questions Steve wont answer
>Why does the American ag appear to be blowing in a breeze?
>In the vacuum of space this should not be possible.
>http://www.astrocentral.co.uk/ag.jpg
>> The answer is, it isnt waving. It looks like that because
of the way
>> the ag was deployed. The ag hangs from a horizontal rod
which
>> telescopes out from the vertical one. In Apollo 11, they
couldnt get
>> the rod to extend completely, so the ag didnt get
stretched fully.
>> It has a ripple in it, like a curtain that is not fully
closed. In
>> later ights, the astronauts didnt fully deploy it on
purpose
>> because they liked the way it looked. In other words, the
ag looks
>> like it is waving because the astronauts wanted it to look
that way.
>> Ironically, they did their job too well. It appears to
have fooled a
>> lot of people into thinking it waved
>> Ibid.
>Why is there no blast crater?
>When the lunar module landed it should have made a large
crater.
>http://www.astrocentral.co.uk/belowlm.jpg
>> When someone driving a car pulls into a parking spot, do
they do it
>> at 100 kilometers per hour? Of course not. They slow down
rst,
>> easing off the accelerator. The astronauts did the same
thing. Sure,
>> the rocket on the lander was capable of 10,000 pounds of
thrust, but
>> they had a throttle. They red the rocket hard to deorbit
and slow
>> enough to land on the Moon, but they didnt need to thrust
that hard
>> as they approached the lunar surface; they throttled down
to about
>> 3000 pounds of thrust.
>> Now here comes a little bit of math: the engine nozzle was
about 54
>> inches across (from the Encyclopaedia Astronautica), which
means it
>> had an area of 2300 square inches. That in turn means that
the thrust
>> generated a pressure of only about 1.5 pounds per square
inch! Thats
>> not a lot of pressure. Moreover, in a vacuum, the exhaust
from a
>> rocket spreads out very rapidly. On Earth, the air in our
atmosphere
>> constrains the thrust of a rocket into a narrow column,
which is why
>> you get long ames and columns of smoke from the back of a
rocket. In
>> a vacuum, no air means the exhaust spreads out even more,
lowering the
>> pressure. Thats why theres no blast crater! Three
thousand pounds of
>> thrust sounds like a lot, but it was so spread out it was
actually
>> rather gentle.
>> http://www.badastronomy.com for his succinct rebuttals to
lying little
>> tommies nonsense.
>>
>>
No comments on the ag and blast craters, lying little tommie?
>> How about the research on Prussian Blue you like about
doing right
>> before you ran away last year?
>You mean the prussian blue that wasnt found in said
gas-chambers?
>> No, I mean the Prussian Blue that does not always form on
exposure to
>> HCN, as can be seen in the fumigation chambers: if PB
always forms,
>> why arent the walls uniformly blue?
Well? if PB *always* forms on exposure, why arent the
fumigation
chambers a nice shade of blue -- you do admit that *they* were
exposed, right?
>> Or are you going to run away from the consequences of your
lies
>> *again*, lying little tommie?
>No!
>> Trying to start a trend, are you?
>> All you have to do is ask nice, and I can tell you how to
prevent your
>> demonstrated ignorance from following you all around
Usenet, despite
>> your use of XNoArchive -- and it doesnt involve concepts
you dont
>> understand, like the difference between an OS and a shell
(and between
>> them and a communications program, and between *them* and
security
>> standards...)
>I hear you window users are real code slingers, how do you
manage to use
>such a complex O/S? I mean wow! WhooooooHooooooooo, You go
Roger!
>> *Im* not the one that didnt even know what program I was
using to
>> read news with, lying little tommie...
===
Subject: Re: EIS sequences by Roger bagula edited by Wilson
> This is the editor who has my email blocked: ( He seems
happy enough
> to have his name on my sequences)
> Sequence numbers of entries in the database (if any, up to
a limit of
> 500) that contain the strings
> wilson AND bagula .
> It will take a few minutes to search the whole database
(the second
> and later lookups are faster)
> %N A037905 a(n) = 9 - (oor(n*Pi) mod 9).
> %N A071641 This is really two sequences: rst, a theta 1
based
> minimal Pisot Fibonacci sequences is produced by the
Marsaglia-Zaman
> carry type of procedure. That sequence is then used to
index the
> primes so that a six letter word pseudorational sequence is
> produced. The idea was to produce a pseudorational number
that didnt
> depend solely on the primes. So the primes are indexed by a
> pseudorandom number sequence to produce a rst digit
pseudorational
> sequence that depends on the theta 1 minimal Pisot instead
of the
> primes.
> %N A071901 n-th decimal digit of the fractional part of the
square
> root of the n-th prime.
> %N A071956 Table in which n-th row list prime factors and
their
> exponents in factorization of prime(n)!.
> %N A071988 Triple Peano sequence: a list of triples (x,y,z)
starting
> at (1,1,1); then x=x+1, y=y+x, z=z+y.
> %N A072049 Floor(2^(n /{Floor(n*log(2)/log(Prime(n)))} )).
> %N A072222 a(n) = mod(abs(n-1-a(n-2)],n) +
mod(abs(n-1-a(n-1)],n-1],
> a(0) = 1, a(1) = 1.
> %N A072231 a(n) = oor(n^2/A005185(n-1)), where A005185 is
> Hofstadters Q-sequence.
> %N A072549 a(n)=Abs(Floor(n+a(n-1)/n-n*log(n))).
> %N A072845 {1, 3, 7, 9} -> Mod[ {1*{1, 3, 7, 9}, 3*{1, 3,
7, 9}, 7*{1,
> 3, 7, 9}, 9*{1, 3, 7, 9}}, 10}
> %N A072851 a(0) = 0, a(1) = a(2) = 1, a(n) = abs ( Sum{( -
> 1)^k*a(abs(n - k))*a(k), k=2..n-1})
> %N A074381 (p-1)/2 mod 2, where p is the n-th prime for
which p+2 is
> also prime; i.e. a(n)=0 if p==1 (mod 4), a(n)=1 if p==3
(mod 4).
> %N A074395 A 7-way classication of the primes.
> %N A074822 Primes p(n) such that p(n) + 4 = p(n+1) and p(n)
== 9 (Mod
10).
> %N A074879 10 - Mod(P(n),10) when Prime(n) + 22 =
Prime(n+1).
> %N A074972 a(n) == - prime(n) (modulo 20).
> %N A075703 a(n) = minimal m such that Sum [
Prime[k],{k,n,m}] >=
> Prime[n]*Prime[m].
> %N A087658 Repeated terms in A087657 (a(n) =
|prime(n)-a(n-1)| +
> |prime(n)-a(n-2)| + |prime(n)-a(n-3)| ).
> %N A087721 Strictly increasing domain of the Hofstadter
batrachian
> sequence A005185.
> %N A090722 a(n) = if 10 - Mod(Prime(n),10) == {1,3,7,9}
respectively
> then {1,2,3,0}.
These sequences are almost without exception trivial or
tedious nonsense.
It takes zero I.Q. to just come up with an arbitrary
function, and iterate
it.
e.g. with my eyes closed, and one hand tied behind my back, I
came up
with these in about a tenth of a second:
a(n)=oor(e*10^n*a(n-1))%n
a(n)=oor(phi*10^n*a(n-1))%n
a(n)=oor(gamma*10^n*a(n-1))%n
a(n)=oor(pi*10^n*a(n-1))%n
a(n)=oor(sqrt(2)*10^n*a(n-1))%n
a(n)=oor(sqrt(pi)*10^n*a(n-1))%n
I bet theyre new! I bet theyre truly original! However, I
also bet
theyre completely worthless crap, just like most of the
above.
And how the heck did you escape from my killle?
*_PUNT_*
*bounce*
*bounce*
~silence~
*_PLONK_*
Phil
1st bug in MS win2k source code found after 20 minutes:
scanline.cpp
2nd and 3rd bug found after 10 more minutes: gethost.c
Both non-exploitable. (The 2nd/3rd ones might be, depending
on the CRTL)
===
Subject: Re: EIS sequences by Roger bagula edited by Wilson
>[...]
>a(n)=oor(e*10^n*a(n-1))%n
>a(n)=oor(phi*10^n*a(n-1))%n
>a(n)=oor(gamma*10^n*a(n-1))%n
>a(n)=oor(pi*10^n*a(n-1))%n
>a(n)=oor(sqrt(2)*10^n*a(n-1))%n
>a(n)=oor(sqrt(pi)*10^n*a(n-1))%n
Oh my gosh, thats amazing! You should publish
this work. (You may run into some resistance,
but eventually the editor will agree its
worthwhile stuff.)
I wish I had the talent to come up with original
results like these.
************************
David C. Ullrich
===
Subject: Re: EIS sequences by Roger bagula edited by Wilson
===
>Subject: Re: EIS sequences by Roger bagula edited by Wilson
>Message-id:
>>[...]
>>a(n)=oor(e*10^n*a(n-1))%n
>>a(n)=oor(phi*10^n*a(n-1))%n
>>a(n)=oor(gamma*10^n*a(n-1))%n
>>a(n)=oor(pi*10^n*a(n-1))%n
>>a(n)=oor(sqrt(2)*10^n*a(n-1))%n
>>a(n)=oor(sqrt(pi)*10^n*a(n-1))%n
>Oh my gosh, thats amazing! You should publish
>this work. (You may run into some resistance,
>but eventually the editor will agree its
>worthwhile stuff.)
Too late, hes gone back to Greece.
>I wish I had the talent to come up with original
>results like these.
>************************
>David C. Ullrich
Mensanator
Ace of Clubs
===
Subject: Flood of maths ebooks on alt.binaries.e-book
In case anyone is interested, a ood of 40 or so ebooks,
mostly
maths but some physics, was posted today on
alt.binaries.e-books.
The multipart posts are complete on Giganews
(www.giganews.com),
which costs about $5 per month (or per gigabyte downloaded
monthly
if greater.
-------------------------------------------------------------
--------------
John R Ramsden (jr@adslate.com)
-------------------------------------------------------------
--------------
Eternity is a long time, especially towards the end.
Woody Allen
===
Subject: Re: Flood of maths ebooks on alt.binaries.e-book
> In case anyone is interested, a ood of 40 or so ebooks,
mostly
> maths but some physics, was posted today on
alt.binaries.e-books.
.technical?
Phil
1st bug in MS win2k source code found after 20 minutes:
scanline.cpp
2nd and 3rd bug found after 10 more minutes: gethost.c
Both non-exploitable. (The 2nd/3rd ones might be, depending
on the CRTL)
===
Subject: Re: Surrogate factoring, update
> James,
> Keep looking into this. Youll learn a lot. But honestly,
this is just
> a variation of Fermats Difference of Squares factorization:
Actually in many ways it is. Its where its different that
things
get interesting.
> pq = n
> M = mean of p and q
> E = error from mean
> M = (p+q)/2
> p = M+E
> q = M-E
> n^2 = M^2 - E^2
> Using quadratic recipcosity you can eliminate many possible
values, but
> then end result is no net improvment in factorization
problem.
Thats just one side of what I gave in my original post.
What Ive done is link the factorization of what you call n
with
another variable that is dependent on the factorization of a
number
*other* than n, which I call the surrogate.
Ive found a way that links two different factorizations
together.
> Do yourself a favour - dont give up on this untill youve
quantied
> your results with equations and numbers (How many steps
will be needed
> to use your technique compared to the one above? How much
time will it
> take for each step?)
Theoretically at its simplest youd simply factor T^2 - 1,
and take
all of its factors in combinations where you get the
difference to
nd a rational j.
You get a head start because T^2 - 1 = (T-1)(T+1), and with T
odd,
both of those are even, and one is divisible by 3.
> The n^2 = M^2 - E^2 can be re-written in a million
different ways with
> even powers of n (as you did below). What are the
advantages? Are
> there any? Quantify (nto qualify) your results.
> JLC
No, I didnt just come up with the standard congruence of
squares.
Here are the equations pulled out:
(jk - Tk + T)(jk + Tk + T) = T^4
k = (-jT +/- T^2 sqrt(j^2 - T^2 + 1))/(j^2 - T^2)
and
j = (-T +/- T sqrt(k^2 + T^2))/k
where youll notice that the second IS the standard
congruence of
squares while for the rst you see something strange as you
have
sqrt(j^2 - T^2 + 1).
To get some appreciation for why this is different, let k =
d/c, and
substitute in the second to get
j = (-cT +/- T sqrt(c^2 + T^2 d^2))/d
and consider that if you get j by using the factors of T^2 -
1, and
the very same congruence of squares that you brought up, then
you get
c and d, and may have just factored T, along with d as well,
by
congruence of squares.
Now *some* difference of factors of T WILL get picked no
matter what,
and at this point I dont know why, if T is not prime, half
the time
it wouldnt be non-trivial factors.
Note, the point again is that SOME factors of T will come out
no
matter what, and if for some reason they are always trivial,
that is,
for instance, T itself and 1, then this idea isnt that big
of a deal.
But at this point there doesnt seem to be any mathematical
reason why
one factorization of T would be selected over another!!!
Thats the scary thing which Id like some answers on, as I
think
there will indeed be reasons why T itself as a factor tends
to pop
out, but even if non-trivial factors pop out a small
percentage of the
time, it still might be enough to affect public key
encryption.
The problem now is a LOT of questions with few answers.
Im just pushing the point that with such an idea, in such an
area,
that if mathematicians are who they say they are, then
someone will
either step forward and eliminate fears in this area by
showing why
this idea is not a threat, or there will be interest in
understanding
how it works.
Basically I found a linkage between factorizations, where if
you
factor T^2 - 1, you may factor T itself as well.
Its like maybe the math doesnt care *what* you factor, as
long as
you factor something.
So, if you factored T, you might get the factors of T^2 - 1,
as well.
Mathematically, at this point, I dont see why the math would
care.
And it certainly doesnt care that some people depend on the
idea that
T is hard to factor for their livelihoods!!!
If this idea does work well, and mathematicians sit back and
ignore
it, if things go badly then they can rightly be blamed by the
world.
They are responsible here.
James Harris
===
Subject: Re: Surrogate factoring, update
James Harris a .8ecrit :
> James,
> Keep looking into this. Youll learn a lot. But honestly,
this is
just
> a variation of Fermats Difference of Squares factorization:
> Actually in many ways it is. Its where its different that
things
> get interesting.
> pq = n
> M = mean of p and q
> E = error from mean
> M = (p+q)/2
> p = M+E
> q = M-E
> n^2 = M^2 - E^2
> Using quadratic recipcosity you can eliminate many possible
values, but
> then end result is no net improvment in factorization
problem.
> Thats just one side of what I gave in my original post.
> [...]
> No, I didnt just come up with the standard congruence of
squares.
> Here are the equations pulled out:
> (jk - Tk + T)(jk + Tk + T) = T^4
> k = (-jT +/- T^2 sqrt(j^2 - T^2 + 1))/(j^2 - T^2)
> and
> j = (-T +/- T sqrt(k^2 + T^2))/k
Your method is essentially no more than a Fermat method.
Take both sides of (jk - Tk + T)(jk + Tk + T) = T^4 modulo T.
It comes (jk)^2 = 0 mod T and, since, T has no square factors
we can write jk = 0 mod T, i.e., jk = aT for some a.
(aT - kT + T)(aT + kT + T) = T^4
(a + 1 - k)(a + 1 + k)T^2 = T^4
(a+1)^2 - k^2 = T^2
Which is equivalent to something like n^2 = M^2 - E^2.
It leads nowhere, this is just a (uselessly complicated)
Fermats
method.
mm
http://www.ellipsa.net/
mm@ellipsa.no.sp.am.net ( suppress no.sp.am. )
===
Subject: Re: Surrogate factoring, update
> James Harris a .8ecrit :
>
Using quadratic recipcosity you can eliminate many possible
values,
but
> then end result is no net improvment in factorization
problem.
>
> Thats just one side of what I gave in my original post.
> [...]
> No, I didnt just come up with the standard congruence of
squares.
> Here are the equations pulled out:
>
> (jk - Tk + T)(jk + Tk + T) = T^4
>
> k = (-jT +/- T^2 sqrt(j^2 - T^2 + 1))/(j^2 - T^2)
Notice that equation for k, and compare with the following
one for j.
>
> and
>
> j = (-T +/- T sqrt(k^2 + T^2))/k
> Your method is essentially no more than a Fermat method.
That is true for the equation for j, but not true for the
equation for
k, which is obvious to the eye.
The important difference is that as is typical with the
Fermat method,
in the equation for j you see sqrt(k^2 + T^2), so k is dened
by the
difference of factors of T^2.
For instance, trivially, let k = (T^2 - 1)/2, then
sqrt(T^4 - 2T^2 + 1 + 4T^2)/2 = T^2 + 1
where I used T^2 and 1, which are, of course, both factors of
T^2.
However, thats just half of the equation set as you also have
k = (-jT +/- T^2 sqrt(j^2 - T^2 + 1))/(j^2 - T^2)
where you have sqrt(j^2 - T^2 + 1), and now its the
difference of
factors of
T^2 - 1
which is clearly different from before.
I know it can be a subtle point, especially if you look at
j = (-T +/- T sqrt(k^2 + T^2))/k
and seize on the familiar.
Basic research can be EXTRAORDINARILY difcult for some
people,
especially if they see something that looks familiar to
escape the
difculty.
Thats just human nature.
Its easier to just try and believe that something is not new,
especially if its difcult to understand.
> Take both sides of (jk - Tk + T)(jk + Tk + T) = T^4 modulo
T.
> It comes (jk)^2 = 0 mod T and, since, T has no square
factors
> we can write jk = 0 mod T, i.e., jk = aT for some a.
> (aT - kT + T)(aT + kT + T) = T^4
> (a + 1 - k)(a + 1 + k)T^2 = T^4
> (a+1)^2 - k^2 = T^2
> Which is equivalent to something like n^2 = M^2 - E^2.
Thats unnecessary work as k is already linked in a simple
way with T
by my own work in my own replies. Youre going in circles.
Consider now how Ill make use of your own equation.
Its the variable j, which is more interesting. Substituting
with k =
aT/j into your own equation gives
(aT/j + 1)^2 - k^2 = T^2, so
(aT + j)^2 - j^2 k^2 = j^2 T^2, which is
(aT + j)^2 = j^2(k^2 + T^2)
which is a far more muddled picture.
I *deliberately* went looking for a factorization which mixed
terms in
such a way that one of the variables could NOT be simply
determined by
congruence of squares while one still is.
The mathematics here is not well-worked out, and the area is
clearly
new, so Im not surprised that several people have clung to
what they
already know.
Basic research is difcult. I suggest for most you just
sitting back
and waiting for experts in the eld to comment is the best
strategy.
> It leads nowhere, this is just a (uselessly complicated)
Fermats
> method.
I can understand your frustration. However, what Im
presenting isnt
textbook, so I dont have *easy* answers, and I can
understand how
youd like to seize upon the familiar.
Its human nature.
My suggestion to you is to sit back and wait for experts in
the eld,
who are willing to face the difculties to emerge.
If mathematicians try to ignore this idea, however, others
may not.
Essentially I found a way to link disparate factorization,
specially
linking
factorizations of T and T^2 - 1 in the simplest form, and
factorization of sT and T^2 - s^2, in the generalized form,
where you can theoretically factor one to get the
factorization of the
other.
If it is a practical idea, then if T = p_1 p_2, you could
shift to
factoring some other number and pull out the factorization of
T by
doing so, which would impact public key encryption.
Im someone who just came up with an idea that Im talking
about, and
mathematicians may choose to ignore it, but if it is viable,
then they
will be responsible for the consequences.
That is, people looking for someone to blame, if things go
badly, will
have every right to go to mathematicians, and ask hard
questions.
I already nd it troubling that I have to emphasize that
point and
deal with clumsy efforts to dismiss the idea, when the
consequences IF
its viable are so huge.
Make no mistake, if I lose money because someone comes off the
Internet exploiting an idea that some of you are trashing
then Id
feel it might right to sue you for damages, and Im the one
who came
up with this idea!!!
Heres where mathematicians prove their love of mathematics,
and
especially of pure math which has here the potential of
practical
application.
If it isnt practical, then its just pure math and no one
(including me) need worry.
If it is practical and mathematicians ignore such a
compelling idea,
then they not only prove their true disdain for mathematics
versus
their claims, they also have the responsibility to cover
damages.
That is, the world can come knocking on the doors of
mathematicians if
things go badly since mathematicians are responsible here.
And in courts of law, liability could extend to personal
property of
mathematicians IF mathematicians behave negligently.
Ignoring a viable idea is negligent.
James Harris
===
Subject: Re: Surrogate factoring, update
BEGIN LUNATIC
RAVINGS___________________________________________________
> Im someone who just came up with an idea that Im talking
about, and
> mathematicians may choose to ignore it, but if it is
viable, then they
> will be responsible for the consequences.
> That is, people looking for someone to blame, if things go
badly, will
> have every right to go to mathematicians, and ask hard
questions.
> I already nd it troubling that I have to emphasize that
point and
> deal with clumsy efforts to dismiss the idea, when the
consequences IF
> its viable are so huge.
> Make no mistake, if I lose money because someone comes off
the
> Internet exploiting an idea that some of you are trashing
then Id
> feel it might right to sue you for damages, and Im the one
who came
> up with this idea!!!
> Heres where mathematicians prove their love of
mathematics, and
> especially of pure math which has here the potential of
practical
> application.
> If it isnt practical, then its just pure math and no one
> (including me) need worry.
> If it is practical and mathematicians ignore such a
compelling idea,
> then they not only prove their true disdain for mathematics
versus
> their claims, they also have the responsibility to cover
damages.
> That is, the world can come knocking on the doors of
mathematicians if
> things go badly since mathematicians are responsible here.
> And in courts of law, liability could extend to personal
property of
> mathematicians IF mathematicians behave negligently.
> Ignoring a viable idea is negligent.
END LUNATIC
RAVINGS___________________________________________________
Say Harris, is your real name Ignatius J. Reilly?
Just wondering...
qui non intelligit, aut taceat, aut discat
===
Subject: Re: Surrogate factoring, update
> Essentially I found a way to link disparate factorization,
> specially linking
> factorizations of T and T^2 - 1 in the simplest form, and
Ok, lets let T=2^8193, show me how to factor the two
well-known
numbers 2^8193-1 and 2^8193+1.
Give me a concrete stepwise algorithm, If you need to use a
step like
nd XYZ so that X + 12 is a prime number, go ahead, but
estimate
the time complexity of it.
> Heres where mathematicians prove their love of
mathematics, and
> especially of pure math which has here the potential of
practical
> application.
While were all showing love, I have to dig a hole in my
yard. Prove
to me your pure love of hard work by digging half of it,
its only
100 or so cubic meters of dirt.
> If it isnt practical, then its just pure math and no one
> (including me) need worry.
Except for lost time and misplaced effort. Just because an
idea
attracts you Magpieishly doesnt mean it will work or anyone
else is
interested. Show how its directly useful, and not OOOOH, I
FOUND
SOMETHING SHINY, and youll get a lot more positive
attention.
Scott
===
Subject: Re: Surrogate factoring, update
James Harris a .8ecrit :
> James Harris a .8ecrit :
Using quadratic recipcosity you can eliminate many possible
values,
but
> then end result is no net improvment in factorization
problem.
Thats just one side of what I gave in my original post.
> [...]
> No, I didnt just come up with the standard congruence of
squares.
> Here are the equations pulled out:
(jk - Tk + T)(jk + Tk + T) = T^4
k = (-jT +/- T^2 sqrt(j^2 - T^2 + 1))/(j^2 - T^2)
> Notice that equation for k, and compare with the following
one for j.
and
j = (-T +/- T sqrt(k^2 + T^2))/k
> Your method is essentially no more than a Fermat method.
> That is true for the equation for j, but not true for the
equation for
> k, which is obvious to the eye.
But not to the mind. Where is the difculty to get k = f(j,T)
here?
> The important difference is that as is typical with the
Fermat method,
> in the equation for j you see sqrt(k^2 + T^2), so k is
dened by the
> difference of factors of T^2.
> For instance, trivially, let k = (T^2 - 1)/2, then
> sqrt(T^4 - 2T^2 + 1 + 4T^2)/2 = T^2 + 1
> where I used T^2 and 1, which are, of course, both factors
of T^2.
> However, thats just half of the equation set as you also
have
> k = (-jT +/- T^2 sqrt(j^2 - T^2 + 1))/(j^2 - T^2)
> where you have sqrt(j^2 - T^2 + 1), and now its the
difference of
> factors of
> T^2 - 1
> which is clearly different from before.
> I know it can be a subtle point, especially if you look at
> j = (-T +/- T sqrt(k^2 + T^2))/k
> and seize on the familiar.
> Basic research can be EXTRAORDINARILY difcult for some
people,
> especially if they see something that looks familiar to
escape the
> difculty.
I nd the word basic quite appropriate here.
> Thats just human nature.
> Its easier to just try and believe that something is not
new,
> especially if its difcult to understand.
> Take both sides of (jk - Tk + T)(jk + Tk + T) = T^4 modulo
T.
> It comes (jk)^2 = 0 mod T and, since, T has no square
factors
> we can write jk = 0 mod T, i.e., jk = aT for some a.
> (aT - kT + T)(aT + kT + T) = T^4
> (a + 1 - k)(a + 1 + k)T^2 = T^4
> (a+1)^2 - k^2 = T^2
> Which is equivalent to something like n^2 = M^2 - E^2.
> Thats unnecessary work as k is already linked in a simple
way with T
> by my own work in my own replies. Youre going in circles.
Indeed? Because, of course, you are sure that when k = (T^2 -
1)/2,
your equation is always solvable? Contrary to what you
believe, you
cannot choose k as you want. Among other constraints, T^2 +
k^2 MUST
be a square and this is not true for any k value.
> Consider now how Ill make use of your own equation.
> Its the variable j, which is more interesting.
Substituting with k =
> aT/j into your own equation gives
> (aT/j + 1)^2 - k^2 = T^2, so
> (aT + j)^2 - j^2 k^2 = j^2 T^2, which is
> (aT + j)^2 = j^2(k^2 + T^2)
> which is a far more muddled picture.
Than what?
> I *deliberately* went looking for a factorization which
mixed terms in
> such a way that one of the variables could NOT be simply
determined by
> congruence of squares while one still is.
> The mathematics here is not well-worked out, and the area
is clearly
> new, so Im not surprised that several people have clung to
what they
> already know.
It is new to you! Thats you who believes something is new
just
because you dont know it already exists.
> Basic research is difcult. I suggest for most you just
sitting back
> and waiting for experts in the eld to comment is the best
strategy.
I agree on the word basic.
> It leads nowhere, this is just a (uselessly complicated)
Fermats
> method.
> I can understand your frustration. However, what Im
presenting isnt
> textbook, so I dont have *easy* answers, and I can
understand how
> youd like to seize upon the familiar.
> Its human nature.
> My suggestion to you is to sit back and wait for experts in
the eld,
> who are willing to face the difculties to emerge.
Sometimes, you are pathetic.
> If mathematicians try to ignore this idea, however, others
may not.
> Essentially I found a way to link disparate factorization,
specially
> linking
But you found nothing, you just uselessly complicated
something
simple.
> factorizations of T and T^2 - 1 in the simplest form, and
> factorization of sT and T^2 - s^2, in the generalized form,
> where you can theoretically factor one to get the
factorization of the
> other.
> If it is a practical idea, then if T = p_1 p_2, you could
shift to
> factoring some other number and pull out the factorization
of T by
> doing so, which would impact public key encryption.
> Im someone who just came up with an idea that Im talking
about, and
> mathematicians may choose to ignore it, but if it is
viable, then they
> will be responsible for the consequences.
> That is, people looking for someone to blame, if things go
badly, will
> have every right to go to mathematicians, and ask hard
questions.
> I already nd it troubling that I have to emphasize that
point and
> deal with clumsy efforts to dismiss the idea, when the
consequences IF
> its viable are so huge.
There is no idea, you bull because of your lack of basic
knowledge and, overall, because of your incredible
pretentiousness.
> Make no mistake, if I lose money because someone comes off
the
> Internet exploiting an idea that some of you are trashing
then Id
> feel it might right to sue you for damages, and Im the one
who came
> up with this idea!!!
You should really follow a therapy.
> Heres where mathematicians prove their love of
mathematics, and
> especially of pure math which has here the potential of
practical
> application.
> If it isnt practical, then its just pure math and no one
> (including me) need worry.
Neither practical nor interesting.
> If it is practical and mathematicians ignore such a
compelling idea,
> then they not only prove their true disdain for mathematics
versus
> their claims, they also have the responsibility to cover
damages.
> That is, the world can come knocking on the doors of
mathematicians if
> things go badly since mathematicians are responsible here.
> And in courts of law, liability could extend to personal
property of
> mathematicians IF mathematicians behave negligently.
> Ignoring a viable idea is negligent.
A viable idea! Ok. I take this once more
>(aT - kT + T)(aT + kT + T) = T^4
>(a + 1 - k)(a + 1 + k)T^2 = T^4
>(a+1)^2 - k^2 = T^2
since a = kj/T
I get this
(kj/T + 1)^2 - k^2 = T^2
(k^2 (j/T)^2 + k 2j/T + 1 - k^2 = T^2
reordering, and taking b = j/T, it comes
(b^2 - 1) k^2 + 2b k + 1 - T^2 = 0
Dont you nd it looks like a degree-2 polynomial on k? Lets
express
k using the polynomial discriminant (in fact, I can use the
reduced
discriminant since I suspect 2b to be even).
D = b^2 - (b^2 - 1)(1 - T^2)
D = b^2 - b^2 + b^2 T^2 + 1 - T^2
but b = j/T thus b^2 T^2 = j^2
nally I get
D = j^2 + 1 - T^2
therefore k = (-b +/- sqrt(D))/(b^2 - 1)
k = (-j/T +/- sqrt(j^2 + 1 - T^2))/ (j^2/T^2 - 1)
multiplying the denominator and the numerator by T^2 (to
simplify) I nally get
k = (-jT +/- T sqrt(j^2 + 1 - T^2) / (j^2 - T^2)
Now, dont you nd it furiously looks like your revolutionnary
> k = (-jT +/- T^2 sqrt(j^2 - T^2 + 1))/(j^2 - T^2)
And what did I use? A degree-2 polynomial and its
discriminant.
As you said The mathematics here is not well-worked out, and
the
area is clearly new. If my memory is not too bad, the Italian
mathematicians of the XVI century already knew how to do
it.
So what? You know nothing about factoring methods. You know
nothing
about the real difculty of programming number theory
problems. What
you know in maths could be written on half a postage stamp.
But you
come and claim you could sue everybody who would dare to
question your
delirium... Yes, I agree, I am wasting my time.
mm
http://www.ellipsa.net/
mm@ellipsa.no.sp.am.net ( suppress no.sp.am. )
===
Subject: Re: Surrogate factoring, update
>James Harris a .8ecrit :
>> [...]which is obvious to the eye.
>But not to the mind.
Youve put your nger on something here - probably you
realized that. Hes never understood that if someone
shows that the solutions to ax^2 + bx + c are x = [etc]
then his solution to the eqution Ax^2 + Bx + C = 0 is
not going to be regarded as a huge advance in human
knowledge.
************************
David C. Ullrich
===
Subject: Re: Surrogate factoring, update
Marcel Martin a .8ecrit :
> multiplying the denominator and the numerator by T^2 (to
> simplify) I nally get
> k = (-jT +/- T sqrt(j^2 + 1 - T^2) / (j^2 - T^2)
^
T^2
mm
http://www.ellipsa.net/
mm@ellipsa.no.sp.am.net ( suppress no.sp.am. )
===
Subject: Re: Surrogate factoring, update
>[...]
>If it is practical and mathematicians ignore such a
compelling idea,
>then they not only prove their true disdain for mathematics
versus
>their claims, they also have the responsibility to cover
damages.
>That is, the world can come knocking on the doors of
mathematicians if
>things go badly since mathematicians are responsible here.
>And in courts of law, liability could extend to personal
property of
>mathematicians IF mathematicians behave negligently.
>Ignoring a viable idea is negligent.
These legal theories of your are fascinating. Can you say
exactly
which statute says that a mathematician who ignores a viable
idea can be held responsible for negligence?
>James Harris
************************
David C. Ullrich
===
Subject: Re: Surrogate factoring, update
> Its been a while since I mentioned surrogate factoring,
and Ill
> composite of two primes (something in the magnitude used
for RSA), and
> challenge yourself to factor it, without looking at the
answer. If your
> method is too slow to do by hand, then try to make a
program to do it
> for you. I guess as soon as you come with real proof,
people might even
> start listening to you. Im no mathematician, so Im in no
position to
> judge your method. The way to prove it to someone like me
would be to
> actually break RSA. Im sure you would gain everybodys
respect if you
> would do it. So? Do it.
> Matthijs.
Theoretical work can be VERY trying to many people. They want
to see
THE RESULT and have most of the details nailed down and have
CERTAINTY.
However, no matter how certain so much knowledge that is
tossed about
today is today, way back there were people at the beginning
who were
lost and looking, trying to gure out what was going on.
Everything around you, everything that is prized or feared
goes back
to some idea that some person was tossing around some time
ago.
Here and now though, theres this idea Im tossing around,
and its at
the beginnings.
Will it be a super idea, a potent idea?
Im not certain, though I denitely think its worth
discussing.
Now I know for some of you thats not the answer you want.
You want
certainty. You want things nailed down and a fully eshed out
product or theory.
Well thats not science or discovery. Thats about time and
persistence with the ideas that pass all the tests.
Most ideas dont pass all the tests.
At the beginning, theres little certainty, much guessing,
and not a
lot of detail.
James Harris
===
Subject: Re: Surrogate factoring, update
>Its been a while since I mentioned surrogate factoring, and
Ill
>>
>>Maybe you should put your method to the test? Let your PC
make a huge
THE RESULT and have most of the details nailed down and have
> CERTAINTY.
It can be trying to mathematicians too. Was it just a waste
of time when
Naom Elkies found out that:
2682440^4 + 15365639^4 + 18796760^4 = 20615673^4 ?
No, because then people could stop looking for a proof that
x^4+y^4+z^4=t^4 doesnt have solutions for positive integers
x,y,z,t,
because this idea obviously turned out to be false.
Then theres the fact that youre posting in sci.crypt, and
not only in
sci.math. In sci.crypt, people are very much interested in
*practical*
as well as theoretical work. Questions like How much faster
is your
method, Can you give us some practical examples, etc., are as
important here as the theory. Its nice to know a certain new
method to
accomplish something takes a time a factor 10^200 less than
an old
method, but if this new method still takes 10^(10^38374646))
years given
todays hardware, then its nice to know but of no practical
value to
cryptography. So I repeat: if theres anything in your method
(assuming
you have one, which I cannot tell), then (at least in
sci.crypt) give us
an example of you factoring a huge composite using your
method.
> However, no matter how certain so much knowledge that is
tossed about
> today is today, way back there were people at the beginning
who were
> lost and looking, trying to gure out what was going on.
They were amazed that e.g. 3^2 + 4^2 = 5^2. People have been
playing
with numbers always. So why dont you want to do this with
your method?
Come on James, give us an example!
Then give us a small beginning of an example. Break RSA a
*little*.
Slightly factor a composite thats just a *little* huge.
After that the
rest of us will tell you whether youll have reached human
cilization or
not.
> Here and now though, theres this idea Im tossing around,
and its at
> the beginnings. Will it be a super idea, a potent idea? Im
not certain,
> though I denitely think its worth discussing.
Break RSA. Then youll have your discussion Im sure.
> Now I know for some of you thats not the answer you want.
You want
> certainty. You want things nailed down and a fully eshed
out
> product or theory.
Isnt that why mathematicians are looking for proofs? They
e.g. wanted
certainty too that x^n + y^n = z^n wouldnt have solutions
for positive
integers x,y,z,n with n>2.
> Most ideas dont pass all the tests.
I guess here in sci.crypt people are interested in practical
tests,
because cryptography has practical as well as theoretical
aspects.
Matthijs Hebly.
===
Subject: Re: Surrogate factoring, update
>Its been a while since I mentioned surrogate factoring, and
Ill
>>
>>Maybe you should put your method to the test? Let your PC
make a huge
> THE RESULT and have most of the details nailed down and have
> CERTAINTY.
