mm-147
 David's point is a good one. Apart from exhaustively
testing> an implementation with all possible inputs of length
less than> 1000 digits, I see no way to prove an
implementation attains> your goal of establishing primality in
the given time limit of no> more than a few hours....> For this
reason the tests commonly used in cryptographic> applications
might be said to be probabilistic in name only. > If you're
asking me, I was responding to the original poster's quest >
for primality testing software. See the OP's requirements,
which > were left in my response, specifying that inputs up to
a thousand > digits should be handled in no more than a few
hours.There are primality proving algorithms out (that do not
rely on thetruth of any hypothesis). Check APR-CL. They have
been extended toway beyond the original 300 digit number for
which they weredesigned. Proving 80 digit number primes is a
question of less thana second. When I 'rst used them on a 
Cray
1, proving a 200 digitnumber prime took 8 minutes; speed has
increased quite a bit sincethat time...-- dik t. winter, cwi,
kruislaan 413, 1098 sj amsterdam, nederland, +31205924131home:
bovenover 215, 1025 jn amsterdam, nederland;
http://www.cwi.nl/~dik/
=What are primative rings and do
they have any particular structure?
=> What are primative
rings and do they have any particular structure? A ring R is
said to be left (right) primitive ringif there is a left
(right) R-module V such that V is a simple
faithfulR-module.The term left and right here is important.
There are right primitiveringwhich are not left pimitive
(Bergman result).There is a well-known classi'cation for
pimitive rings (see I. N.Herstein, Noncommutative rings, The
mathematical Association ofAmerica, 1968.Best wishes
=
>There is a well-known classi'cation for pimitive rings (see
I. N. >Herstein, Noncommutative rings, The mathematical
Association of >America, 1968.about primitive rings. Also, not
knowing what a simple faithful R-moduleis, I'm afraid 
I've not
the background for his book. Additionally I wasfrustrated
trying to locate Noncommutative Rings, at MAA.----
=>[rants that make my point better than I ever could
snipped]David Ullrich got caught once in an interesting
exchange where he>called me an idiot for apologizing to a
*French* newsgroup for not>posting in French.  Nope.
Never happened. (Provide a citation, please).>idiot FOR
APOLOGIZING TO A FRENCH NEWSGROUP FOR NOT POSTING IN
FRENCH.According to the post in question, your comments
were:>Well I must say I'm impressed if Ullrich speaks 
French!Though I'd have been more impressed if he'd 
replied in it!To
which David Ullrich replied:>> Idiot.It is clear that you were
not apologizing to anybody. Therefore, youlied. Since you knew
the post in question, your lie was a knowing lie.
Why do
you take so much trouble to expose such a reasoner as Mr.
Smith? I answer as a deceased friend of mine used to answer on
like occasions - A man's capacity is no measure of his power 
to
do mischief. Mr. Smith has untiring energy, which does
something; self-evident honesty of conviction, which does
more; and a long purse, which does most of all. He has made at
least ten publications, full of 'gures few readers can 
critize.
A great many people are staggered to this extend, that they
imagine there must be the inde'nite something in the
mysterious all this. They are brought to the point of
suspicion that the mathematicians ought not to treat all this
with such undisguised contempt, at least. -- A Budget of
Paradoxes, Vol. 2 p. 129 by Augustus de Morgan
I
thought that I'd posted this, yesterday:is this a conjecture
on the twin primes, UA?be nice! > If one looks at pairs of
consecutive prime numbers separated by only> one non-prime
number - 41,43; 821,823; 8087,8089 etc. - one sees that> the
sum of such two primes is often divisible by 12: (11 + 13)/12
= 2 > (41 + 43)/12 = 7> (821 + 823)/12 = 137> (1931 + 1933)/12
= 322 > (8087 + 8089)/12 = 1348> (104681 + 104683)/12 = 17447
--les ducs d'Enron!http://www.tarpley.net
=>If one looks at
pairs of consecutive prime numbers separated by only>one
non-prime number - 41,43; 821,823; 8087,8089 etc. - one sees
that>the sum of such two primes is often divisible by 12: (11
+ 13)/12 = 2 > (41 + 43)/12 = 7> (821 + 823)/12 = 137> (1931 +
1933)/12 = 322 > (8087 + 8089)/12 = 1348>(104681 + 104683)/12 =
17447 > 3,5 obviously does not work. Use your Harris big mouth
to 'nd>another pair of consecutive primes other than 3,5 
whose
sum is not>evenly divisible by 12.Interesting. I've never 
seen
that before. How would you suggest goingabout 'nding the 
other
pair other than by brute force?
=>[rants that make my point
better than I ever could snipped]David Ullrich got caught once
in an interesting exchange where he>called me an idiot for
apologizing to a *French* newsgroup for not>posting in French.
Nope. Never happened. (Provide a citation, please). > He called
you an idiot for something else.-- dik t. winter, cwi,
kruislaan 413, 1098 sj amsterdam, nederland, +31205924131home:
bovenover 215, 1025 jn amsterdam, nederland;
http://www.cwi.nl/~dik/
=<megasnip Why would Christian Bau
question the accuracy of my prime counting> function?A simple
guess would be jealousy. And it hardly makes sense that 
he'd>
be jealous of a rehash.Oh gosh, why didn't I see all this
before? Of course, everything yousay just must be true. For if
no-one questions its accuracy, we can besure it's true, but 
if
anyone does question its accuracy, the onlypossible
explanation is jealousy, and again we can be sure it's
true.Would this work for me too?<snippettino It is correct
that early on I was certain that my prime counting> function
was the fastest possible. However, in its base form, it's>
rather slow, as implementations 'nd primes on their own and
don't use> the information about found primes.For faster
*algorithms* it pays to use sieves.Hmm. Can you explain the
signi'cance of the ï*' round 
algorithms?Am I right in
understanding that yours is a *function*, not an*algorithm*?>
What's OP?Original PosterBrian
Chandler------http://imaginatorium.org
=... > Nope. Never
happened. (Provide a citation, please). > He called you an
idiot for something else.(He might also have called you idiot
savant...)-- dik t. winter, cwi, kruislaan 413, 1098 sj
amsterdam, nederland, +31205924131home: bovenover 215, 1025 jn
amsterdam, nederland; http://www.cwi.nl/~dik/
=the
§oating-point standard (IEEE-755, -855, I think) inherentlyis
chaotic; and,it's impimentation is completely variable,in 
both
software & hard. > Funny that. Your claim is that your
algorithm is the fastest in the > world, so a value of 2^63
should no problem. What is more funny is that > you get it
wrong again: Your Java program cannot work for values up to >
2^63, because the square root of 2^63 doesn't 
't into an int
(only > values up to 2^31 - 1 work). Not that it cannot be
'xed, but it shows > that you are just incapable of any
coherent thought.--UN HYDROGEN (sic; Methanex (TM)
reformanteurs) ECONOMIE?...La Troi Phases d'Exploitation de 
la
Protocols des Grises de Kyoto:(FOSSILISATION [McCainanites?]
(TM/sic))/BORE/GUSH/NADIR @
http://www.tarpley.net/aobook.htm.Http://www.tarpley.net/
bushb.htm (content partiale, below): 17 -- L'ATTEMPTER de 
COUP
D'ETAT, 3/30/81 23 -- Le FIN d'HISTOIRE 24 -- 
L'ORDEUR du MONDE
NOUVEAU 25 -- THYROID STORK !?!
=>>[rants that make my
point better than I ever could snipped]David Ullrich got
caught once in an interesting exchange where he>called me an
idiot for apologizing to a *French* newsgroup for not>posting
in French.  Nope. Never happened. (Provide a citation,
please).>an idiot for apologizing to a French newsgroup for
not posting inFrench. I called you an idiot for saying you'd
be impressed if _I_had posted in French, like a working
knowledge of that languageis a big deal, attained by only a
few geniuses. A quote from the post you refer to
here:[James]>Well I must say I'm impressed if Ullrich speaks
French!>Though I'd have been more impressed if 
he'd replied
in it![Ullrich]>> Idiot.Once again we see how accurate your
version of events is.It's curious - you say something
happpened, I say it never happenedand ask for a reference. You
give a reference that _shows_ itnever happened, but you 
don't
seem to notice that fact...>When informed that he was on a
French newsgroup>making his posts, he gave some excuse about
not knowing, Btw, this never happened either.>but
never>apologized to me nor to the newsgroup.And ask yourself,
how does it all relate to the poster who noted
the>nitpick?_This_ is _very_ curious. _You_ brought the whole
thing up just now,now _you_ are asking about its
relevance?>James Harris David C. UllrichDavid Ullrich is
a math professor at Oklahoma State University. He is>therefore
paid by the state and by American taxpayers as I'm sure
the>school receives funds from the federal government.My point
is that he should be held to *some* standard, where at
a>minimum public lying is frowned upon.James
Harris**********David C. Ullrich
=>[...]>Seems like James
Harris has an algorithm for counting primes>which is correct,
even if perhaps not totally novel and not>the fastest
available today. Yes (although the word totally is perhaps
overly polite.)>If he has come up with the algorithm>himself,
clearly he is bright enough to do mathematical work of>more
importance, perhaps given some mentor and of course,
actual>interest on his part. Yes. Nobody has ever denied this.
In fact it's happened many timesthat people have pointed out
exactly what you say here and suggestedthat he actually study
some mathematics. But he doesn't appearto have any interest 
in
doing so. One conjectures that this is becauseif he were to
start a serious study of mathematics he would 'rst haveto
admit to himself that he's _not_ at present one of the top
numbertheorists in the world (one of the many curious things
he's statedmany times).>(Anybody wanna offer him a
graduate>fellowship so he has more interesting things to
deal>with and stops posting?)Re on-topic vs off-topic, I think
meta-comments about>a discussion are relevant to the
discussion. The topic>itself is only marginally relevant to
Java as such, but>the comparison to C++ seems to have
generated some interest.**********David C. Ullrich
=> He has
responded to such statements many times, simply stating> that
it's not so. But it is.That is a false statement.Ultimately
Ullrich's case seems to rest on the fact that my work gives>
the e answers as others. But, given that, for instance, there
are> 4 primes up to 10, which are 2, 3, 5, and 7, prime
counting methods,> and any correct prime counting function
will give the e answer.I am more than happy to go into details
about why my prime counting> function is signi'cant and is 
NOT
a rehash.Well, what advantage does your method provide over
existingmethods? Is it signi'cantly faster? Tables of
primesalready exist on the web for very large number of
primes.One could simply do a table search to see if a numberis
a prime or not.The only advantage one might see for a new
method is for assistingin the computation of even newer and
larger primes. If your methodis faster, the people computing
new primes and buildingtables will be happy to use it, I am
sure. You mightwant to contact and convince such people.But if
your method is not _seriously_ faster than what theyare already
using (faster enough to justify rewritingtheir programs,) you
won't hear a peep back from them.And there is nothing else 
in
it for you. Primes are oldstuff. In today's age, 
it's not
something for whichsomebody is going to put you in history
books or giveyou large amounts of grant money. There isn't a
nobelprize in it, either. So why waste your goodcheer over
it?Nobody seems to be arguing seriously that your methodis
incorrect. Even if they are ornery enough notto have come out
right away and told you that your methodwas correct -- 
that's
kind of expected on the usenet.So be happy that your method is
correct, and nobodyhas found an actual fault in it. After that,
if you wantto emulate Newton and 'ght like a bitch over 
credit,
that'syour business. It's a personal choice, 
is it worth it
toyou, enough to get into these 'ghts that deterioriateinto
sleaze quickly, and pull you and everyone else down?> David
Ullrich is commenting on my issue with a post where he talked
of> a racial slur being the perfectly appropriate reply to
me.He also has an interesting post which you can 'nd by going
is the> author, and he uses the word rape.I am not sure what
to make of it. You are exposing that whenMr. Ullrich thinks of
particular vicious nasty crimes, he seemsto think only members
of a certain race are capable of them.Now if that's the 
case,
I would say Mr. Ullrich's upbringingwas sadly wanting and/or
he has not been a particularly thoughtfulindividual since, and
maybe has convinced himself Jeffrey Dahmerwas framed. But none
of that's really related to primes.It would be nicer if both
sides had avoided attackson character of each other. There is
a context whenthe best of us need to be pointed out the errors
inour thinking, but ideally the context is not thatof attacks
on each other.> What's OP?Useful new net shorthand for
Original Poster.
=Yes, I have been seeing this show up on
comp.lang.java.advocacy,> so I am not familiar with the
presumably longer history!Here's a quick summary: For about
EIGHT YEARS James Harris has been> discoveries to sci.math
(and often to other newsgroups). Much of the> time his
arguments are too vague and ill-de'ned for people to make
senseSorry, that's not believable. Something that can be put
intoa Java or C++ program that can be understood by a compiler
isby nature not vague or ill-de'ned. Frankly, vague
andill-de'ned are cop-outs used frequently by many 
incompetent
anddishonest people in academia and on usenet, so you have to
dobetter than that if you want to be taken seriously. E.g.
takea crucial part of the argument and show that it rests
onlack of clear de'nition (ill-de'ned) or can be 
interpretedin
meaningfully and signi'cantly different ways (vague.)
<6jdmgvkm83p1mvup4lie71h55gm4u9trif@4ax.com>
=|| || |
Yes, I have been seeing this show up on
comp.lang.java.advocacy,|| | so I am not familiar with the
presumably longer history!|| || Here's a quick summary: For
about EIGHT YEARS James Harris has been|| discoveries to
sci.math (and often to other newsgroups). Much of|| the time
his arguments are too vague and ill-de'ned for people to||
make sense|| Sorry, that's not believable. Something that 
can
be put into| a Java or C++ program that can be understood by a
compiler is| by nature not vague or ill-de'ned.the 
breakthrough
he claims it is.Wayne was referring to James's other
mathematical arguments, such ashis claimed proof of Fermat's
Last Theorem, his claimed proof thatWiles's proof of FLT is
invalid, and his claimed proof that 
ïcoremathematics' has a
fatal §aw because the ring of algebraic integersis
ïincomplete'.-- http://www.dfan.org
=> [...]> David Ullrich
is commenting on my issue with a post where he talked of>> a
racial slur being the perfectly appropriate reply to me.
He also has an interesting post which you can 'nd by going
is the>> author, and he uses the word rape.I am not sure what
to make of it. You are exposing that when>Mr. Ullrich thinks
of particular vicious nasty crimes, he seems>to think only
members of a certain race are capable of them.Um, maybe
exposing was not the word you meant - it seemsto me that if
you say someone's exposing something it follows that the 
thing
being exposed is actually so. It'scertainly not true that I
think that only members of certainraces are capable of certain
nasty crimes. (Maybe espousingis what you meant? Not sure I
spelled that right.)In case you _do_ think that the posts
James is referring todemonstrate that I think what you say
James is exposing,let me just clarify:Long ago James told us
he was black. Some time later,still long ago, he said
something particularly insultingand dehumanizing - it occured
to me at the time thata racial slur in reply would be
appropriate, simply toillustrate the idea that there is such a
thing as you'renot supposed to talk to people that way. I
refrained,because it wouldn't have been something I 
meant,and
because of course I'm _not_ supposed to talkto people that
way.Then some time later, still long ago, in reply to
someother egregious insult, I said what I say in the
previousparagraph, about things I once considered sayingand
why, and why I did not say them. Again, my pointwas simply to
say that there is such a thing as waysone is simply not
supposed to talk to people - Jameshad stepped way over that
line and I wanted to pointout that there was in fact such a
line.In my post I included a statement as above, to theeffect
that I once (brie§y) considered the idea that aracial slur
would be appropriate - pointed out that ofcourse I decided it
wasn't, in fact it's not something Isaid. 
James replied that a
racial slur was _never_appropriate. This statement is of course
ridiculous;I pointed out that for example, to take an extreme
case,if someone had broken into my home, tied me upand was
about to rape my daughter, if I thoughtthat calling him a
nasty name might distract himuntil the police arrived then a
racial slur would benot only appropriate, refraining from
making sucha comment would be positively wrong.And since then
he's accused me of thinking thatblacks are rapists, or that
rapists are all black,or whatever - he never puts it quite so
baldly, justpoints to that post as evidence of my
attitudes.Which of course is twisting things - the rapistin
the imaginary scenario is in fact black (or amember of some
other unspeci'ed minority,let's say black for 
simplicity's
sake), but that'snot because I think that rapists tend to be
black,it's because the _question_ was whether 
it'scorrect to
say that a racial slur is _never_appropriate - a hypothetical
example illustrating that that's not so is necessarily going
to involve a minority. I mean, duh.>Now if that's the case, 
I
would say Mr. Ullrich's upbringing>was sadly wanting and/or 
he
has not been a particularly thoughtful>individual since, and
maybe has convinced himself Jeffrey Dahmer>was framed. But
none of that's really related to primes.>It would be nicer 
if
both sides had avoided attacks>on character of each other.
There is a context when>the best of us need to be pointed out
the errors in>our thinking, but ideally the context is not
that>of attacks on each other.> What's OP?Useful new net
shorthand for Original Poster.**********David C. Ullrich
=>
...> Nope. Never happened. (Provide a citation, please). He called you an idiot for something else.(He might also
have called you idiot savant...)Hmmm...so Ullrich calls me an
idiot for noting that I'd be impressedif he'd 
written in
French in posting to a French newsgroup, and 'rstyou claim it
was for something else, and *then* you reply again toclaim
that he actually *was* posting in French!!!Fascinating.James
Harris
=>Yes, I have been seeing this show up on
comp.lang.java.advocacy,> so I am not familiar with the
presumably longer history! Here's a quick summary: For
about EIGHT YEARS James Harris has been>> discoveries to
sci.math (and often to other newsgroups). Much of the>> time
his arguments are too vague and ill-de'ned for people to make
senseSorry, that's not believable. Something that can be put
into>a Java or C++ program that can be understood by a
compiler is>by nature not vague or ill-de'ned. He was not
referring to the Prime Counting Function, rather toJames
purely mathematical breakthroughs (things like his proofof
Fermat's last theorem, his Object-Oriented Mathematics,his
Advanced Polynomial Factorization, etc. Years and yearsof
stuff, all of it in fact vague and ill-de'ned. Like
object-oriented mathematics sounds interesting, but he's
nevergiven a coherent de'nition of the basic concepts. (yes,
hewill call what I just said a lie. He doesn't know what a
_coherent de'nition_ _is_ - he _thinks_ he's 
given
them.))>Frankly, vague and>ill-de'ned are cop-outs used
frequently by many incompetent and>dishonest people in
academia and on usenet, so you have to do>better than that if
you want to be taken seriously. E.g. take>a crucial part of
the argument and show that it rests on>lack of clear 
de'nition
(ill-de'ned) or can be interpreted>in meaningfully and
signi'cantly different ways (vague.)How about when James uses
a technical term, it's clear thatwhatever he means by it is
not what the term usually means,and for _years_ (literally) he
simply ignores requests foran explanation of what he _does_
mean by the term?Would you consider that using vague and
ill-de'ned terms?You really need to do some research on
say.**********David C. Ullrich
=>Yes, I have been seeing
this show up on comp.lang.java.advocacy,> so I am not familiar
with the presumably longer history! Here's a quick
summary: For about EIGHT YEARS James Harris has been>>
discoveries to sci.math (and often to other newsgroups). Much
of the>> time his arguments are too vague and ill-de'ned for
people to make sense> Sorry, that's not believable. 
Something
that can be put into> a Java or C++ program that can be
understood by a compiler is> by nature not vague or
ill-de'ned. Frankly, vague and> ill-de'ned are 
cop-outs used
frequently by many incompetent and> dishonest people in
academia and on usenet, so you have to do> better than that if
you want to be taken seriously. E.g. take> a crucial part of
the argument and show that it rests on> lack of clear
de'nition (ill-de'ned) or can be interpreted> in 
meaningfully
and signi'cantly different ways (vague.)Only a tiny fraction
of James' output can be put into a Java or C++program that 
can
be understood by a compiler or has anything atall to do with
computers. I'm not talking speci'cally here of
hisprime-counting algorithm but of the whole body of his work,
mostof which consists of failed attempts to prove Fermat's 
Last
Theorem.There are numerous examples of his vague or 
ill-de'ned
terminologyin the threads archived in Google; of which his use
of factor is aprime (pun intended) example. (He uses
expressions in his proofs likex has a factor of y sometimes to
mean y divides x and sometimes tomean there is a factor, z,
that divides both y and x. The intendedmeaning usually is left
for the reader to guess. He also has a habitof using ring
operations without clearly identifying the ring in whichhe's
working, or assuming that because an argument holds in one
ring,it also holds in another; this unspoken assumption can
cause people tospend days trying to puzzle out his meaning,
especially when they can'ttell which ring he thinks 
he's
using.) I'm not going to start looking upchoose; but here 
are
links to a few recent examples to get you started,if you're
selm=36024859.0307080736.58977a6f%
the presumably longer historywith which you said you were not
familiar demonstrates just why manypeople have no con'dence 
in
Harris or his work. Because of thatrichly-deserved opinion,
anything he does (including programming) isgreeted with
extreme skepticism by many of us. I'm really not trying
toprove anything to you here -- reject everything I've said 
if
you prefer-- I'm just making you aware of the general 
opinion
of himself Jameshas created over a period of years on
USENET.-- rs, Silverlock
= > Seems like James Harris has an
algorithm for counting primes> which is correct,There seems to
be some dispute about that> even if perhaps not totally novel
and not> the fastest available today. If he has come up with
the algorithm> himself, clearly he is bright enough to do
mathematical work of> more importance,!> perhaps given some
mentor and of course, actual> interest on his part. !!>
(Anybody wanna offer him a graduate> fellowship so he has more
interesting things to deal> with and stops posting?)!!!-- Robin
Chapman, www.maths.ex.ac.uk/~rjc/rjc.html The League of
Gentlemen
=>Yes, I have been seeing this show up on
comp.lang.java.advocacy,> so I am not familiar with the
presumably longer history! Here's a quick summary: For
about EIGHT YEARS James Harris has been>> discoveries to
sci.math (and often to other newsgroups). Much of the>> time
his arguments are too vague and ill-de'ned for people to make
senseSorry, that's not believable. No, it happens to be 
true.>
Something that can be put into> a Java or C++ program that can
be understood by a compiler is> by nature not vague or
ill-de'ned.You are asserting that JSH's various 
alleged proof
of Fermat'sLast Theorem can be put intoa Java or C++ program
that can be understood by a compiler.Please justify this.>
Frankly, vague and> ill-de'ned are cop-outs used frequently 
by
many incompetent and> dishonest people in academia and on
usenet,And they are also inevitable when commenting on many
USENET postings :-(> so you have to do> better than that if
you want to be taken seriously. He has done.Have you?> E.g.
take> a crucial part of the argument and show that it rests
on> lack of clear de'nition (ill-de'ned) or can 
be
interpreted> in meaningfully and signi'cantly different ways
(vague.)Been done wish JSH (frequently).-- Robin Chapman,
www.maths.ex.ac.uk/~rjc/rjc.html The League of Gentlemen
=> He has responded to such statements many times, simply
stating>> that it's not so. But it is.That is a false
statement.Ultimately Ullrich's case seems to rest on the 
fact
that my work gives> the e answers as others. But, given that,
for instance, there are> 4 primes up to 10, which are 2, 3, 5,
and 7, prime counting methods,> and any correct prime counting
function will give the e answer.I am more than happy to go
into details about why my prime counting> function is
signi'cant and is NOT a rehash.Well, what advantage does your
method provide over existing> methods? Is it signi'cantly
faster? Tables of primes> already exist on the web for very
large number of primes.> One could simply do a table search to
see if a number> is a prime or not.You're focusing on
algorithms, which isn't a surprise as I take 
ityou're a
computer scientist. But remember I'm arguing
withmathematicians. I doubt Ullrich would be caught dead in a
computerlab unless he was going in to toss something into the
trash if hewandered by it and no other was handy.However, my
prime counting function maps out the entire distributionof
prime numbers over in'nity by telling you how to get them
overin'nity in a difference equation that you can easily
transfer from toa partial differential equation.It may
disprove some interesting assertions in mathematics like
thatthe prime distribution crosses li(x) an in'nite number of
times byproving that it *never* crosses li(x).It may disprove
Riemann's entire approach which is the basis for thefamous
Riemann Hypothesis by showing that certain of his
assumptionswere §awed.I say may because I'm not sure. But 
if
mathematicians can 'ght tonot even properly acknowlede the
mathematics, how will anyone know? > The only advantage one
might see for a new method is for assisting> in the
computation of even newer and larger primes. If your method>
is faster, the people computing new primes and building>
tables will be happy to use it, I am sure. You might> want to
contact and convince such people.And you've been caught in 
the
assumption that it's just somealgorithm.However, the reality 
is
that it's a mathematical function 
that'sapparently never been
seen before, which just might give a newapproach to a lot of
high level mathematics. But if it *has* beendiscovered before
but never put in references or textbooks that justemphasizes
my point.The mathematicians you see me talking about or who
you see posting inreply to me don't know everything.For all
any of us know, someone a hundred years from now might be
theone capable of putting things together in some important
way.But if these mathematicians can get away without even
acknowledging mywork, then you open up the possibility that
some person down the linenever even sees the function as 
it's
not in a textbook.How could any of you defend them not even
giving properacknowledgement?> But if your method is not
_seriously_ faster than what they> are already using (faster
enough to justify rewriting> their programs,) you won't hear 
a
peep back from them.> And there is nothing else in it for you.
