"Plato's diamond throws new light on
finite geometry and combinatorics."
http://m759.freeservers.com
"The Diamond Theory of Truth"
http://www.math16.com/
"The Proof and the Lie"
http://log24.com/log03/1130.htm
As a punishment for unjustly criticising others and for being a
nuisance in general, Steven Cullinane has now been officially declared
a Crank:
http://www.crank.net/maths.html
Public Announcement
Crank Watch International
crankbuster wrote:
>
> "The Proof and the Lie"
> http://log24.com/log03/1130.htm
As so often happens though, if you ignore the "commentary"
he's assembled a useful set of links on elliptic curves
and modular forms!
crankbuster wrote:
[snip]
Not just dubious content, but multiposted too /sigh
If you are going to post to multiple groups (having of course checked
your message is relevant to them all), please crosspost rather than
multipost!
My reply is in alt.math.undergrad

Larry Lard
Replies to group please
Well, when I looked at your reply, on the right margin of the page,
sure enough there was another crank ad from Mr. Steven Cullinane:
Galois Geometry
Surprising symmetry properties
of the smallest Galois spaces
log24.com/theory/GalG.htm
Believe me, this guy is a nut!
> > He preaches his "advanced mathematics" from multiple domains:
> >
> > "Plato's diamond throws new light on
> > finite geometry and combinatorics."
> > http://m759.freeservers.com
>
> _Prima facie_ a collection of and association between a number of
> disparate results from group theory and combinatorics. Nothing that
> immediately appears wrong; a minimal (if that) amount of crankish
> language. Conclusion: not a crank.
O.K. suppose I take an arbitrary array of binary numbers and count its
"symmetries". I quote a huge number, say, 50!/(5!3!2!). I call this the
emerald theorem (because my array is shaped like an emerald I once saw
in a funky dream). Worse, I quote G.H. Hardy, Walt Whitman, T.S. Eliot,
and whatever else comes to mind. I call this "collection of and
association between disparate results"  "Emerald Theory". Then I pay
Google to advertise my site on every page that has matching keywords. I
would be a Crank.
No, Sir you are too kind. Steven Cullinane is a crank of the worse
kind. If he were just doing this much we could just pity the guy and
ignore him. But unfortunately, he thinks he can trash *other*
mathematicians and get away with it!
> >
> > "The Diamond Theory of Truth"
> > http://www.math16.com/
>
> I am hesitant to comment too deeply on philosophical matters, because I
> find it hard to tell apart what is counted legitimate discourse, and
> what is labelled crankish. I will only say that there appears to be
> nothing here that would be out of place in a philosophy textbook.
> Indeed, most of the test on this page is quotation! Conclusion: A
> philosopher. They're either all cranks, or none.
Why so many different domains to spread the same gibberish? Methinks he
spams Google PageRank...
> >
> > "The Proof and the Lie"
> > http://log24.com/log03/1130.htm
>
> The most interesting link you give. This is the one linked to from
> crank.net (see below); when that link was first added, I gave this page
> a look, which I have quickly done again now; nothing major seems to
> have changed.
>
> The thesis of this page is simple:
> Accounts of Wiles' proof of Fermat's Last Theorem (which was done by
> proving (one particular case of) the TaniyamaShimura Conjecture) have
> all stated that the connection TSC makes between elliptic curves (EC)
> and modular forms (MF) is a surprising, unexpected, or (in particular)
> NEW connection to make. This statement is however wrong  connections
> between these two domains were already well and widely known prior to
> Wiles' result.
>
> The adduced evidence seems to provide a cogent argument.
>
> The mistake (imo) the page makes is in the language and tone
> surrounding its thesis  this incorrect assertion (that EC and MF were
> thought completely unrelated) is technically *not* a 'mathematical
> lie', it's more of an error of storytelling; and using such hyperbolic
> language over what is, at heart, a minor issue doesn't inspire
> confidence in the reader.
>
> Conclusion: Eccentric, but not a crank.
Fair enough, but what makes one squirm is the vehemence with which the
page is written and agressively advertised on Google. It's as if you
make a small social error and you are shouted at, beaten up and
murdered. This guy is jealous of the Harvard/Princeton mathematicians.
I'll bet they ignored his "Diamond Theory" so he is taking his
"revenge". Unfortunately for Mr. Steven Cullinane, it backfired on him