> It can be trying to mathematicians too. Was it just a waste
of time when
> Naom Elkies found out that:
> 2682440^4 + 15365639^4 + 18796760^4 = 20615673^4 ?
> No, because then people could stop looking for a proof that
> x^4+y^4+z^4=t^4 doesnt have solutions for positive
integers x,y,z,t,
> because this idea obviously turned out to be false.
I dont disagree.
> Then theres the fact that youre posting in sci.crypt, and
not only in
> sci.math. In sci.crypt, people are very much interested in
*practical*
> as well as theoretical work. Questions like How much faster
is your
> method, Can you give us some practical examples, etc., are
as
> important here as the theory. Its nice to know a certain
new method to
> accomplish something takes a time a factor 10^200 less than
an old
> method, but if this new method still takes
10^(10^38374646)) years given
> todays hardware, then its nice to know but of no
practical value to
> cryptography. So I repeat: if theres anything in your
method (assuming
> you have one, which I cannot tell), then (at least in
sci.crypt) give us
> an example of you factoring a huge composite using your
method.
I dont know if its practical.
But if it is practical or can be made practical then it
probably
affects public key encryption.
Its scary because *theoretically* you can just factor some
really big
number like T^2 - 1 and use its factors to then factor T.
> However, no matter how certain so much knowledge that is
tossed about
> today is today, way back there were people at the beginning
who were
> lost and looking, trying to gure out what was going on.
> They were amazed that e.g. 3^2 + 4^2 = 5^2. People have
been playing
> with numbers always. So why dont you want to do this with
your method?
> Come on James, give us an example!
No matter how many of you are certain that sci.crypt is just
about
practical issues as if theory doesnt matter, I think there
are others
who think that cryptology cares about theoretical approaches
as well
as ones proven by demonstration.
My aim here is to discuss an idea that *might* have huge
implications,
and it might just be interesting, or it might not lead to
much at all.
> Then give us a small beginning of an example. Break RSA a
*little*.
> Slightly factor a composite thats just a *little* huge.
After that the
> rest of us will tell you whether youll have reached human
cilization or
> not.
> Here and now though, theres this idea Im tossing around,
and its at
> the beginnings. Will it be a super idea, a potent idea? Im
not
certain,
> though I denitely think its worth discussing.
> Break RSA. Then youll have your discussion Im sure.
If I knew I could denitely break RSA then I wouldnt be
discussing
this idea here.
> Now I know for some of you thats not the answer you want.
You want
> certainty. You want things nailed down and a fully eshed
out
> product or theory.
> Isnt that why mathematicians are looking for proofs? They
e.g. wanted
> certainty too that x^n + y^n = z^n wouldnt have solutions
for positive
> integers x,y,z,n with n>2.
> Most ideas dont pass all the tests.
> I guess here in sci.crypt people are interested in
practical tests,
> because cryptography has practical as well as theoretical
aspects.
> Matthijs Hebly.
You may guess all you wish, but you cant speak for everyone.
The practical people can just wait and see or dismiss, while
those who
can get pulled in by theory can get involved.
I KNOW that for many of you it can be frustrating to hear
about an
idea when you want a product.
But thats basic research. Its why some people can do it,
and most
cant.
They cant handle the frustration and uncertainty.
James Harris
===
Subject: Re: Surrogate factoring, update
>> Here and now though, theres this idea Im tossing around,
and its at
>> the beginnings. Will it be a super idea, a potent idea?
Im not certain,
>> though I denitely think its worth discussing.
> Break RSA. Then youll have your discussion Im sure.
This is a good idea. Since even if true in a group like
this his idea will not get serious consideration unless he
can actully show a weakness with a break of an example.
David A. Scott
My Crypto code
http://bijective.dogma.net/crypto/scott19u.zip
http://www.jim.com/jamesd/Kong/scott19u.zip old version
My Compression code http://bijective.dogma.net/
**TO EMAIL ME drop the roman ve **
Disclaimer:I am in no way responsible for any of the
statements
made in the above text. For all I know I might be drugged.
As a famous person once said any cryptograhic
system is only as strong as its weakest link
===
Subject: Re: Surrogate factoring, update
> Theoretical work can be VERY trying to many people. They
want to see
> THE RESULT and have most of the details nailed down and have
> CERTAINTY.
Theory is only as valuable as the mind behind it. We as a
society dont
have the time to determine the value of every utterance every
human has
made.
To throw this back in your face, how many high school
students have you
talked to about analytic number theory to see if they have
the next big
theory. If you answer zero then your name be hypocrite and
your argument
dismissed.
> However, no matter how certain so much knowledge that is
tossed about
> today is today, way back there were people at the beginning
who were
> lost and looking, trying to gure out what was going on.
What ego. What ego you have.
> Everything around you, everything that is prized or feared
goes back
> to some idea that some person was tossing around some time
ago.
And we remember most those willing to back their ideas with
the process of
the scientic process. That is
[http://k12science.ati.stevens-tech.edu/exploration/
collaborative/2.htm]
1. Hypothesis.
2. Experiment.
3. Analyze [observer].
4. Compare observations.
5. Determine conclusion.
Stating hypothesis may be interesting and certainly nobody
wants to
discourage people from coming up with new ideas. At some
point you have
follow through though.
For all intents and purposes you have burned your good will
time and time
again. People are simply not interested in what you have to
hypothesize
about because youre not likely to come up with something of
any value
whatsoever.
> Here and now though, theres this idea Im tossing around,
and its at
> the beginnings.
No it isnt. Youve been talking about this idea long enough
that you
either have to shut your trap or go do some real work [e.g.
implement, try
it out and come up with some conclusions].
> Im not certain, though I denitely think its worth
discussing.
Why? You dont even understand academia or the scientic
process. Youre
just an idiot who has newsgroup access. Whoopy.
> Well thats not science or discovery. Thats about time and
> persistence with the ideas that pass all the tests.
> Most ideas dont pass all the tests.
Thats part of the process though. I can respect someone who
wants to
discuss their failed attempts at something cryptographic [why
they thought
it was a good idea *AND* why it failed]. You have yet to show
any merit in
your approach [e.g. why is it a good idea?] or any analysis
as to whether
its effective or not.
Tom
===
Subject: Re: Surrogate factoring, update
> Theoretical work can be VERY trying to many people. They
want to see
> THE RESULT and have most of the details nailed down and have
> CERTAINTY.
> Theory is only as valuable as the mind behind it. We as a
society dont
> have the time to determine the value of every utterance
every human has
> made.
Im talking about an idea where all the information is
upfront.
You can *choose* to consider it or not.
Mathematicians have a duty to consider it because it impacts
an
important area, and may be important (maybe not).
> To throw this back in your face, how many high school
students have you
> talked to about analytic number theory to see if they have
the next big
> theory. If you answer zero then your name be hypocrite and
your
argument
> dismissed.
I can sense that youre emotionally involved here and might
not
understand whats at stake. IF my idea is viable then you
could be
held personally liable for PUBLIC statements you make trying
to get
that idea dismissed.
That is, someone could sue you if they suffer damages from
someone
else who exploits the idea if mathematicians ignore it, and
you helped
create a hostile environment to the idea.
Now Im sure that youve spent a lot of time on Usenet making
lots of
posts without worry of consequences, but here billions of
dollars US
are potentially involved, and people creating a hostile
environment
may be held liable for their statements.
> However, no matter how certain so much knowledge that is
tossed about
> today is today, way back there were people at the beginning
who were
> lost and looking, trying to gure out what was going on.
>
> What ego. What ego you have.
I merely am reminding that the urge to dismiss new ideas
ignores the
reality that everything we have is built on ideas that were
at one
time new.
Thats not ego, its desperation. Im facing a trying and
difcult
situation where I have to ght to get people to acknowledge
an idea
that MIGHT be both valuable and dangerous.
Im trying to remind people that everything was not always as
it is
today.
You cant just dismiss the new, when its small, as if it
cant
someday become big.
Thats dangerous.
> Everything around you, everything that is prized or feared
goes back
> to some idea that some person was tossing around some time
ago.
> And we remember most those willing to back their ideas with
the process
of
> the scientic process. That is
I have a B.Sc. in physics and prize the scientic method.
>
[http://k12science.ati.stevens-tech.edu/exploration/
collaborative/2.htm]
> 1. Hypothesis.
I hypothesized that the factoring problem might be addressed
by
nding a way to link one factorization to another.
> 2. Experiment.
I proceeded to consider a wide variety of factorizations
without much
success until I found:
(jk - Tk + T)(jk + Tk + T) = T^4
and noted that
k = (-jT +/- T^2 sqrt(j^2 - T^2 + 1))/(j^2 - T^2)
showing that I now had a dependency on the factorization of
T^2 - 1.
Success!!!
> 3. Analyze [observer].
I attempted to factor T using the new information, and found
that it
did work, sometimes.
I found I wasnt sure under what conditions it worked.
I began discussing my ndings with others.
> 4. Compare observations.
Some have talked a bit about various aspects of my idea, but
mostly
there has been silence.
Ive done various experiments of my own, but have felt need
to discuss
my research further, and emphasize the danger if it can be
made
practical.
> 5. Determine conclusion.
I decided I needed help, and needed to discuss what I
currently had,
relying on the curiosity of mathematicians and their supposed
love of
pure math.
However, time keeps going by and despite my clear ability to
lay out
the importance and relevance of my work, I nd myself talking
to
strange people on Usenet who chatter about things they
clearly dont
understand, like the Scientic Method.
> Stating hypothesis may be interesting and certainly nobody
wants to
> discourage people from coming up with new ideas. At some
point you have
> follow through though.
> For all intents and purposes you have burned your good will
time and time
> again. People are simply not interested in what you have to
hypothesize
> about because youre not likely to come up with something
of any value
> whatsoever.
Thats not how science works.
You talk about the Scientic Method and then go on to talk
about
social issues as if scientists are some gaggle of little
girls at a
school.
Scientists care about results, not personalities.
Im tired of facing people who are stuck in high school!!!
Its not a popularity contest. I dont care if youre vying
for
Popular Poster or whatever social driven problem you have.
Im trying to discuss research with serious people, who care
about the
data, and not about whether everybody likes everybody else!
> Here and now though, theres this idea Im tossing around,
and its at
> the beginnings.
> No it isnt. Youve been talking about this idea long
enough that you
> either have to shut your trap or go do some real work [e.g.
implement,
try
> it out and come up with some conclusions].
Ive done whats necessary.
> Im not certain, though I denitely think its worth
discussing.
> Why? You dont even understand academia or the scientic
process.
Youre
> just an idiot who has newsgroup access. Whoopy.
And you are the one calling me an idiot. Do you think youre a
scientist?
What warped view of science do you have?
I have to say Im puzzled by your insistence on science as
some social
game.
What happened to you?
> Well thats not science or discovery. Thats about time and
> persistence with the ideas that pass all the tests.
>
> Most ideas dont pass all the tests.
> Thats part of the process though. I can respect someone
who wants to
> discuss their failed attempts at something cryptographic
[why they
thought
> it was a good idea *AND* why it failed]. You have yet to
show any merit
in
> your approach [e.g. why is it a good idea?] or any analysis
as to whether
> its effective or not.
> Tom
The data is in my posts. It is clear, and it has not been
refuted.
You on the other hand insist on insulting me, continually
invoking
social issues, and then act as if what youre taking about has
anything to do with the science.
It seems to me that Ive attracted a newsgroup parasite with
social
issues related to a projected desire for popularity.
You seem trapped in high school (assuming youre American)
with an
inability to get past your social needs and a desire to try
and in
some way inict your pain upon the world.
But, make no mistake, if this idea is viable then you may be
held
liable for your PUBLIC statements. Creating a hostile
environment
might leave a window for hostile exploitation which could
cause
signicant damages IF this idea is viable.
You have been warned. My suggestion for others is to tread
carefully
here.
The situation is NOT a typical one for Usenet.
Your words may be used against you IF theres anything to
this idea,
and you may face claims for damages for public statements
made.
James Harris
===
Subject: Re: Surrogate factoring, update
says...
> Im facing a trying and difcult
> situation where I have to ght to get people to acknowledge
an idea
> that MIGHT be both valuable and dangerous.
Well, you might consider what normal people do when faced
with a possibly
brilliant discovery that they think has potential value. THEY
BUILD A
PRODUCT AND SELL IT. If it as wonderful as you believe, use
it in a
product, and people will beat a path to your door and youll
be living
on the beach in Tahiti in no time at all.
As far as the dangerous claim, Im sure if the NSA thought
your idea was
worth the cost of the electrons used to transmit your posts,
you would
have had a visit from them by now. If they felt it was so
valuable as
to be dangerous, youd probably be dead. Alas, you are still
alive and
kicking, so it is most likely a better option to go with the
rst route
and start selling a product which uses your discovery. There
is so much
snake oil on the market, Im sure you will have no trouble at
all besting
those products with a quality solution, right?
> However, time keeps going by and despite my clear ability
to lay out
> the importance and relevance of my work, I nd myself
talking to
> strange people on Usenet who chatter about things they
clearly dont
> understand, like the Scientic Method.
Then why do you persist here? Obviously you are in the wrong
place.
You need to be talking to a Venture Capital rm (or 10) until
you
nd one that is interested in taking your idea to the next
step.
> But, make no mistake, if this idea is viable then you may
be held
> liable for your PUBLIC statements. Creating a hostile
environment
> might leave a window for hostile exploitation which could
cause
> signicant damages IF this idea is viable.
This is pure, uneducated legal BS.
You may wish to research New York Times Co. v. Sullivan, and
Gertz v.
Robert Welch, Inc. (among a few others) before asserting such
foolishness further.
In the latter case, Justice Powell made the distinction
between public and
private gures, and justied their different treatment in
libel law.
The denition of a public gure:
In some instances an individual may achieve such pervasive
fame or
notoriety
that he becomes a public gure for all purposes and in all
contexts. More
commonly, an individual voluntarily injects himself or is
drawn into a
particular public controversy and thereby becomes a public
gure for a
limited
range of issues. In either case such person assume special
prominence in the
resolution of public questions.
You have clearly injected yourself in just such a fashion in
sci.crypt and
sci.math and thereby removed yourself from any libel claims
involving those
topic, or any topic you raised in such public forums.
The rst remedy of an actual victim of defamation is
self-help -- using
available opportunities to contradict the perceived error and
thereby
minimizing its adverse impact on their reputation.
Public ofcials and gures usually enjoy signicantly greater
access to
the channels of effective communication and hence have a more
realistic
opportunity to counteract false statements than private
individuals normally
have enjoyed in the past. In the case of Usenet and the web
as a whole, you
have full access to the exact same communication as all other
participants,
so there is clearly no need for protection in such cases.
The obvious open access to the Net means that people who feel
they have had
lines of false statements, you have the absolute right to
publish 200 lines
of
refutation, or any other content that you think ameliorates
the problem.
Libel
laws are to protect those that do not have access to means of
protecting
themselves.
Apart from any demonstrated inability to formulate coherent
arguments, its
impossible to argue you have not been given every opportunity
to refute any
and all claims against you.
But, if you insist upon wasting your money, proceed. Starving
lawyers all
over
the world need more money. I am quite condent that you have
never spoken
to
an attorney about this, or you would have been told almost
the exact same
thing.
> You have been warned. My suggestion for others is to tread
carefully
> here.
You need to seek legal counsel before making any further
vacuous threats.
> Your words may be used against you IF theres anything to
this idea,
> and you may face claims for damages for public statements
made.
Good luck.
Randy Howard
To reply, remove FOOBAR.
===
Subject: Re: Surrogate factoring, update
> says...
> Im facing a trying and difcult
> situation where I have to ght to get people to acknowledge
an idea
> that MIGHT be both valuable and dangerous.
> Well, you might consider what normal people do when faced
with a possibly
> brilliant discovery that they think has potential value.
THEY BUILD A
> PRODUCT AND SELL IT. If it as wonderful as you believe, use
it in a
> product, and people will beat a path to your door and
youll be living
> on the beach in Tahiti in no time at all.
Thats the fantasy. The reality is more complex.
What Im doing is talking about an idea which *might* have
major
impact.
I think I can make the case for why the idea needs to be
evaluated.
I note that those who think that they can simply attack ideas
without
consequences could be held liable *IF* the idea turns out to
be
viable, and someone out there uses it to do harm.
> As far as the dangerous claim, Im sure if the NSA thought
your idea was
> worth the cost of the electrons used to transmit your
posts, you would
> have had a visit from them by now. If they felt it was so
valuable as
> to be dangerous, youd probably be dead. Alas, you are
still alive and
> kicking, so it is most likely a better option to go with
the rst route
> and start selling a product which uses your discovery.
There is so much
> snake oil on the market, Im sure you will have no trouble
at all besting
> those products with a quality solution, right?
I contacted the NSA. I didnt hear back from them. If that
sounds
crazy, ok, but I hope you understand that its really about
the
seriousness of the situation as I see it.
Working products are great, yes, but sometimes an idea can be
important even if the person who came up with the idea
doesnt manage
to produce a working product.
Thats because someone else MIGHT produce a working product.
I repeat that I already contacted the NSA. They didnt reply.
> However, time keeps going by and despite my clear ability
to lay out
> the importance and relevance of my work, I nd myself
talking to
> strange people on Usenet who chatter about things they
clearly dont
> understand, like the Scientic Method.
> Then why do you persist here? Obviously you are in the
wrong place.
> You need to be talking to a Venture Capital rm (or 10)
until you
> nd one that is interested in taking your idea to the next
step.
I think youre in a fantasy world.
Im talking about *basic* research with an idea that might
have an
impact in an important area, where it might not, and would
just
qualify as pure math, which some might argue isnt of much
interest.
Research is something that most of you probably just hear
about, but
dont understand what it actually is.
It can be grasping about with an idea where you dont know if
it will
lead to anything, so you talk to others.
Im not a professional mathematician so my options are
limited.
Usenet is a public forum and sci.crypt and sci.math are
supposedly
places where people discuss ideas related to cryptology and
mathematics respectively.
My idea is a mathematical idea related to cryptology (though
not to my
knowledge proven practical as of yet).
> But, make no mistake, if this idea is viable then you may
be held
> liable for your PUBLIC statements. Creating a hostile
environment
> might leave a window for hostile exploitation which could
cause
> signicant damages IF this idea is viable.
> This is pure, uneducated legal BS.
No, it is not.
> You may wish to research New York Times Co. v. Sullivan,
and Gertz v.
> Robert Welch, Inc. (among a few others) before asserting
such
> foolishness further.
> In the latter case, Justice Powell made the distinction
between public and
> private gures, and justied their different treatment in
libel law.
> The denition of a public gure:
> In some instances an individual may achieve such pervasive
fame or
notoriety
> that he becomes a public gure for all purposes and in all
contexts. More
> commonly, an individual voluntarily injects himself or is
drawn into a
> particular public controversy and thereby becomes a public
gure for a
limited
> range of issues. In either case such person assume special
prominence in
the
> resolution of public questions.
> You have clearly injected yourself in just such a fashion
in sci.crypt
and
> sci.math and thereby removed yourself from any libel claims
involving
those
> topic, or any topic you raised in such public forums.
I wouldnt charge libel.
The issue has to do with losses incurred by a person who, for
instance, might lose their business as a result of hackers
capable of
penetrating RSA using methods derived from this idea.
That business could ask if anyone knew that hacker might have
such a
capability.
If it came out that sci.crypt and sci.math posters had
claimed the
idea was not viable in posts and helped to create a hostile
environment to that idea, then posters making such PUBLIC
statements
might be held liable for damages by that business.
That is, you have a responsibility with your speech.
If someone gets harmed by wild hackers roaming freely over the
Internet breaking through RSA encryption because they do the
research
and gure out a way to make this idea work, then people can
come back
to those who attacked the idea publicly and make them pay.
> The rst remedy of an actual victim of defamation is
self-help -- using
> available opportunities to contradict the perceived error
and thereby
> minimizing its adverse impact on their reputation.
> Public ofcials and gures usually enjoy signicantly
greater access to
> the channels of effective communication and hence have a
more realistic
> opportunity to counteract false statements than private
individuals
normally
> have enjoyed in the past. In the case of Usenet and the web
as a whole,
you
> have full access to the exact same communication as all
other
participants,
> so there is clearly no need for protection in such cases.
> The obvious open access to the Net means that people who
feel they have
had
> lines of false statements, you have the absolute right to
publish 200
lines of
> refutation, or any other content that you think ameliorates
the problem.
Libel
> laws are to protect those that do not have access to means
of protecting
> themselves.
> Apart from any demonstrated inability to formulate coherent
arguments,
its
> impossible to argue you have not been given every
opportunity to refute
any
> and all claims against you.
> But, if you insist upon wasting your money, proceed.
Starving lawyers all
over
> the world need more money. I am quite condent that you
have never
spoken to
> an attorney about this, or you would have been told almost
the exact same
> thing.
My position is that mathematicians would be interested in any
simple
idea that turns out to be effective. If my idea turns out to
be
effective then people can *reasonably* conclude that
mathematicians
willfully were negligent in ignoring it, or they are frauds
in terms
of their actual interest in mathematics, versus their claims
and area
of supposed expertise.
Either way they can be made to pay.
> You have been warned. My suggestion for others is to tread
carefully
> here.
> You need to seek legal counsel before making any further
vacuous threats.
Im not threatening legal action.
But I am pointing out that the world may come knocking later
asking
hard questions IF it turns out theres anything to this idea.
> Your words may be used against you IF theres anything to
this idea,
> and you may face claims for damages for public statements
made.
> Good luck.
I wont need luck. I dont plan on making any such claims.
But Ill give you an example to help you see what I mean.
Lets say that a company learns that a toxic waste is being
dumped
into a municipal water supply, and that it would likely lead
to brain
damage for the children of the city.
Lets also say that this company is a leading expert in the
area of
water supplies and protecting them from harm, but for some
reason they
choose NOT to report that theres this issue with the toxic
waste.
Later when children start dying, people research and nd that
this
company knew of the waste but chose not to tell anyone or do
anything
at all.
The company is held liable for damages.
Mathematicians in this area can be held liable for damages
incurred by
ignoring a simple and viable idea if others, trusting people
without
the ability to protect themselves who *depend* on
mathematicians who
are supposed to be experts to protect them, are harmed.
The issue is whether or not the idea is viable.
Im not saying I have the capability to evaluate this idea,
but it
does scare me enough to point out that if it does work or can
be made
to work then people can come back later, if there are
damages, and
point ngers at mathematicians, and make them pay.
James Harris
===
Subject: Re: Surrogate factoring, update
days. My association with the Department is that of an
alumnus.
[.nit picking on a legal observation.]
>You may wish to research New York Times Co. v. Sullivan, and
Gertz v.
>Robert Welch, Inc. (among a few others) before asserting such
>foolishness further.
>In the latter case, Justice Powell made the distinction
between public and
>private gures, and justied their different treatment in
libel law.
>The denition of a public gure:
>In some instances an individual may achieve such pervasive
fame or
notoriety
>that he becomes a public gure for all purposes and in all
contexts. More
>commonly, an individual voluntarily injects himself or is
drawn into a
>particular public controversy and thereby becomes a public
gure for a
limited
>range of issues. In either case such person assume special
prominence in
the
>resolution of public questions.
>You have clearly injected yourself in just such a fashion in
sci.crypt and
>sci.math and thereby removed yourself from any libel claims
involving
those
>topic, or any topic you raised in such public forums.
I dont think this is entirely accurate: the removed yourself
from
any libel claims, that is.
If I recall NY Times v. Sullivan correctly, the situation
with public
gures is that they must meet a considerably stricter burden
of proof
in libel and slander cases, not that they are incapable of
pursuing
such claims. A public gure must prove actual malice, if I
recall
the legal phrase correctly, as part of his or her prima facie
case. A
private gure meets only a much lower threshold.
Its not denial. Im just very selective about
what I accept as reality.
--- Calvin (Calvin and Hobbes)
Arturo Magidin
magidin@math.berkeley.edu
===
Subject: Re: Surrogate factoring, update
>> Theoretical work can be VERY trying to many people. They
want to see
>> THE RESULT and have most of the details nailed down and
have
>> CERTAINTY.
>> Theory is only as valuable as the mind behind it. We as a
society dont
>> have the time to determine the value of every utterance
every human has
>> made.
> Im talking about an idea where all the information is
upfront.
What information though? Equation after equation without
reason is not
information its noise.
> You can *choose* to consider it or not.
Yeah and I *choose* to reply. You can choose not to post it
as well btw.
> Mathematicians have a duty to consider it because it
impacts an
> important area, and may be important (maybe not).
What would you know of duty?
>> To throw this back in your face, how many high school
students have you
>> talked to about analytic number theory to see if they have
the next
big
>> theory. If you answer zero then your name be hypocrite and
your
>> argument dismissed.
> I can sense that youre emotionally involved here and might
not
> understand whats at stake. IF my idea is viable then you
could be
> held personally liable for PUBLIC statements you make
trying to get
> that idea dismissed.
Im not dismissing your ideas so much as Im trying to
dismiss you. Youre
a hypocrite and a waste of time. The only reason Im replying
is because
its sunday and Im taking a break from coding.
> That is, someone could sue you if they suffer damages from
someone
> else who exploits the idea if mathematicians ignore it, and
you helped
> create a hostile environment to the idea.
Um? I dont think so tim. First off, Im Canadian not
American so good
luck trying to sue me. Second, Im not responsible for the
fact that other
people may use RSA [an algorithm invented roughly 5 years
before I was even
born!!!]. People use RSA because they want to. Not because I
think youre
a troll.
> Now Im sure that youve spent a lot of time on Usenet
making lots of
> posts without worry of consequences, but here billions of
dollars US
> are potentially involved, and people creating a hostile
environment
> may be held liable for their statements.
Quite the ego you have. Think your invention is so great?
Prove it.
Either with real math that others can back up or with
practical
implementations.
Your ideas are plain useless. Not because theyre new but
because the
person sponsoring the ideas [namely that would be you] is not
willing to
invest the time and effort into growing the idea into a real
set of theory
that can come to logical conclusions.
Does your idea work? Heck you dont even know. Why does(nt)
it work? Do
you know?
>> However, no matter how certain so much knowledge that is
tossed about
>> today is today, way back there were people at the
beginning who were
>> lost and looking, trying to gure out what was going on.
>>
>> What ego. What ego you have.
> I merely am reminding that the urge to dismiss new ideas
ignores the
> reality that everything we have is built on ideas that were
at one
> time new.
Get it through your thick skull that were not dismissing new
ideas here.
Were dismissing you specically.
I dont remember speaking out about AKS when that was
proposed. That work
[by smart but unheard of people in the eld] was well
accepted and adopted
into academia.
Why?
their invention and drew logical conclusions. They
*contributed* a real
body of work to the eld.
While you on the other hand have yet to contribute anything
other than
noise. Your idea may work, it may work well, but until you
can actually
present your ideas properly nobody will care.
> Im trying to remind people that everything was not always
as it is
> today.
Sadly, people like you are not new.
> You cant just dismiss the new, when its small, as if it
cant
> someday become big.
Not likely. I dont recall seeing your name alongside those
that have
solved the FLT. Whatever happened to that? Got bored? Come
on, where is
your strict scientic principles there? Prove the FLT damn it!
>> Everything around you, everything that is prized or feared
goes back
>> to some idea that some person was tossing around some time
ago.
>> And we remember most those willing to back their ideas
with the process
>> of
>> the scientic process. That is
> I have a B.Sc. in physics and prize the scientic method.
You certainly dont act like it.
>> 1. Hypothesis.
> I hypothesized that the factoring problem might be
addressed by
> nding a way to link one factorization to another.
That wouldnt pass as a grade 9 hypothesis where I came from.
Its not
specic enough. What specically were you intending to test?
[e.g. this
would be part of why you picked those equations, not what
equations but
why]
>> 2. Experiment.
> I proceeded to consider a wide variety of factorizations
without much
> success until I found:
> (jk - Tk + T)(jk + Tk + T) = T^4
> and noted that
> k = (-jT +/- T^2 sqrt(j^2 - T^2 + 1))/(j^2 - T^2)
> showing that I now had a dependency on the factorization of
T^2 - 1.
> Success!!!
Again, this would get a mark of 0. Why did you pick those
equations? What
is T?
What is the full complete closed system algorithm that uses
these equations?
Experiment would also mean TRY your algorithm [which you have
yet to
present
btw] out and see if it works as expected.
>> 3. Analyze [observer].
> I attempted to factor T using the new information, and
found that it
> did work, sometimes.
That would be an experiment. Analyze/observations would be ok
we did
this
test, we got X results. It would be where you organize your
results,
classify them, etc.
> I found I wasnt sure under what conditions it worked.
That would be in your conclusion.
> I began discussing my ndings with others.
Again Conclusions...
>> 4. Compare observations.
> Some have talked a bit about various aspects of my idea,
but mostly
> there has been silence.
No, Compare your observations against your hypothesis. E.g. I
thought
that,
I observed this. This is the section where you discuss what
work you did
vs. the hypothesis you drew.
E.g. I thought these forms of equations would result in
easier factoring, I
observed that X/10 cases it didnt. ... [why it didnt work].
And you prize the scientic process? You dont even know what
it
is!!!
> Ive done various experiments of my own, but have felt need
to discuss
> my research further, and emphasize the danger if it can be
made
> practical.
Why? What danger? GNFS is most certainly faster. But more
importantly
you
say your idea has importance but cant back it up [e.g.
asymtotic running
times].
>> 5. Determine conclusion.
> I decided I needed help, and needed to discuss what I
currently had,
> relying on the curiosity of mathematicians and their
supposed love of
> pure math.
0 marks. Conclusion would be draw a conclusion [it works,
doesnt work],
etc, etc, etc...
Your love for pure math aside, if you cant follow the simple
scientic
process how and why should anyone take you seriously? Youre
not deserving
of worthy attention.
Though you should note that this isnt the rst thread about
your idea.
This is likely the fourth or fth. Each time you start by
posting random
equations and demanding to know why it doesnt work [or why
nobody cares].
Well nobody cares because youre an ignorant arrogant little
prick with
usenet access.
> However, time keeps going by and despite my clear ability
to lay out
> the importance and relevance of my work, I nd myself
talking to
> strange people on Usenet who chatter about things they
clearly dont
> understand, like the Scientic Method.
Thats kinda funny given that you dont know what it is
yourself. This
post
Im replying to is a good example of your ignorance.
>> Stating hypothesis may be interesting and certainly nobody
wants to
>> discourage people from coming up with new ideas. At some
point you have
>> follow through though.
>> For all intents and purposes you have burned your good
will time and
time
>> again. People are simply not interested in what you have
to hypothesize
>> about because youre not likely to come up with something
of any value
>> whatsoever.
> Thats not how science works.
Sadly thats how people work. People will pay attention to
you when they
*want* to. Not when you want them to.
Make people want to pay attention by playing the game.
> You talk about the Scientic Method and then go on to talk
about
> social issues as if scientists are some gaggle of little
girls at a
> school.
For someone who whines about getting no attention at all
maybe you should
care as to why they dont pay attention.
> Scientists care about results, not personalities.
WHAT RESULTS!???!???!?!?!!?
EQUATIONS ARE NOT RESULTS!
> Im tired of facing people who are stuck in high school!!!
I graduated from high school. On my rst try. Which is
probably more
than
I could say of you.
I mean seriously, with comments like yours it would be a
wonder to see if
you actually nished high school on your own without cheating
or bribing
the teachers.
I know when I was in high school science I could write things
like
I hypothesis plants like light.
Or
I hypothesis there are ways to determine the wavelength of
certain
chlorophyll.
We had to be very specic as to what we were thinking. When
we conducted
an experiment we had to detail the process we took. Not just
I put
plants
in bezene. When we observed we had to make charts, graphs,
tables, etc.
We had to organize our observations carefully to get all the
data in the
right places. When we analyzed we had to make very strick
points based on
our observations, etc, etc, etc...
It would be nothing to hand in a 10-15 page writeup once
every 1-2 weeks.
Granted this was at the high school level but still we had to
actually
follow the process and do proper work.
you pass college labs at all?
> Its not a popularity contest. I dont care if youre vying
for
> Popular Poster or whatever social driven problem you have.
I just like pointing out what failure you are. Its fun.
> Im trying to discuss research with serious people, who
care about the
> data, and not about whether everybody likes everybody else!
WHAT DATA????
t^4 = jk-mt+4
OMG Im totally 1337 mafmatician! ROFL LMAO!!!!!!!!!
>> No it isnt. Youve been talking about this idea long
enough that you
>> either have to shut your trap or go do some real work
[e.g. implement,
>> try it out and come up with some conclusions].
> Ive done whats necessary.
Which would be?
>> Im not certain, though I denitely think its worth
discussing.
>> Why? You dont even understand academia or the scientic
process.
>> Youre
>> just an idiot who has newsgroup access. Whoopy.
> And you are the one calling me an idiot. Do you think
youre a
> scientist?
I dont kid myself like you do. Ive made contributions but I
dont think
Im the be-all of the world. I mean you dont see me going
around
PAY ATTENTION TO MY CS^2 PAPER!!! DO IT!!WHY ARENT YOU ALL
READING MY CS^2
PAPER??? READ IT!!!!
No, I posted about it once [or a few times, I dont recall]
and I let it go.
Done with. Over. Finished. Kaput. No more.
> What warped view of science do you have?
The one donated to me by the tax payers of Canada.
> I have to say Im puzzled by your insistence on science as
some social
> game.
What social game? All I ask is that you follow the scientic
process.
Thats not social thats logical.
> The data is in my posts. It is clear, and it has not been
refuted.
Um, Id think the repliers to your earlier threads would beg
to differ.
Specially Martin Marcel has words with you.
> It seems to me that Ive attracted a newsgroup parasite
with social
> issues related to a projected desire for popularity.
No, when I want attention I write software that people use.
Oops..Lets
not
get started there...
> You seem trapped in high school (assuming youre American)
with an
> inability to get past your social needs and a desire to try
and in
> some way inict your pain upon the world.
Ok that just goes to show your researching abilities. Im
Canadian, Ive
mentioned that many times in this group, I put my home
address in various
public places too [my cv, LTC user manual, etc...].
> But, make no mistake, if this idea is viable then you may
be held
> liable for your PUBLIC statements. Creating a hostile
environment
> might leave a window for hostile exploitation which could
cause
> signicant damages IF this idea is viable.
Um, youre no scientist dont play lawyer either.
> You have been warned. My suggestion for others is to tread
carefully
> here.
My suggestion is that you should stop trolling sci.*
newsgroups.
> Your words may be used against you IF theres anything to
this idea,
> and you may face claims for damages for public statements
made.
You know what, go ahead and try to sue me. Put your character
where your
invite you to come up to Canada and sue me.
Tom
===
Subject: Re: Surrogate factoring, update
>> Theoretical work can be VERY trying to many people. They
want to
see
>> THE RESULT and have most of the details nailed down and
have
>> CERTAINTY.
>>
>> Theory is only as valuable as the mind behind it. We as a
society
dont
>> have the time to determine the value of every utterance
every human
has
>> made.
>
> Im talking about an idea where all the information is
upfront.
> What information though? Equation after equation without
reason is not
> information its noise.
> You can *choose* to consider it or not.
> Yeah and I *choose* to reply. You can choose not to post it
as well btw.
> Mathematicians have a duty to consider it because it
impacts an
> important area, and may be important (maybe not).
> What would you know of duty?
You keep making this personal. Im not interested in personal
discussions.
Now you can keep replying and trying to goad me into some
emotional
response, but Im not interested in playing social games.
What I have at this point are several equations:
(jk - Tk + T)(jk + Tk + T) = T^4
k = (-jT +/- T^2 sqrt(j^2 - T^2 + 1))/(j^2 - T^2)
and
j = (-T +/- T sqrt(k^2 + T^2))/k
where signicantly, while j shows a dependency on factors of
T^2 when
it is solved for.
But k shows a dependency on the factors of T^2 - 1.
Those are the facts. At this point no one has shown why
mathematically theres a reason that you cant non-trivially
factor
T^2 by using the factors of T^2-1, which is potentially a big
deal.
If this method is practical or can be made to be practical
then it
could impact public key encryption.
If mathematicians ignore such an idea, then I wonder what in
the world
mathematical actually interests them, when its so
fascinating that
one factorization can be so related to another, and the
social issues
are more of a side thing, but theyre also scary.
If mathematicians do NOT behave as expected here, with
interesting
mathematics, and this idea is more than pure math, then world
society may pay the price.