Primes are old> stuff. In today's age, it's 
not something for
which> somebody is going to put you in history books or give>
you large amounts of grant money. There isn't a nobel> prize
in it, either. So why waste your good> cheer over it?There's
more to the prime distribution than counting primes.And it's
not just about prizes or money.Don't any of you care about
knowledge?Why allow mathematicians to just pick and choose at
their whim?> Nobody seems to be arguing seriously that your
method> is incorrect. Even if they are ornery enough not> to
have come out right away and told you that your method> was
correct -- that's kind of expected on the usenet.So be happy
that your method is correct, and nobody> has found an actual
fault in it. After that, if you want> to emulate Newton and
'ght like a bitch over credit, that's> your 
business. It's a
personal choice, is it worth it to> you, enough to get into
these 'ghts that deterioriate> into sleaze quickly, and pull
you and everyone else down?If necessary I'll tear down the
entire mathematical world as it'scurrently known.> David
Ullrich is commenting on my issue with a post where he talked
of> a racial slur being the perfectly appropriate reply to
me.He also has an interesting post which you can 'nd by going
is the> author, and he uses the word rape.I am not sure what
to make of it. You are exposing that when> Mr. Ullrich thinks
of particular vicious nasty crimes, he seems> to think only
members of a certain race are capable of them.Standards. I say
that a university professor should be held to somestandard, and
people argue with me.> Now if that's the case, I would say 
Mr.
Ullrich's upbringing> was sadly wanting and/or he has not 
been
a particularly thoughtful> individual since, and maybe has
convinced himself Jeffrey Dahmer> was framed. But none of
that's really related to primes.> It would be nicer if both
sides had avoided attacks> on character of each other. There
is a context when> the best of us need to be pointed out the
errors in> our thinking, but ideally the context is not that>
of attacks on each other.Well if you wish to give him a title
why don't you address him asProfessor?He is a professor at
Oklahoma State University, after all.I dare you to stop
calling him Ullrich or Mr. Ullrich and from now onaddress him
as professor Ullrich.Like I'm sure his students do in
Oklahoma.> What's OP?Useful new net shorthand for Original
Poster.James Harris
=which computerized proofs do you
believe,by the lights of thier adequate documentation? in
other words,you've got to be kidding. > Sorry, 
that's not
believable. Something that can be put into> a Java or C++
program that can be understood by a compiler is> by nature not
vague or ill-de'ned. Frankly, vague and> 
ill-de'ned are
cop-outs used frequently by many incompetent and> dishonest
people in academia and on usenet, so you have to do> better
than that if you want to be taken seriously. E.g. take--A
church-school McCrusade (Blair's 
ideals?):Harry-the-Mad-Potter
want's US to kill Iraqis?...For a 1000-year anglo-american
hegemony?HEY, JIMMY; LET'S US and SU FIGHT -then-PM of 
England
& Zbiggy http://www.tarpley.net/bush25.htm (Thyroid Storm ch.)
http://www.rwgrayprojects.com/synergetics/plates/plates.html
http://quincy4board.homestead.com/'les/curriculum/Cosmo.PCX
entire distribution> of prime numbers over in'nity by telling
you how to get them over> in'nity in a difference equation
that you can easily transfer from to> a partial differential
equation. It may disprove some interesting assertions in
mathematics like that> the prime distribution crosses li(x) an
in'nite number of times by> proving that it *never* crosses
li(x). It may disprove Riemann's entire approach which is 
the
basis for the> famous Riemann Hypothesis by showing that
certain of his assumptions> were §awed. I say may because 
I'm
not sure. But if mathematicians can 'ght to> not even 
properly
acknowlede the mathematics, how will anyone know?Even when you
*are* sure, you're usually wrong. Of all the things your 
work
may do, I'll place my money on itcon'rming that 
you don't know
what you're talking about -- not that your ignorance ever 
kept
you from talkingbefore. Your brain appears to be on a
permanent vacation, while your mouth still works
overtime.--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
=>> Yes, I have been
seeing this show up on comp.lang.java.advocacy,>> so I am not
familiar with the presumably longer history!Here's a quick
summary: For about EIGHT YEARS James Harris has been>
discoveries to sci.math (and often to other newsgroups). Much
of the> time his arguments are too vague and ill-de'ned for
people to make senseSorry, that's not believable. Something
that can be put into> a Java or C++ program that can be
understood by a compiler is> by nature not vague or
ill-de'ned.You've misunderstood. Prime-counting 
is only one
tiny piece of what James claims he has done to
revolutionizemathematics. The 8 years of postings are
overwhelminglyconcerned with proofs of Fermat's Last Theorem
and havenothing to do with Java, C++, or algorithms.The vague
and ill-de'ned nature of these argumentshas been discussed at
great length in sci.math. Oneneedn't read too far into any 
of
James' arguments to getto a point where you 
haven't the
foggiest idea of whathe's trying to say. If you read some of
the threadsin sci.math, you'll 'nd many 
explicit discussions
aboutprecisely what terms James is being vague about (oneof
his favorites is has a factor of), what the possiblemeanings
are, how his meaning does not correspond toaccepted 
de'nition,
or how his meaning shifts duringthe course of an argument. -
Randy
=unless you believe every thing taht is put outby the
Second British Church of Christ, Isaac, orby the state schools
as opposed to directlyby the church schools (Public
Schools),that is only apt in that he did aglomeratea lot of
credit, after the putative fact (and AI .-)try searches on
American Almanac, in my sig. > to emulate Newton and 'ght 
like
a bitch over credit, that's--Dec.2000 
ïWAND' Chairman Paul
O'Neill, reelectedto Board.
Newsish?http://www.rand.org/publications/randreview/issues/rr
.12.00/http://members.tripod.com/~american_almanac
=Hash:
SHA1[..]>> David Ullrich is commenting on my issue with a post
where he talked of>> a racial slur being the perfectly
appropriate reply to me. He also has an interesting post
checking
posts where David Ullrich is the>> author, and he uses the word
rape.I am not sure what to make of it. You are exposing that
when> Mr. Ullrich thinks of particular vicious nasty crimes,
he seems> to think only members of a certain race are capable
of them.Now if that's the case, I would say
[snippety-snip]Spoken like a reasonable person. If, however,
you continue to entertain the idea that JSH may be a
reasonable person, you would IMHO double the size of the
minority which holds that as a viable hypothesis.I conclude[1]
that JSH's major contribution, if any, is likely to be as 
part
of a case-study for someone trying to 'nd a more precise
description of JSH's condition than kook. JensJSH) quote 
from
a recent JSH missive, message-ID
=[rants that make my point better than I ever could snipped]David Ullrich got caught once in an interesting exchange
where he>called me an idiot for apologizing to a French
newsgroup for not>posting in French. Nope. Never happened.
(Provide a citation, please).- -- Key ID 0x09723C12,
j.tingleff@ieee.org/jens_tingleff@yahoo.comhttp://
www.imaginet.fr/~jensting/ +44 1223 211
585iD8DBQE/DcfqimJs3AlyPBIRAhKxAKDQ3DdFDUNwRck/
f6MIj0QA2RX8ZwCg3SBmxi42SJhnUKBuVbWdTiiJmkk==BtDH
=[
newsgroups trimmed]>Yes, I have been seeing this show up on
comp.lang.java.advocacy,> so I am not familiar with the
presumably longer history! Here's a quick summary: For
about EIGHT YEARS James Harris has been>> discoveries to
sci.math (and often to other newsgroups). Much of the>> time
his arguments are too vague and ill-de'ned for people to make
senseSorry, that's not believable. Something that can be put
into>a Java or C++ program that can be understood by a
compiler is>by nature not vague or ill-de'ned. Frankly, vague
and>ill-de'ned are cop-outs used frequently by many
incompetent and>dishonest people in academia and on usenet, so
you have to do>better than that if you want to be taken
seriously. E.g. take>a crucial part of the argument and show
that it rests on>lack of clear de'nition 
(ill-de'ned) or can
be interpreted>in meaningfully and signi'cantly different 
ways
thefollowing #1 world wide web page devoted to James Harris:
http://www.crank.net/harris.htmlWhich might provide a degree
of familiarization with the longerhistory referred to.George
Maydwell--Modern Cellular Automata:
www.collidoscope.com/moderncaCollidoscope Hexagonal
Screensaver: www.collidoscope.com
=In case you _do_ think
that the posts James is referring to> demonstrate that I think
what you say James is exposing,> let me just clarify:Long ago
James told us he was black. Some time later,> still long ago,
he said something particularly insulting> and dehumanizing -
it occured to me at the time that> a racial slur in reply
would be appropriate, simply to> illustrate the idea that
there is such a thing as you're> not supposed to talk to
people that way. I refrained,> because it wouldn't have been
something I meant,> and because of course I'm _not_ supposed
to talk> to people that way.Ah, people are not supposed to say
what they're thinking?Okay, David. I haven't 
gone back to the
old postings far enough, butwhat you say here con'rms what I
have suspected.Something in your personal duel with James
reminds me of the classicstory The President's Speech by
Oliver Sacks. It has been so popularthat it was easy to 'nd a
'ne summary of it, so I don't have to givea 
summary myself:
http://www.konformist.com/2001/mickeyz-05.htm(scroll down to
'nd Sack's name, and then read to end). I 
alsorecommend
reading the original story.
= >> [...]> David Ullrich is
commenting on my issue with a post where he talked of>> a
racial slur being the perfectly appropriate reply to me.
He also has an interesting post which you can 'nd by going
is the>> author, and he uses the word rape.>I am not sure
what to make of it. You are exposing that when>Mr. Ullrich
thinks of particular vicious nasty crimes, he seems>to think
only members of a certain race are capable of them.Um, maybe
exposing was not the word you meant - it seems> to me that if
you say someone's exposing something it > follows that the
thing being exposed is actually so. It's> certainly not true
that I think that only members of certain> races are capable
of certain nasty crimes. (Maybe espousing> is what you meant?
Not sure I spelled that right.)In case you _do_ think that the
posts James is referring to> demonstrate that I think what you
say James is exposing,> let me just clarify:Long ago James
told us he was black. Some time later,> still long ago, he
said something particularly insulting> and dehumanizing - it
occured to me at the time that> a racial slur in reply would
be appropriate, simply to> illustrate the idea that there is
such a thing as you're> not supposed to talk to people that
way. I refrained,> because it wouldn't have been something I
meant,> and because of course I'm _not_ supposed to talk> to
people that way.Then some time later, still long ago, in reply
to some> other egregious insult, I said what I say in the
previous> paragraph, about things I once considered saying>
and why, and why I did not say them. Again, my point> was
simply to say that there is such a thing as ways> one is
simply not supposed to talk to people - James> had stepped way
over that line and I wanted to point> out that there was in
fact such a line.In my post I included a statement as above,
to the> effect that I once (brie§y) considered the idea that
a> racial slur would be appropriate - pointed out that of>
course I decided it wasn't, in fact it's not 
something I>
said. James replied that a racial slur was _never_>
appropriate. This statement is of course ridiculous;> I
pointed out that for example, to take an extreme case,> if
someone had broken into my home, tied me up> and was about to
rape my daughter, if I thought> that calling him a nasty name
might distract him> until the police arrived then a racial
slur would be> not only appropriate, refraining from making
such> a comment would be positively wrong.And since then 
he's
accused me of thinking that> blacks are rapists, or that
rapists are all black,> or whatever - he never puts it quite
so baldly, just> points to that post as evidence of my
attitudes.> Which of course is twisting things - the rapist>
in the imaginary scenario is in fact black (or a> member of
some other unspeci'ed minority,> let's say 
black for
simplicity's sake), but that's> not because I 
think that
rapists tend to be black,> it's because the _question_ was
whether it's> correct to say that a racial slur is _never_>
appropriate - a hypothetical example illustrating > that
that's not so is necessarily going to involve > a minority. 
I
mean, duh.>Now if that's the case, I would say Mr. 
Ullrich's
upbringing>was sadly wanting and/or he has not been a
particularly thoughtful>individual since, and maybe has
convinced himself Jeffrey Dahmer>was framed. But none of
that's really related to primes.>It would be nicer if both
sides had avoided attacks>on character of each other. There is
a context when>the best of us need to be pointed out the errors
in>our thinking, but ideally the context is not that>of attacks
on each other.>> What's OP?>Useful new net shorthand for
Original Poster.**********David C. UllrichOk, there is a
complex history here. Sorry if I caused offense.I would agree
with your point too -- if anything at all can be saidto stop a
criminal until police gets there, what was said is not avalid
object of criticism.
=> Only a tiny fraction of James'
output can be put into a Java or C++> program that can be
understood by a compiler or has anything at> all to do with
computers. I'm not talking speci'cally here of 
his>
prime-counting algorithm but of the whole body of his work,
most> of which consists of failed attempts to prove Fermat's
Last Theorem.> There are numerous examples of his vague or
ill-de'ned terminology> in the threads archived in Google; of
which his use of factor is aOk, I get it.>
40agate.berkeley.eduI dunno, this still seems a little like
nitpicking to me: g has a factor of 5, you really mean not
that 5 divides g, but rather that there is an algebraic
integer which divides both 5 and g, then the STANDARD AND
CORRECT way of saying it is g and 5 have a common factor [in
the ring of all algebraic integers].I would say a certain
amount of informal neologism is ok in usenet postsas long as
the meaning is not lost.> Basically, what I've been saying 
is
that the presumably longer history> with which you said you
were not familiar demonstrates just why many> people have no
con'dence in Harris or his work. Because of that>
richly-deserved opinion, anything he does (including
programming) is> greeted with extreme skepticism by many of
us. I'm really not trying to> prove anything to you here --
reject everything I've said if you prefer> -- 
I'm just making
you aware of the general opinion of himself James> has created
over a period of years on USENET.Overall, I guess after seeing
some of the self-evaluation andthe intent and self-assurance
to tear down the entire mathematical worldover the subtle
advantages of a new prime counting function/methodand what it
may (and presmuable may not) do, I suppose I have toagree with
the general opinion...
=>>[...]Ok, there is a complex
history here. Yup. _If_ for whatever reason you want to
understand what's going onin all this then like I keep 
saying,
you need to look at a lot ofposts on sci.math for the last
seven or eight years. Of course there'sno reason you should
actually do that, but until you do you needto realize that you
cannot take anything James says about thecomplex history at
face value - his version of who said what,when and why is
always different from everyone else's.>Sorry if I caused
offense.Okie dokie.>I would agree with your point too -- if
anything at all can be said>to stop a criminal until police
gets there, what was said is not a>valid object of
criticism.**********David C. Ullrich
=...I dare you to stop
calling him Ullrich or Mr. Ullrich and from now on> address
him as professor Ullrich.Like I'm sure his students do in
Oklahoma.How very quaint. Don't university students in the
States call theirprofs by their 'rst names?GC
=>He has
responded to such statements many times, simply stating> that
it's not so. But it is.That is a false statement.Ultimately
Ullrich's case seems to rest on the fact that my work gives>
the e answers as others. But, given that, for instance, there
are> 4 primes up to 10, which are 2, 3, 5, and 7, prime
counting methods,> and any correct prime counting function
will give the e answer.I am more than happy to go into details
about why my prime counting> function is signi'cant and is 
NOT
a rehash. Well, what advantage does your method provide
over existing>> methods? Is it signi'cantly faster? Tables of
primes>> already exist on the web for very large number of
primes.>> One could simply do a table search to see if a
number>> is a prime or not.You're focusing on algorithms,
which isn't a surprise as I take it>you're a 
computer
scientist. But remember I'm arguing with>mathematicians. I
doubt Ullrich would be caught dead in a computer>lab unless he
was going in to toss something into the trash if he>wandered by
it and no other was handy.Your cluelessness remains amazing, as
always. Last time yousaid something in this direction I
clari'ed things for you - maybeyou didn't see 
that post. Lemme
just say this about that: _my_programs do not give incorrect
answers because of roundofferrors.>However, my prime counting
function maps out the entire distribution>of prime numbers
over in'nity by telling you how to get them 
over>in'nity in a
difference equation that you can easily transfer from to>a
partial differential equation.That pde is not a pde, and more
important you've _never_ given_any_ reason to suspect that 
it
has anything to do with countingprimes.>It may disprove some
interesting assertions in mathematics like that>the prime
distribution crosses li(x) an in'nite number of times
by>proving that it *never* crosses li(x).It may do that, even
though there's absolutely nothing novelabout it
mathematically, and you give _no_ reason why someonewould
think it might do that.>It may disprove Riemann's entire
approach which is the basis for the>famous Riemann Hypothesis
by showing that certain of his assumptions>were §awed.e
comment, squared.>I say may because I'm not sure. 
You're not
sure? In fact you have no reason whatever to think eitherof
those two assertions may be so.> But if mathematicians can
'ght to>not even properly acknowlede the mathematics, how 
will
anyone know?>> The only advantage one might see for a new
method is for assisting>> in the computation of even newer and
larger primes. If your method>> is faster, the people computing
new primes and building>> tables will be happy to use it, I am
sure. You might>> want to contact and convince such people.And
you've been caught in the assumption that it's 
just
some>algorithm.However, the reality is that it's a
mathematical function that's>apparently never been seen
before, Never seen before, until about 200 years ago you mean.
Neverseen since then, except by people who've studied
well-knownalgorithms for counting primes. Nothing like it has
ever beenseen, except by the 20% of the grad students in the
'eld that_you_ tell us you were told come up with something
analogous.>which just might give a new>approach to a lot of
high level mathematics. But if it *has* been>discovered before
but never put in references or textbooks that just>emphasizes
my point.The mathematicians you see me talking about or who
you see posting in>reply to me don't know everything.[...]If
necessary I'll tear down the entire mathematical world as
it's>currently known.sanity or lack thereof then 
don't say
things that sound totally crazy.Seems simple enough.> David
Ullrich is commenting on my issue with a post where he talked
of> a racial slur being the perfectly appropriate reply to
me.He also has an interesting post which you can 'nd by going
is the> author, and he uses the word rape. I am not sure
what to make of it. You are exposing that when>> Mr. Ullrich
thinks of particular vicious nasty crimes, he seems>> to think
only members of a certain race are capable of them.Standards. I
say that a university professor should be held to
some>standard, and people argue with me.> Now if that's the
case, I would say Mr. Ullrich's upbringing>> was sadly 
wanting
and/or he has not been a particularly thoughtful>> individual
since, and maybe has convinced himself Jeffrey Dahmer>> was
framed. But none of that's really related to primes.>> It
would be nicer if both sides had avoided attacks>> on
character of each other. There is a context when>> the best of
us need to be pointed out the errors in>> our thinking, but
ideally the context is not that>> of attacks on each
other.Well if you wish to give him a title why don't you
address him as>Professor?He is a professor at Oklahoma State
University, after all.I dare you to stop calling him Ullrich
or Mr. Ullrich and from now on>address him as professor
Ullrich.Like I'm sure his students do in Oklahoma. 
What's
OP? Useful new net shorthand for Original Poster.James
Harris**********David C. Ullrich
=> Don't any of you care
about knowledge?Get off it -- if you truly cared about
knowledge rather thancredit, you would have shut up long ago
and gone onto other things. What you had to say is out
there.It's sitting on archives, you have generated enough
noiseabout it, if it has any truth and super-lasting value to
it,it will be found by those who need it.But you are just
looking for credit over something, ifnot for Fermat's 
theorem,
then by convincing yourselfthat what you maybe have is very
signi'cant. Thematerial is not truly interesting to you, 
*you*
are.So let's don't pretend you are in it for 
knowledge.
=> I
dare you to stop calling him Ullrich or Mr. Ullrich and from
now on> address him as professor Ullrich.Like I'm sure his
students do in Oklahoma. > How very quaint. Don't university
students in the States call their > profs by their 'rst 
names?I
was amazed quite a few years ago when I was taken to task by
someonebecause I had suggested that a professor (whom I called
by his 'rstname) was making a serious error. The professor
acknowledged his errorlater.I think it is cultural. Some
students think very highly of theirprofessors and think they
are not making mistakes, and would neverdare to address them
by their 'rst name. They are putting them ona pedestal. Of
course, in general they know more than the students,but are
liable to make mistakes and errors just like everybody else.--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam,
nederland, +31205924131home: bovenover 215, 1025 jn amsterdam,
nederland; http://www.cwi.nl/~dik/
=> ...> Nope. Never
happened. (Provide a citation, please).> He called you an
idiot for something else.(He might also have called you idiot
savant...) > Hmmm...so Ullrich calls me an idiot for noting
that I'd be impressed > if he'd written in 
French in posting
to a French newsgroup, and 'rst > you claim it was for
something else, and *then* you reply again to > claim that he
actually *was* posting in French!!!Ah, vous .90tes un
idiot.You claimed he said that because you apologised for not
writing in French.But as you *now* so aptly remark, it was for
writing you'd be impressedif he'd written in 
French. And
indeed, the latter is something else.Yes? You are an idiot for
a few reasons. The 'rst is that when you'nd a 
posting by David
in a French newsgroup that is not in French, youronly reply is
about his French abilities in that newsgroup (and you
knownothing about his abilities in that 'eld), not about the
content.Second is your assumption that posting in English in a
French (or Germanor whatever) newsgroup is frowned upon. I have
posted in English inboth French and German newsgroup, simply
because I do not feel comfortablewriting in those languages,
especially when it is technical. I have noproblem either
reading or speaking those languages. None of my
Englishpostings has been frowned upon. And the third reason is
of course thatyou (not so) subtly changed the allegation in
order to make me look afool.Idiot, va-t'en.-- dik t. winter,
cwi, kruislaan 413, 1098 sj amsterdam, nederland,
+31205924131home: bovenover 215, 1025 jn amsterdam, nederland;
http://www.cwi.nl/~dik/
=...I dare you to stop calling him
Ullrich or Mr. Ullrich and from now on> address him as
professor Ullrich.Like I'm sure his students do in 
Oklahoma.>
How very quaint. Don't university students in the States 
call
their> profs by their 'rst names?GCDepends on the professor.
Come on, Americans aren't so easily boxed, you know.James
Harris
=> [newsgroups trimmed]>Yes, I have been seeing this
show up on comp.lang.java.advocacy,> so I am not familiar with
the presumably longer history! Here's a quick summary: 
For
about EIGHT YEARS James Harris has been>> discoveries to
sci.math (and often to other newsgroups). Much of the>> time
his arguments are too vague and ill-de'ned for people to make
sense>Sorry, that's not believable. Something that can be
put into>a Java or C++ program that can be understood by a
compiler is>by nature not vague or ill-de'ned. Frankly, vague
and>ill-de'ned are cop-outs used frequently by many
incompetent and>dishonest people in academia and on usenet, so
you have to do>better than that if you want to be taken
seriously. E.g. take>a crucial part of the argument and show
that it rests on>lack of clear de'nition 
(ill-de'ned) or can
be interpreted>in meaningfully and signi'cantly different 
ways
the> following #1 world wide web page devoted to James Harris:>
http://www.crank.net/harris.html> Which might provide a degree
of familiarization with the longer> history referred to.George
MaydwellWell I just checked the page and while it's clearly
meant to beinsulting, it seems that it's just insults like
crank scatteredaround the page, as the links provided don't
say much.I'm curious as to whether anyone can 
'nd real
justi'cation on thepage for the assertion that 
I'm a
crank.Consider it a dare.James Harris
=> Don't any of you
care about knowledge?Get off it -- if you truly cared about
knowledge rather than>credit, you would have shut up long ago
and gone on>to other things. What you had to say is out
there.>It's sitting on archives, you have generated enough
noise>about it, if it has any truth and super-lasting value to
it,>it will be found by those who need it.But you are just
looking for credit over something, if>not for Fermat's
theorem, then by convincing yourself>that what you maybe have
is very signi'cant. The>material is not truly interesting to
you, *you* are.So let's don't pretend you are 
in it for
knowledge.An unusually fast disillusionment cycle. Usually it
takes a week orso. - Randy
=> Only a tiny fraction of James'
output can be put into a Java or C++>> program that can be
understood by a compiler or has anything at>> all to do with
computers. I'm not talking speci'cally here of 
his>>
prime-counting algorithm but of the whole body of his work,
most>> of which consists of failed attempts to prove 
Fermat's
Last Theorem.>> There are numerous examples of his vague or
ill-de'ned terminology>> in the threads archived in Google; 
of
which his use of factor is aOk, I get it.>
40agate.berkeley.eduI dunno, this still seems a little like
nitpicking to me: g has a factor of 5, you really mean not
that 5> divides g, but rather that there is an algebraic
integer which divides> both 5 and g, then the STANDARD AND
CORRECT way of saying it is g and 5 have a common factor [in
the ring of all algebraic> integers].I would say a certain
amount of informal neologism is ok in usenet posts>as long as
the meaning is not lost.Certainly. But (i) the meaning _is_
lost - it happens all the timethat when he says a has a factor
of b someone foolishly assumesthat what he means is that a has
a factor of b! So they reply,pointing out that what he's 
just
said is wrong. Of course whateverhe's said typically _is_
wrong, but not for the reason someonethinks, because the
someone was not familiar with his privatelanguage. The
irritating and irrational aspect of all of thisis that it has
been pointed out to him _many_ times that he'snot saying 
what
he means, and that this leads to confusion -you'd think 
he'd
say oh, and start using the languagecorrectly. But instead
when people point out that he's notsaying what he means he
insists that his terminology iscorrect and that the way the
language is used by everyoneelse is wrong, and he continues to
speak his own privatelanguage. (You might note that since 
we're
talking just aboutwhat words and phrases _mean_, it's 
literally
impossible forhim to be right and everyone else wrong - 
that's
possiblealthough unlikely regarding matters of fact, but what
wordsmean is de'ned by consensus, the majority _is_ right,by
de'nition. But he doesn't seem to care about 
that.)(ii) He's
not consistent - _sometimes_ when he saysa has a factor of b
he means that a has a factor ofb, and sometimes he means that
a and b share a factor.A certain amount of neoligism is 'ne.