and he got listed on crank.net!
> >
> > As a punishment for unjustly criticizing others and for being a nuisance in general, Steven Cullinane has now been officially declared a Crank:
> > http://www.crank.net/maths.html
>
>  The very page you cite shows that the link to one Cullinane's of
> webpages was added on 26 Feb *2004*. It is surely stretching the bounds
> of 'now' to use that word in connection with this listing.
I beg your pardon! I should have said that Mr. Steven Cullinane was
designated a Crank on the 26th of February, 2004.
>  crank.net is in no way about 'punishment' for 'unjust criticism' or
> general nuisance. It's a collection of links. And there's nothing in
> any way 'official' about it.
Yes, crank.net is too good for Mr. Steven Cullinane! This guy should be
locked up in gitmo!
>  In fact given my argument above, he probably shouldn't be listed at
> crank.net at all!
No, he certainly should be, more often!
> >
> > Public Announcement
> > Crank Watch International
>
> Interesting way to debut on Usenet, I must say.
Never heard of you either!!
> 
> Larry Lard
> Replies to group please
Julie
for
Crank Watch International
Reference your dubious website:
http://m759.freeservers.com/
"The Diamond Theorem:
Inscribe a white diamond in a black square. Split the resulting figure
along its vertical and horizontal midlines into four quadrants so that
each quadrant is a square divided by one of its diagonals into a black
half and a white half. Call the resulting figure D.
Let G be the group of 24 transformations of D obtained by randomly
permuting (without rotating) the four quadrants of D. Let S4 denote the
symmetric group acting on four elements. Then
(1) Every Gimage of D has some ordinary or colorinterchange symmetry,
(2) G is an affine group generated by S4 actions on parts of D, and
(3) Results (1) and (2) generalize, through intermediate stages, to
symmetry invariance under a group of approximately 1.3 trillion
transformations generated by S4 actions on parts of a 4x4x4 cube."
What does (2) mean? By Cullinane's definition of G, G is isomorphic to
S4, the symmetric group on 4 letters, with 24 elements. What does he
mean by saying G is generated by S4 actions? Every group generates
itself as its own subgroup! This is a theorem?
What does (3) mean? Generalize how? What is "approximately 1.3
trillion"? What "parts" of a 4x4x4 cube? Who is Cullinane trying to
fool?
See the "4x4 Case" following the "theorem". Cullinane states that "G is
a group of 322,560 permutations". Where does this number come from?
Going by his own definition, if 4x4=16 objects are to be permuted (this
is the only way to "generalize" his "theorem") then G should be
isomorphic to S16, the symmetric group on 16 letters, with
16!=20922789888000 elements. Why 322560? Huh?
No, Sir you are not a crank but a moron.
Andrew
for
Crank Watch International
crankbuster wrote:
>
> [...]
>
> Andrew
> for
> Crank Watch International
Can we assume you're Andrew during the week, and Julie
at the weekends (5th July for example)?
crankbuster wrote:
> No, Sir you are not a crank but a moron.
Lunatic would be more appropriate!
john_r...@sagittaps.com wrote:
{...}
> Can we assume you're Andrew during the week, and Julie
> at the weekends (5th July for example)?
And Barry. You missed Barry. Down with Cranks!
The statement of the socalled "Diamond Theorem" is trivial, almost a
mere tautology, disguised by some unnecessary terminology about affine
geometry seemingly designed to fool the reader. Obviously, if you take
4 objects and permute them randomly, the total number of permutations
is 4!=24 and the group of permutations is S4. Now, if each of the
permuted objects has some geometrical symmetry, then these resulting
permutations will display symmetries too. Depending on what you start
with, you can always count the symmetries. So does this qualify as a
theorem? Why not start with a pentagonal shape, a hexagonal shape etc.,
colored with 1 or 2 or 3 etc. colors? You can obtain infinitely many
"theorems". That's ridiculous!
> On closer scrutiny, I do find Steven Cullinane's site
> cranky:
Know what I find bizarre (if not cranky)? People adopting aliases
like "crankbuster" and complaining on newsgroups about the crankiness
of people utterly unaffiliated with the group.
I'm also a bit suspect when firsttime posters pop up to agree with
them.
I don't know about other sci.math regulars, but I don't really care
about Steven Cullinane or your opinions regarding him. But good luck
attracting that groundswell of moral and mathematical outrage.