I think that would be a betrayal of the world by the math
community.
James Harris
===
Subject: Re: Surrogate factoring, update
>> What would you know of duty?
> You keep making this personal. Im not interested in
personal
> discussions.
Um because Im trying to tell you to grow up. Id expect that
to be
personal.
> Now you can keep replying and trying to goad me into some
emotional
> response, but Im not interested in playing social games.
good. How about play some scientic ones then?
I dont care about your equations. Present them properly and
then, maybe,
Ill look at them. What about this dont you get?
Why are you so adverse to doing some actualy work? What you
think Fermat,
Euclid, etc are well known because they simply said
HEY LOOK I HAVE AN IDEA!!!
No they did years upon years of hard laborous study where
they invented new
theory and presented it as best they could to their peers.
Christ almighty
youd think someone who protests to be so so smart would
gure this
out.
So you have an idea, great, Im happy for ya. Now do some
work.
Tom
===
Subject: Re: Surrogate factoring, update
>> [...]
>I can sense that youre emotionally involved here and might
not
>understand whats at stake. IF my idea is viable then you
could be
>held personally liable for PUBLIC statements you make trying
to get
>that idea dismissed.
Sounding like a lunatic again, James. Better you should stick
to purely mathematical comments - then you just sound stupid
and ignorant.
>That is, someone could sue you if they suffer damages from
someone
>else who exploits the idea if mathematicians ignore it, and
you helped
>create a hostile environment to the idea.
>Now Im sure that youve spent a lot of time on Usenet
making lots of
>posts without worry of consequences, but here billions of
dollars US
>are potentially involved, and people creating a hostile
environment
>may be held liable for their statements.
For years and years youve been talking about the danger that
people who oppose your work are in. Have you ever got around
to actually talking to a lawyer about any of this?
>[...]
>The data is in my posts. It is clear, and it has not been
refuted.
Perhaps not, but it appears to a casual observer like me that
the
idea that theres anything new about it has been refuted
pretty
well.
You should actually study some math someday. Then youd have
a better chance of actually doing something new. If youre
unaware of the things that have been done in the last few
centuries youre going to tend to reproduce them, leading
to yawns from the audience.
>You on the other hand insist on insulting me, continually
invoking
>social issues, and then act as if what youre taking about
has
>anything to do with the science.
>It seems to me that Ive attracted a newsgroup parasite with
social
>issues related to a projected desire for popularity.
>You seem trapped in high school (assuming youre American)
with an
>inability to get past your social needs and a desire to try
and in
>some way inict your pain upon the world.
>But, make no mistake, if this idea is viable then you may be
held
>liable for your PUBLIC statements. Creating a hostile
environment
>might leave a window for hostile exploitation which could
cause
>signicant damages IF this idea is viable.
>You have been warned. My suggestion for others is to tread
carefully
>here.
These continual warnings really _do_ make you sound extremely
wacky. Honest, they do.
>The situation is NOT a typical one for Usenet.
No? Seems quite typical to me.
>Your words may be used against you IF theres anything to
this idea,
>and you may face claims for damages for public statements
made.
Ah. He may face _claims_ for damages. Thats different. I
agree
that he could face such _claims_. I really really wish youd
get
around to actually making such claims in court some time - it
would be fun to read about.
>James Harris
************************
David C. Ullrich
===
Subject: Re: Surrogate factoring, update
Discussion, linux)
>>Now Im sure that youve spent a lot of time on Usenet
making lots of
>>posts without worry of consequences, but here billions of
dollars US
>>are potentially involved, and people creating a hostile
environment
>>may be held liable for their statements.
> For years and years youve been talking about the danger
that
> people who oppose your work are in. Have you ever got around
> to actually talking to a lawyer about any of this?
[...]
>>Your words may be used against you IF theres anything to
this idea,
>>and you may face claims for damages for public statements
made.
> Ah. He may face _claims_ for damages. Thats different. I
agree
> that he could face such _claims_. I really really wish
youd get
> around to actually making such claims in court some time -
it
> would be fun to read about.
I think youve mis-read him. Now hes not threatening to sue
people.
Hes considering the following:
(1) His method leads to a defeat of RSA encryption;
(2) But the good guys ignore it because Tom made a Usenet
post saying
the method sucks;
(3) So the bad guys break the scheme, empty every bank and
enslave
children;
(4) In this case, a plaintiff sues Tom for billions of dollars
damages. Poor Tom.
Whole different story than the old one in which James sues
mathematicians for failing to give him his due.
Jesse F. Hughes
What I represent is the unknowable future--the power of
change. In
that sense Im a force of Nature, a force of the Universe, a
living
emodiment of change itself. --James Harris and his sense of
humility
===
Subject: Re: Surrogate factoring, update
>Now Im sure that youve spent a lot of time on Usenet
making lots of
>posts without worry of consequences, but here billions of
dollars US
>are potentially involved, and people creating a hostile
environment
>may be held liable for their statements.
>> For years and years youve been talking about the danger
that
>> people who oppose your work are in. Have you ever got
around
>> to actually talking to a lawyer about any of this?
>[...]
>Your words may be used against you IF theres anything to
this idea,
>and you may face claims for damages for public statements
made.
>> Ah. He may face _claims_ for damages. Thats different. I
agree
>> that he could face such _claims_. I really really wish
youd get
>> around to actually making such claims in court some time -
it
>> would be fun to read about.
>I think youve mis-read him. Now hes not threatening to sue
people.
>Hes considering the following:
>(1) His method leads to a defeat of RSA encryption;
>(2) But the good guys ignore it because Tom made a Usenet
post saying
>the method sucks;
>(3) So the bad guys break the scheme, empty every bank and
enslave
>children;
>(4) In this case, a plaintiff sues Tom for billions of
dollars
>damages. Poor Tom.
>Whole different story than the old one in which James sues
>mathematicians for failing to give him his due.
Hmm, you may be right. I guess wed better tread carefully
here...
I know, no matter what stupid thing anyone says we all rise
and say with one voice that hes right. That should keep us
pretty safe.
************************
David C. Ullrich
===
Subject: Re: Surrogate factoring, update
===
>Subject: Re: Surrogate factoring, update
>> Its been a while since I mentioned surrogate factoring,
and Ill
>>
>> Maybe you should put your method to the test? Let your PC
make a huge
>> composite of two primes (something in the magnitude used
for RSA), and
>> challenge yourself to factor it, without looking at the
answer. If your
>> method is too slow to do by hand, then try to make a
program to do it
>> for you. I guess as soon as you come with real proof,
people might even
>> start listening to you. Im no mathematician, so Im in no
position to
>> judge your method. The way to prove it to someone like me
would be to
>> actually break RSA. Im sure you would gain everybodys
respect if you
>> would do it. So? Do it.
>> Matthijs.
>Theoretical work can be VERY trying to many people.
>They want to see THE RESULT and have most of the
>details nailed down and have CERTAINTY.
>However,
In other words, you cant.
>James Harris
Mensanator
Ace of Clubs
===
Subject: Lorentz group - Wikipedia--> special attention to
Robin Chapman
The covering spin group
Like the rotation group SO(3), the restricted Lorentz group
is not
simply connected; rather, it is doubly connected. That is, the
fundamental group
of
SO+(1, 3) is isomorphic
to Z2
.
The universal cover
of
the restricted Lorentz group can be identied with the
special linear
group
SL(2, C). The
restricted Lorentz group is isomorphic to the quotient group
SL(2, C)/{1}
also
known
as the projective linear group
,
PSL(2, C). This
group shows up in another guise as the group of all M.9abius
transformations
of the Riemann sphere
.
In applications to quantum mechanics
the group
SL(2, C) is
sometimes called the Lorentz group.
http://en.wikipedia.org/wiki/Lorentz_group
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca
92040-2905,tel:
619-5610814 :
URL : http://home.earthlink.net/~tftn
URL : http://victorian.fortunecity.com/carmelita/435/
===
Subject: Re: question about Lorentz transformations and the
SU(2) group
The universal covering group of SO(3,1)^uparrow (where the
uparrow
stands for the orthochronous part of the group, i.e., the
part of the
Lorentz group, which is continously connected to the identity
element)
is SL(2,C), i.e., the special linear group, operating on the
2-dim.
complex vector space.
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca
92040-2905,tel:
619-5610814 :
URL : http://home.earthlink.net/~tftn
URL : http://victorian.fortunecity.com/carmelita/435/
===
Subject: OP1 and Lorentzian Geometry
As emphasized by Penrose, this space has a fascinating
connection to
Lorentzian geometry -- or in other words, special relativity.
All
conformal transformations of the Riemann sphere come from
fractional
linear transformations It is easy to see that the group of
such
transformations is isomorphic to PSL(2,C):
http://math.ucr.edu/home/baez/Octonions/node11.html
===
Subject: Enneper Cousins--> Loerntz group L^4 immersion in
SL(2,C) to
give
H^3--> R^3 minimal surfaces
boundary=------------040505030306040201070807
-------------------------------------------------------------
--------
Mean Curvature 1 Enneper Cousins and their Duals in Hyperbolic
3-Space EG-Models Home
image ennepercousin_Preview.gif
image ennepercousindual_Preview.gif
Electronic Geometry Model No. 2001.01.049
Authors
Wayne Rossman, Masaaki Umehara, and Kotaro Yamada
Description
We show a mean curvature 1 Enneper cousin in hyperbolic
3-space.
(Hyperbolic 3-space is shown here using the Poincare model.)
This
surface is isometric to the minimal Enneper surface in
Euclidean
3-space. The second surface we show is the dual surface to
the Enneper
cousin shown here. Only one of four congruent pieces, with
the end cut
away, of each surface is shown.
Robert Bryant, in [1], found a representation for mean
curvature 1
surfaces in hyperbolic 3-space. This representation is
similar to the
Weierstrass representation for minimal surfaces in Euclidean
3-space, in
that it also produces surfaces from a meromorphic function
and a
holomorphic 1-form on a Riemann surface.
Using this representation, Bryant explicitly described the
Enneper
cousins, and there is a one parameter family of these
surfaces,
depending on a positive real parameter mu (see Bryants
work). The value
of mu chosen for the surface here is mu=1.4.
The hyperbolic Gauss map (described in [1] and [2]) of the
Enneper
cousin has an essential singularity at the end. Since the
hyperbolic
Gauss map is the map which takes each point on the surface to
the
asymptotic class of the normal geodesic starting at that
point and
oriented in the mean curvature vectors direction, this
essential
singularity is reected in the fact that the end wraps around
innitely many times as it approaches the sphere at innity.
The dual of a surface with lift F (as in [1]) is the surface
whose lift
is the inverse of F. Note that the dual of the Enneper cousin
has a
periodic series of bulges moving out toward the end of the
surface. The
end in this picture approaches the south pole in the sphere
at innity.
More detailed information about these surfaces can be found
in the LaTeX
and postscript and pdf and Mathematica les included in this
model.
(One of the included Mathematica les is a program for
drawing general
mean curvature 1 surfaces in hyperbolic 3-space, based on
general
Weierstrass data. Also included is a jvx le marking the
boundary of
the Poincare model for the hyperbolic 3-space.)
Model produced with: JavaView v.2.00.a2
Keywords
constant mean curvature surface; minimal surface; Ennepers
surface;
hyperbolic 3-space
MSC-2000 Classication
53A10 (53A35,53A42)
References
1. Robert Bryant: Surfaces of mean curvature one in
hyperbolic space,
Asterisque 154-155 (1987), 321--347.
2. Masaaki Umehara and Kotaro Yamada: Complete surfaces of
constant
mean curvature-1 in the hyperbolic 3-space, Annals of
Mathematics
137 (1993), 611--638.
3. Masaaki Umehara and Kotaro Yamada: A duality on CMC 1
surfaces in
hyperbolic 3-space and a hyperbolic analogue of the Osserman
Inequality, Tsukuba Journal of Mathematics 21 (1997),
229--237.
4. Z. Yu: The inverse surface and the Osserman Inequality,
Tsukuba
Journal of Mathematics 22 (1998), 575--588.
Files
* Master File: ennepercousin_Master.jvx
* Master File: ennepercousindual_Master.jvx
* Applet File: ennepercousin_Applet.jvx
* Applet File: ennepercousindual_Applet.jvx
* Preview: ennepercousin_Preview.gif
* Preview: ennepercousindual_Preview.gif
* Other: ennepercousins.nb
* Other: CMC1surfaces.nb
* Other: CMC1surfaces.tex
* Other: CMC1surfaces.ps
* Other: CMC1surfaces.pdf
* Other: boundary.jvx
Submission information
Submitted: Tue Jan 23 17:56:59 CET 2001.
Revised: Tue Feb 12 09:25:29 CET 2002.
Accepted: Wed Feb 20 12:44:06 CET 2002.
Authors Addresses
Wayne Rossman
Kobe University
Mathematics Department
Faculty of Science
Rokko, Kobe 657-8501
Japan
wayne@math.kobe-u.ac.jp
http://www.math.kobe-u.ac.jp/HOME/wayne/wayne.html
Masaaki Umehara
Hiroshima University
Mathematics Department
Faculty of Science
Higashi-Hiroshima 739-8526
Japan
umehara@math.sci.hiroshima-u.ac.jp
http://www.math.sci.hiroshima-u.ac.jp/~umehara/
Kotaro Yamada
Kyushu University 36, 6-10-1
Faculty of Mathematics
Hakozaki, Higashi-ku, Fukuoka 812-8185
Japan
kotaro@math.kyushu-u.ac.jp
http://www.math.kyushu-u.ac.jp/kotaro/
http://www-sfb288.math.tu-berlin.de/eg-models/models/Surfaces
/Mean_Curvature
_Surfaces/2001.01.049/_preview.html
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca
92040-2905,tel:
619-5610814 :
URL : http://home.earthlink.net/~tftn
URL : http://victorian.fortunecity.com/carmelita/435/
--------------040505030306040201070807--
===
Subject: Re: Classical, theoretical physics
> Galileo discovered - with the crude methods available to
him at the
> time - that the rate of free fall starting from rest, was
16 per
> second, and _changed_: Increasing at a _constant rate_ of
16 per
> second each consecutive second that it continued: This
constant rate
> of change in the rate of free fall can be written in the
language of
> mathematics; as (16/sec)/(1 second) = 16/sec^2, and is a
constant;
> which is only one half [g/2] of Newtons acceleration of
free fall [g
> = (vt-vi)/t = 2s/t^2 = 32/sec^2].
Now tell me; shock me; how can anybody refute Galileos
empirically
> found Constant rate of free fall? Other than improving its
accuracy
> with todays methodology.
>
> I think many of us here are rather more familiar than you
with the
> language of mathematics.
> Dont you wish.
> We know the equations to use when we wish to
> calculate how long an object will take to fall a given
distance, and we
> know the constants to plug in so that our answers are in
full agreement
> with reality. Many of us have actually done the sodding
experiment.
>
> Congratulations: Did you learn anything?
> So, Shead, tell us how far an object falls (on Earth,
neglecting air
> resistance, initial velocity 0) in 5 seconds. You may
assume a constant
> value (of your choice!) for g.
> Ill get back to you on that; but one thing is for sure:
There is no
> choice of g. It is what it is, wherever you are.
Okay; getting back to that big problem you gave me about how
far an
object falls (on Earth, neglecting air resistance, initial
velocity 0)
in 5 seconds. Its going to take a while, and some
explaining,
because its like somebody asked recently: why do some
people take so
long to give a simple answer?
There are some people who require time to consider the
options, and
thats always been a problem for me: I cant give a simple
yes or no
answer, because there are always so many options.
For me the options must be left open: So that a simple d =
1/2 gt^2 =
(16/sec^2)xt^2 = 16 x 25 = 400, is an incomplete answer:
To be
complete; d = (vi)t + (g/2)t^2.
With Newtons a = g = (vt-vi)/t: the velocities (vt-vi) must
be
innitely close together or else they must be integrated -
with a
series of iterations - because the intermediate velocities
might be
something else between the points at which they apply. The
average
(vt-vi)/2t = g/2 would only apply where the change is
constant. Newton
had to invent the innitesimal calculus to assure that
(vt-vi)/t was
surely equal to [2s/t^2 = g].
Using Galileos g/2 = 16/sec^2 we avoid this problem because
it
applies _at_ a point; not over a _period_ of time: So d =
(vi)t +
(g/2)t^2!
For now:
===
Subject: Mathematica notebook for calculating a Bryant cousin
minimal
surface
Based on Pascal Collins paper:
The Geometry of Finite Topology Bryant Surfaces
L^4 group geometery and U(1)*SU(2) and the quaternion
are entires isomorphous in group terms ( that is the elemets
of each can
be transformed by simple comformal transformations to the
other.
Im not really satised with this method.
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===
Subject: Now somebody tell me that Robin Chapman isnt a
troll again?!
Roger L. Bagula
===
Subject: Re: Now somebody tell me that Robin Chapman isnt a
troll again?!
One should not come to help others and be
attack by robbers and cut throats.
Professors are supposed to be wise and good.
Confusion of testosterone with intelligence isnt a good
thing.
Confusion of pedantry with actual understanding is worse.
The idea of newsgroups was to promote learning not to show it
off;
to answer questions and present new and original results,
not ask esoteric questions so professors could demonstrate
erudition and their mastery of the current literature on the
subject.
Not to attack innocents and denigrate those not
accepted as part of an in group of international professors.
No professor owns mathematics
and can defend it as his territory.
We see that the dignity of professors has blinded them to the
fact that
knowledge is independent of them and they have no
real power over it or others except what they earn by
the respect of others for their usefulness in teaching the
subject
or producing new and original mathematics.
Attacking others when they try to answer questions is troll
behavior.
Defending trolls and their action is troll behavior.
Behaving in general like power in the academic community was
actual
understanding or knowledge seems to be defending troll
behavior in this
news group.
In general the shameful behavior in this newsgroup is
something no
gentleman who respects the pursuit of knowledge should be
happy with.
Grow up and behave as grown men.
Learn to respect others and their rights.
Try to be good and actually answer questions.
Try to poke holes in the pompous rhetoric of fools, but
kindly.
Make sci.math a place where men may go in safety to learn
about
mathematics.
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca
92040-2905,tel:
619-5610814 :
URL : http://home.earthlink.net/~tftn
URL : http://victorian.fortunecity.com/carmelita/435/
===
Subject: Re: Now somebody tell me that Robin Chapman isnt a
troll again?!
X-URL:
http://mygate.mailgate.org/mynews/sci/sci.math/
e7f872f45d9a033a998809a2a879e3
7d.48257%40mygate.mailgate.org
> One should not come to help others and be attack
> by robbers and cut throats.
Of course, you dont come to help people, you come
to post delusional accusations and drivel-level
math discoveries, all in the interests of
increasing your fame as a legendary math kook, so
none of your consequential arguments derived from
the above beginning pertain.
You might stop to reect that most people acting
as you do are in profound need of assistance from
mental health professionals, and that it might be
worthwhile for you to stop by and let one of those
professionals kick your tires as it were.
xanthian.
===
Subject: Re: Now somebody tell me that Robin Chapman isnt a
troll again?!
You might stop to reect that most people acting
as you do are in profound need of assistance from
mental health professionals, and that it might be
worthwhile for you to stop by and let one of those
professionals kick your tires as it were.
xanthian.
Hmmm.... speaking of mental health, someone
who signs their stuff xanthian must have some
sort of problem.
===
Subject: Re: Now somebody tell me that Robin Chapman isnt a
troll again?!
>[...]
>Try to poke holes in the pompous rhetoric of fools
Just thought Id point out that he actually issued this
invitation, for the benet of anyone who didnt bother
reading down to the bottom...
>, but kindly.
>Make sci.math a place where men may go in safety
How could sci.math be unsafe?
>to learn about
>mathematics.
>Respectfully, Roger L. Bagula
>tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca
92040-2905,tel:
>619-5610814 :
>URL : http://home.earthlink.net/~tftn
>URL : http://victorian.fortunecity.com/carmelita/435/
************************
David C. Ullrich
===
Subject: Re: Now somebody tell me that Robin Chapman isnt a
troll again?!
> One should not come to help others and be
> attack by robbers and cut throats.
> Professors are supposed to be wise and good.
Incidentally, I am not, and never have been, a professor.
> Attacking others when they try to answer questions is troll
behavior.
Please cease such behaviour, Mr Bagula.
> Behaving in general like power in the academic community
was actual
> understanding or knowledge seems to be defending troll
behavior in this
> news group.
I havent met anyone on this group who does that.
> In general the shameful behavior in this newsgroup is
something no
> gentleman who respects the pursuit of knowledge should be
happy with.
Bravo. Now please cease your ad hominem attacks, Mr Bagula.
> Grow up and behave as grown men.
Sexist.
> Try to be good and actually answer questions.
Hmm, what about those whose attempt at answering questions
merely
aunt their own ignorance?
(for example see
et seq.)
> Try to poke holes in the pompous rhetoric of fools, but
kindly.
> Make sci.math a place where men may go in safety to learn
about
> mathematics.
After you.
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Lacan, Jacques, 79, 91-92; mistakes his penis for a square
root, 88-9
Francis Wheen, _How Mumbo-Jumbo Conquered the World_
===
Subject: Re: Now somebody tell me that Robin Chapman isnt a
troll again?!
Well, I for one agree completely. The fact that youre
able to spam EIS with millions of sequences that have
no particular interest to anyone, and spam sci.math
with messages that answer questions nobody asked,
is denitive proof that Robin Chapman is a troll.
(But btw no, those posts about SL(this and that) do
not prove that a question about SL(2,R) was really
a question about SL(2,C)...)
>Roger L. Bagula
************************
David C. Ullrich
===
Subject: Somebody tell me that Roger Bagula isnt a troll was
Re: Now
somebody tell me that Robin Chapman isnt a troll again?!
Anyone?
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Lacan, Jacques, 79, 91-92; mistakes his penis for a square
root, 88-9
Francis Wheen, _How Mumbo-Jumbo Conquered the World_
===
Subject: Re: Somebody tell me that Roger Bagula isnt a troll
was Re: Now
somebody tell me that Robin Chapman isnt a troll again?!
> Anyone?
At least Robin is not.
===
Subject: Re: Somebody tell me that Roger Bagula isnt a troll
was Re: Now
somebody tell me that Robin Chapman isnt a troll again?!
>Anyone?
Well, I have to say sorry, I would never have thought
of you as particularly trollitudinous, but I never
knew that Bagula has made up so many sequences of
integers. Hes spent hours writing down random
formulas to generate sequences and posting them
on the internet, if he says youre a troll then
youre a troll. (The fact that you still havent
admitted that youre really the guy who works
case much. I mean we all know the truth about that...)
************************
David C. Ullrich
===
Subject: Re: Now somebody tell me that Robin Chapman isnt a
troll again?!
OK - Robin Chapman isnt a troll again.
===
Subject: Re: Now somebody tell me that Robin Chapman isnt a
troll again?!
> OK - Robin Chapman isnt a troll again.
And never was!
===
Subject: An Analysis problem.
a_1, a_2, a_3, ... is a sequence of positive integers such
that a_1 < a_2 <
a_3 < ... .
Put f(x) = x^(a_1) + x^(a_2) + x^(a_3) + ... for -1 < x < 1.
Let g(x) = 1/f(x), and suppose g is the derivative of g.
(f, g, g are functions dened on the interval (-1,1) )
The problem: Is it true that the derivative g(x) converges
as x goes to
1,
that is, lim_{x --> 1-} g(x) exists?
I guess the statement to be true, but I do not know how to
prove it.
I am trying to solve the problem A6 at
http://www.kalva.demon.co.uk/short/sh02.html. The above
problem is related
to the problem A6. Any proof for the above problem implies a
proof for
problem A6.
===
Subject: Re: An Analysis problem.
> a_1, a_2, a_3, ... is a sequence of positive integers such
that a_1 < a_2
<
> a_3 < ... .
> Put f(x) = x^(a_1) + x^(a_2) + x^(a_3) + ... for -1 < x < 1.
> Let g(x) = 1/f(x), and suppose g is the derivative of g.
> (f, g, g are functions dened on the interval (-1,1) )
> The problem: Is it true that the derivative g(x) converges
as x goes to
1,
> that is, lim_{x --> 1-} g(x) exists?
> I guess the statement to be true, but I do not know how to
prove it.
> I am trying to solve the problem A6 at
> http://www.kalva.demon.co.uk/short/sh02.html. The above
problem is
related
> to the problem A6. Any proof for the above problem implies
a proof for
> problem A6.
demon.co.uk tells me it cant nd that URL.
It seems very unlikely to me that your conjecture is correct.
With a
FINITE sum g(x) is of the form
sum a_k x^(a_k-1)
------------------
(sum x^(a_k))^2
and the limit as k --> 1 is (sum a_k)/n^2, where the sum is
from k=1
to n. This suggests we may have problems with a_k = k^2, for
example.
And the innite series for g(x) when a_k = k^2 starts off
-1/x^2 -2*x + 5*x^4 - 7*x^6 - 8*x^7 + 20*x^9 + 11*x^10 -
39*x^12 -
28*x^13 + 15*x^14 + 64*x^15 + 51*x^16 - 54*x^17 - 95*x^18 -
80*x^19 +
126*x^20 + 176*x^21 + 69*x^22 - 240*x^23 - 325*x^24 +
405*x^26 +
560*x^27 - 145*x^28 - 720*x^29 - 806*x^30 + 416*x^31 +
1320*x^32 +
952*x^33 - 875*x^34 - ...
When I plot the partial sums they really seem to blow up as x
--> 1.
Why do you think this limit exists?
--Ron Bruck
===
Subject: Re: An Analysis problem.
> a_1, a_2, a_3, ... is a sequence of positive integers such
that a_1 <
a_2 <
> a_3 < ... .
> Put f(x) = x^(a_1) + x^(a_2) + x^(a_3) + ... for -1 < x < 1.
> Let g(x) = 1/f(x), and suppose g is the derivative of g.
> (f, g, g are functions dened on the interval (-1,1) )
>
> The problem: Is it true that the derivative g(x) converges
as x goes
to 1,
> that is, lim_{x --> 1-} g(x) exists?
>
> I guess the statement to be true, but I do not know how to
prove it.
>
>
> I am trying to solve the problem A6 at
> http://www.kalva.demon.co.uk/short/sh02.html. The above
problem is
related
> to the problem A6. Any proof for the above problem implies
a proof for
> problem A6.
> demon.co.uk tells me it cant nd that URL.
> It seems very unlikely to me that your conjecture is
correct. With a
> FINITE sum g(x) is of the form
> sum a_k x^(a_k-1)
> ------------------
> (sum x^(a_k))^2
> and the limit as k --> 1 is (sum a_k)/n^2, where the sum is
from k=1
> to n. This suggests we may have problems with a_k = k^2,
for example.
> And the innite series for g(x) when a_k = k^2 starts off
> -1/x^2 -2*x + 5*x^4 - 7*x^6 - 8*x^7 + 20*x^9 + 11*x^10 -
39*x^12 -
> 28*x^13 + 15*x^14 + 64*x^15 + 51*x^16 - 54*x^17 - 95*x^18 -
80*x^19 +
> 126*x^20 + 176*x^21 + 69*x^22 - 240*x^23 - 325*x^24 +
405*x^26 +
> 560*x^27 - 145*x^28 - 720*x^29 - 806*x^30 + 416*x^31 +
1320*x^32 +
> 952*x^33 - 875*x^34 - ...
> When I plot the partial sums they really seem to blow up as
x --> 1.
> Why do you think this limit exists?
> --Ron Bruck
Actually worse things than blowing up can happen: We can have
g(x)
oscillating wildly as x -> 1-. Sketch: Given a_1 < ... < a_n
and setting
g_n(x) = 1/[x^(a_1) + ... + x^(a_n)] we have g_n(1) = -(a_1
+ ... +
a_n)/n^2. It follows that we can choose x_n in (0,1) such
that g_n(x_n) is
as close to -(a_1 + ... + a_n)/n^2 as we like. Furthermore if
a_(n+1) >>
a_n, then g(x_n) will be as close to -(a_1 + ... + a_n)/n^2
as we like for
*any* g(x) of the form 1/[x^(a_1) + ... + x^(a_n) +
x^(a_(n+1)) + ...].
(Needs checking, but its easy.)
Next note the expression (a_1 + ... + a_n)/n^2 can be made to
oscillate
between 1/2 and oo: Clearly it can be made as large as we
like: Given a_1 <
... < a_(n-1), just choose a huge a_n. But having chosen such
an a_n, we
can then choose the the subsequent as to increase by 1 for
any nite
number of steps. Suppose we take j such steps. Then were
looking at
(a_1 + ... + a_n + 1 + 2 + ... + j + j*a_n)/(n+j)^2 -> 1/2 as
j ->
oo.
Putting this together with the rst paragraph shows the a_ns
can be
chosen so that the corresponding g gives g(x) oscillating
wildly as x ->
1-.
===
Subject: Re: Innity can not exist
>>
>> Innity may just be a convenient phrase for denoting the
logical
>> limits of human reasoning.It is most understandable in a
geometric way
>> via the relationship between diameter,circumference and
the Pi value
>> Ininite cardinality of sets is very well dened. A set
has innite
>> cardinality if it can be mapped 1-1 onto a proper subset
of it self.
>> Consider, for example, the set of non-negative integers Z.
n <-> 2*n
>> is a 1-1 map of the non-negative integers onto to the even
integers
>> which is a proper subset of the non-negative integers.
Hence Z (by
>> denition) is innite. A set has nite cardinality if it
does not
>> have innite cardinality which denes nite and niteness
for
>> counting the number of elements in a set.
> This is a great illustration Bob...the denition that you
used was
> better than the one that I touched on (a set is innite if
it is not
> nite and a nite set is a set such that there exist a
bijective
> correspondence between it and a section of the positive
integers). I
> like yours much better.
The two denitions are equivalent if you assume the axiom of
choice. In
the
absence of the axiom of choice, the
nite-iff-bijective-with-some-natural-number denition is the
correct
one.
A set that is bijective with a proper subset is called
Dedekind
innite.
Dave Seaman
Judge Yohns mistakes revealed in Mumia Abu-Jamal ruling.
===
Subject: Re: EIS enries of Roger L. Bagula
I while ago I thought that the Yahoo number theory group might
be of some interst and I joined it--you never know. Most of
these groups on Yahoo are pretty inactive, but number theory
was not. Every morning there were several messages
from Roger Bagula.
It doesnt take long to gure out that his number theory
and sequences are nonsense. But he has completely taken over
the group. I unsubscribed from it.
Van
>My response was to add the comment:
>Warning: the management of EIS can be hazardous to innocent
mathematicians.
>I have one editor there who has me on his blocked list:
>A Dr. Bob Wilson V
>That is he can send me insulting email and my replies bounce.
>Robin Chapman has also got me on his blocked list, so he can
do the
same.
>I have a lot of detractors, but in most cases they tend to
admit
>,grudgingly, that my result is new and worthwhile.
> What result?
>Ive become very stoic about this over the years
>and many results.
>Editors seem happy to have their names on my sequences.
>> In many of that sequences there is a paragraph like it:
>>
>> Extension: Warning: Many recent communications from this
author
have
>> contained
>> numerical errors or have been badly formatted. This
entry has
>> not been
>> edited and may contain errors. It is included on a
provisional
>> basis in
>> the hope that some reader will edit it. - njas
>>
>>
> ************************
> David C. Ullrich
===
Subject: Re: EIS enries of Roger L. Bagula
> I while ago I thought that the Yahoo number theory group
might
> be of some interst and I joined it--you never know. Most of
> these groups on Yahoo are pretty inactive, but number theory
> was not. Every morning there were several messages
> from Roger Bagula.
> It doesnt take long to gure out that his number theory
> and sequences are nonsense. But he has completely taken over
> the group. I unsubscribed from it.
Dont let kookery win. Complain to the moderator(s) of the
list.
And complain often.
I say that as a moderator of a whole bunch of vaguely serious
yahoogroups. (Several of which have witnessed these kinds of
Bagularities.)
If the moderator(s) isnt prepared to deal with valid
complaints,
/then/ unsubscribe.
Phil
1st bug in MS win2k source code found after 20 minutes:
scanline.cpp
2nd and 3rd bug found after 10 more minutes: gethost.c
Both non-exploitable. (The 2nd/3rd ones might be, depending
on the CRTL)
===
Subject: Re: July 4th Quiz
> I did not mean to say this. I do not know whats gotten into
me lately.
> Ive been in therapy once a week as of late, and am working
on resolving
my
> abuse as a child.
> Steve
--------------
Liar.
Steve Walz
ath: nntpswitch.com
===
Subject: Re: Zorns lemma for families of subsets of a
countable set
> | I think not (given that ZF is consistent). Force over the
> | constructible universe L to add aleph-one many Cohen
subsets
> | of omega-one. Call the L-generic lter G and the resulting
> | (unordered) set of Cohen subsets of omega-one
> | A = {a_i: i < omega-one}. In L[G] form the class M of sets
> | hereditarily ordinal-denable with parameters drawn from A
> | and the a_i. Then I think M will be a model of ZF + DCR +
-DC.
> I dont remember enough of the results on forcing to be
able to
> check your proof. It seems like the existence of an innite
> subset of a set X without a countable subset should be
typically
> insufcient to imply over ZF the existence of such a subset
of
> a set Y that is enough smaller than X.
I dont really follow you here. Enough smaller for what?
Presumably you have in mind some strategy for proving failure
of DC, but I dont see it.
> Is Bells Boolean Valued Models and Independence Proofs
(still)
> considered a good reference?
> Keith Ramsay
The basic technology of forcing certainly hasnt changed
since it was published, but Id recommend you look in Jechs
book: he presents the details of the model of ZF - AC which
I mentioned in response to your rst question (i.e. adding
Cohen reals rather than Cohen subsets of omega-one), and the
details of the model for ZF + DCR - DC are quite similar.
Bob Beaudoin
===
Subject: Re: Sets of functions
> Your proof (which I omitted) is, as usual, too complicated.
(The
as
> usual is meant not as a dig, but as constructive
criticism.) When
A
> is not empty, the only function in {x}^A is the constant
function;
> that is, A is a singleton. When A is empty, {x}^A = {0}
(where 0
> denotes the empty set}, again a singleton. There is a clear
bijection
> between singletons.
> I tend to be critical of myself, which leads me to ruminate
too
much.
> Comprehending ideas is easier for me, at least at this
point, than
writing a
> formal proof of the ideas. In other words, I can usually
understand
the
> exercises, but have difculty in completing them using
mathematical
> notation. The difculty for me stems from lack of sufcient
condence in
> my knowledge, which manifests itself in my repeatedly
questioning
myself.
> This all results in my spending for more time than
necessary on each
> exercise problem. I try not to complicate things, but
always to no
avail.
> When A is not empty, the only functions in A^{x} are the
constant
> functions; thus, the bijection maps a function to the unique
element in
> its image. When A is empty, so is A^{x}, and the empty set
is
a
> bijection from the empty set to itself.
> The term singleton is unfamiliar to me. Would accept, as a
proof to
> the exercise, what you in your reply? Or was that only for
my benet
and
> not how you would formally present your answer?
A singleton is a set with exactly one element.
an example of all that is needed for such proofs. I truly
hope it
helps.
You seem very diligent and capable to address the material.
However,you suffer from not having a reader not giving you
feedback on
written assignments, though you do get some of that here as
far as
readers patience will allow. Not that the content of your
proofs is
necessarily wrong, but they are very long-winded and
inelegant. A
reader (e.g., I) may just glaze over them when s/he knows a
much
simpler proof will do and not even bother to check the
details; thus,
you may not get the feedback on content that you desire. All
this is
to say that you need to learn something about the style of
writing
proofs.
Again, all this is meant as constructive criticism; by no
means do I
mean any offense. To the contrary, you are to be commended
for your
self-study.
Best,
-SJH
===
Subject: Re: Sets of functions
> an example of all that is needed for such proofs. I truly
hope it
> helps.
Yes, any and all constructive feedback is of help. I
appreciate it.
> You seem very diligent and capable to address the material.
> However,you suffer from not having a reader not giving you
feedback on
> written assignments, though you do get some of that here as
far as
> readers patience will allow. Not that the content of your
proofs is
> necessarily wrong, but they are very long-winded and
inelegant. A
> reader (e.g., I) may just glaze over them when s/he knows a
much
> simpler proof will do and not even bother to check the
details; thus,
> you may not get the feedback on content that you desire.