In mathematics_any_ amount of neologism is 'ne as long as
things areclearly de'ned. But things are never clearly 
de'ned
inhis stuff - there's always some question as to exactlywhat
something means in one of his proofs. [Noting thatof course
sentences containing the word always arealways
exaggerations...]>> Basically, what I've been saying is that
the presumably longer history>> with which you said you were
not familiar demonstrates just why many>> people have no
con'dence in Harris or his work. Because of that>>
richly-deserved opinion, anything he does (including
programming) is>> greeted with extreme skepticism by many of
us. I'm really not trying to>> prove anything to you here --
reject everything I've said if you prefer>> -- 
I'm just making
you aware of the general opinion of himself James>> has created
over a period of years on USENET.Overall, I guess after seeing
some of the self-evaluation and>the intent and self-assurance
to tear down the entire mathematical world>over the subtle
advantages of a new prime counting function/method>and what it
may (and presmuable may not) do, I suppose I have to>agree with
the general opinion...That's not a good thing. 
He's stated that
he's going to sic the Army on us if we don't 
shape up (he has
the power to do this becausegenerals like him). Presumably now
that you've said you supposeyou have to agree with the 
general
opinion you've become partof the establishment 
that's going to
be 'red or worse when theTruth 'nally comes 
out.Good luck with
that.**********David C. Ullrich
=>>[...]Ah, vous .90tes un
idiot.>[...]Idiot, va-t'en.French. I'm
impressed<giggle>.**********David C. Ullrich
=> Don't any of
you care about knowledge?Get off it -- if you truly cared about
knowledge rather than>credit, you would have shut up long ago
and gone on>to other things. He talks a lot about how we have
no regard for Truth. But _he_ is the _only_ person I've ever
seen stateexplicitly in a usenet post that if what he'd just
saidwas wrong people shouldn't bother to say so becausehe
didn't want to
know:<824hn8$i61$1@nntp9.atl.mindspring.net>1999/12/01> If
you're worried that maybe you can't judge its 
correctness for
yourself,> especially since all these real mathematicians
would just as soon let me> mouth off as produce any actual
math in objection, I'll help you out. Where> I have p in the
proof, use 3. That is, try it out with p=3. But if it> fails,
don't tell me. I don't want to know.>What you 
had to say is
out there.>It's sitting on archives, you have generated 
enough
noise>about it, if it has any truth and super-lasting value to
it,>it will be found by those who need it.But you are just
looking for credit over something, if>not for Fermat's
theorem, then by convincing yourself>that what you maybe have
is very signi'cant. The>material is not truly interesting to
you, *you* are.So let's don't pretend you are 
in it for
knowledge.**********David C. Ullrich
checked the page and while it's clearly meant to be>
insulting, it seems that it's just insults like crank
scattered> around the page, as the links provided don't say
much.The term crank isn't an insult, it's an 
identi'cation. If
someone want to insult you they they will call youa jackass.>
I'm curious as to whether anyone can 'nd real 
justi'cation on
the> page for the assertion that I'm a crank. Consider it a
dare. James HarrisCheck your track record of postings to the
internet. Your prior history is suf'cient proof.--It takes a
village to raise an idiot.--Democracy: The triumph of
popularity over principle.--http://www.crbond.com
=> ...>
Nope. Never happened. (Provide a citation, please).> He
called you an idiot for something else.(He might also have
called you idiot savant...)> Hmmm...so Ullrich calls me an
idiot for noting that I'd be impressed> if 
he'd written in
French in posting to a French newsgroup, and 'rst> you claim
it was for something else, and *then* you reply again to>
claim that he actually *was* posting in French!!!Ah, vous
.90tes un idiot.Nope. You're a math groupie, so you 
'ght for
Ullrich even when hedisplayed his true coarseness when I was
being diplomatic.Readers should see:Now consider that in the
previous post--the one to which Ullrichreplied--I said:Well I
must say I'm impressed if Ullrich speaks French!Though 
I'd
have been more impressed if he'd replied in it!Unfortunately 
I
do not speak French so I won't try.Now in thinking back I 
saw
that as an apology to the newsgroup for notspeaking French, in
which I also was pointing out that I wasn'tspeaking French
because I don't know it.> You claimed he said that because 
you
apologised for not writing in French.> But as you *now* so
aptly remark, it was for writing you'd be impressed> if 
he'd
written in French. And indeed, the latter is something else.>
Yes? You are an idiot for a few reasons. The 'rst is that 
when
you> 'nd a posting by David in a French newsgroup that is not
in French, your> only reply is about his French abilities in
that newsgroup (and you know> nothing about his abilities in
that 'eld), not about the content.That's 
irrational. If
someone were posting here completely in French,wouldn't that
be pertinent?How welcoming are all of you to non-English
speakers who post?In noting my inability to speak French I was
at *least* acknowledgingthat fault, and explaining why I
couldn't go to French.> Second is your assumption that 
posting
in English in a French (or German> or whatever) newsgroup is
frowned upon. I have posted in English in> both French and
German newsgroup, simply because I do not feel comfortable>
writing in those languages, especially when it is technical. I
have no> problem either reading or speaking those languages.
None of my English> postings has been frowned upon. And the
third reason is of course that> you (not so) subtly changed
the allegation in order to make me look a> fool.Which is an
expression of arrogance, as if the fact that otherstolerated
your not posting in the language of the newsgroup, it's
ok.Well let someone come on one of these newsgroups and post
entirely inFrench, or Russian or German, and see the
treatement they get.> Idiot, va-t'en.But then again, English
speakers seem to be quite vicious and impolitewith each other
anyway.It's as if so many not only lack proper manners, but
they enjoyinforming the world.James Harris
=>> ...>> I
dare you to stop calling him Ullrich or Mr. Ullrich and from
now on>> address him as professor Ullrich.>> Like I'm sure 
his
students do in Oklahoma.> How very quaint. Don't university
students in the States call their> profs by their 'rst 
names? GCDepends on the professor. Come on, Americans aren't so
easily boxed, you know.James HarrisI know nothing about
pugilism. But you all call your fathers sirdon't you? Very
odd.GC
=> Which is an expression of arrogance, as if the
fact that others> tolerated your not posting in the language
of the newsgroup, it's ok.Well let someone come on one of
these newsgroups and post entirely in> French, or Russian or
German, and see the treatement they get.Generally they get
their questions answered, as you'dknow if 
you've ever read any
threads but your own. I'veseen French, Spanish, Italian, 
German
and Dutch. I thinkI've seen Polish as well. Occasionally
Finnish, but onlyin response when somebody posted from a *.'
address. - Randy
=> Now consider that in the previous
post--the one to which Ullrich> replied--I said:Well I must
say I'm impressed if Ullrich speaks French!That certainly
isn't an apology to the newsgroup fornot speaking
French.Though I'd have been more impressed if 
he'd replied in
it!Nor is that.Unfortunately I do not speak French so I 
won't
try.Nor is that.Now in thinking back I saw that as an apology
to the newsgroup for not> speaking French, in which I also was
pointing out that I wasn't> speaking French because I 
don't
know it.It is a statement about not speaking French. Not
anapology though, nor does it seem addressed to theFrench
here completely in French,> wouldn't that be pertinent?How
welcoming are all of you to non-English speakers who post?>
post entirely in> French, or Russian or German, and see the
treatement they
=200208211233.g7LCXQK14034%40proapp.mathforum.org&prev=/groups
%3Fsafe%3Dimages%26ie%3DISO-8859-1%26as_ugroup%3Dsci.math%26lr
%3Dlang_fr%26num%3D50%26hl%3DenExchanges in other languages
are not hard to 'nd either,but I con'ned myself 
to posts in
sci.math in the last yearor so where the original query was
not in English. - Randy
= Now in thinking back I saw
that as an apology to the newsgroup for not>> speaking French,
in which I also was pointing out that I wasn't>> speaking
French because I don't know it.> It is a statement about not
speaking French. Not an> apology though, nor does it seem
addressed to the> French newsgroup.In the Harris-Universe it
counts as an apology, in the e way thatwell, maybe you 
weren't
lying this time serves as an apology forcalling someone a
liar.-- rs, Silverlock
=...> Well I just checked the page
and while it's clearly meant to be> insulting, it seems that
it's just insults like crank scattered> around the page, as
the links provided don't say much.The term crank 
isn't an
insult, it's an identi'cation. If > someone 
want to insult you
they they will call you a jackass.I disagree; it is no insult
to call a jackass a jackass.I've given this matter some
thought, and now feel certainthat along such lines there is
nothing one can say to Harristhat would be an insult. It seems
that what you have to do if you want to insult him is to ask
him a civil question.-jiw > I'm curious as to whether anyone
can 'nd real justi'cation on the> page for the 
assertion that
I'm a crank.> Consider it a dare.> James Harris...[Page
referred to is http://www.crank.net/harris.html]
= >> Don't
any of you care about knowledge?>Get off it -- if you truly
cared about knowledge rather than>credit, you would have shut
up long ago and gone on>to other things. He talks a lot about
how we have no regard for Truth. > But _he_ is the _only_
person I've ever seen state> explicitly in a usenet post 
that
if what he'd just said> was wrong people 
shouldn't bother to
say so because> he didn't want to know:JSH is a discoverer. 
He
doesn't need to have his errors pointed out tohim. 
Here's how
it's supposed to work:- JSH makes a (wrong) discovery- JSH
posts this discovery on sci.math- the mathematicians _'x_
what's wrong- JSH takes the creditTrouble is, you guys 
arne't
doing step three properly. JSH wants youto correct his
problems, not simply prove that they are wrong. Nowonder 
he's
so frustrated, you're not cooperating.The fact that his
discoveries aren't 'xable is
irrelevant.<824hn8$i61$1@nntp9.atl.mindspring.net 1999/12/01If
you're worried that maybe you can't judge its 
correctness for
yourself,> especially since all these real mathematicians
would just as soon let me> mouth off as produce any actual
math in objection, I'll help you out.> Where> I have p in 
the
proof, use 3. That is, try it out with p=3. But if it> fails,
don't tell me. I don't want to know.What you 
had to say is out
there.>It's sitting on archives, you have generated enough
noise>about it, if it has any truth and super-lasting value to
it,>it will be found by those who need it.>But you are just
looking for credit over something, if>not for Fermat's
theorem, then by convincing yourself>that what you maybe have
is very signi'cant. The>material is not truly interesting to
you, *you* are.>So let's don't pretend you are 
in it for
knowledge.**********David C. Ullrich
=Now consider that in
the previous post--the one to which Ullrich> replied--I
said:Well I must say I'm impressed if Ullrich speaks
French!That certainly isn't an apology to the newsgroup for>
not speaking French.> Though I'd have been more impressed if
he'd replied in it!Nor is that.> Unfortunately I do not 
speak
French so I won't try.Nor is that.I'll concede 
that you can
argue that it's not an apology. I thoughtof it as an 
apology,
but I'll back down from the assertion that it isan apology, 
as
I can see where others can reasonably disagree. Now in thinking
back I saw that as an apology to the newsgroup for not>
speaking French, in which I also was pointing out that I
wasn't> speaking French because I don't know 
it.It is a
statement about not speaking French. Not an> apology though,
nor does it seem addressed to the> French
newsgroup.<deleted>My point was that it would have been polite
to reply in French on aFrench newsgroup, or at least to
acknowledge in some way that somemight be bothered by posting
in English.My explanation for the group was that I didn't 
know
French, or I wouldhave posted at least partly in French. My
sense that was apologeticcan be reasonably disputed by others
as I noted above.James Harris
=> ...>> Well I just checked
the page and while it's clearly meant to be>> insulting, it
seems that it's just insults like crank scattered>> around 
the
page, as the links provided don't say much.The term crank 
isn't
an insult, it's an identi'cation. If > someone 
want to insult
you they they will call you a jackass.I disagree; it is no
insult to call a jackass a jackass.> I've given this matter
some thought, and now feel certain> that along such lines
there is nothing one can say to Harris> that would be an
insult. It seems that what you have to do > if you want to
insult him is to ask him a civil question.> -jiwAs if posters
usually ask me a civil question!!!Consider that there's more
below... >> I'm curious as to whether anyone can 
'nd real
justi'cation on the>> page for the assertion that 
I'm a
crank.>> Consider it a dare.>> James Harris> ...> [Page
referred to is http://www.crank.net/harris.html]So go ahead
and check the link.Consider that a double dare.James
Harris
http://www.crank.net/harris.html] So go ahead and check the
link. Consider that a double dare. James HarrisOK, now what?
Your own track record of publicly §aunting your mistakes,
gaffes, blunders,errors, oversights, omissions, ambiguities,
solipsisms, non-sequiters, gaps, slip-ups,fallacies, etc. has
elevated your status as a crank from convincingly evident
toconclusively proven. In my dictionary the term crank has
your picture for a de'nition.--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
= >> [...]> David Ullrich
is commenting on my issue with a post where he talked of>> a
racial slur being the perfectly appropriate reply to me.
He also has an interesting post which you can 'nd by going
is the>> author, and he uses the word rape.>I am not sure
what to make of it. You are exposing that when>Mr. Ullrich
thinks of particular vicious nasty crimes, he seems>to think
only members of a certain race are capable of them.Um, maybe
exposing was not the word you meant - it seems> to me that if
you say someone's exposing something it > follows that the
thing being exposed is actually so. It's> certainly not true
that I think that only members of certain> races are capable
of certain nasty crimes. (Maybe espousing> is what you meant?
Not sure I spelled that right.)In case you _do_ think that the
posts James is referring to> demonstrate that I think what you
say James is exposing,> let me just clarify:Long ago James
told us he was black. Some time later,> still long ago, he
said something particularly insulting> and dehumanizing - it
occured to me at the time that> a racial slur in reply would
be appropriate, simply to> illustrate the idea that there is
such a thing as you're> not supposed to talk to people that
way. I refrained,> because it wouldn't have been something I
meant,> and because of course I'm _not_ supposed to talk> to
people that way.Well, a while back I ended up in a debate with
a poster from SouthAfrica--before Apartheid was ended--and
during that discussioninformation about my race was pertinent
so I gave it. I don'tremember David Ullrich participating in
that discussion but heapparently gathered the information from
it, based on the timing ofhis comments that he mentions
later.Since then I have made other posts where I've talked 
of
my race.As for this remark he claims was so insulting and
dehumanizing itwas my stating that he'd acted as my lapdog 
in
an instance. > Then some time later, still long ago, in reply
to some> other egregious insult, I said what I say in the
previous> paragraph, about things I once considered saying>
and why, and why I did not say them. Again, my point> was
simply to say that there is such a thing as ways> one is
simply not supposed to talk to people - James> had stepped way
over that line and I wanted to point> out that there was in
fact such a line.Remember Ullrich is talking now about my
saying he'd acted as mylapdog in an instance, and now notice
the paternalistic tone.> In my post I included a statement as
above, to the> effect that I once (brie§y) considered the idea
that a> racial slur would be appropriate - pointed out that of>
course I decided it wasn't, in fact it's not 
something I> said.
James replied that a racial slur was _never_> appropriate. This
statement is of course ridiculous;> I pointed out that for
example, to take an extreme case,> if someone had broken into
my home, tied me up> and was about to rape my daughter, if I
thought> that calling him a nasty name might distract him>
until the police arrived then a racial slur would be> not only
appropriate, refraining from making such> a comment would be
positively wrong.Given Ullrich's claim above I went into the
Google archives.I found that I'd said:<Quote>Now how many of
you think that it's the most natural thing in theworld that
calling someone a racial slur might be
appropriate?</Quote>Later I found that I'd
said:<Quote>Possibly you believe that you are doing yourself
and Professor Ullrichof Oklahoma State University a favor by a
post which I believeindicates that you agree with him that a
racial slur may be in somecases the appropriate
response.</Quote>Now then as to Ullrich's example of a 
someone
breaking into hishouse about to rape his daughter the
implication is obvious enough,but it's actually 
nonsensical.If
you could even imagine such a thing, do you think you'd be
hurlingracial slurs if one would apply? If you had a gun, you
might use it,but not your mouth.Why would Ullrich even come up
with such an example? And why use hisown daughter? > And since
then he's accused me of thinking that> blacks are rapists, 
or
that rapists are all black,> or whatever - he never puts it
quite so baldly, just> points to that post as evidence of my
attitudes.> Which of course is twisting things - the rapist>
in the imaginary scenario is in fact black (or a> member of
some other unspeci'ed minority,> let's say 
black for
simplicity's sake), but that's> not because I 
think that
rapists tend to be black,> it's because the _question_ was
whether it's> correct to say that a racial slur is _never_>
appropriate - a hypothetical example illustrating > that
that's not so is necessarily going to involve > a minority. 
I
mean, duh.Now Ullrich refuses to acknowledge that noxious
smell of theimplication, and seeks to attack me instead,
accusing me of twistingthings.What should fascinate you is
that Ullrich consistently has gotten awaywith his comments as
many posters on sci.math were stalwart in defenseof him.For me
that makes the case fascinating as they apparently have
a*perception* of power based on their refusal to acknowledge
truthsthat don't suit them.I had the feeling that they 
thought
that they were in some waycontrolling me, or at least hurting
my feeling deeply, which I foundextraordinary.If you 'nd that
hard to believe, consider the other post in reply 
toUllrich's
comments here, from soft-eng.>Now if that's the case, I 
would
say Mr. Ullrich's upbringing>was sadly wanting and/or he has
not been a particularly thoughtful>individual since, and maybe
has convinced himself Jeffrey Dahmer>was framed. But none of
that's really related to primes.>It would be nicer if both
sides had avoided attacks>on character of each other. There is
a context when>the best of us need to be pointed out the errors
in>our thinking, but ideally the context is not that>of attacks
on each other.>> What's OP?>Useful new net shorthand for
Original Poster.**********David C. UllrichSo what's the
synopsis? Ullrich acknowledges his statements about aracial
slur being the perfectly appropriate reply but continues
todefend himself.He also defends his scenario involving an
intruder about to rape hisdaughter with the position that a
racial slur would be an appropriateresponse with the
implication that the intruder is someone to whom aracial slur
would apply.He bases his arguments at one point on the
assertion that I deliveredan egregious insult, for stating
that he had acted as my lapdog in aninstance.What he doesn't
add is that once I found he was so upset, deduced fromreplies
that came later, I apologized.I've maintained that David
Ullrich as a professor at a stateuniversity should be held to
some standard, and repeatedly postershave argued with me.
They've also become extremely upset at myactually 
registering
a complaint to Oklahoma State University aboutDavid 
Ullrich's
*public* statements.And in fact I've registered several
complaints and even chatted oncewith the head of the math
department at Oklahoma State University onthe phone.It's a
fascinating case that just keeps going. I wouldn't 
besurprised
if more comes later as I want to remind the readers
that*Ullrich* brought the subject up in this thread.James
Harris
= ...>> Well I just checked the page and while it's
clearly meant to be>> insulting, it seems that it's just
insults like crank scattered>> around the page, as the links
provided don't say much.>> The term crank 
isn't an insult,
it's an identi'cation. If>> someone want to 
insult you they
they will call you a jackass.> I disagree; it is no insult
to call a jackass a jackass.> I've given this matter some
thought, and now feel certain> that along such lines there is
nothing one can say to Harris> that would be an insult. It
seems that what you have to do> if you want to insult him is
to ask him a civil question.> -jiwAs if posters usually ask me
any class of reply exceptderision. You are a troll, a crackpot,
woefully and irremediablyignorant, and vigorously entertain
delusions of personal
competence.http://www.apa.org/journals/psp/psp7761121.html
Unskilled and Unaware of It: How Dif'culties in Recognizing
One'sOwn Incompetence Lead to In§ated Self-Assessments
http://insti.physics.sunysb.edu/~siegel/quack.html<http://
www.'rehead.org/~jessh/'lm/kubrick/Kubrick-Psych
o.html><http:/
/www.naturalchild.com/elliott_barker/prisons.html>When some
git (look in a mirror, Harris) repeatedly presentsbrilliant
discovery trivially demonstrated to be crap, then we
alljusti'ably shouthttp://w0rli.home.att.net/youare.swfHey
Harris, can you pass the Space math test? Fill in
thefollowing, including signs (the 'rst one is mercy
humped):(+1)(+1) = +1(-1)(+1) = ?(+1)(-1) = ?(-1)(-1) = ?Uncle
Al can dance in the pale
moonlight,http://www.mazepath.com/uncleal/eotvos.htm 1)
Footnotes, 2) Footnotes that connect to literature references;
3) Internally self-consistent, 4) Consistent with all empirical
observation; 5) New predicted phenomena, 6) New predicted
phenomena that are testable against empiricalobservation in
existing quali'ed apparatus.Your posts - every one of your
posts - fall short in categories(1)-(4), and short of (6) at
your own insistence. You post ,Harris, you post . What
sort of civil question do youthereafter expect?Uncle Al ays,
Evolution is a hoot if you are one of the survivors.-- Uncle
Alhttp://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for
children and most mammals)Quis custodiet ipsos custodes? The
Net!
a poster from South> Africa--before Apartheid was ended--and
during that discussion> information about my race was
present. You are loathsome,boring, ignorant, and ineducable.
You are the Bell Curvepersoni'ed (p. 279, softcover). You are
a credit... nah, we won't gothere, but... so is Uncle Al -
except at the right side of the bellrather than the left,
amidst his own kind in turn.What made this country great?It
was spics and niggers and wops and kikes with noses as long as
youarm! Firesign Theatre.And chinks and micks and bohunks and
frogs (mostly Canukistan - poorbottom line) and squidjiggers
and squareheads and norsks and svensksand the occasional WASP.
Excise the Liberals and it's a pretty goodcountry. (Hey 
folks,
the new AT&T $0.99 monthly charge is bull. Call the800
number and tell them you won't pay it. The 'rst 
time they
hangup on you. The second time they have a special plan that
is thee as your current plan, but without the new monthly fee.
Uncle Algot to scream into the handset, I'm mad as Hell and 
I'm
not going totake it any more! It was a lot of fun when the
fungible corporateasset at the other end got into the spirit
of the thing.) -- Uncle Alhttp://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)Quis
custodiet ipsos custodes? The Net!
=> which computerized
proofs do you believe,> by the lights of thier adequate
documentation?> in other words,> you've got to be 
kidding.???
If you have been frustrated by someone'sadequate
documentation, I can understand that.But something put into a
program can NEVER bevague or ill-de'ned, though it can be
incorrectfor its purpose. At worst, it could be obfuscatedand
hard to understand. Which is not at allrelated to being vague
and ill-de'ned.This is because (useful) programming languages
have tobe implemented by compilers or interpretersso every
possible nuance has to have been de'nedto exact precision.
Even more so than mathematics,where a certain amount of
hand-waving can possiblyescape the attention of people.
=So
how can such stuff go on for EIGHT years? You folksmust not
have enough entertaining material on sci.math,to want to
provide enough feedback to keep the §ames onfor so long!Does
anybody know the relevance of alt.writing here?
= ...> Well
I just checked the page and while it's clearly meant to be>
insulting, it seems that it's just insults like crank
scattered> around the page, as the links provided don't say
much.>> The term crank isn't an insult, it's 
an identi'cation.
If>> someone want to insult you they they will call you a
jackass.>> I disagree; it is no insult to call a jackass a
jackass.>> I've given this matter some thought, and now feel
certain>> that along such lines there is nothing one can say
to Harris>> that would be an insult. It seems that what you
have to do>> if you want to insult him is to ask him a civil
question.>> -jiwAs if posters usually ask me a civil
class of reply except> derision. You are a troll, a crackpot,
woefully and irremediably> ignorant, and vigorously entertain
delusions of personal
competence.http://www.apa.org/journals/psp/psp7761121.html>
Unskilled and Unaware of It: How Dif'culties in Recognizing
One's> Own Incompetence Lead to In§ated Self-Assessments 
>
http://insti.physics.sunysb.edu/~siegel/quack.html>
<http://www.'rehead.org/~jessh/'lm/kubrick/Kubri
ck-Psycho.html
<http://www.naturalchild.com/elliott_barker/prisons.html > When
some git (look in a mirror, Harris) repeatedly presents>
brilliant discovery trivially demonstrated to be crap, then we
all> justi'ably shouthttp://w0rli.home.att.net/youare.swfHey
Harris, can you pass the Space math test? Fill in the>
following, including signs (the 'rst one is mercy
humped):(+1)(+1) = +1> (-1)(+1) = ?> (+1)(-1) = ?> (-1)(-1) =
?Uncle Al can dance in the pale
moonlight,http://www.mazepath.com/uncleal/eotvos.htm 1)
Footnotes,> 2) Footnotes that connect to literature
references;> 3) Internally self-consistent,> 4) Consistent
with all empirical observation;> 5) New predicted phenomena,>
6) New predicted phenomena that are testable against
empirical> observation in existing quali'ed apparatus.Your
posts - every one of your posts - fall short in categories>
(1)-(4), and short of (6) at your own insistence. You post
,> Harris, you post . What sort of civil question do
you> thereafter expect?Uncle Al ays, Evolution is a hoot if
you are one of the survivors.Uncle Al,You fracture me, man.
Outrageous!
=> So how can such stuff go on for EIGHT years?
You folks> must not have enough entertaining material on
sci.math,> to want to provide enough feedback to keep the
§ames on> for so long!Every time someone succeeds in
convincing James that there is an error.He goes away -- for a
while. Then he comes back as if nothing hadhappened and starts
proliferating threads.> Does anybody know the relevance of
alt.writing here?I don't even know why he posts to any group
other than:alt.delusions.of.grandeur.--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
=...> You claimed he said
that because you apologised for not writing in French.> But as
you *now* so aptly remark, it was for writing you'd be
impressed> if he'd written in French. And indeed, the latter
is something else.> Yes? You are an idiot for a few reasons.