Jesse F. Hughes
"The three principal virtues of a programmer are Laziness, Impatience, and
Hubris." Larry Wall in the Perl5 Manpages
Jesse F. Hughes wrote:
> "Bob Stewart" <bobstew...@hotmail.com> writes:
>
> > On closer scrutiny, I do find Steven Cullinane's site
> > cranky:
>
> Know what I find bizarre (if not cranky)? People adopting aliases
> like "crankbuster" and complaining on newsgroups about the crankiness
> of people utterly unaffiliated with the group.
I think "crankbuster" serves a useful purpose. It is necessary to
expose fraudsters like Cullinane. I found Cullinane's attack on Barry
Mazur and Andrew Wiles particularly disgusting. Especially because such
attacks do not allow the accused any opportunity of defending
themselves. Not that Mazur and Wiles would condescend to defend
themselves against a crank. But how would you feel if you found a paid
advertisement attacking your work (I am assuming you are a
mathematician)?
> I'm also a bit suspect when firsttime posters pop up to agree with
> them.
Do you consider yourself to be superior to make judgements like that?
You have not even bothered to comment upon any of the mathematical
fraud that Cullinane is trying to perpetrate.
> I don't know about other sci.math regulars, but I don't really care
> about Steven Cullinane or your opinions regarding him.
Do you regularly write comments devoid of mathematical content to
math.sci? Is that why you are a regular? I am glad though that you dont
care about Steven Cullinane.
> But good luck
> attracting that groundswell of moral and mathematical outrage.
Cry Havoc and let loose the Dogs of War
Your statement that "if each of the permuted objects has some geometrical symmetry, then these resulting permutations will display symmetries too" is false, as you would know if you had tried to find a counterexample... Such as (for instance) the four diffent square patterns obtained by division of a square into black and white halves by horizontal or vertical (rather than diagonal) midlines.
As for affine geometry, see
http://log24.com/theory/geometry.html.
This site contains an explanation, written for those with some mathematical maturity, of the role played by the affine group AGL(4,2) in the geometry of the 4x4 square.
That group, by the way, is where the number 322,560, quoted by the deeply confused "crankbuster," comes from.
> Jesse F. Hughes wrote:
>
>> I'm also a bit suspect when firsttime posters pop up to agree with
>> them.
>
> Do you consider yourself to be superior to make judgements like
> that?
Why would that convey superiority?
> You have not even bothered to comment upon any of the mathematical
> fraud that Cullinane is trying to perpetrate.
Because I haven't read any of his writings and don't give a damn about
him.
If he can't write like James S. Harris, why should I care about him or
your opinions about him?
>> I don't know about other sci.math regulars, but I don't really care
>> about Steven Cullinane or your opinions regarding him.
>
> Do you regularly write comments devoid of mathematical content to
> math.sci?
sci.math, but you betcha.
> Is that why you are a regular? I am glad though that you dont care
> about Steven Cullinane.
>
>> But good luck
>> attracting that groundswell of moral and mathematical outrage.
>
> Cry Havoc and let loose the Dogs of War
Kinda curious that someone who has never posted on Usenet before has
come over all passionate about Cullinane and so quick to defend
crankbuster's judgment, don'tcha think?
From a throwaway hotmail account, no less.
I don't know about Cullinane, but I know nuts when I sees 'em.

Jesse F. Hughes
"Truth is common stuff, ready to your hand, but lies you have to make
yourself, and you can't be sure they are any good until you've
used them  and then it's too late." John Steinbeck
I think you know "crankbuster" quite well. Posting on occasion from the
same IP.

dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
by the way, have you ever thought much about the affine geometry
ag(2,2) and its symmetry group agl(2,2)? (i'm at least halfway trying
to use your own notation here.)