All this is
> to say that you need to learn something about the style of
writing
> proofs.
I accept that some readers may not look at my proofs in great
detail
before responding, however I know that there are many that
do. My not
having
a teacher or others to discuss my study with in person is a
hinderance,
yes,
but not something that will lead me to failure. I make up for
not having a
teacher by being very critical with myself, and by asking for
assistance
from members of this news group. I cant explain how happy I
am that people
take the time to aid me. It is an odd way to learn
mathematics, but it is
going ne. As Ive said before, I havent been studying set
theory every
day, but I plan to begin studying for hours every day quite
soon. When I
revisit old theorems and prove them again, the most recent
proofs tend to
always be much improved. If you do a search for posts by me,
you will see
that I initially did not even know logic and so asked about
contradictions
and tautologies. Im now know much more than I did before
embarking to
study
set theory. Im sure I will continue to progress because I
truly enjoy
mathematics, as most of the readers here do.
> Again, all this is meant as constructive criticism; by no
means do I
> mean any offense. To the contrary, you are to be commended
for your
> self-study.
Oh no, I do understand the difference. Even if a person were
to
criticize a proof of mine, and call me dummy or something, I
would still
evaluate the criticism and make the best of it. Im glad that
everyone has
been extraordinarly helpful to me. On a side-note, good
things can come
from
ugly motives, and vice-versa.
Take care, and thank you, Adam.
===
Subject: Re: Groupthink
> Yale psychologist Irving Janis coined the term in 1972 to
> describe a decision-making process in which ofcials are
> so wedded to the same assumptions and beliefs that they
> ignore, discount or even ridicule information to the
contrary.
> When members of a cohesive, homogenous group value
> unanimity and agreement on one course of action more
> than a realistic appraisal of alternatives, they are
engaging
> in groupthink.
you noticed? its only a dozen people here, each too afraid to
comment
on any alternate theory for fear of looking stupid in front
of their
mainstream.
really quite ridiculous especially with 1000s of staff on the
truman show
mocking the text hugging group here for their numerous
entrenched errors.
this statement is false lets call it inconsistent
this statement has no proof lets allow it
if you KNOW its true it must have a proof lets dissalow it
xxx
xxx
xxx
yyy is not counted here.
xxx..
yxx..
yyx..
...
cant see yyy here either, its missing too
A function exists that determines whether its input halts or
not,
or whether it is self referential.
halt(f(x) = x+1, 0) = true
halt(f(x) = f(x) + 1, 0) = false
halt(f(x) = if (halt(x,x), f(x), 0), 0) = self_referential
still working on busy beaver..
Herc
===
Subject: Dissecting a regular polygon into rhombs
A regular polygon, with 2n sides of unit length, can be
dissected into n(n-1)/2 rhombs with sides of unit length.
In how many ways can this be done?
===
Subject: Re: Dissecting a regular polygon into rhombs
> A regular polygon, with 2n sides of unit length, can be
> dissected into n(n-1)/2 rhombs with sides of unit length.
> In how many ways can this be done?
Dont know if theres a nice formula, but certainly
a lot of work has been done on these rhombus tilings.
See the preprints at
http://perso.ens-lyon.fr/frederic.chavanon/
for instance.
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Lacan, Jacques, 79, 91-92; mistakes his penis for a square
root, 88-9
Francis Wheen, _How Mumbo-Jumbo Conquered the World_
===
Subject: Re: Dissecting a regular polygon into rhombs
3QLpj-NoP*NzsIC,boYU]bQ]Hy<#4ga3$21:
> A regular polygon, with 2n sides of unit length, can be
> dissected into n(n-1)/2 rhombs with sides of unit length.
> In how many ways can this be done?
> Dont know if theres a nice formula, but certainly
> a lot of work has been done on these rhombus tilings.
> See the preprints at
> http://perso.ens-lyon.fr/frederic.chavanon/
> for instance.
Some other keywords to use in searching for these rhomb
tilings would be
simple pseudoline arrangement (the planar dual to a rhomb
tiling),
circular sequence (a way of representing pseudoline
arrangements as
sequences of permutations), wiring diagram (a standard way of
drawing
circular sequences as pseudoline arrangements) and rank 3
oriented
matroid (another representation in terms of the orientation
of each
triangle formed by three pseudolines).
I lost my copy a few years back but I seem to recall that
Knuths book
_Axioms and Hulls_ has a fair amount of material on counting
these
objects. More recently see [S. Felsner: On the number of
arrangements
of pseudolines, Discrete Comput. Geometry 18 (1997), 257-267].
I think the upper and lower bounds are both of the form
const^{n^2}
and the main question is getting an accurate value of the
constant.
David Eppstein http://www.ics.uci.edu/~eppstein/
Univ. of California, Irvine, School of Information & Computer
Science
===
Subject: Another Mathematicians apology needed asap !!
Please - if you discover a new phenomena, PLEASE, PLEASE,
GIVE IT A DULL
I am getting entirely fed up with all the urry of
misinformation oating
around, even in moves, regarding CHAOS.
Even people who despise mathematics are walking around
proclaiming factoids
about CHAOS.
Seems like everybodys an expert on CHAOS - including folks
who
couldnt
factor y=x^2, and others who divide by zero.
We need one of two things. Either dull and technical naming
of mathematical
phenomena, or documentaries which explain CHAOS to the public
at large.
If I had a nickel for every CHAOS expert I met Id be a
millionaire.
The
urry of misinformation is doing a tremendous disservice to
science.
Read below - postings found on USENET.
------------------------------------------------------snip
> Buttery Effect and Chaos theory are part of modern
sciences
> links to eland - you can believe in both simultaneously,
you
> just cant prove there is a link between them (or disprove
it,
> either).
------------------------------------------------------snip
> Theyre like the buttery effect
> illustration of the chaos theory in that all of the
interaction of the
> initial systems involved make it impossible to calculate
every outcome.
------------------------------------------------------snip
If they had deviated from the Music much at all, I would
think that the principles of chaos would have made it utterly
useless
as a predictive tool very quickly (buttery effect again).
(And in
any situation where _personalities_ are involved, such as
those of the
Ainur, I cant imagine that chaos would not apply.)
------------------------------------------------------snip
See Chaos Science, the Buttery
Effect, and all that. Another manifestation of the Cybernetic
Model coming
to the fore is the new age assertion that crystals work just
like
computer
chips. There are signs that the Cybernetic Model dovetails
back into the
spirit model, and in Chaos Servitors: A User Guide, you
will nd a
reasonably coherent argument to support the idea that
localised
informationelds can, over time, become self-organising to
the extent that
we experience them as autonomous entities - spirits.
------------------------------------------------------snip
Widen you focus, look at history and the stuff of culture. Do
you see
how we are lead by ideas, how we follow fashions? Its about
the focal
point, and the diverse range of people attracted to that
focus. I see
Michael occupying that focus as an enabler, a means by which,
people
celebrate a much larger idea.
::: The buttery effect of Chaos theory comes to mind :::
------------------------------------------------------snip
> Wouldnt that be the other way around?
> I think the idea of a buttery effect (from ancient asia
wisdom)
come
> before the fractals, and fractal geometry and chaos
theory... :)
Really? I was unaware of such a concept in Asian thinking,
but it doesnt
surprise me.
------------------------------------------------------snip
Im not sure whether you are misunderstanding me. Im only
repeating
what is very conventional wisdom (in fact theres a movie
that just
came out about an example of the buttery effect, although I
forget
its name). I would offer a couple possible counter arguments:
a) I
would cite standard works in the philosophy of history that
assert this to
be so. b) develop an
argument based on the theory of negentropic systems that
suggest
that any emergent process is highly subject to the inuence of
contingencies. Which do you prefer that I do? Or perhaps I
could
instead appeal to common sense: how well does your local
weather
forecaster do?
===
Subject: Re: Another Mathematicians apology needed asap !!
> Please - if you discover a new phenomena, PLEASE, PLEASE,
GIVE IT A DULL
Hmm. I cant agree with this. Colorful names make things
easier to
remember. E.g., it is easy to remember what an annhilator is.
And dull
names tend to be long, and of course long names are
inconvenient to write
down and say.
Let us suppose that the importance of chaos theory has been
overestimated
by
the average person. (This seems reasonable to me given the
the style of
discussion about it, which is why I have not bothered to
check by bothering
to acquaint myself with it.) This suggests to me that
manipulation of
public
opinion plays an important role in this eld in deciding what
is
considered
important. The people who are good at such manipulation tend
to also be the
same people who are most easily manipulated. (Why? Because
manipulators
tend
to have manipulative ancestors whose mates are likely to be
easily
manipulated ancestors). So even if some people get confused
about what
important math is, at least they are not likely on the whole
to be the most
innocent types. Even if there is real math involved in that
eld which is
being hurt because of the eld becoming largely silly, at
least chaos
theory could be a magnet that can pull deceptive people
outside of greater
math, thereby leaving the latter more pristine.
Oftentimes it is worse for deceivers to be deceived. For
example, it is bad
that abusive violent people tend to view violence as more
powerful than it
is, a simple consequence of their having gotten to a certain
extent caught
up in their own convenient deceptions as to the potency of
their behaviors.
But it doesnt bother me much what the apparently mostly
silly group of
chaos people are doing and saying. Sure, I pity the poor
serious people
studying, e.g., differential equations in which slight
changes in initial
conditions lead to large changes in results, but oh well.
===
Subject: Re: Another Mathematicians apology needed asap !!
...
>But it doesnt bother me much what the apparently mostly
silly group of
>chaos people are doing and saying. Sure, I pity the poor
serious people
>studying, e.g., differential equations in which slight
changes in initial
>conditions lead to large changes in results, but oh well.
Most mathematically interesting topics that are merchandised
by
chaos theory stem from pure mathematics. I just mention a few
names:
Cantor, Poincare, Birkhoff, Julia, Smale... I think there are
still
many deep theorems lurking. But they will fall into the eld
of
Analysis, Topology, Geometry (under the focus of Dynamical
systems
theory).
If chaos theorists are still around they will cannibalize
those
results. But that shouldnt discourage future mathematicians.
Or
should it?
Thomas
===
Subject: annihilator
|
|> Please - if you discover a new phenomena, PLEASE, PLEASE,
GIVE IT A
|
|Hmm. I cant agree with this. Colorful names make things
easier to
|remember. E.g., it is easy to remember what an annhilator
is. And
|dull names tend to be long, and of course long names are
inconvenient
|to write down and say.
speaking of annihilator, ive often wondered where that
terminology
came from. specically, i wonder whether it came from the
fact that
in quantum mechanics the annihilator ideal of the ground
state of a
harmonic oscillator is generated by the so-called annihilation
operators.
[e-mail address jdolan@math.ucr.edu]
===
Subject: Re: annihilator
>speaking of annihilator, ive often wondered where that
terminology
>came from.
I think that was an album of ZZTop.
Thomas [SCNR]
===
Subject: Re: Another Mathematicians apology needed asap !!
> Please - if you discover a new phenomena, PLEASE, PLEASE,
GIVE IT A DULL
Fuzzy logic keeps cropping up too.
===
Subject: Re: Another Mathematicians apology needed asap !!
> Please - if you discover a new phenomena, PLEASE, PLEASE,
GIVE IT A
DULL
I do not know how someone derives time travel from the
buttery
effect.
Makes about as much sense as deriving potable water from the
term
community urinal.
If they wanted to make a movie about something, they should
have tried to
explain why even though there are billions of butteries, it
is
unreasonable to assume that their wings apping is actually
controlling
the weather. That perhaps there is an opposing phenomena to
the buttery
effect which diminishes the inuence of these seemingly
innite miniscule
perturbations. And then, perhaps there is some type of
feedback or
recursiveness to it acting as a dampening force/inuence.
Sensitive dependence on initial conditions - the buttery
effect. What
Im saying is that this seems like an inuence for which
there may be an
inverse or opposite. Perhaps Robustness Regardless of Initial
Conditions.
Could these act as competing forces ? Or, have I become a
babbling fool
at
last......
===
Subject: Re: Another Mathematicians apology needed asap !!
===
>Subject: Re: Another Mathematicians apology needed asap !!
>Message-id: <3KbIc.69047$Oq2.14181@attbi_s52>
>> Please - if you discover a new phenomena, PLEASE, PLEASE,
GIVE IT A
DULL
>I do not know how someone derives time travel from the
buttery
effect.
>Makes about as much sense as deriving potable water from the
term
>community urinal.
>If they wanted to make a movie about something, they should
have tried to
>explain why even though there are billions of butteries, it
is
>unreasonable to assume that their wings apping is actually
controlling
>the weather. That perhaps there is an opposing phenomena to
the buttery
>effect which diminishes the inuence of these seemingly
innite
miniscule
>perturbations. And then, perhaps there is some type of
feedback or
>recursiveness to it acting as a dampening force/inuence.
Isnt the Hollywood understanding of the Buttery Effect
completely wrong?
Its not that buttery wing aps _cause_ hurricanes, its
that trying to
extrapolate
chaotic functions is pointless since initial conditions that
differ by as
little as
a buttery wing ap become hurricanes.
Excel tells me that 3^(1/2^n) becomes 1 when n=48. Now, do
you belive that?
The Hollywood writers would.
>Sensitive dependence on initial conditions - the buttery
effect.
What
>Im saying is that this seems like an inuence for which
there may be an
>inverse or opposite. Perhaps Robustness Regardless of Initial
Conditions.
>Could these act as competing forces ? Or, have I become a
babbling fool
at
>last......
Mensanator
Ace of Clubs
===
Subject: Re: Another Mathematicians apology needed asap !!
>Please - if you discover a new phenomena, PLEASE, PLEASE,
GIVE IT A DULL
How come Catastrophe Theory isnt en vogue?
>I am getting entirely fed up with all the urry of
misinformation
oating
>around, even in moves, regarding CHAOS.
>Even people who despise mathematics are walking around
proclaiming
factoids
>about CHAOS.
Thats due in part to those wheather people: Look! Do you see
this
beautiful seemingly harmless little buttery? Right now it is
causing
a terrible downpour somewhere in South East Asia!
Crichtons Jurassic Park (and Jeff Goldblum as the brilliant
mathematician) is also to blame.
>Seems like everybodys an expert on CHAOS - including folks
who
couldnt
>factor y=x^2, and others who divide by zero.
>We need one of two things. Either dull and technical naming
of
mathematical
>phenomena, or documentaries which explain CHAOS to the
public at
large.
There are beautiful books on Chaos (e.g. this book by Peitgen
et al.)
Why do we need even more? We need people that object to some
of their
over-simplied conclusions.
>If I had a nickel for every CHAOS expert I met Id be a
millionaire.
The
>urry of misinformation is doing a tremendous disservice to
science.
Is it *that* bad?
>Read below - postings found on USENET.
Let me guess: Do they talk about the buttery effect?
Buttery effect ad nauseum
I was right! BTW: Isnt there a buttery bifurcation in
catastrophe
theory? Why isnt that more popular?
Thomas
===
Subject: Re: Another Mathematicians apology needed asap !!
X-URL:
http://mygate.mailgate.org/mynews/sci/sci.math/
a936a6dd2e9927bc9c5406f0959b08
1f.48257%40mygate.mailgate.org
> I was right! BTW: Isnt there a buttery bifurcation in
catastrophe
> theory? Why isnt that more popular?
Thats what happens when you give your buttery grayscale
wings;
it gets lost in the print.
HTH
xanthian.
===
Subject: Re: Another Mathematicians apology needed asap !!
>Please - if you discover a new phenomena, PLEASE, PLEASE,
GIVE IT A DULL
> How come Catastrophe Theory isnt en vogue?
It was, about 20 years ago.
===
Subject: Re: Another Mathematicians apology needed asap !!
>>
>>
>>Please - if you discover a new phenomena, PLEASE, PLEASE,
GIVE IT A
DULL
>> How come Catastrophe Theory isnt en vogue?
>It was, about 20 years ago.
So thats the solution. Be patient. Wait.
Thomas
===
Subject: Re: Another Mathematicians apology needed asap !!
===
>Subject: Another Mathematicians apology needed asap !!
>Message-id:
>Please - if you discover a new phenomena, PLEASE, PLEASE,
GIVE IT A DULL
>I am getting entirely fed up with all the urry of
misinformation
oating
>around, even in moves, regarding CHAOS.
Wouldnt work. If it had a dull name, someone would just
incorporate
it into a cutesy acronym and youre right back where you
started.
Mensanator
Ace of Clubs
===
Subject: Re: Another Mathematicians apology needed asap !!
> Wouldnt work. If it had a dull name, someone would just
incorporate
> it into a cutesy acronym and youre right back where you
started.
Quite right. This reminds me that Darwins name for his
theory was
theory of descent with modications and that Einsteins name
for
his theory was invariant theory.
JOse Carlos Santos
===
Subject: Does a high SAT score predict mathematical talent?
Im wondering what you think about efforts to identify future
mathematicians of high talent at middle-school (junior high)
age.
I am aware of a long-term research study in the United States,
including young people from around the world, called the
Study of
Mathematically Precocious Youth (SMPY).
http://peabody.vanderbilt.edu/depts/psych_and_hd/smpy/
default.htm
Ascertainment of subjects for SMPY appears to be based almost
entirely on scoring above a specied level on the SAT I math
section before a specied (young) age. Some of the older
cohorts
in SMPY are now old enough to have entered full-time
professional
careers after completing graduate school. Have you
encountered any
SMPY participants in your professional activities? Does a high
score on the SAT I math section
http://www.collegeboard.com/student/testing/sat/about/
SATI.html
well predict who will be a talented mathematician as an adult?
What other signs of incipient talent would you look for in,
say, a
thirteen-year-old child who declares a strong interest in
math?
What are reliable signs that a young person is NOT likely to
reach
the top level of performance in mathematics?
I appreciate any comments or discussion anyone has on this
point.
Karl M. Bunday
(remove .de to email)
===
Subject: Re: Does a high SAT score predict mathematical
talent?
I am of the opinion that excellence in anything has less to
do with
biology,
and much more to do with passion for that thing.
I do not believe in the quantication of intelligence, nor do
I believe in
the quantication of passion. But passion is certainly more
easily
understood than intelligence, which probably has no
satisfactory
denition.
I know what you are thinking at this point - and I dont
really care. Ill
lay it on the line for you just one time only - consider your
opportunity
for fame.
Education fails by killing passion which occurs naturally in
every pupil.
Blame it on your unions, your school boards, your budgets,
whatever you
like. But Ill gurantee that this is why some excell and
others do not.
Some
will escape the educational maze with their passion intact,
while others
will be processed like tuna.
This is why many people actually hate math. Make no mistake,
their
hatred
is just a real as any other. Their hatred of all things
mathematical is the
diametric opposite of passion. If the public school system
would leave
people alone I actually believe that we would have a greater
number of
mathematicians in our society.
And, there WERE prior cultures where mathematics ourished
which lacked
the
educational systems which we posses today, producing an
entirely different
breed as well if you must know.
> Im wondering what you think about efforts to identify
future
> mathematicians of high talent at middle-school (junior
high) age.
> I am aware of a long-term research study in the United
States,
> including young people from around the world, called the
Study of
> Mathematically Precocious Youth (SMPY).
>
http://peabody.vanderbilt.edu/depts/psych_and_hd/smpy/
default.htm
> Ascertainment of subjects for SMPY appears to be based
almost
> entirely on scoring above a specied level on the SAT I math
> section before a specied (young) age. Some of the older
cohorts
> in SMPY are now old enough to have entered full-time
professional
> careers after completing graduate school. Have you
encountered any
> SMPY participants in your professional activities? Does a
high
> score on the SAT I math section
>
http://www.collegeboard.com/student/testing/sat/about/
SATI.html
> well predict who will be a talented mathematician as an
adult?
> What other signs of incipient talent would you look for in,
say, a
> thirteen-year-old child who declares a strong interest in
math?
> What are reliable signs that a young person is NOT likely
to reach
> the top level of performance in mathematics?
> I appreciate any comments or discussion anyone has on this
point.
> Karl M. Bunday
> (remove .de to email)
===
Subject: Re: Does a high SAT score predict mathematical
talent?
X-URL:
http://mygate.mailgate.org/mynews/sci/sci.math/
cbce65bac40bfe0ba617c1207ca5dc
d7.48257%40mygate.mailgate.org
Since the conventional wisdom is that the greatest
mathematicians
have done their greatest work by their young twenties, isnt
all
this prediction a bit beside the point? By the time the
typical
student nishes an undergraduate college degree s/he is 21
already.
Finishing a PhD adds several years to that, and suddenly you
have
young math major out in the world as a professional, and
already
headed downhill from any expected zenith of productivity.
I think you might have better luck predicting the success of
the
also-rans than of the top tier mathematicians by SAT scores.
IMAO
xanthian.
===
Subject: Re: Does a high SAT score predict mathematical
talent?
Counter example: Erdos.
Mind all that amphetamine helped keep his mind sprightly.
===
Subject: Re: Does a high SAT score predict mathematical
talent?
> Since the conventional wisdom is that the greatest
mathematicians
> have done their greatest work by their young twenties,
Fortunately, this conventional wisdom is total bollocks.
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Lacan, Jacques, 79, 91-92; mistakes his penis for a square
root, 88-9
Francis Wheen, _How Mumbo-Jumbo Conquered the World_
===
Subject: Re: Does a high SAT score predict mathematical
talent?
>> Since the conventional wisdom is that the greatest
mathematicians
>> have done their greatest work by their young twenties,
>Fortunately, this conventional wisdom is total bollocks.
I just heard this myth on the news (USA) again yesterday.
The item was about neuron connections during childhood
and neuron disconnections after childhood. The myth is
alive and kicking in medical circles.
/BAH
Subtract a hundred and four for e-mail.
===
Subject: Re: Does a high SAT score predict mathematical
talent?
>> Since the conventional wisdom is that the greatest
mathematicians
>> have done their greatest work by their young twenties,
>Fortunately, this conventional wisdom is total bollocks.
> I just heard this myth on the news (USA) again yesterday.
> The item was about neuron connections during childhood
> and neuron disconnections after childhood. The myth is
> alive and kicking in medical circles.
Im a little puzzled by the relevance of this. Was the item
specically mentioning mathematicians? Or was it discussing
some
relation to the great works of scientists, etc.?
Its a long way from talking about neuron connections to
deducing the
age at which great mathematical work is produced.
===
Subject: Re: Does a high SAT score predict mathematical
talent?
>Since the conventional wisdom is that the greatest
mathematicians
> have done their greatest work by their young twenties,
>>
>>Fortunately, this conventional wisdom is total bollocks.
>>
>> I just heard this myth on the news (USA) again yesterday.
>> The item was about neuron connections during childhood
>> and neuron disconnections after childhood. The myth is
>> alive and kicking in medical circles.
> Im a little puzzled by the relevance of this. Was the item
> specically mentioning mathematicians? Or was it discussing
some
> relation to the great works of scientists, etc.?
> Its a long way from talking about neuron connections to
deducing the
> age at which great mathematical work is produced.
The only mathematician I could think of who had done his
greatest work by his early twenties was Galois :-)
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Lacan, Jacques, 79, 91-92; mistakes his penis for a square
root, 88-9
Francis Wheen, _How Mumbo-Jumbo Conquered the World_
===
Subject: Re: Does a high SAT score predict mathematical
talent?
X-URL:
http://mygate.mailgate.org/mynews/sci/sci.math/
ba26703ece9ebcf840917f48c6d977
a5.48257%40mygate.mailgate.org
> The only mathematician I could think of who had done his
> greatest work by his early twenties was Galois :-)
Far be it from me to suggest that you remain ignorant:
http://www-groups.dcs.st-andrews.ac.uk/~history/
xanthian.
===
Subject: Re: Does a high SAT score predict mathematical
talent?
>
>Since the conventional wisdom is that the greatest
mathematicians
> have done their greatest work by their young twenties,
>>
>>Fortunately, this conventional wisdom is total bollocks.
>>
>> I just heard this myth on the news (USA) again yesterday.
>> The item was about neuron connections during childhood
>> and neuron disconnections after childhood. The myth is
>> alive and kicking in medical circles.
>
> Im a little puzzled by the relevance of this. Was the item
> specically mentioning mathematicians? Or was it discussing
some
> relation to the great works of scientists, etc.?
>
> Its a long way from talking about neuron connections to
deducing the
> age at which great mathematical work is produced.
> The only mathematician I could think of who had done his
> greatest work by his early twenties was Galois :-)
How about Abel? Died when 26.
===
Subject: Re: Does a high SAT score predict mathematical
talent?
reply in this thread:
>Since the conventional wisdom is that the greatest
mathematicians
>have done their greatest work by their young twenties,
>>
>>Fortunately, this conventional wisdom is total bollocks.
> The only mathematician I could think of who had done his
> greatest work by his early twenties was Galois :-)
Thats my LOL for the day, and I appreciate your comments and
the
comments of the other participants in this thread.
I get the impression that the persistent myth about
mathematicians
burning out and becoming unproductive while they are young has
much to do with Hardys line in his Mathematicians Apology
that
mathematics is a young mans game. And I wonder if the
still-inuential writings of the last E. T. Bell contain
similar
suggestions that mathematicians are expected to wash up early?
Web sites that comment on this issue of mathematics being
conned
to the young, and mostly disagree with that proposition by
providing counterexamples, include
http://slate.msn.com/id/2082960/
http://uzweb.uz.ac.zw/science/maths/zimaths/72/youth.html
http://www.math.rutgers.edu/~zeilberg/Opinion46.html
I appreciate the turn the thread has taken in discussing
whether
or not mathematicians can sustain their mathematical activity
into
middle age, because that may have consequences for how young
people are educated in mathematics, which is my concern in
opening
this thread. There does appear to be a line of thought that a
promising young mathematician ought to be sped through the
standard pre-university and undergraduate university
mathematics
curriculum as rapidly as possible, the better to have more
productive years doing new things in math after obtaining a
Ph.D.,
before burnout sets in. Some mathematicians appear to
consciously
disagree with this view, and I know that Tony Gardiner in the
U.K.
says that to build a higher building, one must dig a deeper
foundation, and thus he advocates enrichment rather than
acceleration for the most promising young mathematicians in
Britain. I am raising the question precisely because I havent
made up my mind (fully) as to the answer, and as a
nonmathematician I desire to give sound guidance to some young
people I know who are highly interested in math, and perhaps
initially enjoying good potential to learn more math.
comments anyone has.
Karl M. Bunday
(remove .de to email)
===
Subject: Re: Up/Down/Left/Right: the puzzle
> solution, you can derive a host of others by permuting rows
and/or
> permuting columns. This leads to the following canonical
solution:
> 1 2 * * (Increase to right and down)
> * 3 4 5
> * * * 6
> * * * 7
> So, there is essentially only one solution for n=4.
...
> -jiw
> 1 2 15 16
> 11 3 4 5
> 12 13 14 6
> 10 9 8 7
> 1 2 9 8
> 16 3 4 5
> 14 13 10 6
> 15 12 11 7
...
was printing one too few numbers, making 8-singulars look
like they
were 7-singulars. According to the new program, there are zero
7-singular solutions at n=4 and canonically one 8-singular
solution,
1 2 15 16
11 3 4 5
12 13 14 6
10 9 8 7
which can of course be mutated by
rows/columns/reections/rotations
to form hundreds of equivalent solutions.
In canonical form, Leroys suggested 9-singular and completion
* 2 1 * 15 2 1 16
8 3 * 7 8 3 12 7
9 * * 6 9 10 11 6
* 4 * 5 14 4 13 5
becomes
1 2 16 15
12 3 7 8
13 4 5 14
11 10 6 9
which is indeed on my list of 9-singular solutions.
-jiw
===
Subject: Why are elements in the domain mapped to a single
element in the
codomain?
This may sound like a silly question, but bare with me. Why
do functions
map
elements in their domain to a single element in the codomain?
Is it because
everything in set theory is a set, and since sets can not
contain the same
element more than once, a function can not map a domain
element to more
than
one codomain element? It may be a naive question, but I wish
to understand
this, or at least know how others understand it.
Mapped siblings to fellow siblings in a map, it really
wouldnt work since
a
person may have more than one sibling.
The following are all siblings of eachother: Bart, Lisa, and
Maggie.
Bart | Lisa
Bart | Maggie
Lisa | Bart
Lisa | Maggie
Maggie | Bart
Maggie | Lisa
If I wanted to make the relationship into a standard
function, I couldnt
because each name occurs twice in the left column. However,
if I used a
more
restricted relationship, such as siblings related to the
sibling born right
before them or themselves otherwise, I could have a function.
I think the ages go: Maggie, Bart, Lisa.
Bart | Lisa
Lisa | Lisa
Maggie | Bart
Functions are not good for showing relationships when
elements of the
domain
are related to more than one element in the codomain? What
concept exists
to
support the original relationhips?
Again, I know this may appear to be, or actually are, silly
questions, but
I
would like to know more about how people understand functions
and why it
was
seen that such a concept was a good idea.
Take care, Adam.
Dont just read it; ght it! Ask your own questions, look for
your own
examples, discover your own proofs. Is the hypothesis
necessary? Is the
converse true? What happens in the classical special case?
What about the
degenerate cases? Where does the proof use the hypothesis?
--- Paul Halmos (1916 - )
addam@rogers.com
===
Subject: Re: Why are elements in the domain mapped to a
single element in
the codomain?
> This may sound like a silly question, but bare with me. Why
do functions
map
> elements in their domain to a single element in the
codomain? Is it
because
> everything in set theory is a set, and since sets can not
contain the
same
> element more than once, a function can not map a domain
element to more
than
> one codomain element? It may be a naive question, but I
wish to
understand
> this, or at least know how others understand it.
If a map was assigned one element in the domain to two
elements in the
co-domain, how could the map discern which element to map to?
There can be
two elements in the domain mapped to one in the co-domain,
but not one in
the domain to two in the co-domain. I hope that helps.
Lurch
===
Subject: Re: Why are elements in the domain mapped to a
single element in
the codomain?
> This may sound like a silly question, but bare with me. Why
do functions
> map elements in their domain to a single element in the
codomain? Is it
> because everything in set theory is a set, and since sets
can not contain
> the same element more than once, a function can not map a
domain element
> to more than one codomain element? It may be a naive
question, but I wish
> to understand this, or at least know how others understand
it.
As a high school student, I was also bothered by that. It has
nothing to do
with sets, the reason is that a function is just dened as
mapping each
domain element to one element of the codomain.
Suppose you would allow multiple-valued funtions, eg some f :
X --> Y. Then
this induces a single-valued funtion between the power-sets
P(f) : P(X) -->
P(Y) by mapping a singleton {x} to {multiple values f(x)} and
extending it
on all subsets of X in the obvious way.
Conclusion: multiple-valued functions are not more general
that
single-valued functions.
hang my head drown my fear
till you all just disappear
reverse my forename for mail! - saibot
===
Subject: Re: Why are elements in the domain mapped to a
single element in
the codomain?
> This may sound like a silly question, but bare with me.
bare?
> Why do functions
> map elements in their domain to a single element in the
codomain?
cos thats the denition of function.
> The following are all siblings of eachother: Bart, Lisa,
and Maggie.
> Bart | Lisa
> Bart | Maggie
> Lisa | Bart
> Lisa | Maggie
> Maggie | Bart
> Maggie | Lisa
> If I wanted to make the relationship into a standard
function, I couldnt
> because each name occurs twice in the left column.
The concept you are groping after is relation. A relation
between the
sets
A and B is a subset of A x B.
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Lacan, Jacques, 79, 91-92; mistakes his penis for a square
root, 88-9
Francis Wheen, _How Mumbo-Jumbo Conquered the World_
===
Subject: Re: Why are elements in the domain mapped to a
single element in
the codomain?
> Why do functions
> map elements in their domain to a single element in the
codomain?
> cos thats the denition of function.
And what motivates the denition?
===
Subject: Re: Why are elements in the domain mapped to a
single element in
the codomain?
>> Why do functions
>> map elements in their domain to a single element in the
codomain?
>> cos thats the denition of function.
> And what motivates the denition?
cos thats what functions are like :-)
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Lacan, Jacques, 79, 91-92; mistakes his penis for a square
root, 88-9
Francis Wheen, _How Mumbo-Jumbo Conquered the World_
===
Subject: Re: Why are elements in the domain mapped to a
single element in
the codomain?
> And what motivates the denition?
> cos thats what functions are like :-)
Ah! Now I understand! lol.
===
Subject: Re: Why are elements in the domain mapped to a
single element in
the codomain?
> And what motivates the denition?
> cos thats what functions are like :-)
> Ah! Now I understand! lol.
I think the denition of function* has, in part, the same
motivation as the
order of operations rules studied in arithmetic and
beginning algebra courses: that any expression have at most
one value
associated with it.
Of course, some expressions are undened just as a function
evaluated at an input value not in its domain must be.
I hope you nd this helpful.
Kevin ONeill
_______________________________________
* In particular, I am referring to that part of the denition
that requires
that there is exactly one output
from the function when evaluated at an input in the domain of
the
function -- it is that part that distinguishes function from
relation.
===
Subject: Re: Why are elements in the domain mapped to a
single element in
the codomain?
>
> This may sound like a silly question, but bare with me.
> bare?
> Why do functions
> map elements in their domain to a single element in the
codomain?
> cos thats the denition of function.
>
> The following are all siblings of eachother: Bart, Lisa,
and Maggie.
>
> Bart | Lisa
> Bart | Maggie
> Lisa | Bart
> Lisa | Maggie
> Maggie | Bart
> Maggie | Lisa
>
> If I wanted to make the relationship into a standard
function, I
couldnt
> because each name occurs twice in the left column.
> The concept you are groping after is relation. A relation
between the
sets
> A and B is a subset of A x B.
Or alternatively, you could see it as a function whose
codomain is the
set of subsets P(S) of S:={Bart, Lisa, Maggie}
f:S -> P(S)
f(Bart)={Lisa,Maggie}
...
===
Subject: Re: Why are elements in the domain mapped to a
single element in
the codomain?
> Or alternatively, you could see it as a function whose
codomain is the
> set of subsets P(S) of S:={Bart, Lisa, Maggie}
> f:S -> P(S)
> f(Bart)={Lisa,Maggie}
> ...
Ah!
===
Subject: stochastic differential equation vs differentiation
of probability
function.
hello,
Im confused.
It seems like people are using stochastic differential
equations to
model nance etc.
but it seems like other people are also differentiating a
probability
functions.
what do those two thing above mean? Im sorry for asking such
simpleton question. But Im utterly confused here.
Can you guys suggest soem reference materials and/or websites
for a
math newbie such as myself to understand such things to a
point where
I can solve those systems?
thank you all.
===
Subject: integer~.
hello.....doctor~
nd the root such that (x^2) + x + 1 = 0 (mod 19)
----------------------------
i can~ ^.^
(x^2) + x + 1 = 0 (mod 19)
(x^2) + x - 56 = 0 (mod 19)
(x-7)(x+8) = 0 (mod 19)
so
x = 7 or -8 (mod 19)
but .......um......i want to use ind method.
so
2 is primitive root modulo 19.
and
2^0 = 1
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 13
2^6 = 7
2^7 = 14
2^8 = 9
2^9 = 18
2^10 = 17
2^11 = 15
2^12 = 11
2^13 = 3
2^14 = 6
2^15 = 12
2^16 = 5
2^17 = 10
2^18 = 1
and
(x^2) + x + 1 = 0 (mod 19)
2 {ind_(2)_x} + {ind_(2)_x} = ind_2_(18) (mod 18)
3 ind_(2)_x = 9 (mod 18)
ind_(2)_x = 3, 9, 15 (mod 18)
so
x = 8, 18, 12 (mod 19)
um......not same.
i dont know the reason.
let me advice, please~
thank you very much.
===
Subject: Re: integer~.
mina_world escribi.97:
> hello.....doctor~
> nd the root such that (x^2) + x + 1 = 0 (mod 19)
> ----------------------------
> i can~ ^.^
> (x^2) + x + 1 = 0 (mod 19)
> (x^2) + x - 56 = 0 (mod 19)
> (x-7)(x+8) = 0 (mod 19)
> so
> x = 7 or -8 (mod 19)
Or use the qudratic formula:
x = (-1 +/- sqrt(-3))/2 = 10*(-1 +/- sqrt(16)) = 10(-1 +/- 4)
= 30 or -50
> but .......um......i want to use ind method.