The 'rst is that when you> 'nd a posting by 
David in a French
newsgroup that is not in French, your> only reply is about his
French abilities in that newsgroup (and you know> nothing about
his abilities in that 'eld), not about the content. > 
That's
irrational. If someone were posting here completely in French,
> wouldn't that be pertinent?Yup, it would be pertinent. And 
it
does happen. > How welcoming are all of you to non-English
speakers who post?there are only a few that are *not*
welcoming. I have myself answeredsome of them. > In noting my
inability to speak French I was at *least* acknowledging >
that fault, and explaining why I couldn't go to French.was 
not
posting in French in a French newsgroup, rather you would
havebeen impressed when he had done so. As an afterthought you
mentionthat you did not write in French either. David's 
idiot
was *not*in response to that afterthought.> Second is your
assumption that posting in English in a French (or German> or
whatever) newsgroup is frowned upon. I have posted in English
in> both French and German newsgroup, simply because I do not
feel comfortable> writing in those languages, especially when
it is technical. I have no> problem either reading or speaking
those languages. None of my English> postings has been frowned
upon. And the third reason is of course that> you (not so)
subtly changed the allegation in order to make me look a>
fool. > Which is an expression of arrogance, as if the fact
that others > tolerated your not posting in the language of
the newsgroup, it's ok.How could I communicate otherwise in 
a
French or German newsgroup when I donot feel comfortable
posting in French or German? If you seriously limitthe
languages used in a newsgroup to the main languages used in
that group,you are seriously losing quite a bit of
international communication. > Well let someone come on one of
these newsgroups and post entirely in > French, or Russian or
German, and see the treatement they get.There are only a few
that give them a hard treatment. > Idiot, va-t'en. > But
then again, English speakers seem to be quite vicious and
impolite > with each other anyway.Oh, well, as I am not an
English speaker this does not apply to me, itappears. > It's
as if so many not only lack proper manners, but they enjoy >
informing the world.Yup, you are a prime example. Invading a
French newsgroup only to informthe readers (but not in French)
that you would be impressed if a particularposter had written
something in French.-- dik t. winter, cwi, kruislaan 413, 1098
sj amsterdam, nederland, +31205924131home: bovenover 215, 1025
jn amsterdam, nederland; http://www.cwi.nl/~dik/
=... >
Well, a while back I ended up in a debate with a poster from
South > Africa--before Apartheid was ended--and during that
discussion > information about my race was pertinent so I gave
it.I think this is quite strange. Apartheid ended in South
Africa in 1993,that was years before you started your quest on
FLT. (Nelson Mandelawas released in 1990 and three years after
his release Apartheid ended.)-- dik t. winter, cwi, kruislaan
413, 1098 sj amsterdam, nederland, +31205924131home: bovenover
215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
=[rants that make my point better than I ever could snipped]David Ullrich got caught once in an interesting exchange
where he>called me an idiot for apologizing to a *French*
newsgroup for not>posting in French. Nope. Never happened.
(Provide a citation, please).>When informed that he was on a
French newsgroup>making his posts, he gave some excuse about
not knowing, but never>apologized to me nor to the newsgroup.And ask yourself, how does it all relate to the poster who
noted the>nitpick?>James Harris**********David C.
UllrichDavid Ullrich is a math professor at Oklahoma State
University. He istherefore paid by the state and by American
taxpayers as I'm sure theschool receives funds from the
federal government.My point is that he should be held to
*some* standard, where at aminimum public lying is frowned
upon.James Harris
=>So how can such stuff go on for EIGHT
years? You folks>must not have enough entertaining material on
sci.math,>to want to provide enough feedback to keep the §ames
on>for so long!Although some of his talents exist only in his
imaginationhe _is_ a world-class troll.>Does anybody know the
relevance of alt.writing here?Only James.**********David C.
Ullrich
=> ...> Well, a while back I ended up in a debate
with a poster from South> Africa--before Apartheid was
ended--and during that discussion> information about my race
was pertinent so I gave it.I think this is quite strange.
Apartheid ended in South Africa in 1993,> that was years
before you started your quest on FLT. (Nelson Mandela> was
released in 1990 and three years after his release Apartheid
ended.)You're right. I actually went back to the thread and
also found outthat the other poster merely mentioned being
part Afrikaaner.So in recollecting I got several things wrong,
which looks like asexing up to me, as in fact, Apartheid had
ended, and the poster'sI should have gone back and checked
instead of relying on memory.James Harris
=>So how can
such stuff go on for EIGHT years? You folks>must not have
enough entertaining material on sci.math,>to want to provide
enough feedback to keep the §ames on>for so long!Although some
of his talents exist only in his imagination> he _is_ a
world-class troll.>Does anybody know the relevance of
alt.writing here?Only James.> **********Some words from James
on the subject:>> You see, I looked for major discoveries
using very simple mathematics>> because I feared that
mathematicians and the people who worship them,>> might too
easily avoid the truth, if I couldn't explain it to people>>
outside of the math club.>> They don't play fair. I point 
out
simple neat mathematical truths;>> they try to deliver low
blows.>> On sci.math that's often all you need to handle
people labeled>> cranks. I'm hoping that
alt.math.undergrad and sci.skeptic are different. And as
for alt.writing, writers rule the earth, so prudence
dictates>> that I include them. - Randy
= >
http://www.msnusers.com/AmateurMath/Documents/CountViewer.html
Very stupid to put it at a MSN site... like most reasonable
people, Idon't> have a Microsoft Passport account so I 
can't
go to your site. And I'mreally> not going to create a 
Passport
account... =- Brian Dickens, the NetherlandsI have also tried
<unsuccessfully> try the applet,and I also do not intend to
create a Passport account.It seems to me,that if Harris is
interested in folks seeing his works,that he should make them
more accessible.--Tom Potter http://tompotter.us
=>
Conjecture:> For every prime p, the multiplicative group
Z(modulo p) contains at least> one prime q<p such that q is a
generator of the group.>It fails for p=2 :-)
=I don't
think it works for p = 3 either.Lurch > Conjecture:> For every
prime p, the multiplicative group Z(modulo p) contains atleast>
one prime q<p such that q is a generator of the group.> It
fails for p=2 :-)>
=> I don't think it works for p = 3
either.<2> = {2, 1} Z modulo 3.GREG Lurch> Conjecture:>> For
every prime p, the multiplicative group Z(modulo p) contains
at> least>> one prime q<p such that q is a generator of the
group.> It fails for p=2 :-)>
= If one looks at pairs of
consecutive prime numbers separated by only> one non-prime
number - 41,43; 821,823; 8087,8089 etc. - one sees that> the
sum of such two primes is often divisible by 12:> The post by
Rasmus Villemoes settles that splendidly, but your even>
posing the problem shows you've forgotten that all primes 
over
3 are of the> form 6x+1 or 6x-1, so prime pairs are one of
each.> Or else you hoped this Harris guy would waste major
time> looking for a counterexample -- _Bad_ Uncle Al!
Baaad!Stupidity should be lethal, Robert A. Heinlein.Think of
my original post as evolution in action.-- Uncle
Alhttp://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for
children and most mammals)Quis custodiet ipsos custodes? The
Net!
=Al Littlebigmanwearingbigboypants admits to trolling:
> Al Littlebigmanwearingbigboypants trolls:>> If one looks at
pairs of consecutive prime numbers separated by only>> one
non-prime number - 41,43; 821,823; 8087,8089 etc. - one sees
that>> the sum of such two primes is often divisible by 12:>
The post by Rasmus Villemoes settles that splendidly, but your
even> posing the problem shows you've forgotten that all 
primes
over 3 are of the> form 6x+1 or 6x-1, so prime pairs are one of
each.> Or else you hoped this Harris guy would waste major
time> looking for a counterexample -- _Bad_ Uncle Al! Baaad! >
Stupidity should be lethal, Robert A. Heinlein.> Think of my
original post as evolution in action.Do unto others as 
you've
done unto yourself..... LOL
=Conjecture 1:If p is any odd
prime & p-1 contains at least 1 Quadratic non-residue, thenat
least one prime q which divides p-1 is a primitive
root.Conjecture 2:If p is any prime bigger than 3, then the
multiplicative group Z(modulo p-1)contains at least one
primitive root of p.Conjecture 3:Suppose p is any odd prime
and p-1 is of the form 2q^x, where q is an oddprime. If g is a
quadratic non residue of both p and p-1, then g is aprimitive
root.--So, I'm looking for counterexamples, or reasons why
these wouldn't be true.So far, I'm thinking 
that both 1 & 3
are false, and 2 is true - although Ihaven't found any
counterexamples, or been able to prove them either way.Any
help would be great.GREG
=I have a function proportional to
a probability distribution of interest that is giving me 
'ts.y
= x * I(1-(x^2); y, 1/2)where ïI' is the 
regularized beta
function. What I need is the form of this distribution as
y->+oo and x>0. For large y, it looks awfully like a gamma or
beta distribution, and I'd really like to know if it *is* 
one
of those (or something similar). Can anyone help with
this?Zeus
=Suppose X, Y, Z are positive random variable with
the pdf f_X(t), f_Y(t),f_Z(t), respectively. And F_X(t),
F_Y(t), F_Z(t) are respective cdffunction. The quantity a is a
positive real number. I need to evaluate thefollowing
probabiltiy.P( X<a; Y < X < Z).I develop the following
expresion.P( X<a; Y < X < Z) = int_{0}^{a} f_X(t) P( Y < t <
Z) dt =int_{0}^{a} f_X(t) F_Y(t) [1-F_Z(t) ] dt--ZHANG
Yan
=Suppose X, Y, Z are positive random variable with the
pdf f_X(t), f_Y(t),> f_Z(t), respectively. And F_X(t), F_Y(t),
F_Z(t) are respective cdf> function. The quantity a is a
positive real number. I need to evaluate the> following
probabiltiy.P( X<a; Y < X < Z).I develop the following
expresion.P( X<a; Y < X < Z) = int_{0}^{a} f_X(t) P( Y < t <
Z) dt> =int_{0}^{a} f_X(t) F_Y(t) [1-F_Z(t) ] dt No. As you
have stated it, you have de'nite values for Y and Z, such 
that
0 < Y < X < min(a,Z) Why the last inequality? Because if a < Z
then X < a guarantees x < Z, and vice-versa. Of course the
probability must be 0 if min(a,Z) < Y . Thus P( Y < X <
min(a,Z) ) = int _Y ^{min(a,Z)} {dt f_X (t) ) = [ F_X (
min(a,Z) ) - F_X (Y) ] theta ( min(a,Z) - Y ) You can then
multiply by the pdf's f_Y (u) and f_Z (v), and integrate 
over
u and v to get the probability of 'nding an X that 
satis'es
the restrictions.-- Julian V. NobleProfessor Emeritus of
^^^^^^^^http://galileo.phys.virginia.edu/~jvn/ Science knows
only one commandment: contribute to science. -- Bertolt
Brecht, Galileo.
=In Madrid, 25> I think this is a wellknow
problem but I'm not sure: A street has a length of 10 car
lengths. How many cars can be parked on> average if each
arriving car parks on a random available spot?
=>>I think
this is a wellknow problem but I'm not sure:>>A street has a
length of 10 car lengths. How many cars can be parked on
>>average if each arriving car parks on a random available
spot?> 10> Not if cars park across a car-length boundary.Of
course. But the OP didn't specify that. Very often, the
availablespots are explicitly marked with painted
rectangles.For example, if the street is two car lengths
long,> and a car parks right in the middle, no more cars can
park.
=>Message-id:
<lM_Oa.3433$Vr5.2278@news-binary.blueyonder.co.uk>In Madrid,
25I've heard it said (about circles) It 
doesn't work in
theory, but it's atribute to European drivers that it works 
in
practice.>> I think this is a wellknow problem but I'm not
sure:>> A street has a length of 10 car lengths. How many cars
can be parked on>> average if each arriving car parks on a
random available spot?--Mensanator2 of Clubs
http://members.aol.com/mensanator666/2ofclubs/2ofclubs.htm
=
>>I think this is a wellknow problem but I'm not sure:>>A
street has a length of 10 car lengths. How many cars can be
parked on>>average if each arriving car parks on a random
available spot?> 10>> Not if cars park across a car-length
boundary.Of course. But the OP didn't specify that. Very
often, the available> spots are explicitly marked with painted
rectangles.And very often, people completely ignore those
painted rectangles :p
=>>I think this is a wellknow problem
but I'm not sure:>>A street has a length of 10 car lengths.
How many cars can be parked on>>average if each arriving car
parks on a random available spot?> 10>> Not if cars park
across a car-length boundary.Of course. But the OP didn't
specify that. Very often, the available> spots are explicitly
marked with painted rectangles.And very often, people
completely ignore those painted rectangles :pBut less so when
parking meters are present.
=Hey,Im curious, what would you
guys/gals say the probability of someoneentering a Ph.D.
program in Math or Stats and not 'nishing it. i.e.dropping
out.
=>Im curious, what would you guys/gals say the
probability of someone>entering a Ph.D. program in Math or
Stats and not 'nishing it. i.e.>dropping out.Of not leaving
with a Ph.D.? 75% would be my guess, based on the eightyears
I've been at Colorado.Doug
=>Hey,Im curious, what would you
guys/gals say the probability of someone>entering a Ph.D.
program in Math or Stats and not 'nishing it. i.e.>dropping
out.Wouldn't know about stat, but sad to say a large 
majority
of thepeople who enter the PhD program in math here at OSU
endup without a PhD, one way or another.**********David C.
Ullrich
= >Im curious, what would you guys/gals say the
probability of someone>entering a Ph.D. program in Math or
Stats and not 'nishing it. i.e.>dropping out. Of not leaving
with a Ph.D.? 75% would be my guess, based on the eight> years
I've been at Colorado. DougDepends a lot on the school, of
course. If you want the highestprobability, I would guess in
the states it might be University of Montanaor University of
Idaho or Idaho State. Not disparaging, that's just howthey
are.
=> Hey,Im curious, what would you guys/gals say the
probability of someone> entering a Ph.D. program in Math or
Stats and not 'nishing it. i.e.> dropping out.I just read 
that
it was about 50-50. Long ago, I heard that it isanother 50-50
that one who 'nishes will do nothing after theirthesis. This
suggests that a lot of theses are written by theadvisor.
=>
Hey,> Im curious, what would you guys/gals say the
probability of someone> entering a Ph.D. program in Math or
Stats and not 'nishing it. i.e.> dropping out. I just read
that it was about 50-50. Long ago, I heard that it is> another
50-50 that one who 'nishes will do nothing after their> 
thesis.
This suggests that a lot of theses are written by the>
advisor.Not in the least. In graduate school you are
surrounded by excellentmathematicians and the spirit of
mathematics. Mathematics is everywhere; itis the whole world.
Everybody around you thinks that it's the only thingworth
learning.Then you get a job at Podunk, and discover that your
newfound colleaguesthink that knowing mathematics is knowing
the difference between additionand subtraction. Discussions in
the faculty lounge are about football.You teach 12 to 15
credits a week, e old stuff year after year. You getnumb and
tired and disillusioned (Pirsig mentions this in Zen and the
Art ofMotorcycle Maintenance). You have no real contact with
the living world ofmathematics and mathematicians; all 
you've
got is your Calculus I textbookand your colleagues. With great
effort you can scare up money to go to theoccasional
convention.Some people overcome these obstacles, bless
them.
=...>> I just read that it was about 50-50. Long ago,
I heard that it is>> another 50-50 that one who 'nishes will
do nothing after their>> thesis. This suggests that a lot of
theses are written by the>> advisor.Not in the least. In
graduate school you are surrounded by excellent>mathematicians
and the spirit of mathematics. Mathematics is everywhere; it>is
the whole world. Everybody around you thinks that it's the 
only
thing>worth learning.Then you get a job at Podunk, and discover
that your newfound colleagues>think that knowing mathematics is
knowing the difference between addition>and subtraction.
Discussions in the faculty lounge are about football.You teach
12 to 15 credits a week, e old stuff year after year. You
get>numb and tired and disillusioned (Pirsig mentions this in
Zen and the Art of>Motorcycle Maintenance). You have no real
contact with the living world of>mathematics and
mathematicians; all you've got is your Calculus I 
textbook>and
your colleagues. With great effort you can scare up money to go
to the>occasional convention.Some people overcome these
obstacles, bless them.I like to believe that the advent of
Usenet, later the web, arxiv.org, etc., are helping more
people overcome those obstaclesmore effectively.Lee
Rudolph
=>> Hey, Im curious, what would you guys/gals
say the probability of someone>> entering a Ph.D. program in
Math or Stats and not 'nishing it. i.e.>> dropping out.I just
read that it was about 50-50.50-50 for 'nishing or not
'nishing?;-)-- Rouben Rostamian <rostamian@umbc.edu>
=> I
just read that it was about 50-50. Long ago, I heard that it
is> another 50-50 that one who 'nishes will do nothing after
their> thesis. This suggests that a lot of theses are written
by the> advisor.Most of those PhDs go to positions where
research is not encouraged,rather teaching and service are
encouraged. 4-year colleges, communitycolleges, even high
schools. That could also be a reason for notwriting more
papers. The idea that writing no research papers equalsdoing
nothing shows a warped view of the world.-- G. A. Edgar
http://www.math.ohio-state.edu/~edgar/
=Not in the least. In
graduate school you are surrounded by excellent>mathematicians
and the spirit of mathematics. Mathematics is everywhere;
it>is the whole world. Everybody around you thinks that it's
the only thing>worth learning.Then you get a job at Podunk,
and discover that your newfound colleagues>think that knowing
mathematics is knowing the difference between addition>and
subtraction. Discussions in the faculty lounge are about
football.You teach 12 to 15 credits a week, e old stuff year
after year. You get>numb and tired and disillusioned (Pirsig
mentions this in Zen and the Art of>Motorcycle Maintenance).
You have no real contact with the living world of>mathematics
and mathematicians; all you've got is your Calculus I
textbook>and your colleagues. At this point I would suggest:
Guy's UPINT, GP/PARI, some decent coffee, asupply of good
Scotch Whiskey, and a great wife. Perhaps time on a
troutstream just outside Podunk two evenings a week may be of
some bene't. Asummer working the wheat harvest might help
also. Clearly Podunk ain't MSRI. Southwest will, however, 
get
you to Oakland for$99. I don't know what AC Transit costs
these days, but it can't be much. Even the numb and tired 
and
disillusioned have choices, I would think.Rich
=>Im
curious, what would you guys/gals say the probability of
someone>entering a Ph.D. program in Math or Stats and not
'nishing it. i.e.>dropping out.Of not leaving with a Ph.D.?
75% would be my guess, based on the eight> years I've been 
at
Colorado.DougWow, i never would have thought it be that high.
I would have guessedmaybe 30% drop out rate. I 'gured after
someone got their Masters inMathematics, got straight A's in
their graduate courses that it wouldbe suf'cient to prepare
them for the doctorate program in mathematics/or
statistics.
=> I just read that [chance of completing Ph.D.]
was about 50-50. Long> ago, I heard that it is another 50-50
that one who 'nishes will do> nothing after their thesis.You
mean 50% of mathematics Ph.D.s are unemployed, spending
theirentire lives sitting in their room staring at the walls?
I thinknot. Perhaps there is a much more narrow (-minded)
interpretation ofthe word nothing?I'm going to speculate 
that
nothing is interpreted along the linesnot inconsistent with
the simple observation that something on theorder of 50% of
math or science Ph.D. graduates enter careers otherthan
academics.> This suggests that a lot of theses are written by
the advisor.I would suggest that one for whom this is
suggested by the 50-50'gure should consider investing some
time in the study of logic orstatistics.Kevin.
=>>Im
curious, what would you guys/gals say the probability of
someone>>entering a Ph.D. program in Math or Stats and not
'nishing it. i.e.>>dropping out.Of not leaving with a Ph.D.?
75% would be my guess, based on the eight> years I've been 
at
Colorado.DougWow, i never would have thought it be that high.
I would have guessed> maybe 30% drop out rate. I 'gured after
someone got their Masters in> Mathematics, got straight A's 
in
their graduate courses that it would> be suf'cient to prepare
them for the doctorate program in mathematics> /or
statistics.One thing is that most people enter without a
Masters degree in the'rst place and switch to a Masters 
rather
than 'nish the PhD. Thataccounts for a big portion of the
discrepancy you think is present. Ion the other hand was one
of the few people that had passed most ofthe hurdles of a math
PhD program without actually getting such adegree. I believe
there was one other out of maybe two or three dozenPhD
graduates during the 've year period I was trying for a
PhD.Karl Hallowell
=> <snip >Then you get a job at Podunk,
and discover that your newfound colleagues>think that knowing
mathematics is knowing the difference between addition>and
subtraction. Discussions in the faculty lounge are about
football.>You teach 12 to 15 credits a week, e old stuff
year after year. You get>numb and tired and disillusioned
(Pirsig mentions this in Zen and the Art of>Motorcycle
Maintenance). You have no real contact with the living world
of>mathematics and mathematicians; all you've got is your
Calculus I textbook>and your colleagues. With great effort you
can scare up money to go to the>occasional convention.>Some
people overcome these obstacles, bless them.I like to believe
that the advent of Usenet, later the web, > arxiv.org, etc.,
are helping more people overcome those obstacles> more
effectively.I believe that is quite accurate. I currently (to
be cured in a fewmonths) have no access to a nearby college
library, community, etc.The nearest college is more than
fourty miles away and there I haveonly a few informal contacts
in the aerospace engineering community.My real connections (as
such) are online.Any serious math or physics concept is
Klein models, the inverse Galoisproblem, or the Eight Vertex
model and quickly 'nd relevant researchand expository
material. The USENET might not be able to answer myquestions,
but they never have failed to come up with some insight.I'm
still trying to 'gure out how to use arXiv.org (even after
yearsof playing with it), but it's proving to be an amazing
research tooleven with my limited experience.Karl
Hallowell
=>>Im curious, what would you guys/gals say the
probability of someone>entering a Ph.D. program in Math or
Stats and not 'nishing it. i.e.>dropping out. Of not
leaving with a Ph.D.? 75% would be my guess, based on the
eight>> years I've been at Colorado. DougWow, i never
would have thought it be that high. I would have guessed>maybe
30% drop out rate. I 'gured after someone got their Masters
in>Mathematics, got straight A's in their graduate courses
that it would>be suf'cient to prepare them for the doctorate
program in mathematics>/or statistics.Again, I have no idea
how things are in stat, but no that's not howit is in math 
at
all. A master's degree requires that you learn acertain 
amount
of mathematics - how much and how well you'rerequired to 
learn
it varies from place to place. A PhD requires_much_ more.
First, it requires that you learn much moremathematics - much
deeper mathematics, and you're requiredto understand it much
better than a master's student (tooversimplify that last
point, a master's student gets creditfor knowing facts, 
while
a PhD student only gets credit forknowing how to _prove_ those
facts).And then there's the much more 
signi'cant difference:
APhD requires a thesis, which is supposed to be signi'cant
original research. Of course some theses aremore signi'cant
and original than others, but regardless,it's a totally
different sort of requirement from anythingthat's required 
in
a typical master's degree - at leasttheoretically, when you
'nish your PhD there's supposedto be 
_something_ that you
understand better thananyone else on the
planet.**********David C. Ullrich
=...> I just read that it
was about 50-50. Long ago, I heard that it is> another 50-50
that one who 'nishes will do nothing after their> thesis. 
This
suggests that a lot of theses are written by the> advisor.>>Not
in the least. In graduate school you are surrounded by
excellent>>mathematicians and the spirit of mathematics.
Mathematics is everywhere; it>>is the whole world. Everybody
around you thinks that it's the only thing>>worth
learning.>>Then you get a job at Podunk, and discover that
your newfound colleagues>>think that knowing mathematics is
knowing the difference between addition>>and subtraction.
Discussions in the faculty lounge are about football.>>You
teach 12 to 15 credits a week, e old stuff year after year.
You get>>numb and tired and disillusioned (Pirsig mentions
this in Zen and the Art of>>Motorcycle Maintenance). You have
no real contact with the living world of>>mathematics and
mathematicians; all you've got is your Calculus I
textbook>>and your colleagues. With great effort you can scare
up money to go to the>>occasional convention.>>Some people
overcome these obstacles, bless them.I like to believe that
the advent of Usenet, later the web, >arxiv.org, etc., are
helping more people overcome those obstacles>more
effectively.It can certainly help people stay in touch, or at
least that seemsplausible. Hard to see how it can help with
the huge teachingloads at Podunk, though.>Lee
Rudolph**********David C. Ullrich
=>>I like to believe that
the advent of Usenet, later the web, >>arxiv.org, etc., are
helping more people overcome those obstacles>>more
effectively.It can certainly help people stay in touch, or at
least that seems>plausible. Hard to see how it can help with
the huge teaching>loads at Podunk, though.Why, by providing
the students^Wclients^Wenrollees at Podunkwith sci.math to do
their homework for them, of course.And if you'd read Hyman
Bass's report to the Carnegie Foundationin the latest
_Notices_, you'd realize that teaching load isa
doubleplusungood phrase. Time to talk about research
burdeninstead!Lee Rudolph 
=Most of those PhDs go to
positions where research is not encouraged,> rather teaching
and service are encouraged. 4-year colleges, community>
colleges, even high schools. That could also be a reason for
not> writing more papers. The idea that writing no research
papers equals> doing nothing shows a warped view of the
world.Adding to this ... A PhD program in mathematics that
ONLY prepares theparticipant for writing research papers is a
seriously incompleteprogram at best. Data shows that only
about 20% of math PhDs in the USwill end up at PhD-granting
universities.