But you can`t do it in a additive equation ..
Ignacio Larrosa Ca.96estro
A Coru.96a (Espa.96a)
ilarrosaQUITARMAYUSCULAS@mundo-r.com
===
Subject: Re: Accessing Usenet
> [...] By the way,
The only aspect of beta thats better is its response time.
The rest looks to me like change for its own sake,
regardless of its disfunctionality.
Are you listening, Google?
Keep the old organization -- just speed it up.
===
Subject: Need help with some simple maths
Let rect(x) dene a rectangular function where its values are
1 for |x| <
0.5.
Now I can I prove that
/ a / (x-a/2)
rect(a-x)rect(x) = rect | --- | rect | ------- |
2 / (1 - |a|) /
===
Subject: Re: Need help with some simple maths
> Let rect(x) dene a rectangular function where its values
are 1 for |x|
<
0.5.
> Now I can I prove that
> / a / (x-a/2)
> rect(a-x)rect(x) = rect | --- | rect | ------- |
> 2 / (1 - |a|) /
Assuming that rect(x) =0 for |x| >= 0.5
You should separately analyse for |a| > 1 and for |a| <=1.
If |a| > 1 then (1) there is no overlap so rect(a-x)rect(x)=0
for any x and
a/2 >0.5 --> rect(a/2) = 0.
If |a| <= 1 then there is overlap.
LHS:
For a > 0 rect(a-x)rect(x)=1 for x in (a-0.5,0.5), othervise
its = 0.
For a < 0 rect(a-x)rect(x) = 1 for x in (-0.5,a+0.5),
othervise its =0.
RHS:
|(a/2)|< 0.5 --> rect(a/2) == 1.
For a>0 :
rect((x-a/2)(1-a))= 1 when
-0.5 < (x-a/2)/(1-a) < 0.5
--> -0.5(1-a) < (x-a/2) < 0.5(1-a) (since 1-a >0)
---> (a/2 - 0.5) < x - a/2 < (0.5 - a/2)
----> a-0.5 < x < 0.5
For a<0 analysis is similar.
*****
For a=0
LHS: rect(0-x)rect(x)= rect(-x)rect(x)=rect(x), since
rect(-x)=rect(x)
RHS: rect(0/2)rect((x-0/2)/(1-|0|) = 1*rect(x) = rect(x)
*****
Goran.
===
Subject: Re: Accessing Usenet
The response time is great though--from 8 hrs to a few minutes
is quite an improvement.
The front end is ne with me--I can adjust to the old or new,
though I appreciate some of the new features.
The main thing is response time. Until someone told me about
groups2 I was going to abandon Google for something faster.
Van
> [...] By the way,
--
> The only aspect of beta thats better is its response time.
> The rest looks to me like change for its own sake,
> regardless of its disfunctionality.
> Are you listening, Google?
> Keep the old organization -- just speed it up.
===
Subject: Re: integer~.
> hello.....doctor~
> nd the root such that (x^2) + x + 1 = 0 (mod 19)
> ----------------------------
> i can~ ^.^
> (x^2) + x + 1 = 0 (mod 19)
> (x^2) + x - 56 = 0 (mod 19)
> (x-7)(x+8) = 0 (mod 19)
> so
> x = 7 or -8 (mod 19)
Fine. (-8 = 11 mod 19, but same difference).
> but .......um......i want to use ind method.
What is ind method?
> so
> 2 is primitive root modulo 19.
> and
> 2^0 = 1
> 2^1 = 2
> 2^2 = 4
> 2^3 = 8
> 2^4 = 16
> 2^5 = 13
> 2^6 = 7
> 2^7 = 14
> 2^8 = 9
> 2^9 = 18
> 2^10 = 17
> 2^11 = 15
> 2^12 = 11
> 2^13 = 3
> 2^14 = 6
> 2^15 = 12
> 2^16 = 5
> 2^17 = 10
> 2^18 = 1
So 2 is a primitive root
> and
> (x^2) + x + 1 = 0 (mod 19)
> 2 {ind_(2)_x} + {ind_(2)_x} = ind_2_(18) (mod 18)
> 3 ind_(2)_x = 9 (mod 18)
You cant do this--see below.
> ind_(2)_x = 3, 9, 15 (mod 18)
> so
> x = 8, 18, 12 (mod 19)
> um......not same.
> i dont know the reason.
> let me advice, please~
> thank you very much.
You have order(2) = p-1 = 18, so
x = 2^^m, where m is mod 18, but what does that have to do
with your
eq.?
2^^2m + 2^^m = - 1 = 2^^9
but you cant add the exponents. This is not how one solves
these eqns.
Your original soln. is the only way I know of, though its good
to know about the primitive root.
Van
===
Subject: Re: integer~.
> hello.....doctor~
> nd the root such that (x^2) + x + 1 = 0 (mod 19)
> ----------------------------
> i can~ ^.^
> (x^2) + x + 1 = 0 (mod 19)
> (x^2) + x - 56 = 0 (mod 19)
> (x-7)(x+8) = 0 (mod 19)
> so
> x = 7 or -8 (mod 19)
> Fine. (-8 = 11 mod 19, but same difference).
> but .......um......i want to use ind method.
> What is ind method?
> so
> 2 is primitive root modulo 19.
> and
> 2^0 = 1
> 2^1 = 2
> 2^2 = 4
> 2^3 = 8
> 2^4 = 16
> 2^5 = 13
> 2^6 = 7
> 2^7 = 14
> 2^8 = 9
> 2^9 = 18
> 2^10 = 17
> 2^11 = 15
> 2^12 = 11
> 2^13 = 3
> 2^14 = 6
> 2^15 = 12
> 2^16 = 5
> 2^17 = 10
> 2^18 = 1
> So 2 is a primitive root
> and
> (x^2) + x + 1 = 0 (mod 19)
> 2 {ind_(2)_x} + {ind_(2)_x} = ind_2_(18) (mod 18)
> 3 ind_(2)_x = 9 (mod 18)
> You cant do this--see below.
> ind_(2)_x = 3, 9, 15 (mod 18)
> so
> x = 8, 18, 12 (mod 19)
> um......not same.
> i dont know the reason.
> let me advice, please~
> thank you very much.
> You have order(2) = p-1 = 18, so
> x = 2^^m, where m is mod 18, but what does that have to do
with your
> eq.?
> 2^^2m + 2^^m = - 1 = 2^^9
> but you cant add the exponents. This is not how one solves
these eqns.
thank you. but, um....i cant understand.
i know that ind ab = ind a + ind b
------------------------------------
and i know the other example.
14x = 25 (mod 37)
ind 14 + ind x = ind 25 (mod 36)
33 + ind x = 10 (mod 36)
ind x = -23 = 13 (mod 26)
x = 15 (mod 37)
------------------------------------
i just used this method for original problem.
um.......i dont know the reason that differ the result.
let me advice, please
thank you very much~
===
Subject: Re: integer~.
mina_world escribi.97:
> hello.....doctor~
> nd the root such that (x^2) + x + 1 = 0 (mod 19)
> ----------------------------
> i can~ ^.^
> (x^2) + x + 1 = 0 (mod 19)
> (x^2) + x - 56 = 0 (mod 19)
> (x-7)(x+8) = 0 (mod 19)
> so
> x = 7 or -8 (mod 19)
>> Fine. (-8 = 11 mod 19, but same difference).
> but .......um......i want to use ind method.
>> What is ind method?
> so
> 2 is primitive root modulo 19.
> and
> 2^0 = 1
> 2^1 = 2
> 2^2 = 4
> 2^3 = 8
> 2^4 = 16
> 2^5 = 13
> 2^6 = 7
> 2^7 = 14
> 2^8 = 9
> 2^9 = 18
> 2^10 = 17
> 2^11 = 15
> 2^12 = 11
> 2^13 = 3
> 2^14 = 6
> 2^15 = 12
> 2^16 = 5
> 2^17 = 10
> 2^18 = 1
>> So 2 is a primitive root
> and
> (x^2) + x + 1 = 0 (mod 19)
> 2 {ind_(2)_x} + {ind_(2)_x} = ind_2_(18) (mod 18)
> 3 ind_(2)_x = 9 (mod 18)
>> You cant do this--see below.
> ind_(2)_x = 3, 9, 15 (mod 18)
> so
> x = 8, 18, 12 (mod 19)
> um......not same.
> i dont know the reason.
> let me advice, please~
> thank you very much.
>> You have order(2) = p-1 = 18, so
>> x = 2^^m, where m is mod 18, but what does that have to do
with your
>> eq.?
>> 2^^2m + 2^^m = - 1 = 2^^9
>> but you cant add the exponents. This is not how one
solves these
>> eqns.
> thank you. but, um....i cant understand.
> i know that ind ab = ind a + ind b
> ------------------------------------
> and i know the other example.
> 14x = 25 (mod 37)
> ind 14 + ind x = ind 25 (mod 36)
> 33 + ind x = 10 (mod 36)
> ind x = -23 = 13 (mod 26)
> x = 15 (mod 37)
> ------------------------------------
> i just used this method for original problem.
> um.......i dont know the reason that differ the result.
> let me advice, please
> thank you very much~
Ummm... In that example, there arent additions in the
equation, only
multiplications.
> (x^2) + x + 1 = 0 (mod 19)
You can do
x^2 + x = 18 (mod 19)
ind_(2)(x^2 + x) = ind_2(18) (mod 18)
But from here you cant go to
> 2 {ind_(2)_x} + {ind_(2)_x} = ind_2_(18) (mod 18)
bas you cant do log(a + b) = log(a) + log(b)
Ignacio Larrosa Ca.96estro
A Coru.96a (Espa.96a)
ilarrosaQUITARMAYUSCULAS@mundo-r.com
===
Subject: Re: integer~.
> hello.....doctor~
> nd the root such that (x^2) + x + 1 = 0 (mod 19)
> ----------------------------
> i can~ ^.^
> (x^2) + x + 1 = 0 (mod 19)
> (x^2) + x - 56 = 0 (mod 19)
> (x-7)(x+8) = 0 (mod 19)
> so
> x = 7 or -8 (mod 19)
> Fine. (-8 = 11 mod 19, but same difference).
> but .......um......i want to use ind method.
> What is ind method?
> so
> 2 is primitive root modulo 19.
> and
> 2^0 = 1
> 2^1 = 2
> 2^2 = 4
> 2^3 = 8
> 2^4 = 16
> 2^5 = 13
> 2^6 = 7
> 2^7 = 14
> 2^8 = 9
> 2^9 = 18
> 2^10 = 17
> 2^11 = 15
> 2^12 = 11
> 2^13 = 3
> 2^14 = 6
> 2^15 = 12
> 2^16 = 5
> 2^17 = 10
> 2^18 = 1
> So 2 is a primitive root
> and
> (x^2) + x + 1 = 0 (mod 19)
> 2 {ind_(2)_x} + {ind_(2)_x} = ind_2_(18) (mod 18)
> 3 ind_(2)_x = 9 (mod 18)
> You cant do this--see below.
> ind_(2)_x = 3, 9, 15 (mod 18)
> so
> x = 8, 18, 12 (mod 19)
> um......not same.
> i dont know the reason.
> let me advice, please~
> thank you very much.
> You have order(2) = p-1 = 18, so
> x = 2^^m, where m is mod 18, but what does that have to do
with your
> eq.?
> 2^^2m + 2^^m = - 1 = 2^^9
> but you cant add the exponents. This is not how one solves
these eqns.
> Your original soln. is the only way I know of, though its
good
> to know about the primitive root.
> Van
===
Subject: Re: The relationship between mass, inertia, size and
weight
>>
>>Masses whose relative density is lighter than that of water
are less
>>dense and will oat in it. Masses whose relative density is
heavier
>>than water are more dense than water and will sink in it.
>> Using your tables, would a boat, that is made out of
cement, sink?
>Boats made of seement, tin or steel will sink if they have
paper bottoms
like you.
You did not answer the question. Im still asking it.
/BAH
Subtract a hundred and four for e-mail.
===
Subject: Re: The relationship between mass, inertia, size and
weight
In sci.math, jmfbahciv@aol.com
<40f11b9d$0$1167$61fed72c@news.rcn.com>:
> Masses whose relative density is lighter than that of water
are less
>dense and will oat in it. Masses whose relative density is
heavier
>than water are more dense than water and will sink in it.
>
> Using your tables, would a boat, that is made out of
cement, sink?
>
>>Boats made of seement, tin or steel will sink if they have
paper bottoms
> like you.
> You did not answer the question. Im still asking it.
Its worth noting that many boats are made of steel anyway.
Now steel is heavier than water, but the boats oat anyway.
Hmm! Perhaps its because most of the boat is made of air,
and therefore the density is less than 1 kg/liter -- the
density of the water -- and it oats.
Even a boat with no bottom would oat nicely -- if the top
is enclosed so that the air doesnt leak out. There are
presumably some issues with stability management, though;
if such a boat turns over it will sink like a stone once
the air leaves through the open no-longer-bottom. Also,
Im not sure what would happen as the boat turns into a
submarine and goes deeper into the murky depths, increasing
pressure and decreasing volume of the trapped air --
and bouyancy of the vessel. Most likely, if the boat is
forced beyond a certain depth, it will lose its bouyancy
and continue to sink, even if the air doesnt leak out.
If one is lucky enough to nd such a sunken boat one can
pump air into it to reoat it, assuming the stability
issues, etc, are dealt with -- but that would take a lot
of work. (Literally. Im hoping you saw my previous
computations regarding compressing air in response to a
rather silly proposal of sinking a 1-km shaft into the
ocean to generate electric power.) Id have to compute
it but it would probably take the same amount of work to
attach the boat to a crane and lift it out -- assuming
the crane was near the boat already.
Darn that 2LoT. :-)
> /BAH
> Subtract a hundred and four for e-mail.
#191, ewill3@earthlink.net
Its still legal to go .sigless.
===
Subject: Re: The relationship between mass, inertia, size and
weight
The inertia; size and weight of a given mass of matter are
related
> through its density:
> [snip crap]
>>
>> In free fall, Head?
> No puke: Only on Earths surface.
> So one on a mountain and another in a valley, what then?
In those places a given mass will have - and exert - weight:
So the
relationship seems to apply very well there; but not in free
fall.
Wouldnt you agree?
Shead
===
Subject: Re: Why are elements in the domain mapped to a
single element in
the codomain?
I would just say it this way. For a function, we want to have
a y =
f(x)
for every x. If f were multi-valued, i.e., had more than one
y to an x,
we wouldnt have a unique y for each x, i.e. our function
would not be
well dened.
For a function, we want each x to give a unique y.
> This may sound like a silly question, but bare with me. Why
do
functions
> map elements in their domain to a single element in the
codomain?
Is it
> because everything in set theory is a set, and since sets
can not
contain
> the same element more than once, a function can not map a
domain
element
> to more than one codomain element? It may be a naive
question, but
I wish
> to understand this, or at least know how others understand
it.
> As a high school student, I was also bothered by that. It
has nothing
to do
> with sets, the reason is that a function is just dened as
mapping
each
> domain element to one element of the codomain.
> Suppose you would allow multiple-valued funtions, eg some f
: X -->
Y. Then
> this induces a single-valued funtion between the power-sets
P(f) :
P(X) --P(Y) by mapping a singleton {x} to {multiple values
f(x)} and
extending it
> on all subsets of X in the obvious way.
> Conclusion: multiple-valued functions are not more general
that
> single-valued functions.
> --
> hang my head drown my fear
> till you all just disappear
> reverse my forename for mail! - saibot
===
Subject: Re: Does a high SAT score predict mathematical
talent?
> Counter example: Erdos.
> Mind all that amphetamine helped keep his mind sprightly.
Did he really take speed?
There is an excellent 1 hr bio about him on PBS every once in
a while.
Has anyone else seen it?
Also, was it the Nova about Einsteins wife that talked about
the Hungarians support for mathematicians around 1900?
Or was that the show on Erdos--I cant recall.
I think Erdos mother was also a mathematician, so he had a lot
of support. I had to laugh--his mother had done everything for
him and he could do _nothing_ for himself when he 1st came to
England. And no permanent address--a totally independent
person.
A great life in some ways--if you dont mind no home or love
life.
Anyway, I was impressed with what Hungary used to do.
That is what the US needs to do. There were math clubs
for high school aged students interested in math, and many
journals, like Acta Mathematica.
Van
===
Subject: Re: Does a high SAT score predict mathematical
talent?
> Counter example: Erdos.
> Mind all that amphetamine helped keep his mind sprightly.
> Did he really take speed?
> There is an excellent 1 hr bio about him on PBS every once
in a while.
> Has anyone else seen it?
> Also, was it the Nova about Einsteins wife that talked
about
> the Hungarians support for mathematicians around 1900?
> Or was that the show on Erdos--I cant recall.
> I think Erdos mother was also a mathematician, so he had a
lot
> of support. I had to laugh--his mother had done everything
for
> him and he could do _nothing_ for himself when he 1st came
to
> England. And no permanent address--a totally independent
person.
> A great life in some ways--if you dont mind no home or
love life.
> Anyway, I was impressed with what Hungary used to do.
> That is what the US needs to do. There were math clubs
> for high school aged students interested in math, and many
> journals, like Acta Mathematica.
> Van
Erdoss mother was not a mathematician, but a HS math
teacher. In the
spring term, 1966, the two of them spent a term at the
University of
Illinois (Urbana) and stayed at the student union. Every
afternoon
around 3, many members of the math dept would have coffee at
the union
and she would often join us. And once she told us that her
son was
really a ne mathematician. I dont know if he ever before or
after
had spent a whole term in one place. But you cannot judge the
Hungarian mathematical educational system by Erdos, who was
truly sui
generis. There was an incredible generation of
mathematicians, back
in the early 20th, but I think there were some very special
conditions, not easily reproduced.
I had solid Bs in 7th and 8th grade math. This changed in
HS, but
still I never qualied for AP (my class, graduating in 54,
was the
rst, experimental, class of it, at least in my scholl).
Despite
solid As, math still didnt interest me in the least.
Science did,
until later I discovered I was no good in the lab. But then I
discovered modern (now classical) algebra and the die was
cast.
As for the college boards, well all I can say is that all
three of my
kids did better in the math SATs than I did , and not one of
them had
the slightest interest in majoring in it. Incidentally, my
best work
was done between the ages of 30 and 35. But I have some good
ideas
since.
Do schools kill interest in math (and science)? Yes, I think
they
largely do. The problem is that the elementary school
teachsers
absolutely hate math (in general; obviously there are
exceptions) and
dont do much better with science. As long as they are both
underpaid
and protected by unions, this is unlikely to change. One of
the
unintended side-effects of womens lib has been that smart
young women
have other choices than to be either teachers of nurses. I
wouldnt
turn that clock back, but I would upgrade the status of
teaching as a
profession. We send our kids off to school, but our allergy
to taxes
results in doing it on the cheap.
===
Subject: Re: Does a high SAT score predict mathematical
talent?
>>Counter example: Erdos.
>>Mind all that amphetamine helped keep his mind sprightly.
> Did he really take speed?
Yes. Erdos really did take amphetamines quite habitually. I
have
perused both of the book-length biographies of Erdos
available in
American public libraries.
> I think Erdos mother was also a mathematician, so he had a
lot
> of support. I had to laugh--his mother had done everything
for
> him and he could do _nothing_ for himself when he 1st came
to
> England. And no permanent address--a totally independent
person.
> A great life in some ways--if you dont mind no home or
love life.
It appears that Erdos unusual social life, both growing up
and as
a fully grown adult, had something to do with his sustained
mathematical productivity. A rather intriguing off-hand
suggestion
in a seminar monograph about evolutionary biology and human
intelligence
The Nature of Intelligence (2000) edited by Gregory R. Bock,
Jamie
A. Goode, and Kate Webb (Chichester: Wiley) Novartis
Foundation
Symposium 233)
is that professional output, in mathematics and other
professions,
is related to sexual display. A young mathematician seeking a
life
partner will get a Ph.D. and make tenure, and then settle down
once able to reproduce offspring as well as ideas. The
prediction
of that hypothesis would be that most academics, not just in
mathematics, do their most conspicuous work (or most
energy-consuming work) at the age when they are about to start
their families.
> Anyway, I was impressed with what Hungary used to do.
> That is what the US needs to do. There were math clubs
> for high school aged students interested in math, and many
> journals, like Acta Mathematica.
I agree that the competition culture fostered in secondary
education in Hungary for the last century has had benecial
effects on the mathematics community in that country. An
effort in
the United States, which reaches worldwide, to build a similar
kind of competition culture in the Internet era can be found
at
http://www.artofproblemsolving.com
especially at that sites very useful online forums, which are
fully international in participation. I wish something of that
kind had existed when I was a kid in the early 1970s. I will
tentatively guess, inviting comments from participants in this
sci.math newsgroup, that helping young people nd soulmates
with
whom they can discuss math helps them develop as productive
mathematicians over the course of a LONG [grin] lifetime. Does
that make sense to everyone else reading this thread?
are most welcome.
===
Subject: Re: Atheist MorituriMax
>>We know God by faith (the
>>original meaning of faith is knowledge), but faith is a
gift, and you
>>have to ask for it.
> Funny kind of gift, that you have to ask for it.
I guess he meant youd have to accept it.
Matthijs.
===
Subject: Re: Atheist MorituriMax
> Mitch, there is a lot to say about this subject, and it
would be too
> long to say it all. God transcends physics and math; He
created them.
> God is innite, and the universe contains Him, that is why
the
> universe is innite. There has always been God, that is why
time is
> innite, it did not start at a certain moment, nor will it
end at
> another.
> None of which contributes in any way to the sum of human
understanding.
> Its just meaningless wafe.
> We know God by faith (the
> original meaning of faith is knowledge), but faith is a
gift, and you
> have to ask for it.
> Funny kind of gift, that you have to ask for it. Youd
think an
> omnipotent God would just grant it to everyone. It would
save everyone a
> whole lot of bother, and mean a lot more worshipping for
Him, which He
> seems to like. Why is that, by the way? Why does He get off
on all that
> adoration? Is He mentally ill?
> If you observe things around you, you realize that
> nothing happens by itself, and if you observed some
complicated
> gadget, you realize the person who did it had a lot of very
> specialized knowledge. Observe any plant, animal, or human
being, you
> know they did not make themselves, and the technology and
knowledge it
> must have required to make them, are clearly beyond our
understanding.
> Agree?
> Well obviously rational people dont agree, since this is
just the tired
> old teleological argument so eloquently dismissed by (for
example)
> Richard Dawkins in The Blind Watchmaker.
Let us suppose that somebody invented grammar, and let us
call that
person a grammarian. Could you use grammar to prove the
grammarian
never existed? Trying to use physics to prove God does not
exist is
the same thing. Questioning why God does not do things the
way we
think they should be done, is a bit pretentious, it seems to
me,
considering that, obviously, the intelligence and power of
God are a
zillion orders of magnitude greater than ours.
Peter.
===
Subject: Re: Atheist MorituriMax
X-URL:
http://mygate.mailgate.org/mynews/sci/sci.math/
9c5425d04edc3518e3f2d3d0e5b3bf
39.48257%40mygate.mailgate.org
> obviously, the intelligence and power of God are a
> zillion orders of magnitude greater than ours.
Obviously? Only to the profoundly brainwashed.
If the intelligence of a non-existent God are a
zillion orders of magnitude greater than ours,
Stanford and Binet must have put the wrong arithmetic
sign on the results of human IQ tests.
Do you think you could keep this drooling
feeble-minded drivel out of the sci.* hierarchy and
in the talk.atheism and talk.religion.* newsgroups
where it belongs?
That you are just bubbling over with a need to
chatter about your fairy tale God only means that
decaying matter like your brain tends to ourgas.
People participating in sci.* newsgroups are not
correspondingly bubbling over with needs to read
your outgassing, perhaps because most participants
dont (yet) have brains trying desperately to
recycle themselves.
HTH
xanthian.
===
Subject: Re: Atheist MorituriMax
>>obviously, the intelligence and power of God are a
>>zillion orders of magnitude greater than ours.
> Obviously? Only to the profoundly brainwashed.
> If the intelligence of a non-existent God are a
> zillion orders of magnitude greater than ours,
> Stanford and Binet must have put the wrong arithmetic
> sign on the results of human IQ tests.
> Do you think you could keep this drooling
> feeble-minded drivel out of the sci.* hierarchy and
> in the talk.atheism and talk.religion.* newsgroups
> where it belongs?
> That you are just bubbling over with a need to
> chatter about your fairy tale God only means that
> decaying matter like your brain tends to ourgas.
> People participating in sci.* newsgroups are not
> correspondingly bubbling over with needs to read
> your outgassing, perhaps because most participants
> dont (yet) have brains trying desperately to
> recycle themselves.
Why do you think *you* are the one to decide what people here
want to
read about? Let people speak for themselves plz. You are
certainly not
speaking for me.
M.
===
Subject: Re: Atheist MorituriMax
X-URL:
http://mygate.mailgate.org/mynews/sci/sci.math/
19dfb2fcf69d22e9f1d0f398e5efcc
42.48257%40mygate.mailgate.org
> Why do you think *you* are the one to decide what
> people here want to read about?
Try to suppress muddy thinking before it hits your
keyboard.
The issue is not what people here want to read
about, but what people want to read about here.
There are a long list of other newsgroups where
ranting about the existence of one deity, and the utter
nonexistence of equally unlikely other deities, is
right on charter. I cannot too highly recommend
talk.origins, talk.atheism, and talk.religion.* for
these purposes. I cannot too highly deprecate sci.*
and comp.* being used for these purposes.
Clarifying this issue is the purpose of newsgroup
charters. If you think the charter of, in this case
sci.math, calls for fatuous outpourings from
brain-damaged proponents of theistic psychobabble,
on the topic of the existence or non-existence of
their deity-of-the-week, please take the trouble to
point out the relevant text in the charter.
Otherwise, have the good grace to shut up on the
subject.
> Let people speak for themselves plz. You are
> certainly not speaking for me.
How sad for you. I am, however, speaking for the
utility of newsgroup charters, and against the
years long every newsgroup is appropriate for every
topic we vandals care to discuss there campaign of
David Hayes and his minions, as I have been since
1991 when I rst encountered his cadre of the
clueless, the destructive, and the mindless, forging
approvals to moderated newsgroups.
HTH
xanthian.
===
===
Subject: Re: integer~.
> mina world
escribi:
> hello.....doctor~
> nd the root such that (x^2) + x + 1 = 0 (mod 19)
> ----------------------------
> i can~ ^.^
> (x^2) + x + 1 = 0 (mod 19)
> (x^2) + x - 56 = 0 (mod 19)
> (x-7)(x+8) = 0 (mod 19)
> so
> x = 7 or -8 (mod 19)
> Or use the qudratic formula:
> x = (-1 +/- sqrt(-3))/2 = 10*(-1 +/- sqrt(16)) = 10(-1 +/-
4) = 30
or -50
> ==but .......um......i want to use ind method.
> But you can`t do it in a additive equation ..
Right. Its the rule of exponents. exp(a)*exp(b) = exp(a+b),
but mina, you were trying to do something with
exp(a) + exp(b) = 2^^2m + 2^^m ; you cant do anything with
this.
This is not a way to do this problem.
Van
===
Subject: Re: sci.math trolls: Robin Chapman is the British
version of David
C. Ullrich
>
>>[...]
>>Theyre both very good at spotting
>>mistakes and writing them up in English ASCII.
>
>Im good at writing up _mistakes_? Well *&%! you then.
>>
>>ROTFLMAO.
>So you assume I was just kidding? Kids today, aint
>got no respect, lemme tell ya...
>>Yessir, bosssir.
>Thats more like it. (We can revoke your membership,
>you know.)
Membership?!!! Uh-oh. Now what am I responsible for?
/BAH
Subtract a hundred and four for e-mail.
===
Subject: Re: plausibility argument (sefara) for twin primes
conjecture
. Honestly, who > cares if you can give a rigorous proof of
something
that is almost > certainly true by common sense?
> Craig
Craig forgets that Mathematics is an art and a game. There is
a great
pleasure to nd the logical or arithmetical reason why a
conjecture
is true.
Euclid was not happy until he proved the obvious: There exists
innitely many primes.
In Chess it is delicious to know why there is a mate in n
moves.
Also, it is a thriller the endeavor to demosntrate that the
Twin Prime
Conjecture is undecidable within standard arithmetic (I
particularly
think so)
===
Subject: Re: plausibility argument (sefara) for twin primes
conjecture
|I dont like this example because its one of those examples
where what
|people are thinking and saying are two different things.
When a layman
|hears or says continuous curve s/he has a particular idea of
|something, usually a very tame kind of curve for which the
intuition is
|correct in asserting it cannot ll a region of space. This
is more
|of an example of miscommunication rather than a case of
intuition
|leading one astray.
People seem to have the same intuition, though, even after
having
been given a rigorous denition.
The fact that its possible to have an informal notion like
this without
a denition in mind is one reason for pursuing informal
arguments
like the original poster mentioned. Its also a reason why
its useful
to go beyond them, because one can study curves in an informal
way for a long time before you realize theres any such thing
as
what we call a space-lling curve (whether its the kind of
thing you
had in mind by a curve or not). Having to say what additional
properties you mean to assume of your nice smooth curves adds
to the clarity of the exposition of their properties.
Keith Ramsay
===
Subject: Becoming Human
http://www.becominghuman.org/
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca
92040-2905,tel:
619-5610814 :
URL : http://home.earthlink.net/~tftn
URL : http://victorian.fortunecity.com/carmelita/435/
===
Subject: Re: Becoming Human
>http://www.becominghuman.org/
Now this is curious. I could swear I just read a post from
you where you exhort us to actually answer questions. I
dont see what mathematical question this answers.
Nor what questions are answered by any of your posts in the
last few days...
************************
David C. Ullrich
===
Subject: Re: Becoming Human
> http://www.becominghuman.org/
Any relevance to mathematics?
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Lacan, Jacques, 79, 91-92; mistakes his penis for a square
root, 88-9
Francis Wheen, _How Mumbo-Jumbo Conquered the World_
===
Subject: Re: Continued-Fraction /Recursion Puzzle
Copied previous post as spoiler-space:
> Your mission is to determine a closed form for the sequence
{a(k)}.
>
> (Below, each [....] is a continued fraction of +- rational
terms.)
>
>
> a(1) = 1.
>
> a(2) = 1/2.
>
> For m >= 1,
>
> a(2m+1) *(-1)^m =
>
> [1; 1, a(2), -2a(3), -a(4), 2a(5),
> a(6), -2a(7), -a(8), 2a(9),...,+-a(2m)]
>
> + 2 *sum{k=1 to m} a(2k-1) (-1)^k.
>
> Above, the terms of the continued fraction follow the
pattern:
>
> ..., a(4j-2), -2 a(4j-1), -a(4j), 2 a(4j+1),...
>
> as j = 1, 2, 3,...
>
> For m >= 1,
>
> a(2m+2) *(-1)^m =
>
> (1/2)[1; 1, a(3)/2, -4a(4), -a(5)/2, 4a(6),
> a(7)/2, -4a(8), -a(9)/2, 4a(10),...,+-a(2m+1)/2]
>
> + 2 *sum{k=1 to m} a(2k) (-1)^k.
>
> Above, the terms of the continued fraction follow the
pattern:
>
> ..., a(4j-1)/2, -4 a(4j), -a(4j+1)/2, 4 a(4j+2),...
>
> as j = 1, 2, 3,...
>
> Leroy Quet
> It is simpler to do this instead in terms of the sequence
{b(k)},
> where:
> b(m2) = a(m2)(-1)^(m+1),
> b(m2-1) = a(m2-1)(-1)^(m+1).
> We can then rewrite the above as:
> b(1) = 1.
> b(2) = 1/2.
> For m >= 1,
> b(2m+1) =
> [1; 1, b(2), 2b(3), b(4), 2b(5),
> b(6), 2b(7), b(8), 2b(9),..., b(2m)]
> - 2 *sum{k=1 to m} b(2k-1).
> Above, the terms of the continued fraction follow the
pattern:
> ..., b(2j), 2 b(2j+1),...
> as j = 1, 2, 3,...
> For m >= 1,
> b(2m+2) =
> (1/2)[1; 1, -b(3)/2, 4b(4), -b(5)/2, 4b(6),
> -b(7)/2, 4b(8), -b(9)/2, 4b(10),..., -b(2m+1)/2]
> - 2 *sum{k=1 to m} b(2k).
> Above, the terms of the continued fraction follow the
pattern:
> ..., -b(2j+1)/2, 4 b(2j+2),...
> as j = 1, 2, 3,...
> Leroy Quet
Using the result in Continued Fraction = Sum (the general
result):
I get:
a(m) = (m-1)!!/m!!,
where m!! is the double-factorial,
m!! = m(m-2)(m-4)...*{1 or 2}.
In other words,
a(2m) = (2m)!/(m!^2 *4^m),
a(2m-1) = (m-1)!^2 *4^(m-1)/(2m-1)!,
and
b(2m) = (-1)^(m+1) (2m)!/(m!^2 *4^m),
b(2m-1) = (-1)^(m+1) (m-1)!^2 *4^(m-1)/(2m-1)!
Leroy Quet
===
Subject: Galileos constant [g/2]
Galileo discovered that bodies at Earths surface -
regardless of
their mass - will fall with a constant; average rate of
change in
position: This rate of change is a ratio of its change in
position
[s], per a unit of time [t], and can be written
mathematically as: s/t
= (about) 16/sec.
Furthermore, they will continue to fall at this rate [s/t =
16/sec]
for each consecutive second thereafter: Which constant can be
written
mathematically as: s/t^2 = 16/sec^2.
Among other things, this constant is useful in nding the
change in
position of a free falling mass at any instant; point in
time: Where s
= (16/sec^2)t^2: Without the calculus!
Any questions? Shead
===
Subject: Re: Galileos constant [g/2]
> Galileo discovered that bodies at Earths surface -
regardless of
> their mass - will fall with a constant; average rate of
change in
> position: This rate of change is a ratio of its change in
position
> [s], per a unit of time [t], and can be written
mathematically as: s/t
> = (about) 16/sec.
> Furthermore, they will continue to fall at this rate [s/t =
16/sec]
> for each consecutive second thereafter: Which constant can
be written
> mathematically as: s/t^2 = 16/sec^2.
> Among other things, this constant is useful in nding the
change in
> position of a free falling mass at any instant; point in
time: Where s
> = (16/sec^2)t^2: Without the calculus!
> Any questions? Shead
Yeah. I got some.
Don, why dont you take some junior college courses in
calculus or
maybe some non-calculus physics courses? Then go for physics
with
calculus. Start small, and work your way up. Youve got some
time
left. You might need to learn more algebra rst but maybe
there are
some remedial high school courses offered in your vicinity,
and that
might only take half a year. Youll quickly learn what a
complete
fool youve been but in the end youll have a real sense of
accomplishment.
You know, if you learn enough you might even be able to help
some
young person to get into math and science. Right now youll
only
confuse them and put them on the road to failure.
---DPM
===
Subject: Re: Galileos constant [g/2]
> Galileo discovered that bodies at Earths surface -
regardless of
> their mass - will fall with a constant; average rate of
change in
> position: This rate of change is a ratio of its change in
position
> [s], per a unit of time [t], and can be written
mathematically as: s/t
> = (about) 16/sec.
> Furthermore, they will continue to fall at this rate [s/t =
16/sec]
> for each consecutive second thereafter: Which constant can
be written
> mathematically as: s/t^2 = 16/sec^2.
> Among other things, this constant is useful in nding the
change in
> position of a free falling mass at any instant; point in
time: Where s
> = (16/sec^2)t^2: Without the calculus!
> Any questions? Shead Don, why dont you take some junior college courses in
calculus or
> maybe some non-calculus physics courses? Then go for
physics with
> calculus. Start small, and work your way up. Youve got
some time
> left. You might need to learn more algebra rst but maybe
there are
> some remedial high school courses offered in your vicinity,
and that
> might only take half a year. Youll quickly learn what a
complete
> fool youve been but in the end youll have a real sense of
> accomplishment.
> You know, if you learn enough you might even be able to
help some
> young person to get into math and science. Right now youll
only
> confuse them and put them on the road to failure.
> ---DPM
...putting them on the road to failure.
===
Subject: Re: Galileos constant [g/2]
> Galileo discovered that bodies at Earths surface -
regardless of
> their mass - will fall with a constant; average rate of
change in
> position:
You could enter for the next Olympic games if they had an
event
called stupidity. In the art of demonstrating maximum
stupidity
and lack of understanding in the fewest words you are
something
of a genius.
Martin Hogbin
===
Subject: Re: Galileos constant [g/2]
Nothing.
> Galileo discovered
Galilei, Galileo. Discorsi e Dimostrazioni Matematiche
Intorno a
Due Nuove Scienze (Appresso gli Elsevirii, Leida: 1638)
1638, Dumb Donny Head. Your watch is slow, Dumb Donny
Head.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
===
Subject: Re: Galileos constant [g/2]
> Galileo discovered that bodies at Earths surface -
regardless of
> their mass - will fall with a constant; average rate of
change in
> position: This rate of change is a ratio of its change in
position
> [s], per a unit of time [t], and can be written
mathematically as: s/t
> = (about) 16/sec.
> Furthermore, they will continue to fall at this rate [s/t =
16/sec]
> for each consecutive second thereafter: Which constant can
be written
> mathematically as: s/t^2 = 16/sec^2.
> Among other things, this constant is useful in nding the
change in
> position of a free falling mass at any instant; point in
time: Where s
> = (16/sec^2)t^2: Without the calculus!
You own Galileo an apology.
===
Subject: Re: Galileos constant [g/2]
>
> Galileo discovered that bodies at Earths surface -
regardless of
> their mass - will fall with a constant; average rate of
change in
> position: This rate of change is a ratio of its change in
position
> [s], per a unit of time [t], and can be written
mathematically as: s/t
> = (about) 16/sec.
>
> Furthermore, they will continue to fall at this rate [s/t =
16/sec]
> for each consecutive second thereafter: Which constant can
be written
> mathematically as: s/t^2 = 16/sec^2.
>
> Among other things, this constant is useful in nding the
change in
> position of a free falling mass at any instant; point in
time: Where s
> = (16/sec^2)t^2: Without the calculus!
>
> You own Galileo an apology.
No! Its you and the church who owe Galileo an apology; for
not
appreciating his talent.
Shead
===
Subject: Re: Galileos constant [g/2]
> Galileo discovered that bodies at Earths surface -
regardless of
> their mass - will fall with a constant; average rate of
change in
> position: This rate of change is a ratio of its change in
position
> [s], per a unit of time [t], and can be written
mathematically as: s/t
> = (about) 16/sec.
The acceleration due to gravity varies by latitude. It is
higher at the
poles and less at the equator. See Newtons law of graviation.
Tell me sHead, what is g at an altitute of 22,000 km msl.
The accerlation is proprtional to the Mass of the Earth and
inversely
proportion to the square of the distance from the center of
mass of the
Earth. That is why things acclerate more gently on the Moon.
Bob Kolker
===
Subject: Re: Galileos constant [g/2]
> Galileo discovered that bodies at Earths surface -
regardless of
> their mass - will fall with a constant; average rate of
change in
> position: This rate of change is a ratio of its change in
position
> [s], per a unit of time [t], and can be written
mathematically as: s/t
> = (about) 16/sec.
> The acceleration due to gravity varies by latitude. It is
higher at the
> poles and less at the equator. See Newtons law of
graviation.
You probably know that it has to do with the centrifugal
effect of
Earths rotation around the center of mass of the Earth-moon
system;
which affects the tides.
> Tell me sHead, what is g at an altitute of 22,000 km msl.
I dont know or care, maybe you do? Some years ago I gured
that g
for the moons acceleration toward Earth; at 240,000 miles
above Earth
was almost 22 miles/hour^2, and Earths acceleration [g]
toward the
moon was almost 0.27 miles/hour^2.
Id guess that _thats_ about what they are now; a ratio of
about
1/80.45; or vice versa.
> The accerlation is proprtional to the Mass of the Earth and
inversely
> proportion to the square of the distance from the center of
mass of the
> Earth. That is why things acclerate more gently on the Moon.
OH, I see said the blind man;^)
Shead >The acceleration due to gravity varies by latitude. It is
higher at the
>>poles and less at the equator. See Newtons law of
graviation.
> You probably know that it has to do with the centrifugal
effect of
> Earths rotation around the center of mass of the
Earth-moon system;
> which affects the tides.
The lack of spherical symmetry of the earth makes the
gravitational
acceleration variable from place to place. If the earth were
attened
and it did not rotate, gravity would be greater at the poles
and less at
the equator.
Bob Kolker
===
Subject: Re: Galileos constant [g/2]
> You probably know that it has to do with the centrifugal
effect of
> Earths rotation around the center of mass of the
Earth-moon system;
> which affects the tides.
It would be true even if the earth did not rotate.
Bob Kolker
===
Subject: Re: Galileos constant [g/2]
>> You probably know that it has to do with the centrifugal
effect of
>> Earths rotation around the center of mass of the
Earth-moon system;
>> which affects the tides.
>It would be true even if the earth did not rotate.
>Bob Kolker
So, if we have to pick between two fools who each pick only
one of the
causes (Bob Kolker only called our attention to one of them
as well,
saying See Newtons law of graviation), which one should we
go with?
Id go with Shead, since his cause accounts for 65% of the
difference.
===
Subject: Integer Sequence Language Equations
I am posting this guess-the-sequences-rule puzzle with an
added
element (so that it is harder, though not impossible, to
argue that
there are many many solutions for each sequence).
As in the typical language equation, replace each letter with
a word
that starts with the same letter so as to describe the
sequences
rules.
(None of these sequences are, as of now, in the EIS yet.)
(And the same letter repeated in each description may refer
to a
different word.)
(Hopefully, I have calculated the sequences correctly, since
I gured
each by hand.)
1)
1, 1, 2, 3, 24, 5, 720, 315,...
a(m) = L D of m F C T m.
2)
1, 1, 2, 2, 4, 2, 6, 2, 7, 3, 10, 3,...
a(m) = N of P T of S R P T m.
3)
0, 1, 5, 2, 34, 324,...
a(m) = m F T F P of mth H N.
4)
1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0,...
If a(m) = 0, P C S I R,
If a(m) = 1, P C S I F B 0, T I R.
Leroy Quet
===
Subject: Re: Integer Sequence Language Equations
>I am posting this guess-the-sequences-rule puzzle with an
added
>element (so that it is harder, though not impossible, to
argue that
>there are many many solutions for each sequence).
>As in the typical language equation, replace each letter
with a word
>that starts with the same letter so as to describe the
sequences
>rules.
>(None of these sequences are, as of now, in the EIS yet.)
>(And the same letter repeated in each description may refer
to a
>different word.)
>(Hopefully, I have calculated the sequences correctly, since
I gured
>each by hand.)
>2)
>1, 1, 2, 2, 4, 2, 6, 2, 7, 3, 10, 3,...
>a(m) = N of P T of S R P T m.
Im not sure about this one. I thought I had a denition that
tted, but applying it strictly would give each term zero.
(What if there is no P T?)
John Roberts-Jones
===
Subject: Inertial motion
Whereas Galileos natural inertial motion may have been
unaccelerated
circular motion; around the world (?): Newtons natural
inertial
motion was unaccelerated motion in a straight line; at a
constant
speed.
Newton postulated his circular motion as being accelerated
from his
inertial unaccelerated motion; by a centripetally directed
force;
which he called the force of gravity.
Todays inertial unaccelerated motion may include orbital,
and any
other motion in between; including free fall.
Shead
===
Subject: Re: Inertial motion
> Whereas Galileos
Galilei, Galileo. Discorsi e Dimostrazioni Matematiche
Intorno a
Due Nuove Scienze (Appresso gli Elsevirii, Leida: 1638)
Do you speak Italian, Dumb Donny Head? 1638, Dumb Donny
Head. Your watch is slow, Dumb Donny Head.
> Todays inertial unaccelerated motion may include orbital,
Hey Dumb Donny ehad, acceleration is a vector. Orbital
motion is accelerated, you ing imbecile - and in a divergent
gravitational eld with tidal forces, Dumb Donny Head.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
===
Subject: Re: Inertial motion
Cut<
Orbital
> motion is accelerated,
Shame on you. Orbital motion beyond the atmosphere is free
fall;
generally falling toward, and passing by; then falling toward
again;
which continues until the atmosphere or something else
captures it.
Shead
===
Subject: Re: Jordans Curve Theorem for polygons
> I wonder whether there does not exists an elementary (or at
least an
> easier) proof
> of a version of Jordans curve theorem for polygons.
Il know there is a proof using differentiable topology and
degree theory.
Its more analytic, but I sincerely doubt that its easier.
Check Milnors
/Topology from the Differentiable Viewpoint/, Princeton
University Press. I
/think/ Jordans theorem is proved, along with usual results
of Algebraic
topology.
===
Subject: Re: Jordans Curve Theorem for polygons
> ...
>Theres also a more or less straightforward approach (but
somewhat
>tricky) using induction on the number of sides. The basic
idea is to
>chop up the polygon and then apply the induction hypothesis.
This is
>described by Bing in his book on 3-dimensional topology.
> Bings method has (or can be made to have) the virtue of
yielding,
> not just the Jordan Curve Theorem, but the Schoenies
Theorem
> (in a strong form: the union of the polygon and its
interior is PL
> ambient isotopic to the union of a
triangle-with-lotsa-extra-vertices
> and *its* interior), I believe.
One can show using induction and a simple lemma on chopping
up a
polygon (this is somewhat misleadingly phrased, see below)
that a
polygon on the plane bounds a disc, or a stronger version
that says it
is PL isotopic to a triangle using a series of pushes.
Heres the lemma and its proof:
Lemma: Given a polygon with more than three vertices, there
is a
segment connecting two vertices so that the segment only
touches the
polygon at its ends.
Remark: Since at this point we cant assume something is
either inside
or outside (we havent shown a polygon separates the plane),
we cant
talk about whether such a segment is inside or outside. I
think the
phrase chop up which I originally used, implicitly assumes
this
segment is inside. So its best to avoid this kind of
terminology.
Proof: Pick three consecutive vertices v_1, v_2, v_3. Look at
the
segment [v_1, v_3]. If it doesnt touch the polygon in its
interior,
were done. So assume it does. This means the polygon either
just
touches [v_1, v_3] in its interior, meaning there is a vertex
in its
interior, or there is a vertex contained inside the triangle
spanned by
the vertices v_1, v_2, v_3. In the former case, pick such a
vertex
and connect it to v_2. This gives the necessary segment. In
the
latter case, pick the vertex in the triangle closest to v_2.
Connecting it to v_2 gives the segment. QED.
To prove a polygon bounds a disc, just use the induction
hypothesis
that any polygon with number of sides less than or equal to n
bounds a
disc. Given a polygon with number of sides n+1, use the lemma
to nd
a segment that only touches the polygon at vertices x and y.
The
polygon together with this segment forms whats called a
theta curve:
three simple arcs such that each pair shares the same distinct
endpoints. Call the arcs corresponding to pieces of the
original
polygon a_1 and a_2. We can apply the induction hypothesis to
a_i
union [x, y] for each i, to get two discs, D_1, D_2. One may
be inside
the other, or they may be disjoint except where they meet
along [x, y].
The latter case is easily seen to give a disc, since two
discs that are
joined along an arc in each boundary gives a disc. In the
rst case,
say the disc bound by a_2 and [x, y], D_2. is inside the
other D_1. We
can push [x, y] keeping its endpoints xed, across D_2 to
a_2. This
is an isotopy of the plane mapping the boundary of D_2 to our
polygon,
a_1 union a_2. This shows the polygon bounds a disc.
To prove the stronger version of the Schoeniess theorem, use
the
induction hypothesis that any polygon with number of sides
less than or
equal to n can be PL-isotoped by a series of pushes to a
triangle. A
push here refers to a PL-isotopy of the plane that has
compact support,
in particular, you pick a point and look at a star
neighborhood of it.
Suppose theres another point in the neighborhood so that the
neighborhood is also a star of it, i.e. the neighborhood is a
cone on
two different points p and q. You can realize the map that
sends the
cone on p to the cone on q by an isotopy that slides p along
a segment
to q. This is a push. Ill refer to a series of pushes also
as a
push, for brevity.
The idea here is to nd the segment [x,y] and form the theta
curve.
Basically here all you have to do is use the fact that two
pairs of
arcs in the theta curve bound discs that can be pushed to a
triangle
and then argue that the third pair of arcs can also be pushed
to a
triangle. As before youll either have two discs touching
along an arc
or one inside the other. In the rst case, push one disc into
a
triangle. Then you can use the triangle and a push across it
to force
everything into the other disc (which probably doesnt look
like a
triangle). So by pushes, youve moved the original polygon
onto
something that can be pushed into a triangle. The second case
Ill
leave to the reader. In this case, instead of sucking
everything into
a disc, you have to blow it out onto a disc.
===
Subject: Re: Jordans Curve Theorem for polygons
>> ...
>>Theres also a more or less straightforward approach (but
somewhat
>>tricky) using induction on the number of sides. The basic
idea is to
>>chop up the polygon and then apply the induction
hypothesis. This is
>>described by Bing in his book on 3-dimensional topology.
>> Bings method has (or can be made to have) the virtue of
yielding,
>> not just the Jordan Curve Theorem, but the Schoenies
Theorem
>> (in a strong form: the union of the polygon and its
interior is PL
>> ambient isotopic to the union of a
triangle-with-lotsa-extra-vertices
>> and *its* interior), I believe.
> One can show using induction and a simple lemma on chopping
up a
> polygon (this is somewhat misleadingly phrased, see below)
that a
> polygon on the plane bounds a disc, or a stronger version
that says it
> is PL isotopic to a triangle using a series of pushes.
> Heres the lemma and its proof:
> Lemma: Given a polygon with more than three vertices, there
is a
> segment connecting two vertices so that the segment only
touches the
> polygon at its ends.
> Remark: Since at this point we cant assume something is
either inside
> or outside (we havent shown a polygon separates the
plane), we cant
> talk about whether such a segment is inside or outside. I
think the
> phrase chop up which I originally used, implicitly assumes
this
> segment is inside. So its best to avoid this kind of
terminology.
> Proof: Pick three consecutive vertices v_1, v_2, v_3. Look
at the
> segment [v_1, v_3]. If it doesnt touch the polygon in its
interior,
> were done. So assume it does. This means the polygon
either just
> touches [v_1, v_3] in its interior, meaning there is a
vertex in its
> interior, or there is a vertex contained inside the
triangle spanned by
> the vertices v_1, v_2, v_3. In the former case, pick such a
vertex
> and connect it to v_2. This gives the necessary segment. In
the
> latter case, pick the vertex in the triangle closest to v_2.
> Connecting it to v_2 gives the segment. QED.
No. This might not work.
Suppose that v_1, v_2 and v_3 have coordinates (10,0), (0,0)
and (0,10)
respectively. Suppose the other vertices of the polygon are
v_4 = (1,8),
v_5 = (8,1) and v_6 = (5,5). Your algorithm would pick the
vertex
v_6. But the segment v_2 v_6 meets the side v_4 v_5.
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Lacan, Jacques, 79, 91-92; mistakes his penis for a square
root, 88-9
Francis Wheen, _How Mumbo-Jumbo Conquered the World_
===
Subject: Re: Jordans Curve Theorem for polygons
> Lemma: Given a polygon with more than three vertices, there
is a
> segment connecting two vertices so that the segment only
touches the
> polygon at its ends.
>
[snipped my irrelevant remark]
> Proof: Pick three consecutive vertices v_1, v_2, v_3. Look
at the
> segment [v_1, v_3]. If it doesnt touch the polygon in its
interior,
> were done. So assume it does. This means the polygon
either just
> touches [v_1, v_3] in its interior, meaning there is a
vertex in its
> interior, or there is a vertex contained inside the
triangle spanned by
> the vertices v_1, v_2, v_3. In the former case, pick such a
vertex
> and connect it to v_2. This gives the necessary segment. In
the
> latter case, pick the vertex in the triangle closest to v_2.
> Connecting it to v_2 gives the segment. QED.
> No. This might not work.
> Suppose that v_1, v_2 and v_3 have coordinates (10,0),
(0,0) and (0,10)
> respectively. Suppose the other vertices of the polygon are
v_4 = (1,8),
> v_5 = (8,1) and v_6 = (5,5). Your algorithm would pick the
vertex
> v_6. But the segment v_2 v_6 meets the side v_4 v_5.
there arent vertices in the interior of the triangle
v_2v_2v_3,in
which case there is a vertex in the interior of [v_1, v_3],
or there
are vertices in the interior of the triangle. So the fth
sentence
in my proof should be replaced by this new statement.
===
Subject: Re: Jordans Curve Theorem for polygons
>> Lemma: Given a polygon with more than three vertices,
there is a
>> segment connecting two vertices so that the segment only
touches the
>> polygon at its ends.
>>
> [snipped my irrelevant remark]
>> Proof: Pick three consecutive vertices v_1, v_2, v_3. Look
at the
>> segment [v_1, v_3]. If it doesnt touch the polygon in its
interior,
>> were done. So assume it does. This means the polygon
either just
>> touches [v_1, v_3] in its interior, meaning there is a
vertex in its
>> interior, or there is a vertex contained inside the
triangle spanned
by
>> the vertices v_1, v_2, v_3. In the former case, pick such
a vertex
>> and connect it to v_2. This gives the necessary segment.
In the
>> latter case, pick the vertex in the triangle closest to
v_2.
>> Connecting it to v_2 gives the segment. QED.
>> No. This might not work.
>> Suppose that v_1, v_2 and v_3 have coordinates (10,0),
(0,0) and (0,10)
>> respectively. Suppose the other vertices of the polygon
are v_4 = (1,8),
>> v_5 = (8,1) and v_6 = (5,5). Your algorithm would pick the
vertex
>> v_6. But the segment v_2 v_6 meets the side v_4 v_5.
> there arent vertices in the interior of the triangle
v_2v_2v_3,in
> which case there is a vertex in the interior of [v_1, v_3],
or there
> are vertices in the interior of the triangle. So the fth
sentence
> in my proof should be replaced by this new statement.
Still doesnt work.
Try v_1, ..., v_6 = (12,0), (0,0), (0,12), (1,8), (8,1),
(5,5).
Your algorithm still picks v_6 but v_2 v_6 isnt a diagonal.
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Lacan, Jacques, 79, 91-92; mistakes his penis for a square
root, 88-9
Francis Wheen, _How Mumbo-Jumbo Conquered the World_
===
Subject: Re: Jordans Curve Theorem for polygons
>
>>
>
>> Lemma: Given a polygon with more than three vertices,
there is a
>> segment connecting two vertices so that the segment only
touches the
>> polygon at its ends.
>>
> [snipped my irrelevant remark]
>> Proof: Pick three consecutive vertices v_1, v_2, v_3. Look
at the
>> segment [v_1, v_3]. If it doesnt touch the polygon in its
interior,
>> were done. So assume it does. This means the polygon
either just
>> touches [v_1, v_3] in its interior, meaning there is a
vertex in its
>> interior, or there is a vertex contained inside the
triangle spanned
by
>> the vertices v_1, v_2, v_3. In the former case, pick such
a vertex
>> and connect it to v_2. This gives the necessary segment.
In the
>> latter case, pick the vertex in the triangle closest to
v_2.
>> Connecting it to v_2 gives the segment. QED.
>>
>> No. This might not work.
>>
>> Suppose that v_1, v_2 and v_3 have coordinates (10,0),
(0,0) and
(0,10)
>> respectively. Suppose the other vertices of the polygon
are v_4 =
(1,8),
>> v_5 = (8,1) and v_6 = (5,5). Your algorithm would pick the
vertex
>> v_6. But the segment v_2 v_6 meets the side v_4 v_5.
>
> there arent vertices in the interior of the triangle
v_2v_2v_3,in
> which case there is a vertex in the interior of [v_1, v_3],
or there
> are vertices in the interior of the triangle. So the fth
sentence
> in my proof should be replaced by this new statement.
> Still doesnt work.
> Try v_1, ..., v_6 = (12,0), (0,0), (0,12), (1,8), (8,1),
(5,5).
> Your algorithm still picks v_6 but v_2 v_6 isnt a diagonal.
No, it doesnt pick v_6, since v_6 is not in the interior of
the
triangle. However, its easy to see how to modify the example
so it
still is a counterexample. So let me make another change.
Sentence eight of the proof (which has had sentence 5
replaced by the
above) should be replaced by Pick a vertex inside the
triangle that is
*furthest* away from [v_1, v_3].
Im pretty sure it works now.
The complete text is now:
Proof: Pick three consecutive vertices v_1, v_2, v_3. Look at
the
segment [v_1, v_3]. If it doesnt touch the polygon in its
interior,
were done. So assume it does. Either there arent vertices
in the
interior of the tirangle v_1v_2v_3, in which case there is a
vertex in
the interior of [v_1, v_3], or there are vertices in the
interior of
the triangle. In the former case, pick such a vertex and
connect it to
v_2. This gives the necessary segment. In the latter case,
pick a
vertex inside the triangle that is furthest away from [v_1,
v_3].
Connecting it to v_2 gives the segment. QED.
As I said before, its straightforward, but somewhat tricky.
:-) I
hope anybody reading this doesnt get the impression this is
more
complicated than it is.
===
Subject: Geometric series question
The following geometric series is convergent if |x|<1
(1-x)^(-1)=1+x+x^2+...
Suppose i take the derivative of LHS and RHS
-(1-x)^(-2)=1+2x+3x^2+...
Does this equality always hold, also for higher order
derivatives? What is
known about
convergence of these series?
===
Subject: Re: Geometric series question
> The following geometric series is convergent if |x|<1
> (1-x)^(-1)=1+x+x^2+...
> Suppose i take the derivative of LHS and RHS
> -(1-x)^(-2)=1+2x+3x^2+...
I dont think so. Just plug in 0 for x!!
Are you sure that you took the derivative of (1-x)^(-1)
correctly??
> Does this equality always hold, also for higher order
derivatives? What
is
known about
> convergence of these series?
===
Subject: Re: Geometric series question
>The following geometric series is convergent if |x|<1
> (1-x)^(-1)=1+x+x^2+...
>Suppose i take the derivative of LHS and RHS
> -(1-x)^(-2)=1+2x+3x^2+...
Well, almost.
>Does this equality always hold, also for higher order
derivatives? What is
known about
>convergence of these series?
One of the amazing things about power series (thats a series
f(x) = a_0 + a_1 x + a_2 x^2 + ...)
is that if the series converges for |x| < R then its
legitimate to calculate the derivative by term-wise
differentiation, as above - the differentiated series
is guaranteed to converge to the derivative of the
sum for |x| < R as well.
Not true for most sorts of series, just power series.
You nd a proof when you study complex analysis.
************************
David C. Ullrich
===
Subject: Re: Geometric series question
> The following geometric series is convergent if |x|<1
> (1-x)^(-1)=1+x+x^2+...
This is not a series; it is an equality between a series and
its sum.
> Suppose i take the derivative of LHS and RHS
> -(1-x)^(-2)=1+2x+3x^2+...
Wrong. What youll get on the left is (1 - x)^{-2}.
> Does this equality always hold, also for higher order
derivatives?
Yes.
> What is known about convergence of these series?
They converge if and only if |x| < 1.
Jose Carlos Santos
===
Subject: Need help solving a differential equation
Hi all,
I am attempting to solve the following ordinary linear
differential equation with some boundary conditions.
y/y = b cosh ax
where a, b are constants.
I havent had much success in getting an analytical solution.
I would
appreciate any suggestions for deriving a close form solution.
Amal
===
Subject: Re: Need help solving a differential equation
> Hi all,
> I am attempting to solve the following ordinary linear
> differential equation with some boundary conditions.
> y/y = b cosh ax
> where a, b are constants.
> I havent had much success in getting an analytical
solution. I would
> appreciate any suggestions for deriving a close form
solution.
> Amal
Maple says:
> DE := diff(y(x),x,x)/y(x) = b*cosh(a*x);
2
d
---- y(x)
2
dx
DE := --------- = b cosh(a x)
y(x)
> dsolve(DE,y(x));
/ 2 b /1 (1/2)
y(x) = _C1 MathieuC|0, - ---, arccos|- (2 cosh(a x) + 2) ||
| 2 2 /|
a /
/ 2 b /1 (1/2)
+ _C2 MathieuS|0, - ---, arccos|- (2 cosh(a x) + 2) ||
| 2 2 /|
a /
or, written linearly:
y(x) = _C1*MathieuC(0, -2*b/a^2,
arccos(1/2*(2*cosh(a*x)+2)^(1/2)))
+_C2*MathieuS(0, -2*b/a^2, arccos(1/2*(2*cosh(a*x)+2)^(1/2)))
where _C1 and _C2 are two arbitrary constants.
Note that arccos of something > 1 is imaginary.
The help says:
The Mathieu functions MathieuC(a, q, x) and MathieuS(a, q, x)
are
solutions of the Mathieu differential equation:
y + (a - 2 q cos(2 x)) y = 0
MathieuC and MathieuS are even and odd functions of x,
respectively.
===
Subject: thank you for helping.
A N Niel
AB
Abraham Buckingham
Achava Nakhash, the Loving Snake
Acid Pooh
Adam
Alain Verghote
Alan E. Feldman
Alex.Lupas
Amitabha Roy
Angelos TSIRIMOKOS
Artur
Arturo Magidin
Bill Dubuque
Bill Jones
Bill Taylor
Boudewijn Moonen
Brian VanPelt
briggs@encompasserve.org
Bruce B
Carsten Hansen
Chan-Ho Suh
Christian Bau
Cron
Daniel Grubb
Daniel McLaury
DanKage
Dave Rusin
Dave Seaman
David Bernier
David C. Ullrich
David McAnally
David R. MacIver
David W. Cantrell
Denis Feldmann
Derek Holt
Doug Norris
Douglas Scot Gillman
Dr. Michael Ulm
dreamvigile
Ed Hook
Eli
Elisabeth E. Korelines
FDH
shfry
ip
Fred Eckertson
G. A. Edgar
George Cox
Gib Bogle
Goran Jakupovic
GrandNord
Herman Rubin
Hero
hubert
Hubert Quatreville
Ignacio Larrosa Canestro
Imam Tashdid ul Alam
Ioannis
Jaakko Suomala
James Buddenhagen
James Wong
Jason Pawloski
Jeremy Boden
Jesse F. Hughes
Jim Heckman
Jim Nastos
jk
jmfbahciv@aol.com
Jodi
Johan Kullstam
John Baez
Jon Haugsand
Jonathan Miller
Joona I Palaste
Jose Carlos Santos
Julien Santini
Justin
Justin Davis
K. P. Hart
keith
Keith A. Lewis
Lance Lamboy
Larry Hammick
Lee Rudolph
Leonard Blackburn
lydia
Lynn Kurtz
M.Sugure
Marc Olschok
mareg@mimosa.csv.warwick.ac.uk
markus
Martin Penderis
mathedman
Mathieu
mathman
matt grime
Maxi
mensanator
Michael Barr
Michael Jrgensen
Michael N. Christoff
Michael Varney
Mike Kent
Mitch Harris
mjc
Narasimham G.L.
Nat Silver
Nicolas Le Roux
Niraj Prasad
Nobody
Oscar Lanzi III
panh
Peter L. Montgomery
Peter Webb
Phil Holman
Phil Smith
Poker Joker
r.e.s.
Rakoto Ramparany
rickO
Rob Johnson
Robert Israel
Robert Vienneau
Robin Chapman
Ross A. Finlayson
saccade
Salix
Sanford A. Geraci
Sekhmet
Sheikh Yabooti
Shmuel (Seymour J.) Metz
Stephen J. Herschkorn
Sylvain Croussette
Ted Hwa
The Ghost In The Machine
The Last Danish Pastry
The World Wide Wade
Thomas Nordhaus
Tim Brauch
Tim Smith
Timothy Murphy
Tobias Fritz
Toni Lassila
Tonio
Torkel Franzen
Tralfaz
Tralfaz
Troubled
Van Jacques
Virgil
W. Dale Hall
Wayne Brown
Wilbert Dijkhof
Will Twentyman
William Elliot
Yogi
Yves De Cornulier
Z Zag
Zdislav V. Kovarik
ZZBunker
===
Subject: Re: thank you for helping.
Gosh I feel so special.
===
Subject: Re: Inertial motion
> Whereas Galileos natural inertial motion may have been
unaccelerated
> circular motion; around the world (?): Newtons natural
inertial
> motion was unaccelerated motion in a straight line; at a
constant
> speed.
Unaccelerated circular motion?? You mean it just sort of
naturally
goes in a circle, without any force acting?
Any deviation from a straight line requires force.
> Newton postulated his circular motion as being accelerated
from his
> inertial unaccelerated motion; by a centripetally directed
force;
> which he called the force of gravity.
> Todays inertial unaccelerated motion may include orbital,
and any
> other motion in between; including free fall.
Say what??
> Shead
===
Subject: Re: Another Mathematicians apology needed asap !!
I thought the point of the buttery effect was that
small changes in initial conditions sometimes produce large
effects as time increases.
Van
> Please - if you discover a new phenomena, PLEASE, PLEASE,
GIVE IT
A DULL
> I do not know how someone derives time travel from the
buttery
effect.
> Makes about as much sense as deriving potable water from
the term
> community urinal.
> If they wanted to make a movie about something, they should
have
tried to
> explain why even though there are billions of butteries,
it is
> unreasonable to assume that their wings apping is actually
controlling
> the weather. That perhaps there is an opposing phenomena to
the
buttery
> effect which diminishes the inuence of these seemingly
innite
miniscule
> perturbations. And then, perhaps there is some type of
feedback or
> recursiveness to it acting as a dampening force/inuence.
> Sensitive dependence on initial conditions - the buttery
effect.
What
> Im saying is that this seems like an inuence for which
there may
be an
> inverse or opposite. Perhaps Robustness Regardless of
Initial
Conditions.
> Could these act as competing forces ? Or, have I become a
babbling
fool at
> last......
===
Subject: Re: Another Mathematicians apology needed asap !!
> I thought the point of the buttery effect was that
> small changes in initial conditions sometimes produce large
> effects as time increases.
> Van
Precisely. Now, what this has to do with time travel - I will
never know.
In fact, the movie does not really demonstrate the butterty
effect at
all.
In the movie, things are caused to change and the protagonist
experiences
all of the different scenarios which are due to the butt.
eff..
But what the butt. eff. implies is that small changes at t1
would cause
drastic changes at t2, and I dont see any drastic changes in
the movie -
just subtle ones. Maybe instead of blond, his girlfriend
becomes brunette
or
whatever. That aint right. The butt eff could cause his whole
galaxy to
exist or not, but I guess that wouldt make much of a movie.
===
Subject: faugere gb
I have problems getting the program Gb by Faugere to run on
my Windows XP
computer.
(http://fgbrs.lip6.fr/jcf/Software/Gb/Download/index.html)
I can complete the installation, but I cannot execute the
program.
Does anybody has some experience with this tool?
joerg
===
Subject: Re: Why are elements in the domain mapped to a
single element in
the codomain?
> Why do functions map elements in their domain to a single
element in
> the codomain? Is it because everything in set theory is a
set, and
> since sets can not contain the same element more than once,
a
> function can not map a domain element to more than one
codomain
> element?
[...]
> Functions are not good for showing relationships when
elements of the
domain
> are related to more than one element in the codomain? What
concept
exists to
> support the original relationhips?
These are the *denitions*: A relation from a to b is a subset
of the Cartesian product a x b. A function f from a to b is a
relation from a to b with the propery that for each c in a
there
exists a unique d in b such that (c,d) in f.
Relations are perfectly ne structures in their own right. For
example, your sibling example (omitted in the quote) can be
modeled
using a relation. Orderings, both partial and total, are
common
relations that appear in mathematics.
Functions serve a different usage. Recall that these
set-theoretic
denitions arose rather recently in the history of
mathematics. Prior
to 1875 or so, mathematicians thought of functions as rules,
e.g., the
map of a number to its square. In these cases, you want a
single
output for each input. And surely by now in your study of
mathematics
you have seen functions and their application and analysis
all over the
place.
One does occasionally see reference to multiple-valued
functions (e.g.,
square root), particularly in complex analysis. One could
translate a
multiple-valued function from a to b to a function from a to
P(b), where P indicates power set. (I.e., P(b) is the set of
all
subsets of b.)
Does the book you are studying not spell out the denitions of
relation and function? If not, I strongly urge you to ditch
the book
and switch to Halmos, Naive Set Theory. Or at least look at
both of
them simultaneously.
And hurry up, man! I am waiting for you to learn enough to
help me out
with Hartogss aleph function. :-)
===
Subject: Re: limitation to induction on nite bounds
responding to |-|erc
Please insert short and direct answers where I have
inserted lines containing only question marks.
HERC > I answered the last one by *demonstrating* the example.
HERC > to show that 0.333... does not occur, you have to show
HERC > En e N,
HERC > Ai,
HERC > !digitsmatchupton2(i, d, n)
PRD > To show that a given inferrence is an example or
instance of
PRD > a rule, do you need to provide an assignment between
terms
PRD > and variables in the rule?
????
PRD > If you assign to the variable d, the sequence
PRD > .333...
PRD > does not the rule Non-Occurence Introduction 1
PRD > become the following?
PRD > En e N, if( nite(length(.333...)), n<= length(.333...))
PRD > Ai,
PRD > !digitsmatchupton(i,.333...,n)
PRD > -> .333... does not occur in S
????
PRD > Why did you remove nite(length(d) from your
PRD > example of the rule?
????
PRD > Can your example be an instance of the rule
PRD > if it does not follow the form of the rule
PRD > faithfully?
????
**** REFERENCE ****
(Non-Occurence Introduction 1)
En e N, if( nite(length(d)), n<= length(d))
Ai,
!digitsmatchupton(i, d, n)
-> d does not occur in S
===
Subject: Re: limitation to induction on nite bounds
> responding to |-|erc inserted lines containing only question marks.
> HERC > I answered the last one by *demonstrating* the
example.
> HERC > to show that 0.333... does not occur, you have to
show
> HERC > En e N,
> HERC > Ai,
> HERC > !digitsmatchupton2(i, d, n)
> PRD > To show that a given inferrence is an example or
instance of
> PRD > a rule, do you need to provide an assignment between
terms
> PRD > and variables in the rule?
> ????
yes.
> PRD > If you assign to the variable d, the sequence
> PRD > .333...
> PRD > does not the rule Non-Occurence Introduction 1
> PRD > become the following?
> PRD > En e N, if( nite(length(.333...)), n<=
length(.333...))
> PRD > Ai,
> PRD > !digitsmatchupton(i,.333...,n)
> PRD > -> .333... does not occur in S
yes
> PRD > Why did you remove nite(length(d) from your
> PRD > example of the rule?
E n, n <= length(oo)
E n
The clause on the quantier is not necessary.
> PRD > Can your example be an instance of the rule
> PRD > if it does not follow the form of the rule
> PRD > faithfully?
no
> **** REFERENCE ****
> (Non-Occurence Introduction 1)
> En e N, if( nite(length(d)), n<= length(d))
> Ai,
> !digitsmatchupton(i, d, n)
> -> d does not occur in S
Ghosty can you check my Occurence defn?
Herc
===
Subject: Re: limitation to induction on nite bounds
responding to |-|erc
HERC, your responses to my messages are verbose, but I have
difculty nding the answers to the specic questions
I have asked. If the answers to my questions are embedded
in your response, I apologize for failing to nd them.
Please answer the questions below in as short and direct a
manner as possible, and please answer the questions
immediately after they appear. If you wish to add
comments or explanations, please added them at the
very end after a clear sign indicating that comments
follow.
PRD > (Non-Occurence Introduction 1)
PRD > En e N, if( nite(length(d)), n<= length(d))
PRD > Ai,
PRD > !digitsmatchupton(i, d, n)
PRD > -> d does not occur in S
PRD > Could you please state the rule Non-Occurence
PRD > Introduction 1 as an English sentence?
HERC > if there exists a number n less than or equal to the
HERC > length of string d, and there is no set member that
HERC > matches the digits of d from digit 1 up to digit n,
HERC > then d does not occur in S.
PRD > Is this a direct translation?
PRD > The term nite(length(d)) occurs in the symbolic
PRD > version of the rule. It does not occur in the English
PRD > version. What happened to the nite(length(d))?
PRD > How was that translated?
PRD > If your translation wsa not a direct translation,
PRD > please provide a direct translation.