= Most of those PhDs go to positions
where research is not encouraged,>> rather teaching and
service are encouraged. 4-year colleges, community>> colleges,
even high schools. That could also be a reason for not>>
writing more papers. The idea that writing no research papers
equals>> doing nothing shows a warped view of the world.Adding
to this ... A PhD program in mathematics that ONLY prepares
the>participant for writing research papers is a seriously
incomplete>program at best. Data shows that only about 20% of
math PhDs in the US>will end up at PhD-granting
universities.There is neither a logical nor a pragmatic
connection between yourlast two sentences. Many universities
and colleges which do notgrant PhDs (in mathematics)
nonetheless have (however unreasonablyand/or unrealistically)
a requirement that their (mathematics)faculty members write
and publish research papers, at leastif they expect to get
tenure and/or merit raises. Lee Rudolph
=>Im curious, what
would you guys/gals say the probability of someone>entering a
Ph.D. program in Math or Stats and not 'nishing it.
i.e.>dropping out.Of not leaving with a Ph.D.? 75% would be my
guess, based on the eight> years I've been at
Colorado.DougWell, at my University you need an A average in
your graduate coursesto be aloud entrance into the PH.D.
program. Would it still be a 75%failure rate you think
??
=>> Hey, Im curious, what would you guys/gals say
the probability of someone>> entering a Ph.D. program in Math
or Stats and not 'nishing it. i.e.>> dropping out.>I just 
read
that it was about 50-50. Long ago, I heard that it is>another
50-50 that one who 'nishes will do nothing after 
their>thesis.
This suggests that a lot of theses are written by
the>advisor.How in the hell does it suggest that? If I go into
industry after 'nishing,maybe I'm not writing 
papers, but that
doesn't mean that my thesis waswritten for me.Doug
=>
Clearly Podunk ain't MSRI. Southwest will, however, get you 
to
Oakland for> $99. I don't know what AC Transit costs these
days, but it can't be much. > Even the numb and tired and
disillusioned have choices, I would think.if you've got the
patience to ride the bus from Oakland, kudos to you. It's 
only
$2.25, but it takes over an hour and a half just to get
todowntown Berkeley. if you take the BART, it's 4.25 total,
and worththe $2.Ben
=>> Most of those PhDs go to positions
where research is not encouraged,>> rather teaching and
service are encouraged. 4-year colleges, community>> colleges,
even high schools. That could also be a reason for not>>
writing more papers. The idea that writing no research papers
equals>> doing nothing shows a warped view of the
world.>Adding to this ... A PhD program in mathematics that
ONLY prepares the>participant for writing research papers is a
seriously incomplete>program at best. Data shows that only
about 20% of math PhDs in the US>will end up at PhD-granting
universities.Such a program will only prepare the participant
for doingresearch in a narrow area. Unfortunately, these seem
to bemost of what is being done now, especially in
statistics.The emphasis on interdisciplinary programs mainly
producesthose who do not know the basics of anything, but
theseprograms have high rates of 'nishing.Students are not
getting the basics of set theory, algebra,analysis, and
topology these days. Learning how to computeand how to solve
certain types of problems fails if basicmaterial not covered
in that is needed. Abstract conceptsare needed for
understanding, even if the details of themare not used. --
This address is for information only. I do not claim that
these viewsare those of the Statistics Department or of Purdue
University.Herman Rubin, Deptartment of Statistics, Purdue
University
=>Hey,>Im curious, what would you guys/gals say
the probability of someone>entering a Ph.D. program in Math or
Stats and not 'nishing it. i.e.>dropping out.No one seems to
have mentioned it, but I think it may depend on thespeci'c
university and what its criteria are for being admitted
intothe program. Averaging over all U.S. schools would
probably not providea meaningful statistic. My guess is that
there is a signi'cant variation.Hard data could be obtained 
by
asking the Director of Graduate Studiesfor various programs. At
my school I'll ask him the next time we're 
onthe tennis
courts.--John E. PrussingUniversity of Illinois at
Urbana-ChampaignDepartment of Aerospace
Engineeringhttp://www.uiuc.edu/~prussing
=available online
in PDF format at
http://www.ams.org/employment/asst.pdfEveryone thinking about
graduate school in mathematics should look atthis booklet. For
example, the 'rst institution that I looked at in the booklet
had72 full time graduate students, 15 part time graduate
students, and 15full time 'rst year graduate students. The
department had graduated18 MS students in the past year, and
an average of 3 PhD's per yeargets an MS, but only about one
in 've entering graduate students goeson to get a PhD. Of
course, you should go back to previous years booklets to see
whether there have been any signi'cant changes inenrollment
patterns. Looking at about a dozen schools in this booklet,
the ratio of full time 'rst year graduate students to 
PhD's
per year (notethat PhD's for the last four years are given 
in
the book, so this hasto be divided by four) runs from about
5-to-1 down to 2-to-1. Of course, some students enter the
graduate program intending to getan MS degree. Unfortunately,
I can't think of any way to distinguishthose students from
students who were given an MS as a consolationprize. In many
cases, the total number of MS and PhD degrees per yearis very
similar to the number of full time 'rst year students,
indicatingthat most students get at least an MS. In other
cases, far fewer degreesare awarded than there are entering
students. For the big picture, it's worth pointing out that
there areapproximately 15,000 graduate students in PhD
granting departments ofmath and statistics in the US, and that
these departments producesomething like 1,000-1,200 PhD
graduates per year. These numbershaven't changed 
dramatically
for the numbers.)-- Brian Borchers borchers@nmt.eduDepartment
of Mathematics http://www.nmt.edu/~borchers/Socorro, NM 87801
FAX: 505-835-5366-- Brian Borchers borchers@nmt.eduDepartment
of Mathematics http://www.nmt.edu/~borchers/Socorro, NM 87801
FAX: 505-835-5366 
=> In
curious, what would you guys/gals say the probability of
someone>entering a Ph.D. program in Math or Stats and not
'nishing it. i.e.>dropping out. No one seems to have 
mentioned
it, but I think it may depend on the> speci'c university and
what its criteria are for being admitted into> the program.
Averaging over all U.S. schools would probably not provide> a
meaningful statistic. My guess is that there is a signi'cant
variation. Hard data could be obtained by asking the Director
of Graduate Studies> for various programs. At my school I'll
ask him the next time we're on> the tennis courts. --> John 
E.
Prussing> University of Illinois at Urbana-Champaign>
Department of Aerospace Engineering>
http://www.uiuc.edu/~prussingI did mention it, when this
thread started. I also suggested a few schoolswhere I guessed
(I have no data) that the probability of 'nishing might
behighest.
=>Wow, i never would have thought it be that
high. I would have guessed>maybe 30% drop out rate. I 'gured
after someone got their Masters in>Mathematics, got straight
A's in their graduate courses that it would>be 
suf'cient to
prepare them for the doctorate program in mathematics>/or
statistics.But that ability to do well in classes is not
particularly well correlatedwith the ability to generate new
mathematical ideas. You don't get aPhD for taking a lot of
classes, you know. (In some places, you don'ttake _any_
classes to get a PhD.)I would also object to a phrase like
drop out. In secondary schooland below, there is a clear
expectation that degree completion is thenecessary goal for
everyone of that age. At the graduate level, and evenat the
undergraduate level, leaving a program is not necessarily
anindication of some kind of failure. Students' eyes are
opened in schoolto the reality of the career choices for which
they are preparing, andthey may well decide they don't like
that image -- even if they're doingwell and can continue to 
do
well. Even if your mathematical skills aresuperb, if what you
want to do is make a lot of money, or to have timeto raise a
family, or to work with some of the world's needy 
people,then
you would be making a mistake to complete a PhD in
mathematics.dave
= This suggests that a lot of theses are
written by the advisor.Right. After all, why *wouldn't* a
professor want to forego his orher own research activities for
a couple years to write an enormouspaper under a student's
name?Maybe you meant to say something less hilarious.-- Kevin
<buhr@telus.net>
=>> Hey,>> Im curious, what would you
guys/gals say the probability of someone>> entering a Ph.D.
program in Math or Stats and not 'nishing it. i.e.>> dropping
out.> I just read that it was about 50-50. Long ago, I heard
that it is> another 50-50 that one who 'nishes will do 
nothing
after their> thesis. This suggests that a lot of theses are
written by the> advisor.Not in the least. In graduate school
you are surrounded by excellent> mathematicians and the spirit
of mathematics. Mathematics is everywhere; it> is the whole
world. Everybody around you thinks that it's the only thing>
worth learning.Then you get a job at Podunk, and discover that
your newfound colleagues> think that knowing mathematics is
knowing the difference between addition> and subtraction.
Discussions in the faculty lounge are about football.You teach
12 to 15 credits a week, e old stuff year after year. You get>
numb and tired and disillusioned (Pirsig mentions this in Zen
and the Art of> Motorcycle Maintenance). You have no real
contact with the living world of> mathematics and
mathematicians; all you've got is your Calculus I textbook>
and your colleagues. With great effort you can scare up money
to go to the> occasional convention.Some people overcome these
obstacles, bless them.Ok, let me put it this way. I KNOW that a
lot of PhD theses arewritten by the advisors. Let me see, I
have had 8 PhD students. Ofhad only the most minimal help;
four had a lot of help and explanationdescribed a PhD thesis
as a work by the advisor under adversecircumstances and I know
for a fact that that was true in his case. Wherever I have been
there is always one supervisor who is known towrite all or
nearly all of his students' theses. One once complainedthat 
he
didn't mind writing them, it was having to explain them 
thathe
objected to.But yes, there are other explanations for why
people don't go on to dotheir own work, but as I look at my
students there is a strongcorrelation between what they did in
grad school and what they didafterwards.
=>> This suggests
that a lot of theses are written by the advisor.Right. After
all, why *wouldn't* a professor want to forego his or>her 
own
research activities for a couple years to write an
enormous>paper under a student's name?Maybe you meant to say
something less hilarious.A lot of people have pointed out that
this does not necessarilysuggest that. Barr just posted a
reply, saying let me put itthis way and then asserting that in
_fact_ a lot of PhD thesesare written by advisors. That's 
not
really putting it anotherway, it's a separate assertion.And
whether you believe it or not, it's a _fact_ that a lot 
ofPhD
theses are essentially written by the advisor. Barrsays he's
seen a lot of this - so have I. Have you spent alot of time on
the faculty in a PhD-granting math department,or is your
disbelief just motivated by your wonderment asto why a
professor would do such a thing?(Regarding why a professor
would do such a thing: First,it doesn't mean 
he's putting his
own research on hold forthose years. Anyway, there are all
sorts of reasons: youhave a student who possibly should have
been kickedout years ago but wasn't - after the 
guy's been
here for've or six years, passed his exams and courses 
andall,
you really hate to kick him out just because hecan't do the
thesis. Or in more cynical vein: If noneof the students get
degrees then sooner or later thebean counters will remove the
PhD program from thedepartment, and then the professor will
have to teachtrigonometry instead of advanced course. All
sorts ofreasons it happens.Not that _I_'ve ever done such a
thing of course...)**********David C. Ullrich
=>> Hey,
Im curious, what would you guys/gals say the probability of
someone>> entering a Ph.D. program in Math or Stats and not
'nishing it. i.e.>> dropping out.>I just read that it was
about 50-50.50-50 for 'nishing or not
'nishing?;-)Yes.;-)
= And whether you believe it or
not, it's a _fact_ that a lot of>> PhD theses are 
essentially
written by the advisor.Yes, there's something 
signi'cant
hidden in the word essentially.>I am certainly willing to
believe that theses are written with highly>variable degrees
of guidance from the advisor, from here's a concept>look at 
so
why don't we meet again in two months to for tomorrow,>why
don't you try showing this class of functions is
uniformly>continuous, and I'd suggest you start by using 
these
estimates I>highlighted in this paper I photocopied for
you---you'll want to take>beta=1/2 in this formula (and
beyond).In any event, Michael said he'd read that only 50% 
of
those who 'nish>their PhDs go on to do any useful research
after the thesis and then>inferred that lots of theses were
written by the advisor. Whether the>inference was logically
correct or not, the implication was that>Michael 'gured
somewhere around 50% of theses (let's be charitable>and say
about 25% or so) are written by advisors, a claim I
'nd>dif'cult to swallow, especially without the 
word
essentially to>dicker over, since Michael didn't quality
written by.At a guess---and I admit it is a guess---I would
say that somewhere>around 1% of theses (in math and stats
departments, let's say) are>written by the advisor in the
sense that it would be considered>substantial plagiarism in a
different context. Signi'cantly more,>say 5% (or perhaps even
10%), involve the advisor leading the student>by the nose to
the extent that it would be obvious to an unbiased>observer
that the student hasn't demonstrated *any* capability to
do>independent research. These seem to be the cases you have
in mind>when you say essentially written.I imagine that
substantially more often, perhaps in as many as 50% of>the
cases, the advisor contributes most of the important ideas,
rough>statements of most main results, and just generally
mostly or even>completely determines the overall direction of
the research with the>student primarily 'lling in the
details.Am I being naive? You seem to think the last estimate
should be>somewhere close to 100%.Huh? How do you get from a
lot of to close to 100%?For the record, when I said a lot of I
wasn't referring toa large _percentage_ of PhD theses. (Otoh 
in
the casesI had in mind the percentage of the thesis written by
theadvisor is indeed _very_ close to 100%.)>> Have you spent
a>> lot of time on the faculty in a PhD-granting math
department,I have spent a lot of time (too much time) as a
Ph.D. student in a>statistics department interacting with both
stats and math>Ph.D. students at that institution. I've also
spent some time as a>postdoc in a math department interacting
with faculty and their>Ph.D. students. The students that I
remember (even a few lifers>who'd been there many years) 
were
obviously writing their own theses>in any reasonable sense. I
was probably fortunate enough to interact>mostly with strong
(though sometimes slow-working!) students.**********David C.
Ullrich
=> Does a Ph.D. program for Mathematics have a time
period for validly> completing> the program? At my university,
one must 'nish within four years.-- Robin Chapman,
www.maths.ex.ac.uk/~rjc/rjc.html The League of
Gentlemen
=Huh? How do you get from a lot of to close to
100%?question:>Do you mean that the advisor has
contributed>almost every original idea in the thesis? with:>
Yes. Sometimes it appears to be somewhat more> than almost
every.and I didn't read carefully enough. I mistakenly 
thought
you weresaying that it sometimes seemed to you that this
happened in almostevery case.> For the record, when I said a
lot of I wasn't referring to> a large _percentage_ of PhD
theses.Yes, now I understand.-- Kevin <buhr@telus.net>
=
Does a Ph.D. program for Mathematics have a time period for
validly completing> the program?It depends on the university
and even the department. My department(stats at
Wisconsin---Madison) had various deadlines you had to meetto
indicate progress. You had to take a certain series of
corecourses within two or three semesters of starting. You had
to takeand pass your written qualifying exam within four
semesters ofcompleting that series of courses, and a pass on
your qualifying examwas only good for a limited amount of time
('ve years, maybe?). Onthe other hand, if you let that lapse,
you could always take and passyour qualifying exam again.I
believe there were requirements to take a full course load up
untilthe time you passed your preliminary exam (an oral
defense of the'rst part of your thesis, essentially). After
that, you haddissertator status, and I'm not aware that 
there
was any particularreason a student couldn't go on 
inde'nitely
passing a qualifying examevery 've years as long as his or 
her
advisor continued to indicatesatisfactory progress.The graduate
school was considering introducing some time limits atsome
point. I don't know if anything came of it.For the most 
part,
it's probably not worth the trouble. Lifers areprominent
'xtures because of their longevity, not their numbers.They
aren't particularly a drain on the university; in some
cases,they may be a source of cheap teaching or research
labour, as pointedaround campus doing odd jobs for low wages,
why go out of your way toregulate against the practice?--
Kevin <buhr@telus.net>
=One wonders also about the ethics of
the department. People> have brains and can use them to make
decisions on a case by> case basis, and that's why we have
extensions. But oh how easy> it is to take advantage of these
lifers as cheap help.On the §ip side, the lifers have brains,
too. If they really thoughtthey were being taken advantage of,
they could always get real jobs.The fact is, a university
campus is a wonderful place to be for abright person with a
wide variety of interests. (Less charitably,these people
undoubtedly have laziness and directionless in somewhatlarger
shares than other students, but even these qualities
aren'twholly without their virtues.) That kind of person, in
that kind ofenvironment, may see no earthly reason for rushing
to 'nish a thesiswhen there are so many other neat things to 
do
every day.There undoubtedly are graduate students that are
taken advantage of,but I suspect it's easier to take 
advantage
of a student thatdesperately wants or needs to graduate
quickly. A department doesn'thave as much leverage over a
lifer.> It is a disservice to a graduate student to not only
let him> waste 7 years of his life pretending to write his
disseration,I wasn't a lifer, but I took my time. 
I'd hardly
consider the manyinteresting things I did while pretending to
write my dissertation awaste of my life. (Since my marriage
was one of them, I imagine mywife would agree.)> When things
are down to the wire, he ought to be _supported_ in his>
efforts by a department interested in the furthering of the>
discipline, not _distracted_ from them by a department
interested in> avoiding hiring a faculty member at 4 times the
cost.I think most departments are extremely supportive of
students whoactually want to graduate. In fact, half of this
thread has beenconcerned with advisors who are far *too*
supportive of thosestudents.I really think you've got it all
wrong. These aren't poor, dumb kidswho don't 
know any better
than to let the greedy corporate universitysteal all their
money. These are grown men and women who happen tolove the
life they're leading and have found a mutually
bene'cialarrangement with a cash-strapped institution to 
allow
them to leadthat life.If anyone feels taken advantage of, 
I'll
bet it's the poor soul whoagreed to be a 
lifer's advisor many,
many years ago and has regrettedit ever since.Are there any
lifers (or near-lifers) out there that feel differently?--
Kevin <buhr@telus.net>
=> I really think you've got it all
wrong. These aren't poor, dumb kids> who don't 
know any better
than to let the greedy corporate university> steal all their
money. These are grown men and women who happen to> love the
life they're leading and have found a mutually 
bene'cial>
arrangement with a cash-strapped institution to allow them to
lead> that life.I would only have it all wrong if I thought
that allthe cases were that way. I've just seen _some_ 
lifers
whowould have bene'tted from a kick in the pants, 
who's
wiveswould have dearly loved to see the quadrupling of the
salary,who would have continued to do essentially the e work
inthe e environment, but with the the quadrupled salary
andquadrupled respect, but it was just too easy for all
involvedto shirk their responsibility.And yes, I'm with you
unless you let them. My point was that the departments should
not enable (in theAlcoholics Anonymous sense of the word)
slacking behavior.These are stipends, not salaries. In my
case, the department got in big hurry to rush people
through.While there was a generous time allowance for 
'nishing
the program,there was only a short allowance for stipends.
Finish quickly orget your support somewhere else was the
message. I resented thisalso, for some of the reasons you hint
at. I was busy trying tostudy mathematics, and this was my
chance. I wasn't at a diplomafactory, and it 
wasn't my goal to
help a department boost theirstatistics. This was my only
chance to take courses from andinteract with certain talented
mathematicians. I would go off andlikely end up at a small
college with no colleagues or library.Here was my one shot,
and some administrator wanted to make sureit was as antiseptic
as possible. So I did mine in 5 years. Anotheryear would have
been nice, so I know what you're saying.Dammit, it was _my_
Ph.D., so I was, by golly, going to forge it_my_ way, at least
to some extent.But my post was addressing other cases. There
are adults whoallow people to take advantage of them. That
doesn't mean it'sA-OK for departments to use 
them. If a
student is not makingprogress on his degree then he is not
really a student, and he doesn'tdeserve a stipend. 
He's
stagnant.There's an ethical question here: The department
believes, intheory, that every professor is engaged in
research at some level.At least they expect it. And every TA
is chasing a degree.So everyone teaching courses is an
_active_ participant in thepursuit of knowledge. We advertize
that this is important in theclassroom. Even the smallest of
colleges insist on professionaldevelopment for promotion and
tenure. In academia, we're againststagnance (is that a 
word?)
We want (don't we?) people who areexcited pursuers of truth
and beauty teaching others to beexcited pursuers of truth and
beuaty. Just to be clear, I don't think every 12-year Ph.D.
student is stagnant. I said at the beginning that we have
brains andwe should use them to make decisions. It's that I
think thatsome of those decisions are made in favor of slave
labor.Bart
=Consider the product h = n(n+1)(n+2)(n+3) for
integer n>0, and assumeh=a^b for some positive intgers a and
b. Any prime p>3 that divides ncannot divide the other n+i
factors, so p^b must divide n, from which itfollows n=
(product of primes >3 dividing n)^b * 3's and 
2's.
Similarlyfor the other factors. Thus we can writen = 2^i 3^j
(prod primes p>3)^bn+1 = 2^x 3^y (prod primes q>3)^bgiving
that1+2^i 3^j (prod primes p>3)^b = 2^x 3^y (prod primes
q>3)^bAnalyze this last equation. If i or x is nonzero, divide
both sides by2^min(i,x), giving one side to be in integer, and
the other not, acontradiction. Thus i=x=0. Similarly, j=y=0.
Thus we have two bth powersof integers that differ by 1, which
is impossible, i.e.1+c^b=d^bhas no integer solutions for b>1,
c>0,d>0, since bth powers differ by morethan 1.Thus no product
of 4 consecutive integers is a poerfect power.Chris Lomont>
Does anyone know of a simple, elementary proof for the result
that the> product of four consecutive positive integers is
never a perfect power> (exponent >= 2)? I know that Erdos and
Selfridge proved a more> general result, but their proof was
neither elementary nor simple.>
=[...]> Thus no product of 4
consecutive integers is a poerfect power.> Chris LomontChris,
nicely done and nicely explained.
=Surely, either n or n + 1
is even, so how can i = x = 0? What am I missing?Robert
Consider the product h = n(n+1)(n+2)(n+3) for integer n>0, and
assume> h=a^b for some positive intgers a and b. Any prime p>3
that divides n> cannot divide the other n+i factors, so p^b
must divide n, from which it> follows n= (product of primes >3
dividing n)^b * 3's and 2's. Similarly> for 
the other factors.
Thus we can write n = 2^i 3^j (prod primes p>3)^b> n+1 = 2^x
3^y (prod primes q>3)^b giving that 1+2^i 3^j (prod primes
p>3)^b = 2^x 3^y (prod primes q>3)^b Analyze this last
equation. If i or x is nonzero, divide both sides by>
2^min(i,x), giving one side to be in integer, and the other
not, a> contradiction. Thus i=x=0. Similarly, j=y=0. Thus we
have two bth powers> of integers that differ by 1, which is
impossible, i.e. 1+c^b=d^b has no integer solutions for b>1,
c>0,d>0, since bth powers differ by more> than 1. Thus no
product of 4 consecutive integers is a poerfect power.> Chris
Lomont > Does anyone know of a simple, elementary proof for
the result that the> product of four consecutive positive
integers is never a perfect power> (exponent >= 2)? I know
that Erdos and Selfridge proved a more> general result, but
their proof was neither elementary nor simple.> 
=Consider
the product h = n(n+1)(n+2)(n+3) for integer n>0, and
assume>h=a^b for some positive intgers a and b. Any prime p>3
that divides n>cannot divide the other n+i factors, so p^b
must divide n, from which it>follows n= (product of primes >3
dividing n)^b * 3's and 2's. Similarly>for the 
other factors.
Thus we can writen = 2^i 3^j (prod primes p>3)^b>n+1 = 2^x 3^y
(prod primes q>3)^bgiving that1+2^i 3^j (prod primes p>3)^b =
2^x 3^y (prod primes q>3)^bAnalyze this last equation. If i or
x is nonzero, divide both sides by>2^min(i,x), giving one side
to be in integer, and the other not, a>contradiction. Thus
i=x=0. You have only shown that min{i, x} = 0.John
Roberts-Jones
=Good, you just shortened the proof a bit.
Similarly, you can't have both nand n+1 being a multiple of
3.> Surely, either n or n + 1 is even, so how can i = x = 0?
What am Imissing?> Robert> Consider the product h =
n(n+1)(n+2)(n+3) for integer n>0, and assume> h=a^b for some
positive intgers a and b. Any prime p>3 that divides n> cannot
divide the other n+i factors, so p^b must divide n, from which
it> follows n= (product of primes >3 dividing n)^b * 3's and
2's. Similarly> for the other factors. Thus we can write> n
= 2^i 3^j (prod primes p>3)^b> n+1 = 2^x 3^y (prod primes
q>3)^b> giving that> 1+2^i 3^j (prod primes p>3)^b = 2^x
3^y (prod primes q>3)^b> Analyze this last equation. If i or
x is nonzero, divide both sides by> 2^min(i,x), giving one side
to be in integer, and the other not, a> contradiction. Thus
i=x=0. Similarly, j=y=0. Thus we have two bth powers> of
integers that differ by 1, which is impossible, i.e.>
1+c^b=d^b> has no integer solutions for b>1, c>0,d>0, since
bth powers differ bymore> than 1.> Thus no product of 4
consecutive integers is a poerfect power.> Chris Lomont>
Does anyone know of a simple, elementary proof for the result
that the>> product of four consecutive positive integers is
never a perfect power>> (exponent >= 2)? I know that Erdos and
Selfridge proved a more>> general result, but their proof was
neither elementary nor simple.>
=> Chris, nicely done and
nicely explained.But not, unfortunately, correct.Eg 1 + 2^3 =
3^2.-- Timothy Murphy tel: +353-86-233 6090
= >1+2^i 3^j
(prod primes p>3)^b = 2^x 3^y (prod primes q>3)^b>Analyze
this last equation. If i or x is nonzero, divide both sides
by>2^min(i,x), giving one side to be in integer, and the other
not, a>contradiction. Thus i=x=0. I think you mean, If BOTH i
and x are nonzero then ... [ e ]. Thus> either i = 0 or x = 0.
But now you've got more work to do!Ah yes, correct :) I only
spent a few minutes thinking..... Actually,since one is n, and
one is n+1, then only one of them has any factor oftwo
anyways... So exactly one of i and x are nonzero. Also, since
n andn+1 are relatively prime, at most one of j and y can be
nonzero, and the pare distince from the q.You might be able to
complete this proof using these facts. For example,if the 2 and
3 are with the n, then noting that each of n+1 , n+2, and
n+3must be (prod primes)^b times some 2 or 3 factors, you
might getcontradictions since powwers of b should be large...
But I have no proof,and must work now.Perhaps after work 
I'll
'nish this if possibleChris Lomont Obviously if both i and x
are zero, you've got 1 + odd = odd, which> is already a
contradiction. dave>
<Pine.GSO.4.44.0307091700190.27326-100000@
morse.math.purdue.edu>
<vgp7g6tfrnl2f6@corp.supernews.com>
=> [...] > Thus no
product of 4 consecutive integers is a poerfect power.>
Chris Lomont Chris, nicely done and nicely explained.>doodled
with it again this afternoon, but it is harder than I
thought.Chris Lomont
=I have found an elegant proof that the
derivative of sin(x) is cos(x).I have studied two a-levels in
maths and read lots of math books buthave not come across this
particular proof before.Obviously, this is not a groundbreaking
proof, it is simply adifferent way of proving a fundamental
result. (without using limitsor in'ntesimals). However, for
personal interest I would like to knowif it is original.Is
there anywhere I can 'nd a catalogue of existing proofs for
thederivative of sin(x)?If it turned out this proof was
original should I consider getting itpublished or is it not
worth it, since it is such a tiny proof.Among these things, I
am also working on some integration techniques.Again, I have a
similiar problem: I do not know whether this stuff Iam 'nding
is original. I have done 6 modules of pure maths at schoolso I
am not a complete novice, but on the other hand I am aware
thatthere is many things that I do not know of pure maths
since I have yetto start my maths degree. Can anyone suggest a
website that providesinformation on advanced integration
techniques, and for that matterinformation on higher level
maths?Any responses to the above would be gratefully
received.Flame.
=> I have found an elegant proof that the
derivative of sin(x) is cos(x).Put your money where your mouth
is.> If it turned out this proof was original should I consider
getting it> published or is it not worth it, since it is such a
tiny proof.>Don't count your chickens before they hatch.> 
Among
these things, I am also working on some integration
techniques.> Again, I have a similiar problem: I do not know
whether this stuff I> am 'nding is original.Apply 
William's
Metatheorem: Whatever math I dream up is already old hat.> Any
responses to the above would be gratefully received.>Let us
know when or if you've the courage for a peer review.
=> I
have found an elegant proof that the derivative of sin(x) is
cos(x).> I have studied two a-levels in maths and read lots of
math books but> have not come across this particular proof
before.Obviously, this is not a groundbreaking proof, it is
simply a> different way of proving a fundamental result.
(without using limits> or in'ntesimals).Hmmm. The 
de'nition of
differentiation involves limits ....> However, for personal
interest I would like to know> if it is original.Why not post
it? For such a basic result it's probablyunlikely that 
it's
totally new, but who knows?> Is there anywhere I can 'nd a
catalogue of existing proofs for the> derivative of
sin(x)?Sounds a bit unlikely.> If it turned out this proof was
original should I consider getting it> published or is it not
worth it, since it is such a tiny proof.If you have a novel
angle on any elementary mathematics,the Mathematical Gazette
might publish it.-- Robin Chapman,
www.maths.ex.ac.uk/~rjc/rjc.html The League of Gentlemen
= I
have found an elegant proof that the derivative of sin(x) is
cos(x).> I have studied two a-levels in maths and read lots of
math books but> have not come across this particular proof
before. Obviously, this is not a groundbreaking proof, it is
simply a> different way of proving a fundamental result.
(without using limits> or in'ntesimals). However, for 
personal
interest I would like to know> if it is original. Is there
anywhere I can 'nd a catalogue of existing proofs for the>
derivative of sin(x)? If it turned out this proof was original
should I consider getting it> published or is it not worth it,
since it is such a tiny proof. Among these things, I am also
working on some integration techniques.> Again, I have a
similiar problem: I do not know whether this stuff I> am
'nding is original. I have done 6 modules of pure maths at
school> so I am not a complete novice, but on the other hand I
am aware that> there is many things that I do not know of pure
maths since I have yet> to start my maths degree. Can anyone
suggest a website that provides> information on advanced
integration techniques, and for that matter> information on
higher level maths? Any responses to the above would be
gratefully received. Flame.Learning by doing has helped many,
including myself - along withlearning by questioning. Don't
get discouraged when you 'nd outthat often you are
re-discovering.Could you share your proof of the derivative
result? It will notdiminish your claims to originality, if
that is indeed the case.(I wonder how the use of limits can be
avoided!)There are journals of high-school mathematics; in
Canada, thereis Crux Mathematicorum with Mathematical Mayhem,
published bythe Canadian Mathematical Society; there should be
a counterpartknown facts, although the main part of its
contents arecompetition type problems, with best solutions
published.And there is American Mathematical Monthly, of
course.Best wishes, ZVK(Slavek).
=>> I have found an
elegant proof that the derivative of sin(x) is cos(x).>> I
have studied two a-levels in maths and read lots of math books
but>> have not come across this particular proof before.
Obviously, this is not a groundbreaking proof, it is simply
a>> different way of proving a fundamental result. (without
using limits>> or in'ntesimals).Hmmm. The 
de'nition of
differentiation involves limits ....> Yeah, I'm kind of
wondering also. I think what he means is that there isno limit
explictly being taken, i.e. you don't take the
differencequotient of sine and then compute it directly. For
example, here's a nice little proof that derivative of sine 
is
cosine that may be what he'stalking about:Consider the unit
circle in R^2, with some parametrization t |--> (x(t),y(t)).
The derivative (x'(t), y'(t)) must be 
orthogonal to the
positionvector (x(t), y(t)) (by differentiating the equation
x(t)^2 + y(t)^2 = 1).So (x'(t), y'(t)) = ( 
-f(t)y(t), f(t)x(t)
) for some function f. However,if we had taken the
parametrization by arc length, then we would have unitspeed,
i.e. f = 1. So we can assume that x'(t) = -y(t), 
y'(t) = x(t).
Also, since we've parametrized by arc length, we see that
(x(t), y(t))makes angle t with the x axis (going
counterclockwise). This is preciselythe de'nition of cosine
and sine (or equivalent to whatever yourde'nition is).
Therefore we have shown derivative of cosine is -sine
andderivative of sine is cosine.>Robin Chapman,
www.maths.ex.ac.uk/~rjc/rjc.html> The League of GentlemenI
presume this is from the graphic novel by Alan Moore. But the
questionis, is the movie any good?
=>>Robin Chapman,
www.maths.ex.ac.uk/~rjc/rjc.html>> The League of GentlemenI
presume this is from the graphic novel by Alan Moore. But the
question> is, is the movie any good?Oh, never mind; I noticed
that I misread The League of Gentlemen as TheLeague of
Extraordinary Gentlemen. The former is apparently a British
TVshow.
= I have found an elegant proof that the derivative
of sin(x) is cos(x).> I have studied two a-levels in maths and
read lots of math books but> have not come across this
particular proof before. Obviously, this is not a
groundbreaking proof, it is simply a> different way of proving
a fundamental result. (without using limits> or 
in'ntesimals).
However, for personal interest I would like to know> if it is
original.I too would like to see your proof.> Is there
anywhere I can 'nd a catalogue of existing proofs for the>
derivative of sin(x)? If it turned out this proof was original
should I consider getting it> published or is it not worth it,
since it is such a tiny proof. Among these things, I am also
working on some integration techniques.Since you say ... also
working on some integration techniques I hope thatyour
reasoning is not circular.(Actually the pun is not intended)>
Again, I have a similiar problem: I do not know whether this
stuff I> am 'nding is original. I have done 6 modules of pure
maths at school> so I am not a complete novice, but on the
other hand I am aware that> there is many things that I do not
know of pure maths since I have yet> to start my maths degree.
Can anyone suggest a website that provides> information on
advanced integration techniques, and for that matter>
information about different disciplines you could lookat some
to the links mentioned in this news group. Some of the links
arecranks, but by reading the responses to various post, you
will determinewhich ones are worth while. Enjoy the
discovery.> Any responses to the above would be gratefully
received. Flame.
=> ----> Learning by doing has helped many,
including myself - along with> learning by questioning. 
Don't
get discouraged when you 'nd out> that often you are
re-discovering.Could you share your proof of the derivative
result? It will not> diminish your claims to originality, if
that is indeed the case.> (I wonder how the use of limits can
be avoided!)----Before I begin, a correction: I have made no
claims to originality.Obviously I hope it to be original, but
do not know this, hence meposting onto this group.I will post
this proof onto this newsgroup since I noticed a ring
ofpessimism in some of the replies. However, before this, how
can I besure I wont lose the claim to its discovery? (if, of
course, itsoriginal).Note: I apologise for any confusion when
I said no limits were used. Imeant this in the sense that
limits or in'ntesimals were not usedexplicitly (not by 
'rst
principles or otherwise)The integration techniques I referred
to are not related to this proofthis is a separate thing I am
working on.I am currently working on other areas of pure
maths, and I amfrequently 'nding new things that I have not
come accross before. Iam con'dent at least one of these 
things
is quite signi'cant, but donot know what to do with them.
Should I just send them off somewhereto get published? I do
not have a clue in this area, I am only in myteens. --------->
There are journals of high-school mathematics; in Canada,
there> is Crux Mathematicorum with Mathematical Mayhem,
published by> the Canadian Mathematical Society; there should
be a counterpart> known facts, although the main part of its
contents are> competition type problems, with best solutions
published. ----Crux Mathematicorum with Mathematical Mayhem: I
have not been able to'nd a counterpart to this. Can anyone
suggest a UK publicationsimiliar to this? 
=> Before I
begin, a correction: I have made no claims to originality.>
Obviously I hope it to be original, but do not know this,
hence me> posting onto this group. I will post this proof onto
this newsgroup since I noticed a ring of> pessimism in some of
the replies. However, before this, how can I be> sure I wont
lose the claim to its discovery? (if, of course, its>
original).>It's published here with date stamp and your
alias.If you want your name on it, then publish it here with
your name.Records of news groups are kept for some years, so
you can lay claim toyour notions via the archives of sci.math.
Otherwise go thru hassle ofarchiving which is much less hassle
than copy writing or publishing.yourself. Post of'ce time
stamps envelopes and as long as you don't openit, upon 
public
opening, it will give you some claim to authorship of
yourfantasies.> I am currently working on other areas of pure
maths, and I am> frequently 'nding new things that I have not
come across before. I> am con'dent at least one of these
things is quite signi'cant, but do> not know what to do with
them. Should I just send them off somewhere> to get published?
I do not have a clue in this area, I am only in my>
teens.You'll need to have you ideas peer 
reviewed.You'll need
to have presentation that'll be noticed by the referee
asnotable and worth his volunteer efforts to consider your
paper forpublishing. Claim what you may, The proof of the
pudding is in the eating.So again I remind you of William
Metatheorem Whatever math I dream up is already old hat.I've
never been able to produce a counterexample and I bet you
won'teither. Yet it's not certain William 
Metatheorem has no
unnoticedloop holes.
=Crux Mathematicorum with Mathematical
Mayhem: I have not been able to> 'nd a counterpart to this.
Can anyone suggest a UK publication> similiar to this?I
already did: The Mathematical Gazette.-- Robin Chapman,
www.maths.ex.ac.uk/~rjc/rjc.html The League of Gentlemen
=I
have found an elegant proof that the derivative of sin(x) is
cos(x).>I have studied two a-levels in maths and read lots of
math books but>have not come across this particular proof
before.Obviously, this is not a groundbreaking proof, it is
simply a>different way of proving a fundamental result.
(without using limits>or in'ntesimals). However, for personal
interest I would like to know>if it is original.Is there
anywhere I can 'nd a catalogue of existing proofs for
the>derivative of sin(x)?If it turned out this proof was
original should I consider getting it>published or is it not
worth it, since it is such a tiny proof.Among these things, I
am also working on some integration techniques.>Again, I have
a similiar problem: I do not know whether this stuff I>am
'nding is original. I have done 6 modules of pure maths at
school>so I am not a complete novice, but on the other hand I
am aware that>there is many things that I do not know of pure
maths since I have yet>to start my maths degree. Can anyone
suggest a website that provides>information on advanced
integration techniques, and for that matter>information on
higher level maths?Any responses to the above would be
gratefully received.Flame.1. There's no money in math. So if
someone steals your idea, you haven't lost any money.2. If
you're doing original work, you'll continue to 
do original
work. If someone steals an idea, just stay away from that
person in the future and keep doing your original work.3. The
only fame you can expect from doing math is among other
mathematicians.4. There is money in applying mathematical
ideas to other disciplines. Not deep mathematical ideas, but a
little math and some logic and organization to business
problems (and translating your results to English for your
colleagues) will keep you steadily employed at quite
reasonable rates. Thinking original thoughts is using time
that could be spent thinking pro'table thoughts. (Of course,
if you get paid well enough, you can afford to spend some time
thinking original thoughts. It's much easier to take the 
lower
salary and be a university professor.)Jon Miller
= >I have
found an elegant proof that the derivative of sin(x) is
cos(x).>I have studied two a-levels in maths and read lots of
math books but>have not come across this particular proof
before.>Obviously, this is not a groundbreaking proof, it is
simply a>different way of proving a fundamental result.
(without using limits>or in'ntesimals). However, for personal
interest I would like to know>if it is original.>Is there
anywhere I can 'nd a catalogue of existing proofs for
the>derivative of sin(x)?>If it turned out this proof was
original should I consider getting it>published or is it not
worth it, since it is such a tiny proof.>Among these things,
I am also working on some integration techniques.>Again, I have
a similiar problem: I do not know whether this stuff I>am
'nding is original. I have done 6 modules of pure maths at
school>so I am not a complete novice, but on the other hand I
am aware that>there is many things that I do not know of pure
maths since I have yet>to start my maths degree. Can anyone
suggest a website that provides>information on advanced
integration techniques, and for that matter>information on
higher level maths?>Any responses to the above would be
gratefully received.>Flame. 1. There's no money in math. So
if someone steals your idea, you > haven't lost any money.I
made no reference to money. To quote myself: ...for
personalinterest I would like to know if it is original> 2. If
you're doing original work, you'll continue to 
do original
work. > If someone steals an idea, just stay away from that
person in the > future and keep doing your original work.If
someone steals an idea as you put it, then i would lose
priorityas the discoverer. I think that as unfair, strange
though it maysound.> 3. The only fame you can expect from
doing math is among other > mathematicians.I do not expect
fame. I do not understand where you derived this ideafrom my
post.> 4. There is money in applying mathematical ideas to
other disciplines. Please see my response to 1.> Not deep
mathematical ideas, but a little math and some logic and >
organization to business problems (and translating your
results to > English for your colleagues) will keep you
steadily employed at quite > reasonable rates. Thinking
original thoughts is using time that could > be spent thinking
pro'table thoughts. Please see my response to 1.(Of course, 
if
you get paid well > enough, you can afford to spend some time
thinking original thoughts. > It's much easier to take the
lower salary and be a university professor.)Jon MillerI am
currently making enquiries with other professional
mathematiciansregarding my work so far. If any developments
occur, I will post themhere along with my work.Flame
=And
don't forget that I've provided access to my 
work at one
locationwhere you can go to see the mathematics that underpins
so many ofthese discussions:1. The short proof of Fermat's 
Last
Theorem where you see the powerof techniques that are also used
in the paper Advanced PolynomialFactorization.2. THE prime
counting function, or my prime counting function as
Idifferentiate it from those so-called prime counting
functions. At mywebsite you can see the function, get a C++
program to run it, readsome of my thoughts on it, join the
group and get a Java algorithmicimplementation, and most
importantly, see the partial differentialequation for the J
function, which is a prime suspect for theconnection between
the prime distribution and the continuous functionslike li(x)
and x/ln x.3. Join the group and you can access the pdf 'le 
to
read my paperAdvanced Polynomial Factorization, where a
polynomial factorizationinto non-polynomial factors proves an
error in taught
mathematics.http://groups.msn.com/AmateurMathSee what all the
arguing is about, judge for yourselves themathematics
presented, and step away from just waiting for people totell
you what to think.Mathematics is not owned by any group of
people. It's beautiful inthat logic and consistency rule the
day, while unfortunately, peoplecan lie about just about
anything, even mathematics.And they can even lie when 
they're
mathematicians. Yes, evenmathematicians can lie. > And don't
forget that I've provided access to my work at one location>
where you can go to see the mathematics that underpins so many
of> these discussions:1. The short proof of Fermat's Last
Theorem where you see the power> of techniques that are also
used in the paper Advanced Polynomial> Factorization.2. THE
prime counting function, or my prime counting function as I>
differentiate it from those so-called prime counting
functions. At my> website you can see the function, get a C++
program to run it, read> some of my thoughts on it, join the
group and get a Java algorithmic> implementation, and most
importantly, see the partial differential> equation for the J
function, which is a prime suspect for the> connection between
the prime distribution and the continuous functions> like li(x)
and x/ln x.3. Join the group and you can access the pdf 'le 
to
read my paper> Advanced Polynomial Factorization, where a
polynomial factorization> into non-polynomial factors proves
an error in taught
mathematics.http://groups.msn.com/AmateurMathSee what all the
arguing is about, judge for yourselves the> mathematics
presented, and step away from just waiting for people to> tell
you what to think.Mathematics is not owned by any group of
people. It's beautiful in> that logic and consistency rule 
the
day, while unfortunately, people> can lie about just about
anything, even mathematics.And they can even lie when 
they're
mathematicians. Yes, even> mathematicians can lie.> James
HarrisI just went for a stroll, as advised. Much of your work
is based on your object math. The problem is, you have
something called an operator that you haven't clearly 
de'ned.
Your de'nition of Objects is also unclear at best. Why not
either use the e math as everyone else or be clear and use
examples? If all your work is based on this, it's no wonder
you are making very little progress in convincing people.--
Will Twentyman
my prime counting function as I> differentiate it from those
imbecile Harris, Uncle Al will give you a discrete primenumber
task to redeem yourself and your incredible manure pile
ofbull theories and proofs. If one looks at pairs of
consecutive prime numbers separated by onlyone non-prime
number - 41,43; 821,823; 8087,8089 etc. - one sees thatthe sum
of such two primes is often divisible by 12: (11 + 13)/12 = 2
(41 + 43)/12 = 7 (821 + 823)/12 = 137 (1931 + 1933)/12 = 322
(8087 + 8089)/12 = 1348(104681 + 104683)/12 = 17447 3,5
obviously does not work. Use your Harris big mouth to
'ndanother pair of consecutive primes other than 3,5 whose 
sum
is notevenly divisible by 12. Put up and demonstrate your
claimed expertise, or shut up for beingthe dysfunctional
ing imbecile that you are. Uncle Al bets thatyou don't
have the balls or the brains to perform. Are you going torun
crying to your mama, Harris?-- Uncle
Alhttp://www.mazepath.com/uncleal/eotvos.htm (Do something
naughty to physics)
=> Put up and demonstrate your claimed
expertise, or shut up for being> the dysfunctional ing
imbecile that you are. Uncle Al bets that> you don't have 
the
balls or the brains to perform. Are you going to> run crying
to your mama, Harris?Can you refer me to a proof (in the
literature) that consective primes whose sum is >= 12 add up
to a number divisible by 12. Is this a known theorem or is
this an open problem?Bob Kolker
<LR%Oa.20246$N7.2676@sccrnsc03>
=> Put up and demonstrate
your claimed expertise, or shut up for being>> the
dysfunctional ing imbecile that you are. Uncle Al bets
that>> you don't have the balls or the brains to perform. 
Are
you going to>> run crying to your mama, Harris? Can you refer
me to a proof (in the literature) that consective primes>
whose sum is >= 12 add up to a number divisible by 12. Is this
a known> theorem or is this an open problem?>Well, if you
accept this is literature, here is a proof:Let p be an odd
prime such that p+2 is also a prime, and assume p /=3.If p ==
1 (mod 4) we have 2p == 2 (mod 4) and consequently p + p+2
=2p+2 == 0 (mod 4), that is, 4 divides 2p+2.If p == 3 (mod 4)
we also have 2p == 2 (mod 4), so also in this casewe have that
4 divides 2p+2.Now 3 does not divide p; thus p == 1 or p == 2
(mod 3); but since p+2is also prime, 3 does not divide p+2,
from which we may conclude thatp == 2 (mod 3) and p+2 == 1
(mod 3); then 2p+2 == 0 (mod 3), and 3divides the sum. Since 3
and 4 are coprime, and they both divide 2p+2,34=12 divides
2p+2. QED (quite elementary, actually)./Rasmus-- 
=> And
don't forget that I've provided access to my 
work at one
location> where you can go to see the mathematics that
underpins so many of> these discussions:1. The short proof of
Fermat's Last Theorem where you see the power> of techniques
that are also used in the paper Advanced Polynomial>
Factorization.2. THE prime counting function, or my prime
counting function as I> differentiate it from those so-called
prime counting functions. At my> website you can see the
function, get a C++ program to run it, read> some of my
thoughts on it, join the group and get a Java algorithmic>
implementation, and most importantly, see the partial
differential> equation for the J function, which is a prime
suspect for the> connection between the prime distribution and
the continuous functions> like li(x) and x/ln x.3. Join the
group and you can access the pdf 'le to read my paper>
Advanced Polynomial Factorization, where a polynomial
factorization> into non-polynomial factors proves an error in
taught mathematics.I think that is speled undermines!
= Put
up and demonstrate your claimed expertise, or shut up for
being> the dysfunctional ing imbecile that you are. Uncle
Al bets that> you don't have the balls or the brains to
perform. Are you going to> run crying to your mama, Harris?Can
you refer me to a proof (in the literature) that consective
primes > whose sum is >= 12 add up to a number divisible by
12. Is this a known > theorem or is this an open problem?If by
consective you mean primes p and q with q-p = 2 then I would
refer you to the use of your brain instead of looking for a
proof in the literature. Two minutes without using pen and
paper maximum. .Every prime except 2 and 3 is of the form 6k-1
or 6k+1. If p and q are primes, q = p+2, and p is not equal to
3, then p is of the form 6k-1 and q of the form 6k+1, so p+q =
12k. <LR%Oa.20246$N7.2676@sccrnsc03>
<u0l7k6rz79w.fsf@imf.au.dk>
=>> Put up and demonstrate
your claimed expertise, or shut up for being>> the
dysfunctional ing imbecile that you are. Uncle Al bets
that>> you don't have the balls or the brains to perform. 
Are
you going to>> run crying to your mama, Harris?> Can you
refer me to a proof (in the literature) that consective
primes> whose sum is >= 12 add up to a number divisible by 12.
Is this a known> theorem or is this an open problem? Well, if
you accept this is literature, here is a proof:Let p be an odd
prime such that p+2 is also a prime, and assume p /=> 3.If p ==
1 (mod 4) we have 2p == 2 (mod 4) and consequently p + p+2 =>
2p+2 == 0 (mod 4), that is, 4 divides 2p+2.If p == 3 (mod 4)
we also have 2p == 2 (mod 4), so also in this case> we have
that 4 divides 2p+2.Now 3 does not divide p; thus p == 1 or p
== 2 (mod 3); but since p+2> is also prime, 3 does not divide
p+2, from which we may conclude that> p == 2 (mod 3) and p+2
== 1 (mod 3); then 2p+2 == 0 (mod 3), and 3> divides the sum.
Since 3 and 4 are coprime, and they both divide 2p+2,> 34=12
divides 2p+2. QED (quite elementary, actually).Very elegant!
Must I now propose something new for Harris to be
anineffectual jackass about, or do you think the original
challenge isstill suf'cient? 8^>)-- Uncle
Alhttp://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for
children and most mammals)Quis custodiet ipsos custodes? The
Net!
=>> Put up and demonstrate your claimed expertise, or
shut up for being> the dysfunctional ing imbecile that you
are. Uncle Al bets that> you don't have the balls or the 
brains
to perform. Are you going to> run crying to your mama,
Harris?>> Can you refer me to a proof (in the literature) that
consective primes>> whose sum is >= 12 add up to a number
divisible by 12. Is this a known>> theorem or is this an open
problem?>>Well, if you accept this is literature, here is a
proof:Let p be an odd prime such that p+2 is also a prime, and
assume p /=>3.If p == 1 (mod 4) we have 2p == 2 (mod 4) and
consequently p + p+2 =>2p+2 == 0 (mod 4), that is, 4 divides
2p+2.If p == 3 (mod 4) we also have 2p == 2 (mod 4), so also
in this case>we have that 4 divides 2p+2.Now 3 does not divide
p; thus p == 1 or p == 2 (mod 3); but since p+2>is also prime,
3 does not divide p+2, from which we may conclude that>p == 2
(mod 3) and p+2 == 1 (mod 3); then 2p+2 == 0 (mod 3), and
3>divides the sum. Since 3 and 4 are coprime, and they both
divide 2p+2,>34=12 divides 2p+2. QED (quite elementary,
actually).>Nice, very nice.Mati Meron | When you argue with a
fool,meron@cars.uchicago.edu | chances are he is doing just
the e
= >> Put up and demonstrate your claimed expertise, or
shut up for being>> the dysfunctional ing imbecile that you
are. Uncle Al bets that>> you don't have the balls or the
brains to perform. Are you going to>> run crying to your mama,
Harris?> Can you refer me to a proof (in the literature) that
consective primes> whose sum is >= 12 add up to a number
divisible by 12. Is this a known> theorem or is this an open
problem?Well, if you accept this is literature, here is a
proof: Let p be an odd prime such that p+2 is also a prime,
and assume p /=> 3. If p == 1 (mod 4) we have 2p == 2 (mod 4)
and consequently p + p+2 => 2p+2 == 0 (mod 4), that is, 4
divides 2p+2. If p == 3 (mod 4) we also have 2p == 2 (mod 4),
so also in this case> we have that 4 divides 2p+2. Now 3 does
not divide p; thus p == 1 or p == 2 (mod 3); but since p+2> is
also prime, 3 does not divide p+2, from which we may conclude
that> p == 2 (mod 3) and p+2 == 1 (mod 3); then 2p+2 == 0 (mod
3), and 3> divides the sum. Since 3 and 4 are coprime, and they
both divide 2p+2,> 34=12 divides 2p+2. QED (quite elementary,
actually).Let me suggest a simpler statement of the last part.
p+1 must be divisibleby 3, since neither p nor p+2 are.