HERC > OK, what might have been clearer is
===
Subject: Re: Does a high SAT score predict mathematical
talent?
>>Counter example: Erdos.
>>
>>Mind all that amphetamine helped keep his mind sprightly.
> Did he really take speed?
> Yes. Erdos really did take amphetamines quite habitually. I
have
> perused both of the book-length biographies of Erdos
available in
> American public libraries.
> It appears that Erdos unusual social life, both growing up
and as
> a fully grown adult, had something to do with his sustained
> mathematical productivity. A rather intriguing off-hand
suggestion
> in a seminar monograph about evolutionary biology and human
> intelligence
> The Nature of Intelligence (2000) edited by Gregory R.
Bock, Jamie
> A. Goode, and Kate Webb (Chichester: Wiley) Novartis
Foundation
> Symposium 233)
> is that professional output, in mathematics and other
professions,
> is related to sexual display. A young mathematician seeking
a life
> partner will get a Ph.D. and make tenure, and then settle
down
> once able to reproduce offspring as well as ideas. The
prediction
> of that hypothesis would be that most academics, not just in
> mathematics, do their most conspicuous work (or most
> energy-consuming work) at the age when they are about to
start
> their families.
In the documentary on Erdos that I referred to, he said that
he found sexual pleasure painful, or distasteful. Kind of a
strange reaction to sex.
> Anyway, I was impressed with what Hungary used to do.
> That is what the US needs to do. There were math clubs
> for high school aged students interested in math, and many
> journals, like Acta Mathematica.
> I agree that the competition culture fostered in secondary
> education in Hungary for the last century has had benecial
> effects on the mathematics community in that country. An
effort in
> the United States, which reaches worldwide, to build a
similar
> kind of competition culture in the Internet era can be
found at
> http://www.artofproblemsolving.com
> especially at that sites very useful online forums, which
are
> fully international in participation. I wish something of
that
> kind had existed when I was a kid in the early 1970s. I will
> tentatively guess, inviting comments from participants in
this
> sci.math newsgroup, that helping young people nd soulmates
with
> whom they can discuss math helps them develop as productive
> mathematicians over the course of a LONG [grin] lifetime.
Does
> that make sense to everyone else reading this thread?
I took a quick look at this URL. Looks good to me.
Van
===
Subject: Rings and their intuitive meaning
Group elements represent processes that can be performed in
sequence
on the identity and undone. The most natural application of
groups is
to the symmetries of a mathematical object.
What is a good way to visualize rings? What are they used
for? Im
looking for a use in mathematics analogous to the use of
groups to
represent symmetry.
===
Subject: Re: Rings and their intuitive meaning
|Group elements represent processes that can be performed in
sequence
|on the identity and undone. The most natural application of
groups is
|to the symmetries of a mathematical object.
|
|What is a good way to visualize rings? What are they used
for? Im
|looking for a use in mathematics analogous to the use of
groups to
|represent symmetry.
ring elements represent _linear_ processes that can be
performed in
sequence. linearity makes it possible to combine processes
not only
by sequential composition, but also by means of pointwise
addition;
thats why rings have an addition operation as well as a
multiplication operation. (prove to yourself that the
pointwise sum
of two parallel linear processes is another linear process!)
on the other hand, linearity discourages us from requiring all
processes to be capable of being undone, because subtraction
and zero
are natural things to include when youre already dealing with
linearity and addition, and the zero process that takes
everything
to zero is a conspicuous example of a process that in general
cant be
undone by any other deterministic process. thats part of why
there
isnt any clause in the denition of ring that requires
division to
be everywhere dened.
[e-mail address jdolan@math.ucr.edu]
===
Subject: Use of a rational tiling group in sl(2,R) to get a
3d surface
This method was suggested by the Bryant cousin surface.
It gives an hyperboloid of one sheet that is very like a
catenoid in shape.
A determinant one group is assumed through out.
This result is very different that the intent of Lagarias
in terms of a upper half plane rational tiling.
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca
92040-2905,tel:
619-5610814 :
URL : http://home.earthlink.net/~tftn
URL : http://victorian.fortunecity.com/carmelita/435/
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(************************************************************
***********
End of Mathematica Notebook le.
*************************************************************
**********)
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca
92040-2905,tel:
619-5610814 :
URL : http://home.earthlink.net/~tftn
URL : http://victorian.fortunecity.com/carmelita/435/
===
Subject: Re: Use of a rational tiling group in sl(2,R) to get
a 3d surface
>This method was suggested by the Bryant cousin surface.
Im so confused. Just now you told us we should use sci.math
to answer questions. I dont recall any questions here about
how to use a rational tiling group in sl(2,R) to get a 3d
surface.
Please use sci.math to answer questions. If everyone
posted everything they know and every bit of code
theyd written there would be literally millions
of posts a day and the group would be totally useless.
Um, also, please when you use sci.math to answer questions
make certain that you actually understand the relevant
mathematics before speaking up. When people recognize
some of the words in the question and post answers
that make no sense that also wastes valuable space.
************************
David C. Ullrich
===
Subject: Re: Use of a rational tiling group in sl(2,R) to get
a 3d surface
===
>Subject: Re: Use of a rational tiling group in sl(2,R) to
get a 3d surface
>Message-id:
>>This method was suggested by the Bryant cousin surface.
>Im so confused. Just now you told us we should use sci.math
>to answer questions. I dont recall any questions here about
>how to use a rational tiling group in sl(2,R) to get a 3d
>surface.
>Please use sci.math to answer questions. If everyone
>posted everything they know and every bit of code
>theyd written there would be literally millions
>of posts a day and the group would be totally useless.
>Um, also, please when you use sci.math to answer questions
>make certain that you actually understand the relevant
>mathematics before speaking up.
Hey, some of us dont realize our understanding is faulty
and if we never spoke up, we would not get corrected and
never learn anything. A troll knows his understanding is wrong
and speaks up anyway with no intention of trying to learn.
So please dont lump us ignoramuses in with the fools.
>When people recognize
>some of the words in the question and post answers
>that make no sense that also wastes valuable space.
>************************
>David C. Ullrich
Mensanator
Ace of Clubs
===
Subject: Re: The Double or One Half Paradox
> Why must people confuse things? All you needed to say was
that you
> pick a box and there is 100 bucks in it. And you may switch
if you
> wish and go for twice as much or half as much.
> Of course in this case, its better to switch, since X is
xed.
Thats silly and annoying.
===
Subject: a noise with a better histogram
I used an inversion of a Gaussian to
get my amplitudes instead of a Gaussian.
It seems to work somewhat better in terms of the histogram.
Im indepted to the patient work of Ray Kooperman and Dr.
Bobby Treat
on Kurtosis excess calculations and Cauchy distribution
calculations.
As I am giving this information to the egroup for comment,
I must take the good with the bad.
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca
92040-2905,tel:
619-5610814 :
URL : http://home.earthlink.net/~tftn
URL : http://victorian.fortunecity.com/carmelita/435/
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(************************************************************
***********
End of Mathematica Notebook le.
*************************************************************
**********)
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca
92040-2905,tel:
619-5610814 :
URL : http://home.earthlink.net/~tftn
URL : http://victorian.fortunecity.com/carmelita/435/
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca
92040-2905,tel:
619-5610814 :
URL : http://home.earthlink.net/~tftn
URL : http://victorian.fortunecity.com/carmelita/435/
===
Subject: Re: a noise with a better histogram
> I used an inversion of a Gaussian to
>get my amplitudes instead of a Gaussian.
>It seems to work somewhat better in terms of the histogram.
>Im indepted to the patient work of Ray Kooperman and Dr.
Bobby Treat
>on Kurtosis excess calculations and Cauchy distribution
calculations.
>As I am giving this information to the egroup for comment,
>I must take the good with the bad.
Im so confused. Just now you told us we should use sci.math
to answer questions. I dont recall any questions here about
noise with a better histogram.
Please use sci.math to answer questions. If everyone
posted everything they know and every bit of code
theyd written there would be literally millions
of posts a day and the group would be totally useless.
Um, also, please when you use sci.math to answer questions
make certain that you actually understand the relevant
mathematics before speaking up. When people recognize
some of the words in the question and post answers
that make no sense that also wastes valuable space.
************************
David C. Ullrich
===
Subject: Re: Question about the distinction between set and
element
> It seems to go without saying that there is some intrinsic
difference
> between the concepts of set and element.
> Does it? Not to me.
> However, I wonder if this is not merely an illusion,
> Indeed, an illusion. In set theory and most of mathematics
(logic and
> category theory being the primary excpetions), *everything*
is a set.
Correction: *everything* can be *coded* as a set, i.e.
mathematics can
be embedded in set theory (and not in a unique way).
-Leonard
> x in y is a relationship between sets.
===
Subject: Re: Question about the distinction between set and
element
question in more precise terms.
Kerry Soileau
> It seems to go without saying that there is some intrinsic
difference
> between the concepts of set and element.
> Does it? Not to me.
> However, I wonder if this is not merely an illusion,
> Indeed, an illusion. In set theory and most of mathematics
(logic and
> category theory being the primary excpetions), *everything*
is a set.
> x in y is a relationship between sets.
> In ZF (or related theories), one assumes that any epsilon
chain is
> nite. That is, if you take a set, an element of that set
(in ZF,
> the elements are sets too), an element of that element, an
element of
> THAT elements,..., after a nite number of steps you nd a
set that
> has no elements (that is, you get the empty set at the
bottom).
> Usually, at each stage, you have lots of choices and the
number of
> steps will depend on that, but will always be nite. Going
up, on
> the other hand, is not limited and can obviously be
innite. So
> there is one place for asymmetry. Could there be a set
theory with an
> actual duality like this? One way would be to insist on
> co-well-foundedness along with well-foundedness. I think
that would
> work, but all sets would be nite. The only other way would
be to
> drop the well-founded axiom. This can be done, but I dont
know if
> the resultant axioms are truly self-dual, although it would
be
> interesting if it were.
> The question is not silly, but I dont know if anyone has
looked at it
> seriously.
===
Subject: When you major/ only product is abuse you are a troll
And it is obvious who they are.
No productive worth in sight
except to slight others.
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca
92040-2905,tel:
619-5610814 :
URL : http://home.earthlink.net/~tftn
URL : http://victorian.fortunecity.com/carmelita/435/
===
Subject: Re: When you major/ only product is abuse you are a
troll
X-URL:
http://mygate.mailgate.org/mynews/sci/sci.math/
13b5ac9af66b02b1992f45ab28fd1a
a2.48257%40mygate.mailgate.org
> Re: When you major/ only product is abuse you are a troll
Right, and since your major/only product is abuse of newsgroup
charters and participants, that would make you a _______?
xanthian.
===
Subject: Re: When you major/ only product is abuse you are a
troll
>And it is obvious who they are.
>No productive worth in sight
> except to slight others.
Clever of you not to mention names this time -
must be embarassing when people explain that
_they_ nd the obvious trolls to be useful
people to have around.
I wonder how this would happen? A nds B very
helpful, while C nds B nothing but a source
of abuse. Hmm, gotta think about that...
>Respectfully, Roger L. Bagula
>tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca
92040-2905,tel:
>619-5610814 :
>URL : http://home.earthlink.net/~tftn
>URL : http://victorian.fortunecity.com/carmelita/435/
************************
David C. Ullrich
===
Subject: Re:
=?ISO-8859-15?Q?paper_claiming_p=3Dnp_and_soap_bubbles?=
Besides the paper claiming NP=P:
1. cs.CC/0406056 [abs, ps, pdf, other] :
Title: P=NP
Authors: Selmer Bringsjord, Joshua Taylor
Subj-class: Computational Complexity; Articial Intelligence
There are also papers that say NP!=P :
4. cs.CC/0310060 [abs, ps, pdf, other] :
Title: Evidence that P is not equal to NP
Authors: Craig Alan Feinstein
Comments: 4 pages. Modied to improve writing style
Subj-class: Computational Complexity
ACM-class: F.1.3
so the false ones have to be sorted out rst.
===
Subject: Re: Pointless Topology
>To nd out more, try to obtain Johnstones Stone spaces book
from
>some library (last time a looked, the US did have libraries
:-).
> Deliberately under funded by excuse of Budget Busting
Bushs Blunders for
> being a despised anti-capitalistic remnant of American
socialism within
US
> modern socially engineered hyper-commercial society wherein
money is the
> measure of all things human and divine. What the local
public library
> does offer pertinent to order theory, tho not the lastest
edition, is
> Davey, B. A., Introduction to Lattices and Order
On the other hand...
http://www.independent.org/tii/content/press_rel/press_040624
.html
http://hertzlinger.blogspot.com
===
Subject: Re: Mathematicians and scientists become wealthy and
rule the
world
> I dont think the main arguments before the Supreme Court
were on the
> benets of a Creative Commons. That wouldnt seem to get
far. As
> I understand it, the arguments were (1) Congress is only
authorized to
> make copyright law insofar as it furthers the advancement
of the
> useful arts and (2) a *retroactive* extension cannot
encourage more
> creativity.
Is it up to an unelected court to second-guess Congress?
http://hertzlinger.blogspot.com
===
Subject: Re: Mathematicians and scientists become wealthy and
rule the
world
>> In the US, 10 % of the people used to own 90 % of the
wealth.
Source?
>> Today, the
>> number has changed to 1% of the people own 90% of the
wealth. Hey,
nothing
>> wrong with making money, but there also needs to be better
balance for
us
>> all.
>> Okay, sorry for the diatribe.
> I agree, but would argue that these things should be
illegal and arent,
> and existing laws arent enforced.
> I agree with you for the most part, especially about the
concentration
> of wealth, and power. They have taken over the media, and
between
> the media and advertising and propaganda, you have to dig
to nd out
> what is really going on.
We have people shouting from the rooftops theyre afraid to
speak above
a whisper.
http://hertzlinger.blogspot.com
===
Subject: Lab experiments on control of dark energy?
PS
It is important to understand why Hal Puthoffs previous
attempts to
explain this very same data of Ken Shoulders did not work.
Hal did not
ask the right question. He is not alone in that of course.
Hal made the
false assumption that it was the QED Casimir force that would
hold the
100 billion electrons together in the charge cluster. In fact
what is
really going on is a completely different physical effect. It
is ZPF
induced gravity dependent on partial vacuum coherence. BTW
when one
reads Science and Ultimate Reality it is obvious how the
string-brane
theorists are shining strong lights in the wrong part of the
Dark Cave.
You do not now seem to need exorbitant new mathematical
superstructures
like colliding branes to explain any of the new cosmological
PS: Kens lab experiments seem to be relevant to this
discussion.
His charge clusters (AKA EVO) that I interpret as glued
together by
strong short-range effective gravity induced by micro-quantum
zero
point energy exotic vacuum cores on the mesoscopic scale are
self-propelled charged geons. The self-propulsion comes for
temporary
unstable inhomogeneous distributions of positive and negative
zero
point quantum pressures at different parts of the EVO.
SUPERLUMINAL PARTICLE MEASUREMENTS
by
Ken Shoulders and Dr. Jack Sarfatti
Abstract
Measurements made on clusters of electrons operating as
Exotic Vacuum
Objects, or EVOs, show velocities exceeding that of light. A
theory of
this behavior is presented based on manipulation of parameters
available in this new eld of exotic vacuum engineering.
This paper can be downloaded from: http://www.svn.net/krscfs/
Ken Shoulders
Note that Ken was a long-time collaborator of Hal Puthoffs
way back in
Hals National Security Agency days. Ken has many patents in
micro-wave
miniaturization and has devoted many decades to these EVO
measurements.
On testing macro-quantum theory of emergent gravity in
cosmology
This is the one to shoot down.
http://qedcorp.com/destiny/CoherentCosmos.pdf
(expanded version posted last night)
If you can?
Show it is wrong, or not even wrong.
Happy Hunting.
:-)
Paul
On issue of the tidal stretch-squeeze liquid drop local
measurement of
the curvature tensor in free oat LIF that is not a problem.
As Ray
Chiao points out in his Conceptual Tensions paper in Science
and
Ultimate Reality you need to distinguish the center of mass
motion
from the relative motion of a spatially extended object like
even a
small liquid drop with small enough surface tension. The
g-force
argument of local vanishing of the connection eld applies
only to
not to the tidal stretch-squeeze relative motions of the
pieces of the
get a good measurement.
Now, in terms of nonlocality of the pure gravity energy.
Obviously we can trivially dene a local stress-energy
density tensor
for the pure vacuum gravity eld as simply
tuv(Geometry) = (c^4/G)Guv
Guv = Ruv - (1/2)Rguv
Einsteins 1916 eld equation is then simply
tuv(Geometry) + Tuv(Matter) = 0
In the classical vacuum with zero micro-quantum ZPF i.e. /zpf
= 0
and with Tuv(Matter) = 0
Then trivially
tuv(Geometry) = 0 in non-exotic vacuum.
MTW say this.
The problem is that you cannot get a global Pu from
integrating this
tuv(Geometry) over 3D space for a Geon in Wheelers sense.
You need to split the tensor tuv(Geometry) into two
pseudo-tensor
pieces, one is a kind of background frame for the other,
which when
integrated gives a Pu for gravity waves from the rotating
vibrating
Geon.
Note, in terms of metric engineering.
When /zpf = 0, at the given scale, with zero torsion and zero
other
elds from NOT locally gauging complete conformal group,
Tuv(Matter)^;v = 0
tuv(Geometry)^;v = 0
Separately. No intermixing between the geometrodynamics and
the matter
elds that live on the geometrodynamics.
This FORBIDS metric engineering. But the situation changes
when /zpf
=/= 0!
I leave for airport to London in a few hours.
------------------------ Yahoo! Groups Sponsor
--------------------~-->
Yahoo! Domains - Claim yours for only $14.70
http://us.click.yahoo.com/Z1wmxD/DREIAA/yQLSAA/GSwxlB/TM
-------------------------------------------------------------
-------~->
Yahoo! Groups Links
PS: Kens lab experiments seem to be relevant to this
discussion.
His charge clusters (AKA EVO) that I interpret as glued
together by
strong short-range effective gravity induced by micro-quantum
zero point
energy exotic vacuum cores on the mesoscopic scale are
self-propelled
charged geons. The self-propulsion comes for temporary
unstable
inhomogeneous distributions of positive and negative zero
point quantum
pressures at different parts of the EVO.
SUPERLUMINAL PARTICLE MEASUREMENTS
by
Ken Shoulders and Dr. Jack Sarfatti
Abstract
Measurements made on clusters of electrons operating as
Exotic Vacuum
Objects, or EVOs, show velocities exceeding that of light. A
theory of
this behavior is presented based on manipulation of
parameters available
in this new eld of exotic vacuum engineering.
This paper can be downloaded from: http://www.svn.net/krscfs/
Ken Shoulders
Note that Ken was a long-time collaborator of Hal Puthoffs
way back in
Hals National Security Agency days. Ken has many patents in
micro-wave
miniaturization and has devoted many decades to these EVO
measurements.
On testing macro-quantum theory of emergent gravity in
cosmology
This is the one to shoot down.
http://qedcorp.com/destiny/CoherentCosmos.pdf
(expanded version posted last night)
If you can?
Show it is wrong, or not even wrong.
Happy Hunting.
:-)
Paul
On issue of the tidal stretch-squeeze liquid drop local
measurement of
the curvature tensor in free oat LIF that is not a problem.
As Ray
Chiao points out in his Conceptual Tensions paper in Science
and
Ultimate Reality you need to distinguish the center of mass
motion from
the relative motion of a spatially extended object like even
a small
liquid drop with small enough surface tension. The g-force
argument of
local vanishing of the connection eld applies only to the
center of
stretch-squeeze relative motions of the pieces of the liquid
drop, which
Now, in terms of nonlocality of the pure gravity energy.
Obviously we can trivially dene a local stress-energy
density tensor
for the pure vacuum gravity eld as simply
tuv(Geometry) = (c^4/G)Guv
Guv = Ruv - (1/2)Rguv
Einsteins 1916 eld equation is then simply
tuv(Geometry) + Tuv(Matter) = 0
In the classical vacuum with zero micro-quantum ZPF i.e. /zpf
= 0
and with Tuv(Matter) = 0
Then trivially
tuv(Geometry) = 0 in non-exotic vacuum.
MTW say this.
The problem is that you cannot get a global Pu from
integrating this
tuv(Geometry) over 3D space for a Geon in Wheelers sense.
You need to split the tensor tuv(Geometry) into two
pseudo-tensor
pieces, one is a kind of background frame for the other,
which when
integrated gives a Pu for gravity waves from the rotating
vibrating Geon.
Note, in terms of metric engineering.
When /zpf = 0, at the given scale, with zero torsion and zero
other
elds from NOT locally gauging complete conformal group,
Tuv(Matter)^;v = 0
tuv(Geometry)^;v = 0
Separately. No intermixing between the geometrodynamics and
the matter
elds that live on the geometrodynamics.
This FORBIDS metric engineering. But the situation changes
when /zpf =/=
0!
I leave for airport to London in a few hours.
===
Subject: Re: Lab experiments on control of dark energy?
> PS
Credits of JS:
Jack has been working on the post-quantum physics of
consciousness and the paranormal since he directed the famous
Esalen
Seminars in 1976 described by Gary Zukav in The Dancing Wu Li
Masters.
He
is also working on the connection of the warp drive physics
of ying
saucers to the new cosmology observations of anti-gravity
dark energy.
Oddly enough I was contacted by I.J. Good in 1980 because a
paper I had
published in Psychoenergetic Systems on such an entity was
almost identical
including a reference to New Age Death Cults in an obscure
talk he had
given
in Chicago before some paranormal group. This was in the wake
of the
Jonestown mass murder. I had never seen or read or even heard
of his talk
of
course. Hence, it appears that we were both channeling the
same information
from what Jorge Luis Borges simply called The Author.
Therefore, Jack is a paranormal channeler of warp-drive
physics of
ying saucers.
(Smoked and Mirrored.)
===
Subject: redene what is a win Re: There exists a Nim version
that is a
draw
OS
> A combinatorial game such as Nim can not be a draw.
> Here is a distant relative that can be a draw:
http://home.no.net/zamunda/split.htm
> I beg to differ.
--- quoting from the above reference ---
Split and Take by Jan Kristian Haugland
This game is almost as simple as nim, and yet it has the
advantage of more
complex games in that one
can have an idea about who is ahead without solving the
endgame. The game
starts with some stones
lying in one or more heaps. The total number of stones should
be divisible
by
3. The two players
alternately split any heap with at least two stones into two
smaller ones.
If
three heaps of equal size are
present after such a move, the last player captures them. It
is possible
that
there are four equal heaps, in
which case only three of them are captured. Thus, all the
stones will
eventually be captured, and whoever
manages to capture more stones wins the game.
--- end quoting ---
Yes, I sort of like those ideas. That the winner is not who
takes off the
last matchstick/s or who does not take off the last
matchsticks but rather
instead *who has the most matchsticks*.
In this fashion, one can see that the concept of win or loss
in Nim was a
decient concept or a stupid concept.
Let me see if I can make a stupid concept of win for checkers
or chess or
tictactoe which is as equally stupid as what win is for Nim.
I think I can. For tictactoe to have an equally stupid
concept of win and
still be a VonNeumann game is to say that the win in
tictactoe is the
person
who makes the last move wins. Hence X always wins in the OS
of this version
of tictactoe. So regardless of what O does, X always wins,
just like in Nim
where second player always wins. Isnt that a nice and stupid
VonNeumann
game
just as Nim is nice and stupid.
Let me see if I can make chess and checkers equally stupid
but still a
VonNeumann game. Chess is easy. If we redene win in chess as
saying the
person with the most pieces at the end of the game in which
the end is
dened as the striking of the chess clock is the winner.
Checkers I leave to the interested reader.
I think Haugland has hit upon the aw of Nim in that the
concept of win of
the game is what is out of proportion to the game.
As I have shown above, you can alter the concept of win of a
game and still
be a VonNeumann game.
It maybe as simple of an adjustment to the game of Nim to say
that the win
is
the largest number of pieces gathered by either player,
rather than the win
dened as the last pickup or not the last pickup.
Archimedes Plutonium
www.archimedesplutonium.com
www.iw.net/~a_plutonium
whole entire Universe is just one big atom where dots
of the electron-dot-cloud are galaxies
===
Subject: A general solution format for this ODE?
THe ODE is in the general format of:
[(ax)^2+bx]*Y + [cx]*Y + kY = 0
xx x
Here all a, b, c and k are constants.
The solution of it cannot be polynomial, cos its singular..
Could anyone suggest on what possible terms (other than
higher order
polynomial terms) the solution might have, so that at least i
can play
around to guess it...I have no clue whatsoever..
A million Thx!
===
Subject: Re: Theorem 4.4.4.
days. My association with the Department is that of an
alumnus.
[.snip.]
>> But if we have that the domain of f is empty, and in
addition we have
>> that f o g = f o h for some functions g and h, then the
codomain of g
>> and h must be empty, which means the domain of both is
empty, and g
>> and h are both the empty function from the empty set to
itself.
>Sure. My main (subconcious) concern was, that the statement
is still
>true, for topological spaces and continuous maps instead of
sets and maps,
>and that with just a little variation, Adams proof would
catch these
>situations too.
Ah, but the real reason that one-to-one/injective is
equivalent to
cancellable on the left for topological spaces (and
surjective is
equivalent to cancellable on the right) is something else:
it is
that given any set there is a topological structure on it
that makes
any map of sets into it continuous (the indiscrete space),
and a
topological structure that makes any map of sets that has it
as domain
continuous (the discrete space); respectively.
So you have a good notion of free topological space in one
element,
which gives you that monomorphisms (maps which can be
cancelled on the
left) must be injective; and the discrete space gives you that
epimorphisms (maps which can be cancelled on the right) must
be
surjective.
But restrict the situation even a little, say, to Hausdorff
spaces,
and the proof no longer works: cancellable on the right now
becomes
equivalent to image is dense, not to surjective. You still
have a
free Hausdorff space on one element which gives you that
cancellable
on the left is equivalent to injective, but you lose the
other clause
of the theorem. And in other concrete natural categories you
lose the
injectivity clause as well (e.g., in the category of divisble
groups,
the quotient map Q -> Q/Z is a monomorphism, so it can be
cancelled on
the left, even though it is not injective).
Its not denial. Im just very selective about
what I accept as reality.
--- Calvin (Calvin and Hobbes)
Arturo Magidin
magidin@math.berkeley.edu
===
Subject: Re: Tensors for mathematicians
> In response to why not just call them matrices or linear
maps?
> Tensors are to matrices what vector elds or 1-forms are to
vectors.
> They live on the tangent (or cotangent) spaces of
manifolds, and in
> the language of Misner, Thorne, and Wheeler, Gravitation,
which
> is where I learned my 1st differential geometry, they map
vector elds
> to scalar functions.
So what you are saying is that a tensor takes a base point x
in the manifold
M,
and then is a multi-linear map of say n vectors from T_x M
> Instead of a vector eld like the electric eld, think of
the
> EM eld tensor eld at each point of some manifold.
> (Proong this, I read EM eld tensor eld--I mean the
> electromagnetic eld tensor is represented as a tensor
eld.)
I cant do this :(
E and B as vector elds can at least be visualized to some
degree; that
4-tensor object is just too mysterious...
> Tensors at a point of a manifold X are dened on the tangent
> space T_x to the manifold at that point, so are just like
tensors on
R^n.
> He then denes them as multilinear maps from
> T_x X T*_x --> R
> Then form the tensor bundle of tensors at all points x in
X, and
> a tensor eld is a section of that bundle.
> The thing is we want to be able to do everything on curved
spaces--
> the universe is not R^n, as we know from Einsteins GR.
> Also see Spivak, Intro to Differential Geometry I and II,
also his
> Calculus on Manifolds, and again I mention Nelson, Tensor
Analysis,
> Princeton Univ. press.
> Grueb does a good job on multilinear algebra, but there are
many good
> treatments of multilinear algebra.
> The study of the antisymmetric algebra, exterior
differential forms,
> differerntial geometry, Stokes thm., Hodges thm., etc. is
fascinating--
> one of the most rewarding things I studied when studying
physics.
> Also, for math-physics, see Analysis, Manifolds, and
Physics, Vol I and
II
> by Choquet-Bruhat et. al. I found these 2 books right at my
level
> (Ph.D. in physics), and very good, IMO.
> Van
All this is true, but as I said earlier in this thread, it is
a huge
amount of abstract machinery to learn, and then it is almost
utterly
useless
for working with real things like the Cauchy stress tensor,
the inertia tensor, etc... Granted, the original poster was
talking about
special relativity, (at the undergraduate level I believe),
but
bringing in the full machinery of GR would seem to me to
obscure, rather
than clarify, the basic ideas.
-Jeff
===
Subject: Re: Tensors for mathematicians
> So why not just throw away the word tensor and call it a
linear
map?
> Im not sure, but I guess the word persists for historical
reasons and
> because of this physical interpretation.
> Linear maps are tensors,
> but not all tensors are linear maps,
> eg bilinear maps.
Good point. So physics books should drop the mysterious word
tensor
and just say the more descriptive term multi-linear map! ....
?
--Jeff
===
Subject: Re: Tensors for mathematicians
> at 09:21 PM, jjensen14@hotmail.com (J Jensen) said:
>You established it for one O.N.basis,
>but the same argument would show it for another O.N. basis,
so the
>two linear maps must be related in the standard way of
changing bases
>in linear algebra.
> Try that with the Gamma symbols and watch what happens. Not
everything
> that has numbers associated with coordinate systems
transforms like a
> tensor.
I assume you are talking about the Cristoffel symbols? I
havent
studied
that yet, so I cant agree or disagree. But, in my above
postings,
I am specically referring to a linear map relating 2 physical
quantities, which are naturally represented as vectors, in an
orthogonal basis.
In that scope, I am still convinced that the things I said in
my rst
posting in this thread are correct, because I havent seen a
real
error
pointed out yet...
--Jeff
===
Subject: Re: Tensors for mathematicians
X-CompuServe-Customer: Yes
X-Coriate: interspeed.co.nz
X-Ecrate: tanandtanlawyers.com
X-Pose: George Cox
X-Punge: Micro$oft
X-Sanguinate: The MVS Guy
X-Terminate: SPA(GIS)
X-Tinguish: Mark Grifth
X-Treme: C&C,DWS
at 07:03 PM, glhansen@indiana.edu (Gregory L. Hansen) said:
>If youre a math person, you might feel comfortable with the
>inexpensive Dover book by Lovelock and Rund, Tensors,
Differential
>Forms, and Variational Principles.
Highly doubtful; the denition that you give seems to have
been
written for a Physicist, not for a Mathematician. I would
expect him
to be more comfortable with coordinate-free denitions.
>A dual is what you need to form a dot product.
No. Its true that given a dual you can dene a dot product,
but
thats putting the cart before the horse. The conventional
way to
dene a dot product is with a metric tensor, and you can then
trivially dene the corresponding dual.
>In particular, special relativity has the metric
> ds^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2
Thats only one formulation; a signature of (- + + +) works
just as
well as (+ - - -). Theres also the ict approach, but AFAIK
nobody
uses it these days.
Shmuel (Seymour J.) Metz, SysProg and JOAT
Unsolicited bulk E-mail 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: is there a Great Attractor in Gametheory of
VonNeumann?? Re: There
exists a Nim version that is a draw OS
> A combinatorial game such as Nim can not be a draw.
> Here is a distant relative that can be a draw:
http://home.no.net/zamunda/split.htm
> I beg to differ.
> Yesterday I was working on a game of Nim, a morph of Nim
where there
are
> no draws in the game itself but where either player can win
in the OS
> and not automatically that one player always wins the OS.
Call it a
> pseudodraw.
> The minimax theorem says a singular point. Thus a
pseudodraw is
> nonexistent.
> Unless there is a draw within the game itself can the OS be
a draw.
> Secondly, I was looking for another Nim morph where it
actually has a
> draw within the game itself and the OS is a draw.
> Thirdly I was looking for a Tictactoe morph that was _not_
a draw in
the
> OS and where either X or O can win in the OS. Call it a
pseudodraw.
> Here is what I come up with:
> Nim-morph with pseudodraw OS: Let me call the person with
rst move as
> white and let me call the person with second move as black.
The rst
> move in this game is not the removal of any matchsticks but
is the
> actual layout of the number of rows and the number of
matchsticks
within
> each row. Black then proceeds as in normal nim. I contend,
thence, that
> this nim morph will end up as a win for one of the players
but not
> automatically the black player (provided regular nim is
considered a
> loss for the one who is forced to pick up the last
matchstick).
> This is a erroneous claim. Even if I added the rule that
only one or two
> matchsticks can be removed per move.
> Nim-morph with a Draw in the game itself: This is where
white with
rst
> move determines the number of rows of matchsticks and the
number of
> matchsticks in each row. And nally, determines that at
least one row
> is a Draw row so that if this row or any of its matchsticks
is
picked
> up last then the entire game is a draw.
> This is possible. It perhaps needs the rule of only one or
two
matchsticks
> removed per move.
> TicTacToe-morph with pseudodraw OS: this one was a tough
one to work
out
> last night. I would have thought that Nim was going to be
the tougher
> challenge. We have several rule changes to normal
tictactoe. Call the
> rst mover as X and the second mover as O. In this morph, O
gets two
> rst moves so that at the end of the game there will be ve
O on the
> board to four X. And the other change in rule is that if
there are no
> three-in-a-row for a outright win then the win goes to the
person who
> has the most two-in-a-row. Now I have not fully played out
all the
> consequences. But I suspect, not sure of this suspection,
that the OS
of
> this morph tictactoe is a win for either X or O or a
pseudodraw. And
> that every game played of this morph will produce a winner
whether it
be
> X or O.
> Trouble with whether end row middles would count as
2-in-a-row rather
> than having only shortened 3-in-a-rows count as 2-in-a-row.
When X
makes
> rst move with placing an X in center square then X has the
most
> 2-in-a-row unless we count end-row-middles as 2 in a row
for O.
> Here again, the concept of Pseudodraw is erroneous, and
that unless a
draw
> exists in the game itself can the OS be a draw. And the
minimax theorem
> says as much.
> Now, the most important aspect of the above, if true,
implies that
there
> exists a Pseudodraw for the games of checkers and chess,
but more
> importantly, that those games OS is a draw with their
current and
> present rules.
> But the above is not all lost and wasted. I can salvage the
idea that to
> make Nim a draw is to add the rule that the player with
rst move
decides
> the arrangement of how many rows and number of matchsticks
per row and
> which row is the Draw row.
> The implications for chess and checkers still remain. That
if a game has
a
> draw possibility, then the OS of that game ends up into
that draw play.
> Nim OS is a win for one of the players always, well,
because there is no
> draw possibility while playing the game.
> I never played Go. I suspect it has a draw possibility. If
it does, then
> that is its OS-- a draw. Chess has a draw possibility, thus
chess OS is a
> draw.
> This claim can be made into a assertion and then a theorem.
> Devise a game that is a VonNeumann game which has a draw
possibility but
> has a nonDraw OS. Nim has a nondraw OS but nim has no draw
within the
game
> itself. So when we inject a draw possibility into Nim then
does the one
> player always win the OS??????
Initially I was tempted to call a draw game in any VonNeumann
game as a
gravity attractor such as gravity equilibrium or
gravitational center so
that
if you introduce a draw game inside of Nim that the OS of Nim
shifts
and
then becomes something different from its automatic win for
second player.
That the moment you introduce a possible draw game that the
entire OS of
Nim
shifts and becomes that draw end result.
But there is another concept in physics that is like
gravitational
attraction. And I suppose a good physicist not the usual run
of the
mill
sort can tell you the conceptual difference between gravity
attraction and
Great Attractor in chaos theory.
I like to think of Great Attractors in EM of electricity and
magnetism.
Anyway, Nim is VonNeumann gametheory and the OS is a certain
victory for
second player. But introduce just one possibility of a draw
outcome, then,
does the entire OS of this Nim change to the draw outcome? As
like a Great
Attractor, the draw outcome forces itself as the Optimal
Strategy.
Archimedes Plutonium
www.archimedesplutonium.com
www.iw.net/~a_plutonium
whole entire Universe is just one big atom where dots
of the electron-dot-cloud are galaxies
===
Subject: Re: is there a Great Attractor in Gametheory of
VonNeumann?? Re:
There exists a Nim version that is a draw OS
>>A combinatorial game such as Nim can not be a draw.