Therefore: 2(p+1) = 2p+2 must bedivisible by 3.I was working
on a similar statement to show that 2p+2 must be divisible
by4, and decided to check what had already been posted. Good
work.
=>> Put up and demonstrate your claimed expertise,
or shut up for being> the dysfunctional ing imbecile that
you are. Uncle Al bets that> you don't have the balls or the
brains to perform. Are you going to> run crying to your mama,
Harris?>> Can you refer me to a proof (in the literature) that
consective primes>> whose sum is >= 12 add up to a number
divisible by 12. Is this a known>> theorem or is this an open
problem?> Well, if you accept this is literature, here is a
proof:> Let p be an odd prime such that p+2 is also a prime,
and assume p /=> 3.> If p == 1 (mod 4) we have 2p == 2 (mod
4) and consequently p + p+2 => 2p+2 == 0 (mod 4), that is, 4
divides 2p+2.> If p == 3 (mod 4) we also have 2p == 2 (mod
4), so also in this case> we have that 4 divides 2p+2.> Now
3 does not divide p; thus p == 1 or p == 2 (mod 3); but since
p+2> is also prime, 3 does not divide p+2, from which we may
conclude that> p == 2 (mod 3) and p+2 == 1 (mod 3); then 2p+2
== 0 (mod 3), and 3> divides the sum. Since 3 and 4 are
coprime, and they both divide 2p+2,> 34=12 divides 2p+2. QED
(quite elementary, actually). Very elegant! Must I now propose
something new for Harris to be an> ineffectual jackass about,
or do you think the original challenge is> still suf'cient?
8^>)Does he understand the notation p == 2 (mod3)?
=> Every
prime except 2 and 3 is of the form 6k-1 or 6k+1.Of course. I
should remember this trick for puzzles for the kids
(yesterdaythey understood my explanation of the proof of why
there can be no largestprime number). This is obvious once I
read it, but not something Ipreviously knew (or remembered).
The resulting proof is then obvious.> If p and q are> primes,
q = p+2, and p is not equal to 3, then p is of the form 6k-1
and> q of the form 6k+1, so p+q = 12k.
=> Can you refer me
to a proof (in the literature) that consective primes > whose
sum is >= 12 add up to a number divisible by 12. Is this a
known > theorem or is this an open problem?If p>3 is prime,
then p is congruent either to 1 or to -1 modulo 6.Likewise p+2
is congruent to either 1 or -1 modulo 6; if p=1 (mod 6)we have
p+2 = 3 (mod 6). So, p = 6k-1, p+2 = 6k+1, and p+p+2 = 12k.
<LR%Oa.20246$N7.2676@sccrnsc03> <u0l7k6rz79w.fsf@imf.au.dk>
=>> Put up and
demonstrate your claimed expertise, or shut up for being>> the
dysfunctional ing imbecile that you are. Uncle Al bets
that>> you don't have the balls or the brains to perform. 
Are
you going to>> run crying to your mama, Harris? Can you refer
me to a proof (in the literature) that consective primes>
whose sum is >= 12 add up to a number divisible by 12. Is this
a known> theorem or is this an open problem?>> Well, if you
accept this is literature, here is a proof: Let p be an
odd prime such that p+2 is also a prime, and assume p /=>>
3. If p == 1 (mod 4) we have 2p == 2 (mod 4) and
consequently p + p+2 =>> 2p+2 == 0 (mod 4), that is, 4 divides
2p+2. If p == 3 (mod 4) we also have 2p == 2 (mod 4), so
also in this case>> we have that 4 divides 2p+2. Now 3
does not divide p; thus p == 1 or p == 2 (mod 3); but since
p+2>> is also prime, 3 does not divide p+2, from which we may
conclude that>> p == 2 (mod 3) and p+2 == 1 (mod 3); then 2p+2
== 0 (mod 3), and 3>> divides the sum. Since 3 and 4 are
coprime, and they both divide 2p+2,>> 34=12 divides 2p+2. QED
(quite elementary, actually). Very elegant! Must I now propose
something new for Harris to be an> ineffectual jackass about,
or do you think the original challenge is> still suf'cient?
8^>)>Well, assuming he can interpret _standard_ mathematical
arguments in_standard_ terminology and using the usual meaning
of words likedivides, conclude, sum etc., you should 'nd
something else forhim to do. I leave it for you to
decide.../Rasmus-- http://home.imf.au.dk/burner/
<LR%Oa.20246$N7.2676@sccrnsc03> <u0l7k6rz79w.fsf@imf.au.dk>
<3f0c3c90$1@cpns1.saic.com>
= Let me suggest a simpler
statement of the last part. p+1 must be divisible> by 3, since
neither p nor p+2 are. Therefore: 2(p+1) = 2p+2 must be>
divisible by 3. I was working on a similar statement to show
that 2p+2 must be divisible by> 4, and decided to check what
had already been posted. Good work.>Well, you're almost
already there. Being divisible by 4 is the e asbeing divisible
by 2 twice. But 2p+2 is even, and so is (2p+2)/2 =p+1, since p
the simpli'cation./Rasmus-- 
=>And don't forget that I've
provided access to my work at one location>where you can go to
see the mathematics that underpins so many of>these
discussions:You should send your texts to your local FBI. They
like to hearfrom scientists like you.---I spewed bodily §uids.
- Shydavidhttp://www.skeptictank.org/
http://www.RonTheNut.ORG/-- You love drugs! You love drugs,
don't you?! You betternot say anything about my mother! 
Don't
you DARE say anythingabout my mother! -- Scientology's
International President (Audio'les of this nutter at
http://www.linkline.com/personal/frice
=Can you refer me to
a proof (in the literature)> that consecutive primes > 3 have
sum divisible by 12. > Is this a known theorem or is this an
open problem?Twin primes p, p+2 have sum divisible by 12 if p
> 3.It's well-known and easy. Let x|y denote x divides
y.METHOD 1: It's obvious every prime p > 3 has form 6n+-1,so
twin primes > 3 have form 6n-1, 6n+1 with sum 12n.METHOD 2:
Suppose p, p+2 are both primes > 3.Then 4|2(p+1) since p odd
=> p+1 even and 3|2(p+1) since not 3|p, not 3|p+2 => 3|p+1Thus
12|2(p+1) = p + p+2i.e. 12 divides the sum of two twin primes >
3.You said consecutive primes but surely you meant twin
primessince it's obviously false for consecutives, e.g. not
12|7+11.-Bill Dubuque
=| Can you refer me to a proof (in the
literature) that consective primes| whose sum is >= 12 add up
to a number divisible by 12. Is this a known| theorem or is
this an open problem?Twin primes is a better term than
consecutive primes. 13 and 17 areconsecutive in the sequence
of primes, but of course this is not whatwe're talking 
about.|
Let p be an odd prime such that p+2 is also a prime, and assume
p /= 3.| | If p == 1 (mod 4) we have 2p == 2 (mod 4) and
consequently p + p+2 =| 2p+2 == 0 (mod 4), that is, 4 divides
2p+2.| | If p == 3 (mod 4) we also have 2p == 2 (mod 4), so
also in this case| we have that 4 divides 2p+2.| | Now 3 does
not divide p; thus p == 1 or p == 2 (mod 3); but since p+2| is
also prime, 3 does not divide p+2, from which we may conclude
that| p == 2 (mod 3) and p+2 == 1 (mod 3); then 2p+2 == 0 (mod
3), and 3| divides the sum. Since 3 and 4 are coprime, and they
both divide 2p+2,| 34=12 divides 2p+2. QED (quite elementary,
actually).I think it's a little better if you 
don't divide
into the cases wherep is of the form 4n+1 and of the form
4n+3. Because p is of the form2n+1, p+(p+2) is 4n+4 which is
divisible by 4.A slightly different approach is to consider
the remainder left by pwhen you divide it by 6 (or
equivalently the congruence class of p mod6). If p is of the
form 6n, 6n+2, or 6n+4 it's even, and 2 is the onlyeven 
prime.
If p is of the form 6n+3 it's a multiple of 3, and 3 isthe 
only
such prime. For p>3, p is always of the form 6n+1 or 6n+5.In
order to be a twin prime, p has to be of the form 6n+5,
andp+(p+2)=12n+12 is divisible by 12.An exercise is to see
what one can say about prime triples, eitherthree primes of
the form p, p+2, and p+6, or of the form p, p+4, p+6.It's a
famous conjecture that given a sequence a1=0,...,an 
o'ntegers,
there exist in'nitely many p such that p+a1,p+a2,...,p+anare
primes if and only if there doesn't exist a prime q such 
that
thea1,...,an leave all q possible remainders on division by q.
That's inturn just a special case of a more general 
conjecture
on the thicknessof the set of m such that A1(m),...,An(m) are
simulataneously prime,where A1,...,An are polynomials in m.The
upshot is that the kind of quite elementary reasoning
RasmusVillemoes just gave us is expected to be good enough to
answer a wholerelated family of questions about primes, when
the answer is thatthere are only 'nitely many examples.On the
other hand, even to show that there are in'nitely 
manyexamples
of twin primes is already extremely hard and hasn't 
beendone,
so the possibility that all large enough twin primes p
havep+(p+2) divisible by 120 can't be ruled out; it just 
seems
ratherimplausible.Keith Ramsay
=METHOD 2: Suppose p, p+2 are
both primes > 3.Then 4|2(p+1) since p odd => p+1 even and
3|2(p+1) since not 3|p, not 3|p+2 => 3|p+1Thus 12|2(p+1) = p +
p+2 i.e. 12 divides the sum of two twin primes >
3.Alternatively 6|p(p+1)(p+2) via binomial coef (p+2:3)
integral.So it must be 6 | p+1 since 6 coprime to p & p+2
(primes > 3).Finally then 12|2(p+1) = p + p+2.More simply:
Among any n or more consecutive integersmust occur a multiple
of n. So among p, p+1, p+2 occurs a multiple of 2 and 3; it
must be p+1 in both cases sincep and p+2 are primes > 3. So
6|p+1 => 12|2(p+1) = p + p+2.-Bill Dubuque
= METHOD 2:
Suppose p, p+2 are both primes > 3. Then 4|2(p+1) since p
odd => p+1 even and 3|2(p+1) since not 3|p, not 3|p+2 =>
3|p+1 Thus 12|2(p+1) = p + p+2>> i.e. 12 divides the sum
of two twin primes > 3.Alternatively 6|p(p+1)(p+2) via
binomial coef (p+2:3) integral.>So it must be 6 | p+1 since 6
coprime to p & p+2 (primes > 3).>Finally then 12|2(p+1) = p +
p+2.More simply: Among any n or more consecutive integers>must
occur a multiple of n. So among p, p+1, p+2 occurs >a multiple
of 2 and 3; it must be p+1 in both cases since>p and p+2 are
primes > 3. So 6|p+1 => 12|2(p+1) = p + p+2.>Lovely.Mati Meron
| When you argue with a fool,meron@cars.uchicago.edu | chances
are he is doing just the e
=And don't forget that I've
provided access to my work at one location> where you can go
to see the mathematics that underpins so many of> these
discussions:1. The short proof of Fermat's Last Theorem 
where
you see the power> of techniques that are also used in the
paper Advanced Polynomial> Factorization.2. THE prime counting
function, or my prime counting function as I> differentiate it
from those so-called prime counting functions. At my> website
you can see the function, get a C++ program to run it, read>
some of my thoughts on it, join the group and get a Java
algorithmic> implementation, and most importantly, see the
partial differential> equation for the J function, which is a
prime suspect for the> connection between the prime
distribution and the continuous functions> like li(x) and x/ln
x.3. Join the group and you can access the pdf 'le to read my
paper> Advanced Polynomial Factorization, where a polynomial
factorization> into non-polynomial factors proves an error in
taught mathematics.I think that is speled undermines!I think
he means underlies, not undermines!Also, I think you mean
spelled, not speled!(...Starblade Riven Darksquall...)
=>
And don't forget that I've provided access to 
my work at one
location> where you can go to see the mathematics that
underpins so many of> these discussions:You have been
thoroughly discredited, James Harris. Your attempt at aproof
is a failure. It's time to take down your site as you
promised. Orhas any remaining ounce of integrity you once
possessed long sincedeparted?--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
=> I think that is speled
undermines!I think that is spelled spelled. GibI think its
spiel myself.-- New de'nition of 
irony:'Today's liberal
Democrats are like the supporters of the Third Reich of
the'30's and 
ï40's- they absolutely trusted the government to
make things right. ï-Comment made on the internet by an ardent
GW Bush supporter.>
=In sci.physics, Rasmus
Villemoes<burner+usenet@imf.au.dk><u0l7k6rz79w.fsf@imf.au.dk>:
Put up and demonstrate your claimed expertise, or shut up for
being> the dysfunctional ing imbecile that you are. Uncle
Al bets that> you don't have the balls or the brains to
perform. Are you going to> run crying to your mama, Harris?>>
Can you refer me to a proof (in the literature) that
consective primes>> whose sum is >= 12 add up to a number
divisible by 12. Is this a known>> theorem or is this an open
problem?Well, if you accept this is literature, here is a
proof:Let p be an odd prime such that p+2 is also a prime, and
assume p /=> 3.If p == 1 (mod 4) we have 2p == 2 (mod 4) and
consequently p + p+2 => 2p+2 == 0 (mod 4), that is, 4 divides
2p+2.If p == 3 (mod 4) we also have 2p == 2 (mod 4), so also
in this case> we have that 4 divides 2p+2.Now 3 does not
divide p; thus p == 1 or p == 2 (mod 3); but since p+2> is
also prime, 3 does not divide p+2, from which we may conclude
that> p == 2 (mod 3) and p+2 == 1 (mod 3); then 2p+2 == 0 (mod
3), and 3> divides the sum. Since 3 and 4 are coprime, and they
both divide 2p+2,> 34=12 divides 2p+2. QED (quite elementary,
actually)./Rasmus> Damn, you beat me to it. I need a bigger
left margin....But yeah, you must have noticed that the center
numberis always divisible by 6. ;-)-- #191,
ewill3@earthlink.netIt's still legal to go .sigless.
=In
sci.physics, Uncle
proof snipped for brevity]> Very elegant! Must I now propose
something new for Harris to be an> ineffectual jackass about,
or do you think the original challenge is> still suf'cient?
8^>)> Well, you could ask him to prove Goldbach's 
Conjecture,
ifyou're into serious sadism. :-)-- #191,
ewill3@earthlink.netIt's still legal to go
.sigless.
=Trivially false.23 + 29 = 5223,29 are consecutive
primes. 12 does notdivide 52
=| Can you refer me to a proof
(in the literature) that consective primes> | whose sum is >=
12 add up to a number divisible by 12. Is this a known> |
theorem or is this an open problem?Twin primes is a better
term than consecutive primes. 13 and 17 are> consecutive in
the sequence of primes, but of course this is not what> 
we're
talking about.Twin primes is the proper term, and so is
searchable. I gave idiotHarris the bene't of the doubt that 
he
could use Google and triviallydiscover he was being made a
fool, again. In retrospect this waswholly unjusti'ed and
silly. Harris is an irremediable cripple.-- Uncle
Alhttp://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for
children and most mammals)Quis custodiet ipsos custodes? The
Net!
=> Twin primes is the proper term, and so is
searchable. I gave idiot> Harris the bene't of the doubt that
he could use Google and trivially> discover he was being made
a fool, again. In retrospect this was> wholly unjusti'ed and
silly. Harris is an irremediable cripple.Do you have a
reference to a proof that twin primes whose sum is greater
than 12 have a sum which is divisible by 12?Bob
Kolker
=>Trivially false.23 + 29 = 5223,29 are consecutive
primes. 12 does not>divide 52_What_ is trivially false,
exactly? Go back to the top:> If one looks at pairs of
consecutive prime numbers separated by only>one non-prime
number - 41,43; 821,823; 8087,8089 etc. - one sees that>the
sum of such two primes is often divisible by 12:It's 
trivially
false that 23, 29 are consecutive primes separated byonly one
non-prime number: 23 < 24 < 25 < 29. **********David C.
Ullrich
=>> Twin primes is the proper term, and so is
searchable. I gave idiot>> Harris the bene't of the doubt 
that
he could use Google and trivially>> discover he was being made
a fool, again. In retrospect this was>> wholly unjusti'ed and
silly. Harris is an irremediable cripple.Do you have a
reference to a proof that twin primes whose sum is greater>
than 12 have a sum which is divisible by 12?> Why should
anyone wish to publish such a triviality?-- Robin Chapman,
www.maths.ex.ac.uk/~rjc/rjc.html The League of Gentlemen
=>
Twin primes is the proper term, and so is searchable. I gave
idiot> Harris the bene't of the doubt that he could use 
Google
and trivially> discover he was being made a fool, again. In
retrospect this was> wholly unjusti'ed and silly. Harris is 
an
irremediable cripple.Do you have a reference to a proof that
twin primes whose sum is greater > than 12 have a sum which is
divisible by 12?There already is a short one in this thread.
Here'sa summary of my scribbling, a slightly different
tack,that convinced me why this is true.Let p and p+2 be two
primes both >3. First of all,p + (p+2) = 2(p+1). Since p is
odd, p+1 is even and2(p+1) is a multiple of 4.What is p mod 3?
It can't be 0 (p is prime, not divisible by 3). It 
can't be 1
(because then p+2 would be equal to 0 mod 3). Soit must be 2.
Thus we have p = 2 mod 3 p+2 = 1 mod 3and p+(p+2) = (2+1) mod
3 = 0 mod 3,So p+(p+2) is divisible by both 3 and 4. - RandyWe
also have that p+(p+2) = 2(p+1). Since p
=>> Twin primes is
the proper term, and so is searchable. I gave idiot>> Harris
the bene't of the doubt that he could use Google and
trivially>> discover he was being made a fool, again. In
retrospect this was>> wholly unjusti'ed and silly. Harris is
an irremediable cripple.Do you have a reference to a proof
that twin primes whose sum is greater >than 12 have a sum
which is divisible by 12?This is trivial - also proofs have
been posted right here in thisthread.Let's see if even I can
'gure it out. Say p and p+2 are both prime,and p > 3. Then p
mod 12 must be one of 1, 5, 7, 11, as mustbe p + 2 mod 12; any
other case would imply that p (or p+2)was not prime. Since p +
2 is two more than p it follows thatp mod 12 must be 5 or 11,
and in either case p + p + 2 is divisibleby 12 (5 + 7 = 12, 11
+ 1 = 12).I didn't read the posted proofs, but I noticed 
people
saying theywere very nice. So I imagine they are more elegant
than the above...>Bob Kolker>**********David C. Ullrich
=>
Proof of FLTAh, how disappointing, I 'gured that for Free
Lunch Theorem,and guessed you'd found a way to be honored as 
a
mathematicianwhile acting with dishonor. No such luck, 
you've
just addedpoor abused Fermet to your attempts to steal what
you can't earn.xanthian.-- 
=In sci.physics, Robert J.
Kolker<bobkolker@comcast.net><dFfPa.26768$Ph3.1918@sccrnsc04>:
>> Twin primes is the proper term, and so is searchable. I
gave idiot>> Harris the bene't of the doubt that he could use
Google and trivially>> discover he was being made a fool,
again. In retrospect this was>> wholly unjusti'ed and silly.
Harris is an irremediable cripple.Do you have a reference to a
proof that twin primes whose sum is greater > than 12 have a
sum which is divisible by 12?You need a reference?Try this
one.If a prime p and its pair p+2 are around a number m =p+1,
what is m divisible by? It turns out that m has tobe divisible
by 6. This is mostly because p and p+2 areboth odd and neither
are divisible by 3; the only numberswhich satisfy both
conditions are 6n - 1 and 6n + 1, forsome positive n (unless
one of the primes is in fact 3,of course). The sum of those
numbers is 12n.QED> Bob Kolker-- #191,
ewill3@earthlink.netIt's still legal to go .sigless.
=x,y
and z are nonzero and coprime integers, p is an odd prime, and
v is avariable integer. That's just x2+y2+vz2 = x2+y2+vz2,
which might seem strange, but the point hereis to allow me to
introduce v, which I can set to any value I choose 
becauseit's
based as it is on this beginning.Whee, what fun! You can set v
to anything you want. So your proof starts with v = vfrom
which, since v = v is already an axiom, you can deduce
NOTHING!Yours,Doug Goncz, Replikon Research, Seven Corners, VA
Fair use and Usenet distribution without restriction or
feeCivil and criminal penalties for circumvention of any
embedded encryption
=| Let's see if even I can 'gure it out.
Say p and p+2 are both prime,| and p > 3. Then p mod 12 must be
one of [...]| I didn't read the posted proofs, but I noticed
people saying they| were very nice. So I imagine they are more
elegant than the above...The only real way to go is by a
congruence argument, so in a sensethey're all minor 
variations
of the e thing. It's very natural toconsider p mod 12, but I
would say that I prefer considering p mod 6Just a little bit.
p and p+2 are of the form 6n-1 and 6n+1 for thee n, so their
sum is 12n.The one approach shows that p and p+2 lie in a pair
of congruenceclasses having the property that any two numbers p
and q lying inthem add up to a multiple of 12. But if we know
q-p, in order todetermine the congruence class of p+q mod 2n,
it's enough to knowthe congruence classes of p and q only 
mod
n.I have a sense that I've often seen little forks in the 
road
inmathematical proofs which are analogous to this. Going from A
to C,one either passes through B, or passes through a slightly
weakerB' which however is still suf'cient for 
C, given A. It
seems likeoften I prefer the former argument, which in a sense
disposes ofthe original information more quickly, but not
always of course.Keith Ramsay
=if the question seems really
easy to everyone else. I wasn't sure if I haddone it right.I
know that between any two rational numbers there is an
irrational number, andthis makes sense because there are many
more irrational numbers than rationalones. However, I am
having problems understanding why there is always arational
number between any 2 irrational numbers (it seems like it
would notwork since there are more irrational numbers). 
=>
I know that between any two rational numbers there is an
irrational number, > and> this makes sense because there are
many more irrational numbers than rational> ones. However, I
am having problems understanding why there is always a>
rational number between any 2 irrational numbers (it seems
like it would not> work since there are more irrational
numbers). > The statements should be in the form of stateintg
that there is at least one rational/irrational betwen any two
reals.The complete truth is that between any two distinct
reals (rational or not) there are a countable in'nity of
rationals and an uncountable in'nity of irrationals.
=> I
know that between any two rational numbers there is an
irrational number, and> this makes sense because there are
many more irrational numbers than rational> ones. However, I
am having problems understanding why there is always a>
rational number between any 2 irrational numbers (it seems
like it would not> work since there are more irrational
numbers).> Making sense is not good enough; for example, it
makes goodsense (to me) that Euler's constant should be
irrational (afterall, most real numbers are irrational), but
so far no one has'gured out whether it is irrational or not.
What is important here is there are enough integer numbers
toget bigger than any prescribed real number. So: suppose you
give me two different real numbers (you wouldbe interested in
irrational ones); call the smaller one x andthe other y. Easy
case: If the interval (x,y) contains an integer number, weare
done. Harder case: The interval (x,y) is too short (and
tooinconveniently located) to contain an integer. But among
theintervals (2*x, 2*y), (3*x, 3*y), ..., (n*x, n*y), ...there
will be one that is longer than 1, so it will contain aninteger
number; call it m (if there are more, choose thesmallest of
them). Then for suitable n, m: n*x < m < n*yand divide by n to
squeeze m/n between x and y.(Good night, Mr. Archimedes,
wherever you are...)
=>I know that between any two rational
numbers there is an irrational number, and>this makes sense
because there are many more irrational numbers than
rational>ones. However, I am having problems understanding why
there is always a>rational number between any 2 irrational
numbers (it seems like it would not>work since there are more
irrational numbers). >It's because between any two distinct
numbers there is a 'nitedistance, and you can always 
'nd both
a rational number and anirrational number on any 'nite
interval. There are uncountably manyirrationals and countably
many rationals on EVERY 'nite interval.Here's 
one easy
construction to 'nd such a number:Consider two distinct
irrational numbers, a and b. Let b be the largerof the two.