>>Here is a distant relative that can be a draw:
>>
>>http://home.no.net/zamunda/split.htm
>I beg to differ.
>Yesterday I was working on a game of Nim, a morph of Nim
where there are
>no draws in the game itself but where either player can win
in the OS
>and not automatically that one player always wins the OS.
Call it a
>pseudodraw.
>>The minimax theorem says a singular point. Thus a
pseudodraw is
>>nonexistent.
>>Unless there is a draw within the game itself can the OS be
a draw.
>Secondly, I was looking for another Nim morph where it
actually has a
>draw within the game itself and the OS is a draw.
>Thirdly I was looking for a Tictactoe morph that was _not_ a
draw in the
>OS and where either X or O can win in the OS. Call it a
pseudodraw.
>Here is what I come up with:
>Nim-morph with pseudodraw OS: Let me call the person with
rst move as
>white and let me call the person with second move as black.
The rst
>move in this game is not the removal of any matchsticks but
is the
>actual layout of the number of rows and the number of
matchsticks within
>each row. Black then proceeds as in normal nim. I contend,
thence, that
>this nim morph will end up as a win for one of the players
but not
>automatically the black player (provided regular nim is
considered a
>loss for the one who is forced to pick up the last
matchstick).
>>This is a erroneous claim. Even if I added the rule that
only one or two
>>matchsticks can be removed per move.
>Nim-morph with a Draw in the game itself: This is where
white with rst
>move determines the number of rows of matchsticks and the
number of
>matchsticks in each row. And nally, determines that at
least one row
>is a Draw row so that if this row or any of its matchsticks
is
picked
>up last then the entire game is a draw.
>>This is possible. It perhaps needs the rule of only one or
two
matchsticks
>>removed per move.
>TicTacToe-morph with pseudodraw OS: this one was a tough one
to work out
>last night. I would have thought that Nim was going to be
the tougher
>challenge. We have several rule changes to normal tictactoe.
Call the
>rst mover as X and the second mover as O. In this morph, O
gets two
>rst moves so that at the end of the game there will be ve
O on the
>board to four X. And the other change in rule is that if
there are no
>three-in-a-row for a outright win then the win goes to the
person who
>has the most two-in-a-row. Now I have not fully played out
all the
>consequences. But I suspect, not sure of this suspection,
that the OS of
>this morph tictactoe is a win for either X or O or a
pseudodraw. And
>that every game played of this morph will produce a winner
whether it be
>X or O.
>>Trouble with whether end row middles would count as
2-in-a-row rather
>>than having only shortened 3-in-a-rows count as 2-in-a-row.
When X
makes
>>rst move with placing an X in center square then X has the
most
>>2-in-a-row unless we count end-row-middles as 2 in a row
for O.
>>Here again, the concept of Pseudodraw is erroneous, and
that unless a
draw
>>exists in the game itself can the OS be a draw. And the
minimax theorem
>>says as much.
>Now, the most important aspect of the above, if true,
implies that there
>exists a Pseudodraw for the games of checkers and chess, but
more
>importantly, that those games OS is a draw with their
current and
>present rules.
>>But the above is not all lost and wasted. I can salvage the
idea that to
>>make Nim a draw is to add the rule that the player with
rst move
decides
>>the arrangement of how many rows and number of matchsticks
per row and
>>which row is the Draw row.
>>The implications for chess and checkers still remain. That
if a game has
a
>>draw possibility, then the OS of that game ends up into
that draw play.
>>Nim OS is a win for one of the players always, well,
because there is no
>>draw possibility while playing the game.
>>I never played Go. I suspect it has a draw possibility. If
it does, then
>>that is its OS-- a draw. Chess has a draw possibility, thus
chess OS is a
>>draw.
>>This claim can be made into a assertion and then a theorem.
>>Devise a game that is a VonNeumann game which has a draw
possibility but
>>has a nonDraw OS. Nim has a nondraw OS but nim has no draw
within the
game
>>itself. So when we inject a draw possibility into Nim then
does the one
>>player always win the OS??????
> Initially I was tempted to call a draw game in any
VonNeumann game as a
> gravity attractor such as gravity equilibrium or
gravitational center so
that
> if you introduce a draw game inside of Nim that the OS of
Nim shifts
and
> then becomes something different from its automatic win for
second
player.
> That the moment you introduce a possible draw game that the
entire OS of
Nim
> shifts and becomes that draw end result.
> But there is another concept in physics that is like
gravitational
> attraction. And I suppose a good physicist not the usual
run of the
mill
> sort can tell you the conceptual difference between gravity
attraction
and
> Great Attractor in chaos theory.
> I like to think of Great Attractors in EM of electricity
and magnetism.
> Anyway, Nim is VonNeumann gametheory and the OS is a
certain victory for
> second player. But introduce just one possibility of a draw
outcome,
then,
> does the entire OS of this Nim change to the draw outcome?
As like a
Great
> Attractor, the draw outcome forces itself as the Optimal
Strategy.
> Archimedes Plutonium
> www.archimedesplutonium.com
> www.iw.net/~a_plutonium
> whole entire Universe is just one big atom where dots
> of the electron-dot-cloud are galaxies
The intellectual midget doth return.
===
Subject: a complex analysis question
f(z)=(z_0 - z) / (1 - bar{z_0} z) abs(z_0)<1 conformal
mapping.(unit
disk to unit disk)
Suppose f maps a disk (center s, radius s) on to a disk
(center 0
radisu r)
where s>0, 2s<1, r<1
(1) For s=1/4, determine f(z) and r.
(2) Show that, in general, r and s are related by the equation
r^2s-r+s=0
---------------(sorry for clumsy notation)-----------
I think, there might be some symmetric relation between those
two
disks in a unit disk. But I cannot gure that out. How can I
solve
this problem?
===
Subject: Re: a complex analysis question
> f(z)=(z_0 - z) / (1 - bar{z_0} z) abs(z_0)<1 conformal
mapping.(unit
> disk to unit disk)
> Suppose f maps a disk (center s, radius s) on to a disk
(center 0
> radisu r)
> where s>0, 2s<1, r<1
> (1) For s=1/4, determine f(z) and r.
Clearly f is a linear fractional map, and so z_0 must be s.
Hope this helps, Bill
> (2) Show that, in general, r and s are related by the
equation
> r^2s-r+s=0
> ---------------(sorry for clumsy notation)-----------
> I think, there might be some symmetric relation between
those two
> disks in a unit disk. But I cannot gure that out. How can
I solve
> this problem?
===
Subject: Re: a complex analysis question
> Clearly f is a linear fractional map, and so z_0 must be s
Scratch this thought, I answered to fast. Still I might try
to use the
fact
that f is a linear fractional map, and preserves circles, to
help obtain
the
formula.
===
Subject: comprehensive theoretical textbook
Are there any good comprehensive handbook/textbooks of
Mathematics that
present all the theories of elementary and advanced
Mathematics
(undergraduate level), including Algebra, Number Theory,
Discrete
Mathematics, Geometry, Calculus and Analysis, etc. using an
axiomatic/formalistic approach - axioms, theorems with
complete proofs,
corollaries etc.? Which one would you recommend?
Frank
===
Subject: Re: Mathematical Induction and a Train Set
> Hi Guys.
> I have a Train Set with a small problem. If I set it at max
speed it will
go
> around 3 or 4 times and then get stuck or roll over.
> My question is, if it can go around once, shouldnt it
continue to do
that
> because its back to its original state of being back to
the starting
point?
> Any suggestions?
The state of the train should include its instantaneous
velocity, as
well as
its position. *This* will not be the same each time around.
The state of the *system* also includes the position of the
track. If
this isnt constant (for example if the sucessful runnings are
shifting the track slightly), then again the conditions have
changed
For a model train set I would lean to the explanation offered
by
others, that either the train or the track is being modied
during
the succcessful running period.
Larry Lard
Replies to group please.
===
Subject: Re: Mathematical Induction and a Train Set
>> Hi Guys.
>> I have a Train Set with a small problem. If I set it at
max speed it will
go
>> around 3 or 4 times and then get stuck or roll over.
>> My question is, if it can go around once, shouldnt it
continue to do
that
>> because its back to its original state of being back to
the starting
point?
>> Any suggestions?
>The state of the train should include its instantaneous
velocity, as
>well as
> its position. *This* will not be the same each time around.
>The state of the *system* also includes the position of the
track. If
>this isnt constant (for example if the sucessful runnings
are
>shifting the track slightly), then again the conditions have
changed
>For a model train set I would lean to the explanation
offered by
>others, that either the train or the track is being modied
during
>the succcessful running period.
Or more generally from a mathematical point of view the
equations
describing the system need to have a term added that
represents random
uctuations, ie noise, that at some point in the orbit
creates a
condition that represents train derailed or jammed.
Physically this
can represent twisting of the trucks, bouncing over rough
sections in
the track etc. Of course, if the track is not nailed down,
then, as
suggested, it is very likely that track will be moved or
joints opened
as the train is operated.
===
Subject: Re: EIS enries of Roger L. Bagula
X-Reply-Etiquette: No copy by email, please
Originator: legalize@deuce.xmission.com (Rich)
[Please do not mail me a copy of your followup]
Relevance? What does it have to do with these newsgroups?
The Direct3D Graphics Pipeline-- code samples, sample
chapter, FAQ:
Pilgrimage: Utahs annual demoparty
===
Subject: Re: EIS enries of Roger L. Bagula
>My response was to add the comment:
>Warning: the management of EIS can be hazardous to innocent
mathematicians.
>I have one editor there who has me on his blocked list:
>A Dr. Bob Wilson V
>That is he can send me insulting email and my replies bounce.
>Robin Chapman has also got me on his blocked list, so he can
do the same.
>I have a lot of detractors, but in most cases they tend to
admit
>,grudgingly, that my result is new and worthwhile.
What result?
>Ive become very stoic about this over the years
>and many results.
>Editors seem happy to have their names on my sequences.
>> In many of that sequences there is a paragraph like it:
>> Extension: Warning: Many recent communications from this
author have
>> contained numerical errors or have been badly formatted.
This entry has not been
edited and may contain errors. It is included on a
provisional basis in
the hope that some reader will edit it. - njas
===
Subject: JSH: Groupthink
So now senators in the United States are trying to put all
the blame
on the CIA for intelligence failurs as if Bush and company
did nothing
wrong, and I think you can see what groupthink is in a
dramatic area.
Now sci.math is a groupthink area as well, since for some
time now
Ive been able to demonstrate my mathematical points with
precision
rarely seen in ANY mathematical proofs, but the *group* years
ago
decided that I couldnt have any correct results.
That group think was why some of you could send emails to
question a
math journals on process of formal peer review--putting your
judgement
over that of its editors and referees--and much of the group
just
yawned.
Group think.
Now then, youre just a gaggle of people, but the United
States is the
most powerful country in the world. If it can fall to group
think,
why should anyone be surprised that sci.math does as well.
The sad thing is the weakness it shows as none of you care
enough for
mathematics itself to stand up and holler when people say
false
things.
Luckily for me, math society is bigger than sci.math, which
you
learned when my paper was published despite years of people
calling me
names here, but maybe you learned the wrong lesson when
sci.math
posters with their coordinated email campaign succeeded in
getting it
yanked.
But you were dealing with a journal mostly created by one
man--Ioannis
Argyros--in a state school in Oklahoma.
See http://rattler.cameron.edu/swjpam/vol2-03.html
So several posters on sci.math got to *one* man who felt that
he had
the right with a journal he created to make a drastic
decision that it
turns out was the wrong one.
Dont get too happy or feel that sci.math is more powerful
than it is
because some of you could so easily inuence just one
mathematician.
I learned from what happened.
I picked journals more carefully and have more than one
paper, so that
at least one should get through.
The battle will be joined again sci.math, and this time you
will be
faced with a far harder task.
That is, I will beat the entire sci.math newsgroup, and show
you all
why groupthink is no match for mathematics. Its kind of
weird how
people can convince themselves of things they wish to believe
and
continue against all evidence.
Its math society itself that will break you. And when you are
condemned by mathematicians you thought were your peers, and
see
papers published in journals you dare not question, dare not
send
emails to, then what will you think?
I doubt youll groupthink then.
Im curious to see how you do. My guess is that you have less
than
six months before all the papers play out, including the
paper with
The Hammer.
James Harris
===
Subject: Re: Groupthink
> Ive been able to demonstrate my mathematical points with
precision
> rarely seen in ANY mathematical proofs, ....
I have had the opportunity to read some of what you have
written over the
last couple of years. Its theres one think you HAVENT
done, its
demonstrate your mathematical points with precision! I say
this as a
mostly neutral bystander.
===
Subject: Re: JSH: Groupthink
Oh, God, James, go get a bottle of Zyprexa or whatever it is
youre
missing.
Yours,
Doug Goncz ( ftp://users.aol.com/DGoncz/ )
Student member SAE for one year.
===
Subject: Re: JSH: Groupthink
> Its kind of weird how
> people can convince themselves of things they wish to
believe and
> continue against all evidence.
Is it? Examine your own record, and heal thyself.
> Im curious to see how you do. My guess is that you have
less than
> six months before all the papers play out, including the
paper with
> The Hammer.
Im equally curious about how your Hammer will sound when
it clanks
against the Anvil of Truth.
Mark the current date!
> James Often in error, but never in doubt! Harris
--
There are two things you must never attempt to prove: the
unprovable --
and the obvious.
--
Democracy: The triumph of popularity over principle.
--
http://www.crbond.com
===
Subject: Wiles
for participation in threads Modular Arithmetic and
Periodicity of a^n
mod
Is this related to Wiles proof, or was he referring to a
different set of
curves?
1: 0 < a < b < c < a+b
1.1: 2 < n
2: a, b, c, pairwise coprime
3: a^n + b^n = c^n
4: A.0 = a^0 mod c
5: B.0 = b^0 mod c
6: A.n = (A.(n-1) * a ) mod c
7: B.n = (B.(n-1) * a ) mod c
8: The period of A is a divisor of phi(c)
9: The period of B is a divisor of phi(c)
10:?The period of (A+B) is a divisor of phi(c)
11: n < phi(c); Pythagoras, 8, 9
11.1: 1 < m < oo
11.2: c = product from i = 1 to m of prime p.i, to the e.i
power
11.3: j.i = phi(p.i ^ e.i) = phi( (p.i-1) * (p.i - 1) );
Euler totient
formula
11.4: q = LCM of elements j.i; private email
11.5: n <= q; 11.4, 8, 9
12: ( a^n + b^n ) / c^n = 1; 3
13: (a/c)^n + (b/c)^n = 1
To be shown:
9999:?In the a,b plane, the set of curves (13) and {(a,b)} do
not intersect
Yours,
Doug Goncz ( ftp://users.aol.com/DGoncz/ )
Student member SAE for one year.
===
Subject: Svara that the Twin Primes Conjecture is Unprovable
For fun, one could argue that twin primes is unprovable. As
to whether
the argument is rigorous or not, you be the judge:
Let S be the set of all n in which 6n-1 is prime.
Let T be the set of all n in which 6n+1 is prime.
Proving the twin primes conjecture is equivalent to showing
that the
intersection of sets S and T is innite.
First of all, we know that sets S and T are both innite by
Dirichlets Theorem. Now, the condition which denes set S,
that 6n-1
is prime for each n in S, indicates nothing about the factors
of 6n+1
when n is in S, and therefore nothing about whether 6n+1 is
prime when
n is in S.
And the condition which denes set T, that 6n+1 is prime for
each n
in T, indicates nothing about the factors of 6n-1 when n is
in T, and
therefore nothing about whether 6n-1 is prime when n is in T.
Therefore, the two conditions which dene the two sets are
independent from one another, meaning that the only way to
determine
the cardinality of the intersection of the two sets, S and T,
is to
directly calculate the elements in the intersection of S and
T. But
this would take an innite amount of time, since one would
have to
test each natural number n. Therefore, Twin Primes is
unprovable. QED
For those of you who dont buy the argument, let me explain
this in
which twins were born in hospital A. And dene set T as the
days in
different hospitals in different parts of the world.) The
conditions
which dene sets S and T have nothing to do with one another,
i.e.,
they are independent from one another. Therefore, the only
way to
determine the cardinality of the intersection of sets S and T
is to
directly calculate the elements in the intersection of sets S
and T.
This is obviously feasible to do since the number of days in
the year
that twins were born in hospitals A and B respectively from
the year
if the intersection of these sets is innite or not, since
one would
have to wait an eternity to do such.
Anyway, I welcome comments.
Craig
===
Subject: Analysis Differentiation question
X-AUTHid: shrest10
Let f be differentiable on [a,b] (some closed interval).
How would I go about constructing a function so that the
range of f is
a). an open interval
b). open on one side and closed on the other side interval.
===
Subject: Analysis Differentiation question
X-AUTHid: shrest10
Let f be differentiable on [a,b] (some closed interval).
How would I go about constructing a function so that the
range of f is
a). an open interval
b). open on one side and closed on the other side interval.
===
Subject: Re: Another Dini Derivate question
X-AUTHid: shrest10
> dont quite understand the relationship between
countable/uncountable
> sets and Dini Derivates.
> I dont even know where to start on this question -
> Show that the set
> {D^+ f(x) < D_- f(x)}
> cannot be uncountable.
> Also, give an example where {D^+ f(x) < D_- f(x)} on an
innite set.
> Here,
> D^+ f(x) = lim sup _ {x -> x0+} (f(x)-f(x0))/(x-x0)
> the upper right dini derivate
> and,
> D_- f(x) = lim inf _ { x -> x0-} (f(x)-f(x0))/(x-x0)
> the lower left dini derivate
No-one has any idea on this?
===
Subject: Re: Another Dini Derivate question
> No-one has any idea on this?
They just did not decide to do your work for you.
===
Subject: Re: Analysis Differentiation question
> Let f be differentiable on [a,b] (some closed interval).
> How would I go about constructing a function so that the
range of f
is
> a). an open interval
> b). open on one side and closed on the other side interval.
First you need to travel to an alternate universe. In this
one,
differentiability implies continuity, and the continuous
image of a
compact set is compact
===
Subject: Re: Analysis Differentiation question
X-AUTHid: shrest10
> Let f be differentiable on [a,b] (some closed interval).
> How would I go about constructing a function so that the
range of f
> is
> a). an open interval
> b). open on one side and closed on the other side interval.
> First you need to travel to an alternate universe. In this
one,
> differentiability implies continuity, and the continuous
image of a
> compact set is compact
You must be mis-understanding my question.
Im not saying the derivative has to be continuous !!!
[a,b], then the set of derivatives must also be an interval.
Im asking how
we can construct a function f and show that the range of its
derivative is
an open interval.
===
Subject: Re: Logic Book
> Perhaps, but I dont see the evidence for that here. What I
see is
> that readability, like beauty, is in the eye of the
beholder. I
> found much of Bourbaki to be an easy read, even though it
wasnt in
> my native language, but A Tale of Two Cities was a far
duller book
> than I had ever read.
It is a far, far duller book that I read, than I have ever
read...
http://hertzlinger.blogspot.com
===
Subject: Re: Masonic Inltrated Churches
>> And I spoke out in 1988 against the churches and
>> media censoring acts of cannibalism and Scriptural passages
>> referring to cannibalism, then for years I had to listen to
>> psychiatrists telling people on the psychiatric appeal
panel
>> hearings that I was obsessed with penises and cannibals
(but
>> it is not me that thinks so much about penises that I would
>> place them on the roofs of churches, and it is not me that
>> thinks so much about cannibals that I would systematically
>> censor all Scriptural references to them).
> Dammit, my Patented Kook-O-Meter blew a fuse. To borrow a
line from
> Maxwell Smart: Thats the third time thats happened this
> week... :O|
The Freemasons are behind everything. For example, as part of
their
scheme to x energy prices they placed Satanic symbols into
the
street map of Washington, DC in order to send coded messages
to the
Elders of Zion (headquarters at 666 Fifth Avenue in
Manhattan) to back
the leveraged buyout of renegade Objectivist
extraterrestrials from
Zeta Reticuli who might otherwise tell us how to make
cold-fusion
reactors reliable. They are deliberately ddling with energy
prices
to keep us from being able to afford to achieve humanitys
highest
aspiration, namely the attempt to
BLOW UP THE MOON
Is there some way to work Enron and Halliburton into this?
http://hertzlinger.blogspot.com
===
Subject: JSH: Sweep likely
At this point Im fairly condent that Ill get complete
vindication
from more than one major math journal.
It should all play out in less than six months.
Im curious about how people on this newsgroup will react to
hearing
that I was right and others were wrong.
Will you accept it as groupthink, or maybe come up with some
other
answer?
Will your faith in your own mathematical ability be shaken?
Will any of you want accountability from posters like David
Ullrich or
Arturo Magidin when the mainstream mathematicians stand by me
and
repudiate both them, their tactics and their claims?
Oh, and in case youre wondering, yes, a Ph.D can be taken
away for
gross fraud.
In a little while, Magidin and Ullrich may no longer have
Ph.Ds.
Its that serious.
James Harris
===
Subject: Re: JSH: Sweep likely
!3KEIp?*w`|bL5qr,H)LFO6Q=qx~iH4DN;i;/yuIsqbLLCh/!U#X[S~(
5eZ41to5f%E@ELIi
$t^
VcLWP@J5p^rst0+(>Er0=^1{]M9!p?&:z]|;&=NP3AhB!B_bi^]Pfkw
> At this point Im fairly condent that Ill get complete
> vindication from more than one major math journal.
Youve never run short on claims.
> Im curious about how people on this newsgroup will react
to hearing
> that I was right and others were wrong.
Weve been hearing it for several years from you now. It does
not
get true by repetition.
> Oh, and in case youre wondering, yes, a Ph.D can be taken
away for
> gross fraud.
It is the tragedy of your life that a Ph.D. cant be issued
for gross
fraud.
> In a little while, Magidin and Ullrich may no longer have
Ph.Ds.
> Its that serious.
You are being delusional again. It is not the rst time. Take
a
look at your expansive record of similar claims and your
reasons for
stating them. And how often you have been eating your words
afterwards. Just swallow your medication instead for once.
David Kastrup, Kriemhildstr. 15, 44793 Bochum
===
Subject: Re: JSH: Sweep likely
We will be waiting anxiously for this to come to pass ;-)
> At this point Im fairly condent that Ill get complete
vindication
> from more than one major math journal.
> It should all play out in less than six months.
> Im curious about how people on this newsgroup will react
to hearing
> that I was right and others were wrong.
> Will you accept it as groupthink, or maybe come up with
some other
> answer?
> Will your faith in your own mathematical ability be shaken?
> Will any of you want accountability from posters like David
Ullrich
or
> Arturo Magidin when the mainstream mathematicians stand by
me and
> repudiate both them, their tactics and their claims?
> Oh, and in case youre wondering, yes, a Ph.D can be taken
away for
> gross fraud.
> In a little while, Magidin and Ullrich may no longer have
Ph.Ds.
> Its that serious.
> James Harris
===
Subject: Absolute convergence => convergence a. e.?
Hi all,
Let f_1, f_2, f_3, ... be a sequence of Lebesgue-integrable
functions
from [0,1] in the reals such that the sum of their norms
converges
(the norm here being ||f|| = int |f|). Is it true or false
that the
series sum(f_n(x), 1 <= n < +oo) converges a. e.? All that I
was able
to prove was that if s_n = f_1 + f_2 + ... + f_n, then some
subsequence of the sequence (s_n)_n converges a. e.; on the
other
hand, I was not able to nd any counterexample.
Jose Carlos Santos
===
Subject: Re: Absolute convergence => convergence a. e.?
> Hi all,
> Let f_1, f_2, f_3, ... be a sequence of Lebesgue-integrable
functions
> from [0,1] in the reals such that the sum of their norms
converges
> (the norm here being ||f|| = int |f|). Is it true or false
that the
> series sum(f_n(x), 1 <= n < +oo) converges a. e.?
int_[0,1] sum |f_n| = sum int_[0,1] |f_n| < oo.
This implies sum |f_n(x)| < oo for a.e. x. For any such x,
f_n(x)
converges.
===
Subject: Re: Atheist MorituriMax
> God is absolute.
> In your mind and ego only. If God was absolute in the real
world,
I couldnt do
> this.
> dOG
> You can deny the existence of God, no problem. But then you
are left
> with the task of explaining something you cannot deny: your
own
> painful existence.
> Peter
This is a repeat of the argument the reason there is
something instead
of nothing is because god put it there.
If god is responsible for our existence, who is responsible
for gods?
This just pushes the question back a step, but into fantasy,
for there
is no evidence for any god, no reason to think god exists,
except for
authority, which is no reason at all.
No one can shed any light on why we are here. The universe
just
exists. There is no why involved.
I think why are we here is a nonsense question.
People thought the world was at for a long time.
They have believed in god for a long time, but I think
eventually people will realize the truth.
There is no god. I curse him and utter obscenities about him
and challenge him to do something--but nothing ever happens.
Van
===
Subject: Re: a noise with a better histogram
> I used an inversion of a Gaussian to
>get my amplitudes instead of a Gaussian.
>It seems to work somewhat better in terms of the histogram.
>Im indepted to the patient work of Ray Kooperman and Dr.
Bobby
Treat
>on Kurtosis excess calculations and Cauchy distribution
calculations.
>As I am giving this information to the egroup for comment,
>I must take the good with the bad.
> Im so confused. Just now you told us we should use sci.math
> to answer questions. I dont recall any questions here about
> noise with a better histogram.
> Please use sci.math to answer questions. If everyone
> posted everything they know and every bit of code
> theyd written there would be literally millions
> of posts a day and the group would be totally useless.
> Um, also, please when you use sci.math to answer questions
> make certain that you actually understand the relevant
> mathematics before speaking up. When people recognize
> some of the words in the question and post answers
> that make no sense that also wastes valuable space.
> ************************
> David C. Ullrich
Amen to that. I already had to unsubscribe to the Yahoo
number theory group because of this idiot, and his posts here
are getting on my nerves.
I try to ignore them, but they seem to be everywhere and
increasing in length and frequency.
Van
===
Subject: Re: Analysis Differentiation question
> Let f be differentiable on [a,b] (some closed interval).
How would I go about constructing a function so that the
range of
f
> is
a). an open interval
> b). open on one side and closed on the other side interval.
> First you need to travel to an alternate universe. In this
one,
> differentiability implies continuity, and the continuous
image of a
> compact set is compact
> You must be mis-understanding my question.
> Im not saying the derivative has to be continuous !!!
Nor did I.
Lets quote your rst sentence: Let f be DIFFERENTIABLE on
[a,b].
In other words, at each x in [a,b], the derivative f(x) of f
exists at x. Which implies that f is continuous at each point
in
[a,b]. I.e., f is continuous on [a,b].
on
> [a,b], then the set of derivatives must also be an interval.
Huh???
> Im asking how
> we can construct a function f and show that the range of
its
derivative is
> an open interval.
Whoa, now you are changing the question. Do you want the
range of f
to be open (as you asked originally), or do you refer to the
range of
the derivative f?
-SJH
===
Subject: Re: MY LIST of the subsets of N
> This takes into account Cantors diagonal argument which
purports
to
> show that there is no complete list of the nite Natural
numbers.
> iF YOU CONSIDER THE SET OF NATURAL NUMBERS TO HAVE A
DEFINITE
> CARDINALITY xO, THEN: THE SUMS REFERNCED HERE ARE (I HOPE)
ALL
HAVE A
> DEFINED NUMBER OF TERMS
>
>
>
>
> IF A = N+ then Ind(A)=1+2+4+8+16+etc... (Xo terms)
>
> This is the sum of the numbers listed in collumn 2 of the
printout.
> The set N+ itself id the last entry in the list because its
index
> number is greater than the INDEX NUMBER of any proper
subset of
> itself.
>
>
> The latter phrase is true for any other unbounded subset
also.
>
>
> Since 0 is not an elt of N+; I can use 0 as a place
holder to
> represent elt of N+ not in a listed set.
>
>- - - - - - - -- -- - - - -- - - - - - - - -- - - - - -- - -
- - - -
> --
> Comment 1
> This seems interesting to me but I wish you would explain
it so I
> can understand it better: I note that you claim that the
range?
is
> the set of natural numbers: I think that this practice of
presuming
> the range to be something is dangerous. We know that every
set{even
> the set N) has more subsets than elements. This means that
N is a
> proper subset of the range of the function if the domain is
the set
of
> all subsets of N. --or not?--
> f:Domain=> range. Right?
>
>
> Every function has a domain and a range. I think now I
misinterpreted
> what you were doing, especially with respect to 0. Below I
offer an
> alternative explanation. First a side note -
>
> You dened N+ as follows:
>
> N+ = {1, 2, 3, 4, ... | n elt N+}
>
> which is of course a circular denition: the denition of N+
> has N+ itself on the right side of the equation. Perhaps you
> had a misprint.
>
>
> The following is my current understanding of what you were
> trying to do:
>
> You are dening an index for every subset A of N as follows:
>
> If A = {a1, a2, a3, ... } then
>
> Ind(A) = 2^(a1 - 1) + 2^(a2 - 1) + 2^(a3 - 1) + ...
>
> For nite sets, this is not an unreasonable index, and
> in fact it is a one-to-one function from the set of nite
> subsets of N into N itself: that is, if Ind(A) = Ind(B),
> then A = B. You can show this by noting that there is a
> correspondence between Ind(A) and a binary expansion: for
> example, if A = {2, 5, 6, 8}, then you could represent your
> index in binary as:
>
> Ind(A) = .01001101
>
> But for innite sets, what is the meaning of Ind(A) ?
> I believe you are thinking of it as a member of some kind
of ordered
> innite set. You are thinking that bigger subsets are
farther
> along in the list: that is, if A is contained in B, then
> Ind(A) < Ind(B).
>
> Again writing the index in reverse binary,
>
> Ind(N) = .111111111...
>
> Note that if E = {2, 3, 4, 5, 6, ...} then
>
> Ind(E) = .011111111...
>
> Note that if D = {1}, then
>
> Ind(D) = .100000000...
>
> So what your index denes is actually a function from the
> subsets of N to the real numbers between 0 and 1. It is not
> a one-to-one function (because Ind(E) = Ind(D), for
example), but
> it is a surjection. This is sufcient to show that the set
of
> all subsets of N has cardinality at least as large as that
of the
> set of all real numbers between 0 and 1. The binary version
of
> your index function also does have the property that if A
is a subset
> of B, then
>
> Ind(A) < Ind(B).
>
> There is clearly a partial inverse function: given a real
number
> between 0 and 1, express it in binary and nd the
corresponding
> subset of N: for example,
>
> x = .011011001,
>
> then dene H(x) = {2, 3, 5, 6, 9}.
>
> The function H is ambiguous for numbers which terminate in
> all 1s because there are two ways to write such numbers.
To remove
> the ambiguity, always take the expansion terminating in
0s: for
> example, if
>
> x = .01001000111111111..., then also
>
> x = .01001001000000000...,
>
> so dene H(x) = {2, 5, 8}.
>
> With this denition, H is a well-dened function and it
> is one-to-one. Moreover,
>
> Ind(H(x)) = x,
>
> although it is not true that H(Ind(A)) = A.
>
>
> I think this is a clearer way of describing what you were
> actually doing: dening a function from the subsets of N
> onto the real numbers between 0 and 1. This is the sense in
> which you were creating a list. What most mathematicians
> would mean by list is a sequence of items indexed by the
> positive integers. Clearly your list is longer than
> the positive integers.
>
> None of this is new. You have only rephrased very well known
> results in your own language.
>
> Andrzej
> This is sure some juicy feedback,Andrzej! You are a product
of your
> experience and education, just as I am. I have been working
under the
> delusion that we can consider not only 0.00011100110000000*
> as an ACTual number but also the number0.00011101111111111*
> We might be able to proceed with some not impossible working
> assumptions.
> We consider ther to be a MASTER number
much in
> the sense that the ordinal number omega or its cardinal
assciate Xo
> are greater than any pf their predecessors. We might than
be able to
> express the cardinality ]
> of a set A = {1,4,6,25,39} to be [1/1+4/4+6/6+25/25+39/39]
and
> similarly for the so called innite sets.
> If the set is innite then its cardinality is an innite
set
> of summands. In like manner we can consider each and every
> binary expression to have a unique value or identity. No
more any of
> this stuff about numbers having an ambiguious
representation.
> We have then the ability to say that A is a proper subset of
> B.(lease use the notation A < B.) implies that Card(A) is <
Card(B).
> and so on. All this is somewhat classied and I cant go
into full
> detail now since my ideas are still in formative stage. I
am going to
> give you comment all the attention I am sure it deserves. I
am
> impressed so far and I hope to have a better reply
soonDavid P. Ferguson 7/8/04
>
>>>>>>>>>
Thanx for the comments. I must note again that you are not
using the standard denition of cardinality. You have dened
a function g from P(N) to [0, 1] which is one-to-one on all
but
a countable set of subsets, where P(N) is the set of all
subsets
of N. Moreover, it has the nice property that if A is a
proper subset
of B (i.e., A < B), then g(A) < g(B). Thus you have a function
which is one-to-one except on the set of complements of nite
sets,
and which preserves (partial) order.
But it is wrong to assume that g(A) can be identied as the
cardinality of A. That is simply not the standard denition
and not equivalent to it. You can invent your own terminology
of course, but it is not a good idea to re-invent standard
terminology. It just leads to confusion.
Andrzej
> Ferguson 7/3/04
> - - - - - - - - - - -- - - - - - - - - - - - - - - - - - -
- - - --
-
> - --
> You thus appear to be dening a function f(S) whose domain
includes
> any subset S of N, and which takes values in N + {0}.
>
> What you need is that this function is 1-1.
>
> It isnt. Any unbounded subset S of N is such that f(S) = 0.
> - - - - - - - - - -- - - - - - - - - - - - - - - - -- - - -
- --
-- - -
> I wish someone would explain the Any unbounded.... f(s) =
0. to
> me.
> Ferguson 7/3/04
> - - - - - -- - - - - -- - -- - - - - - -- - - - - -- - - --
- - -
> - - -
>
>
> Cantor DID prove that every set has more subsets than
subsets.
>
> Doubtful!
>
> In the process he proved that the the cardinality of the
set of
subsets
> of N ia greater thsn the cardinality of N (Xo). But he did
not
prove
> that there is no list of the subsets of N what-so-ever.
>
>
> He did, if by list you mean a function from the subsets of N
> into N itself which is one-to-one. If this is not what you
mean
> by list, then either (1) you need to dene exactly what you
mean,
> or (2) a trivial construction is possible.
>
>
> Andrzej
>
> This I respectfully submit.
> david.ferguson1@cox.net
===
Subject: Re: Garry Denkes Gold & Brass Plates @ Westbury
White Horse Eye
> Therein the reason we need the number 0 rule, and the
number - rule,
> and the number + rule.
> Only if we have all three numbers. Since 0 = + and 0 = -,
theres
> no real need for the other two.
Repeatedly toss a coin (inntie times)
What is the probability of HHHHHHHHHHHHHH.... ?
# desired outcomes 1
_____________________ = __________________________
# total outcomes # total outcomes
as total outcomes -> oo, P(H..) > 0
It CAN happen, so the probability is NOT 0.
Herc
===
Subject: Prime Number Void
Originator: edlee@chinet.com (Edward Lee)
Is there an open interval (p, p*p) where p is a prime number
such that there
are
no prime numbers in this interval?
-Ed L
Due to the volume of spam that I receive, any email message
which does not
have the word, mail, somewhere in the subject will be
automatically
deleted. Someone has also been forging the return address of
spam messages
to make it look as though they are coming from me.
Due to the volume of spam that I receive, any email message
to me which
does
not contain the word, mail, in the subject will be
automatically
deleted.
===
Subject: Re: matrix
> hello,
> what does it mean to solve a matrix?
> It means that Neo has saved the world.
In the immortal word(s) of C. Montgomery Burns, Excellent!
Kevin ONeill
===
Subject: Re: complexity of the subgroup problem in free groups
actually, from what i read about free groups and todd coxeter
enumeration, and stuff,
1. The problem of nding whether some word lies in this
sub-group is
decidable only if the index of the subgroup is nite.
2. And it is undecidable in general to compute the index of
the
subgroup.
So, can this be exploited to generate instances of the word
problem
that are undecidable?
or am i wrong in my understanding of facts 1 and 2
bye
abi