Let N be the 'rst position in which they differ, and b_Nbe 
the
digit that b has in that position.Let c be a number which
consists of the 'rst N digits of b and thenterminates
(continues with all 0s). This number is strictly less thanb,
strictly greater than a, and is rational. - Randy
=> (Good
night, Mr. Archimedes, wherever you are...)I think it's time
some university gave Archimedes an honorary doctorate.--
=obvious..> Is my solution to this question
correct?Almost! The algebra is correct, the English needs some
help.> => QUESTION> Consider the following recurrence relation:
a(n) = a sub (n-1) + n,> with a0 = 1> Prove by induction that
a(n) = 1 + (1/2)(n)(n + 1) is a closed formed> expression for
the above recurrence relation for all nonnegative> integers
n.> => MY SOLUTION:> - Basic step: Show the statement is true
when there is only one term.> Left: A0 = 1> Right: 1 +
(1/2)(0)(0 + 1) = 1 + 0 = 1> 1 = 1> A0 = 1 + (1/2)(0)(0 + 1)>
- Inductive step:> Assume the statement is true.Oops!Usually
expressed the strong way: Assume the statement is true for all
numbers of terms up to n.Also sometimes expressed the weak way:
Assume the statement is true for some number of terms n.> Show
it is true when there are (n + 1) terms.> An+1> = An + (n +
1)> = 1 + (1/2)(n)(n + 1) + (n + 1)> = 1 + (1/2)(n + 1)(n +
2)> = 1 + (1/2)(n + 1)[(n + 1) + 1] > Since it is true for (n
+ 1) terms, it is also true for n terms.Usually
expressed:Since we have shown that it is true for (n + 1)
terms assuming it istrue for n terms, and since we have shown
that the induction has a validstarting case n = 1, then it is
true for any positive integer n.xanthian, assuming I haven't
said something stupid, of course.-- 
=Of course there are
several ways to *construct* the exponential function, but
isthere also a pure existence proof? I am very interested in
such a theorem if itexists.Peace,EJ
=>Of course there are
several ways to *construct* the exponential function, but
is>there also a pure existence proof? I am very interested in
such a theorem if it>exists.Peace,>EJ>Off the top of my head,
I would say that one of the existance proofsfor ODEs
guaarantees that y-y'=0 has a solution, and if you add
theright intial condition, you get e^x.Larry(this space
unintentially left blank .....
=Can someone give me a hint
(not solution) on the following problem. It is number 2.29 in
Rotman's Introduction to Homological Algebra.Given: g
A------>B | |f| Prove the following diagram is a pushout: | V
C g A-------->B | | | | f| f'| | | V g' V 
C-------->DWhere
D=(C /osum B)/W, W={(fa,-ga):a /in A}, f':b-->(0,b)+W and
g':c-->(c,0)+W.What do I need to prove to prove the diagram 
is
a pushout and what is the signi'cance of the set W?
=>Can
someone give me a hint (not solution) on the following
>problem. It is number 2.29 in Rotman's Introduction to
>Homological Algebra.Given:> g> A------>B> |> |>f| Prove the
following diagram is a pushout:> |> V> C g> A-------->B> | |>
| | >f| f'|> | |> V g' V> C-------->DWhere 
D=(C /osum B)/W,
W={(fa,-ga):a /in A}, f':b-->(0,b)+W and 
>g':c-->(c,0)+W.>What
do I need to prove to prove the diagram is a pushoutThe diagram
is a pushout if it satis'es the following two conditions:1.
COMMUTATIVITY: f'g = g'f (I am applying 
functions on the left,
so they should be read right-to-left; f'g means g 
'rst, then
f').2. UNIVERSAL PROPERTY: Given any K and maps b:B->K, 
c:C->K
such that bg=cf, there exists a unique map d:D->K such that
b=df' and c=dg'.> and >what is the 
signi'cance of the set
W?You can think of a pushout as a co-equalizer; you are 
'nding
thelargest object on which you can make f and g 
ïequal'. W is a
measureof how far they are on being ïequal' (not 
exactly, since
we aredealing with the dual notion, but maybe that makes some
sense toyou?). In order for f'g(a) to be equal to 
g'f(a) for
all a, you needto make sure that (f(a),0) is the e as
(0,g(a)); for them to bethe e, you need to mod out by
(f(a),-g(a)); so W is the closure ofall those identities in
Cosum B; moding out by W is the e asimposing those identities
on Cosum B.
It's not denial. I'm just very selective
about what I accept as reality. --- Calvin (Calvin and
Hobbes)
satis'es the following two conditions:1. COMMUTATIVITY: 
f'g =
g'f (I am applying functions on the left, so> they should be
read right-to-left; f'g means g 'rst, then 
f').2. UNIVERSAL
PROPERTY: Given any K and maps b:B->K, c:C->K such that>
bg=cf, there exists a unique map d:D->K such that b=df' and
really obvious. Theuniversal property is the part giving me
the most trouble. I amassuming that one must use a previously
proved universal property toobtain the one in question. I am
not seeing how to construct or provethe existence of such a
map d:D->K, for any K. I don't mind if youspoil the problem
now, unless you think you can give me a
suitablehint.Chris
it satis'es the following two conditions: 1.
COMMUTATIVITY: f'g = g'f (I am applying 
functions on the left,
so>> they should be read right-to-left; f'g means g 
'rst, then
f'). 2. UNIVERSAL PROPERTY: Given any K and maps b:B->K,
c:C->K such that>> bg=cf, there exists a unique map d:D->K
the
commutativity. That part was really obvious. The>universal
property is the part giving me the most trouble. I am>assuming
that one must use a previously proved universal property
to>obtain the one in question. I am not seeing how to
construct or prove>the existence of such a map d:D->K, for any
K. I don't mind if you>spoil the problem now, unless you 
think
you can give me a suitable>hint.I don't follow what you 
mean.
Assume you have an object K, and mapsb:B->K and c:C->K such
that bg = cf. f A ---> C | | g | | g' | | V V B ----> D 
f'We
know that D is de'ned as (Boplus C)/W; so to 
de'ne a map from
Dto K, we can de'ne a map from Boplus C to K whose kernel
contains W,and factor it through the quotient. f' and 
g' are
the obviousinclusions, and W is the subgroup generated by
allpairs (g(a),-f(a)) for a in A.So let's consider what the 
d
HAS to be. First, we want b=df' andc=dg'. So 
given any x in B,
we know what b(x) is (we are GIVEN themaps b and c); and we
know that f'(x) = (x,0) in Boplus C. So we map(x,0) to
b(x).Likewise, we will need to map (0,y) to c(y) for all y in
C.That means that we need to map an element (x,y) in Boplus C
tob(x)+c(y).That de'nes a map, call it e: B oplus C -> K.Now
we need to verify that e factors through the quotient D, that
is,that W is contained in the kernel of e.So let's take an
element of W, which is of the form (g(a),-f(a)) for ain A.
According to the de'nition of e, we mape(g(a),-f(a)) =
b(g(a))+c(-f(a)) = b(g(a)) - c(f(a)) = bg(a) - cf(a).But we
are assuming futher that b and c are such that bg=cf;
sobg(a)-cf(a)=0 for all a in A. Therefore, e takes W to 0, and
so W iscontained in the kernel of e.Therefore, e factors
through the quotient p:Boplus C -> (Boplus C)/W = D.So de'ne 
d
to be the unique map from (Boplus C)/W to K such that
commutativity condition, b=df' and 
c=dg'.Moreover, since the
de'nition of e was forced by the commutativity ofthe diagram,
the choice of d is also forced, so that d is the onlyfunction
that will 't in that diagram. Thus, d is unique.In general,
when you have a universal construction, IF you have
an->explicit<- construction of the object, then the universal
propertyis easy to verify, because you will have no choice
about how to de'nethe map in question. it should be obvious
what the map has to be inan object.
It's not denial. I'm
just very selective about what I accept as reality. --- Calvin
(Calvin and Hobbes)
to this question, which has
been driving me a bit nuts. Some quickbackground: as a
role-player, I use a lot of dice. At times, therules call for
one to roll multiple dice (say, 've six-sided dice, or5d6),
then to drop the lowest two and total the other three.
Thebasic question is: is there a formula for determining the
probabilityof rolling a certain result, given these
conditions?Determining the probability of a particular outcome
when just rollingmultiple dice is relatively straightforward
(there's a briefdiscussion here:
http://mathforum.org/library/drmath/view/52207.html). I can
'nd a pattern to the summation needed when dropping a
singledie from a set; but once I try to remove two dice from
the set, thepattern disappears and I 'nd myself lost again.
(The numbers can bedetermined by brute force, of course, but
that's neither practical norinteresting.)So, I guess the 
base
question is: Is there a formula for calculatingthe probability
of achieving a result R on n dice with d sides,dropping the k
lowest dice?
=Background...An exponent function ful'lls an
equation:f(A+B)=f(A)*f(B)For example:a^(A+B)=(a^A)*(a^B)A
logarithmic function ful'lls an equationf(A*B)=f(A)+f(B)For
example: log(A*B)=log(A)+log(B)Question: What is the name of
the following function that ful'llsf(A)*f(B)=f(A)+f(B)
orf(A)*f(B)=f(A*B)For example:ln(A)*ln(B)=ln(A)+ln(B) or
ln(A)*ln(B)=ln(A*B)(This kind of function indeed exists, if
you (xy)-plot a hyperbola in adouble logarithmic cartesian
co-ordination (ln(x), ln(y)As You know the hyperbola is the
product of asymptotes).Hopefully someone
knows....Tapio
=>Background...>An exponent function ful'lls
an equation:>f(A+B)=f(A)*f(B)>For
example:>a^(A+B)=(a^A)*(a^B)A logarithmic function ful'lls an
equation>f(A*B)=f(A)+f(B)>For example:
log(A*B)=log(A)+log(B)Question: What is the name of the
following function that ful'lls>f(A)*f(B)=f(A)+f(B) 
orI'd call
it either 0 or 2.>f(A)*f(B)=f(A*B)This might be called a
multiplicative function, or a homomorphism ofthe group R{0}
under multiplication.>For example:>ln(A)*ln(B)=ln(A)+ln(B) or
ln(A)*ln(B)=ln(A*B)?????!Robert Israel
israel@math.ubc.caDepartment of Mathematics
http://www.math.ubc.ca/~israel University of British Columbia
Vancouver, BC, Canada V6T 1Z2
=> Background...> An exponent
function ful'lls an equation:> f(A+B)=f(A)*f(B)> For 
example:>
a^(A+B)=(a^A)*(a^B) A logarithmic function ful'lls an 
equation>
f(A*B)=f(A)+f(B)> For example: log(A*B)=log(A)+log(B) Question:
What is the name of the following function that ful'lls>
f(A)*f(B)=f(A)+f(B) orf(a)^2 = 2f(a)f(a)(f(a)-2) = 0if some a
with f(a) = 0, then for all b, f(b) = f(a) + f(b) = f(a)f(b) =
0otherwise for all a, f(a) /= 0, hence f(a) = 2.>
f(A)*f(B)=f(A*B)>Exponentation a^n b^n =
(ab)^n
=>Background...>An exponent function ful'lls an
equation:>f(A+B)=f(A)*f(B)>For example:>a^(A+B)=(a^A)*(a^B)A logarithmic function ful'lls an
equation>f(A*B)=f(A)+f(B)>For example: log(A*B)=log(A)+log(B)Question: What is the name of the following function that
ful'lls>f(A)*f(B)=f(A)+f(B) or I'd call it 
either 0 or 2.
>f(A)*f(B)=f(A*B) This might be called a multiplicative
function, or a homomorphism of> the group R{0} under
multiplication. >For example:>ln(A)*ln(B)=ln(A)+ln(B) or
ln(A)*ln(B)=ln(A*B) ?????!Ah, how to get those
equations?hyperbola in adouble logarithmic cartesian
co-ordination (ln(x), ln(y)As You know the hyperbola is the
product of asymptotes).I start with two asymptotes of a
hyperbola that goes through origo indouble logarithmic
cartesian co-ordination:ln(g) = kln(a)-t andln(g) =
-qln(a)-swhere st>0 and -q and k are slopes.The equation of
the hyperbola is the product of the asymptotes, like
this(-qln(a)-ln(g)-s)(kln(a)-ln(g)-t)=st=>
(ln((a^(-q))/g)-s)(ln((a^(k))/g)-t)=stlhs is expanded by
multiplication=> (ln((a^(-q))/g))(ln((a^(k))/g))
-t(ln((a^(-q))/g))-s(ln((a^(k))/g))+st=stAfter elimination of
st and after rearrangement=>
(ln((a^(-q))/g))(ln((a^(k))/g))=t(ln((a^(-q))/g))+s(ln((a^(k))
/g))Dividing both sides by st and collecting and grouping s
and t on lhs=> ((ln((a^(-q))/g))/s)((ln((a^(k))/g))/t)
=Equation 1((ln((a^(-q))/g))/s)+((ln((a^(k))/g))/t)the
coef'cients 1/s and 1/t before ln() can be used as exponents
like doneearlier with slopes (above):((a^(-q))/g)^(1/s) = A
and ((a^(k))/g)^(1/t) =B and it
follows:ln(A)*ln(B)=ln(A)+ln(B) or ln(A)*ln(B)=ln(A*B) or
1=(1/ln(A)) +1/(ln(B))Done,assuming there is no error.Clearly
A=xB, but substitution does not help to reduce the equation.
Neithere^lhs=e^rhs.I confess I'm blind to see simple 
solution
for (a/g)=f(q,k,s,t).Of course, I can solve ln(g), but 
that's
a standard solution, which has nocommon interest.Any help to
develop Equation 1 further?Tapio> Robert Israel
israel@math.ubc.ca> Department of Mathematics
http://www.math.ubc.ca/~israel> University of British
Columbia> Vancouver, BC, Canada V6T 1Z2
= > Background...>
An exponent function ful'lls an equation:> f(A+B)=f(A)*f(B)>
For example:> a^(A+B)=(a^A)*(a^B)> A logarithmic function
ful'lls an equation> f(A*B)=f(A)+f(B)> For example:
log(A*B)=log(A)+log(B)> Question: What is the name of the
following function that ful'lls> f(A)*f(B)=f(A)+f(B) or 
f(a)^2
= 2f(a)> f(a)(f(a)-2) = 0> if some a with f(a) = 0,> then for
all b, f(b) = f(a) + f(b) = f(a)f(b) = 0> otherwise for all a,
f(a) /= 0, hence f(a) = 2.Yes, You are right. My Q was badly
formulated - sorry!But, starting from the product of two
asymptotes ( a hyperbola) in thedouble logarithmic
coordination system, then f(A) is not constant
2.(2*2=2+2)Please - refer my other post today. The hyperbola
goes through the origo. Itis true for some a , f(a)=0 , namely
as a=1 and g=1 (refer my post today)when the point of the
hyperbola is the origo.> f(A)*f(B)=f(A*B)> Exponentation> a^n
b^n = (ab)^nYou are right again, but I'm too blind to apply
Your result in theasymptote problem.Do You see more clear? Can
You help me?Tapio
=> Background...> An exponent function
ful'lls an equation:> f(A+B)=f(A)*f(B)> For example:>
a^(A+B)=(a^A)*(a^B)A logarithmic function ful'lls an 
equation>
f(A*B)=f(A)+f(B)> For example: log(A*B)=log(A)+log(B)Question:
What is the name of the following function that ful'lls>
f(A)*f(B)=f(A)+f(B) or> f(A)*f(B)=f(A*B)For example:>
ln(A)*ln(B)=ln(A)+ln(B) or ln(A)*ln(B)=ln(A*B)Are you claiming
that this is true when ln representsthe natural log, for
arbitrary A and B?For instance, are you claiming that
ln(2)*ln(3) = ln(2)+ln(3)and thatln(2)*ln(3) = ln(2*3)??? -
Randy
=> Background...> An exponent function ful'lls an
equation:> f(A+B)=f(A)*f(B)> For example:>
a^(A+B)=(a^A)*(a^B)> A logarithmic function ful'lls an
equation> f(A*B)=f(A)+f(B)> For example:
log(A*B)=log(A)+log(B)> Question: What is the name of the
following function that ful'lls> f(A)*f(B)=f(A)+f(B) or>
f(A)*f(B)=f(A*B)> For example:> ln(A)*ln(B)=ln(A)+ln(B) or
ln(A)*ln(B)=ln(A*B) Are you claiming that this is true when ln
Randy,The background of my Q was presented today more
precisely in my reply toprof. Robert Israel. (See the thread).
The equation was derived consideringa hyperbola (with two
asymptotes) in the double logarithmic cartesianco-ordination
system.Here is a link into the similar
problem.http://www.ica1.uni-stuttgart.de/Recent_publications/
Papers/frank/PRE16115.pdfLook at the plots and recognize the
hyperbola!Maybe I have done a failure, maybe I'm blind, but
I'm still tackling withthe 'nal solution.If You 
can give any
help, it's welcome!Tapio For instance, are you claiming that
ln(2)*ln(3) = ln(2)+ln(3) and that ln(2)*ln(3) = ln(2*3)??? -
Randy
=>ln(A)*ln(B)=ln(A)+ln(B) or ln(A)*ln(B)=ln(A*B)>>
?????!>Any help to develop Equation 1 further?The measurable
functions f:(0,in'nity) -> R such that f(A)*f(B) = f(A*B) are
f(x) = x^c for real constants c.Robert Israel
israel@math.ubc.caDepartment of Mathematics
http://www.math.ubc.ca/~israel University of British Columbia
Vancouver, BC, Canada V6T 1Z2
=>The measurable functions
f:(0,in'nity) -> R such that f(A)*f(B) = f(A*B) >are f(x) =
x^c for real constants c.And for f:R -> R, it would be f(0) =
0,f(x) = |x|^c otherwise; or f(0) = 0,f(x) = (sgn x) |x|^c
otherwise; or f(x) = 1 for all x.Robert Israel
israel@math.ubc.caDepartment of Mathematics
http://www.math.ubc.ca/~israel University of British Columbia
Vancouver, BC, Canada V6T 1Z2
= For example:>
ln(A)*ln(B)=ln(A)+ln(B) or ln(A)*ln(B)=ln(A*B)>> Are you
claiming that this is true when ln represents>> the natural
was presented today more precisely in my reply to>prof. Robert
Israel. (See the thread).I posted my question after skimming
through that reply.> The equation was derived considering>a
hyperbola (with two asymptotes) in the double logarithmic
cartesian>co-ordination system.I'm not asking about the
derivation. I'm asking about what it is youclaim to have
proved. Are you saying that the above equations hold forthe
natural logarithm, for arbitrary A and B? - Randy
= > For
example:> ln(A)*ln(B)=ln(A)+ln(B) or ln(A)*ln(B)=ln(A*B)>> Are
you claiming that this is true when ln represents>> the natural
my Q was presented today more precisely in my reply to>prof.
Robert Israel. (See the thread). I posted my question after
skimming through that reply. > The equation was derived
considering>a hyperbola (with two asymptotes) in the double
logarithmic cartesian>co-ordination system. I'm not asking
about the derivation. I'm asking about what it is you> claim
to have proved. Are you saying that the above equations hold
for> the natural logarithm, for arbitrary A and B?Considering
the terms of the derivation from hyperbola and assuming there
isno errors, then the equation should hold for A and B, but
you have torecognize that A is a function of B (or vice versa)
as derived in my earliermessage:((a^(-q))/g)^(1/s) = A and
((a^(k))/g)^(1/t) =BAt least, it was fun to notice after
derivation such a strange andunexpectable equation.At the 
'rst
glance, it should not be valid at all.Therefore, I still
consider an error. There are few reasons:1) a and g are
variables, but plot ln(a) against ln(g) makes hyperbola
andtherefore f(a)=b or vice versa.2) slopes (-q and k) and
constants (s and t) can be - in principle - anyreals, which
gives too many possibilities to choose them for arbitrary A
andB, which results in impossible answers. As we can choose
slopes andconstants quite freely, they nail ln(a) and ln(g).I
assume or guess, but I do not know, that iff the equation
could be true,then there should be some more simple relation
or function between slopesand constants and a and g.As said
earlier, I still consider an error - too.Tapio> - Randy>
= >
For example:>> ln(A)*ln(B)=ln(A)+ln(B) or ln(A)*ln(B)=ln(A*B)>>
Are you claiming that this is true when ln represents> the
background of my Q was presented today more precisely in my
replyto>>prof. Robert Israel. (See the thread).> I posted my
question after skimming through that reply.> The equation was
derived considering>>a hyperbola (with two asymptotes) in the
double logarithmic cartesian>>co-ordination system.> I'm not
asking about the derivation. I'm asking about what it is 
you>
claim to have proved. Are you saying that the above equations
hold for> the natural logarithm, for arbitrary A and B?Some
additional ideas to consider:The double logarithmic plotting
that results in conic sections has generalinterest.Why?
Physical phenomena are based on differential equations that
havesolutions of harmonic oscillations, i.e wave equations.
For example: anoverdamped harmonic oscillator has phase-space
plot that is hyperbola. Onthe other hand, the real exponents
can be sometimes considered as fractaldimensions, which can
indicate the packing density etc. As may physicalphenomena are
exponential, it does not mean that a line in log-plot is
theonly solution. It's even expectable that also conic
sections appear in thedouble logarithmic plotting of
data.Tapio
=I'm trying to 'nd the name for the following
property of a matrixnorm.We have matrix norm |.| over the
reals. Norm |.| has the aboveproperty, if for every pair of
matrices A,B with nonnegativecoef'cients, |A+B| >= |A|. Also,
does anyone know of matrix normsthat don't have this
property?Karl Hallowell
=>I'm trying to 'nd the name for the
following property of a matrix>norm.I don't know of a name 
for
it.>We have matrix norm |.| over the reals. Norm |.| has the
above>property, if for every pair of matrices A,B with
nonnegative>coef'cients, |A+B| >= |A|. Also, does anyone know
of matrix norms>that don't have this property?If |.|_1 is 
one
matrix norm and U is any invertible matrix, you canget another
matrix norm by |A|_2 = |U A U^(-1)|_1. Take |.|_1 to beany
matrix norm satisfying your property, [ 1 1 ] [ 1 0 ] [ 0 b ]
[ 1 1-b ]U = [ 0 -1 ], A = [ 0 0 ], B = [ 0 0 ], U (A+B)
U^(-1) = [ 0 0 ].Thus if 0 < b < 1, |A+B|_2 <= |A|_2 (and in
most cases the inequalitywill be strict). Robert Israel
israel@math.ubc.caDepartment of Mathematics
http://www.math.ubc.ca/~israel University of British Columbia
Vancouver, BC, Canada V6T 1Z2
=>I'm trying to 'nd the name
for the following property of a matrix>norm.I don't know of 
a
name for it.Too bad. Guess I'll look around some more.>We 
have
matrix norm |.| over the reals. Norm |.| has the
above>property, if for every pair of matrices A,B with
nonnegative>coef'cients, |A+B| >= |A|. Also, does anyone know
of matrix norms>that don't have this property?If |.|_1 is 
one
matrix norm and U is any invertible matrix, you can> get
another matrix norm by |A|_2 = |U A U^(-1)|_1. Take |.|_1 to
be> any matrix norm satisfying your property, > [ 1 1 ] [ 1 0
] [ 0 b ] [ 1 1-b ]> U = [ 0 -1 ], A = [ 0 0 ], B = [ 0 0 ], U
(A+B) U^(-1) = [ 0 0 ].> Thus if 0 < b < 1, |A+B|_2 <= |A|_2
(and in most cases the inequality> will be strict). looked at
these norms is that I was trying to 'nd convexity resultsfor
matrices with nonnegative coef'cients that were convex
upfunctions of some parameter. Eg, let matrix A(x) with
parameter xbelonging to some real interval have nonnegative
coef'cients thatare all convex up functions in x. Then |A(x)|
is a convex up functionof x, if |.| satis'es the above
property.The most interesting case is the operator two norm
over squarematrices which is the absolute value of the largest
eigenvalue of thematrix. In the case where the matrix has
nonnegative coef'cients thenby one of the variants of the
Perron-Frobenious Theorem we know thatthere is a largest
eigenvalue which is equal to the operator two norm.Hence, for
A(x) de'ned as above, the largest nonnegative eigenvalueis a
convex up function of x.The trace of A(x) is also a convex up
function of x.Karl Hallowell
=I place a quarter (coin) on
the table. Exactly how many quarters can I putaround this
centered quarter?
=I place a quarter (coin) on the table.
Exactly how many quarters can I put> around this centered
quarter?Six. Think honeycomb.--
Ioannishttp://users.forthnet.gr/ath/jgal/___Eventually,
_everything_ is understandable.
=> I place a quarter (coin)
on the table. Exactly how many quarters can I put> around this
centered quarter?De'ne put.
=>I place a quarter (coin) on the
table. Exactly how many quarters can I put>around this centered
quarter?That depends, of course, on the size of the table.
:-)-- Stan Brown, Oak Road Systems, Cortland County, New York,
USA http://OakRoadSystems.com/You 'nd yourself amusing,
Blackadder.I try not to §y in the face of public
opinion.
=>>I place a quarter (coin) on the table. Exactly
how many quarters can I put>>around this centered quarter?>
That depends, of course, on the size of the table. :-)It also
depends on the de'nition of around. If we consider it ina
three-dimensional sense and place nolimits on distance, then
everyquarter on Earth is around it.And since quarter isn't
de'ned, we could take it to mean one-fourthof anything, which
raises the total a bit higher... :-)-- rs, Silverlock
=hi
all,I am actually trying to understand this mathematical
notion that is soweird to me (I am far from being a god at
maths...).could someone drop the light onto the following for
me ?We will compute a rotation about the unit vector, u by an
angle . Thequaternion that computes this rotation is q = (s,v)
s = cos(teta/2) v = u * sin(teta/2)We will represent a point p
in space by the quaternion P=(0,p) Wecompute the desired
rotation of that point by this formula: P = (0,p) Protated =
qPq^-1The 'rst thing I don't understand at all 
here is where
the s and vvalues come from ?!? It might sound stupid but I
don't understandthis.Any help ?thanx
=hi all,I am actually
trying to understand this mathematical notion that is soweird
to me (I am far from being a god at maths...).could someone
drop the light onto the following for me ?We will compute a
rotation about the unit vector, u by an angle . Thequaternion
that computes this rotation is q = (s,v) s = cos(teta/2) v = u
* sin(teta/2)We will represent a point p in space by the
quaternion P=(0,p) Wecompute the desired rotation of that
point by this formula: P = (0,p) Protated = qPq^-1The 'rst
thing I don't understand at all here is where the s and
vvalues come from ?!? It might sound stupid but I don't
understandthis.
=