[email address jdo...@math.ucr.edu]
Steven H. Cullinane wrote:
> On the off chance that "Bob Stewart" is not "crankbuster" under another name, here is a reply:
You are paranoid!
> Your statement that "if each of the permuted objects has some geometrical symmetry, >then these resulting permutations will display symmetries too" is false,
What an idiot you are! If I arranged 16 identical objects in a 4X4
array and let the symmetric group S16 act on them then I would have 16!
"symmetries".
>as you would know if you had tried to find a counterexample... Such as (for instance) >the four diffent square patterns obtained by division of a square into black and white >halves by horizontal or vertical (rather than diagonal) midlines.
Why horizontal and vertical lines? Surely there are other shapes
possible. And more colors than just two. There are lots of examples
other than the one you have that would display symmetries. Silly!
> As for affine geometry, see
> http://log24.com/theory/geometry.html.
>
> This site contains an explanation, written for those with some mathematical maturity, of the role played by the affine group AGL(4,2) in the geometry of the 4x4 square.
There does not seem to be any natural association of AGL(4,2) with the
4X4 array. Why not just take any set with 16 elements? And by the way,
what does this have to do with T.S. Elliot's "Four Quartets"?! Yeah
right, the affine geometry of free verse! Crank!!
> That group, by the way, is where the number 322,560, quoted by the deeply confused "crankbuster," comes from.
No, it is you who are confused. The question was, why do you restrict
the complete symmetric group S16 to just this subgroup? In the 2X2 case
you take the complete symmetric group S4. Then you claim that the 4X4
case is a "generalization". Why a smaller group? Just to get the result
you want. You dont fool anyone! You dont have any generalization of
your silly trivial "Diamond Theorem". What about the nxn array? Why not
state the theorem for the nxn array? Because you cant! You have no idea
of how many elements the group will have because you have not defined
it!
Bob
The answer to your question is "yes."
As for the notation, a Google search on "AGL(n,q)" should convince you that it is standard, and not my own invention.
Don't feel bad. Your bafflement at standard grouptheoretic notation was shared by the brilliant John Baez. See his sci.math post of March 29, 1993, on "Symplectic structures on finite groups"
"I don't understand the 'AGL' business...."
> Steven H. Cullinane wrote:
>> On the off chance that "Bob Stewart" is not "crankbuster" under
>> another name, here is a reply:
>
> You are paranoid!
Well, it is surely curious that both "Bob Stewart" and "crankbuster"
post from touchtelindia.net IP addresses and that neither have posted
to Usenet prior to this Cullinane nonsense.
What remarkable coincidences!
Whether Cullinane is a crank or not, you people is nuts.

Jesse F. Hughes
"Such behaviour is exclusively confined to functions invented by
mathematicians for the sake of causing trouble."
Albert Eagle's _A Practical Treatise on Fourier's Theorem_
perhaps you were baffled by the meaning of the phrase "your own
notation"? i wasn't suggesting that you invented the notation or that
it isn't a standard notation in some community, rather just commenting
on the fact that i myself don't ordinarily use it, having dozens of
other notations to use in its place, of some degree of standardness in
some community.
my current favorite way of thinking about the homomorphism 4! > 3! is
as the "line at infinity in the projective completion" functor from
affine planes to projective lines over the field z/2.

[email address jdo...@math.ucr.edu]
> my current favorite way of thinking about the homomorphism 4! > 3! is
> as the "line at infinity in the projective completion" functor from
> affine planes to projective lines over the field z/2.
Er.. Do 3!, 4! mean S(3), S(4)?
If so, you have only saved two rightbrackets.

Timothy Murphy
email (<80k only): tim /at/ birdsnest.maths.tcd.ie
tel: +353862336090, +35312842366
smail: School of Mathematics, Trinity College, Dublin 2, Ireland
Jesse F. Hughes wrote:
> "Bob Stewart" <bobstew...@hotmail.com> writes:
>
> > Steven H. Cullinane wrote:
> >> On the off chance that "Bob Stewart" is not "crankbuster" under
> >> another name, here is a reply:
> >
> > You are paranoid!
>
> Well, it is surely curious that both "Bob Stewart" and "crankbuster"
> post from touchtelindia.net IP addresses and that neither have posted
> to Usenet prior to this Cullinane nonsense.
Dude, in case you didn't know, there are lots of Americans in India.
When your job is outsourced, you follow the job! Not a bad place,
democratic, quite a tech hub. Almost everybody here uses either
touchtel or reliance, each of which are vast networks (much like
comcast or aol back home).
> What remarkable coincidences!
Not really, billions of people using hotspots in a global network.
> Whether Cullinane is a crank or not, you people is nuts.
Who is "you people"? Do I know you? Have you seen Cullinane's cranky
website? Why are you writing in this thread?
The question is, what do you mean by "genralization" in the statement
of your "Diamond Theorem". As stated, your "Theorem" makes no sense and
is a trivial tautology at best. Given an nxn array, how exactly is the
associated group defined? The theorem is not accompanied by a proof
(obviously, because you cannot prove something that is not even
defined!). You give a 2X2 case and a 4x4 case. There is no connection
between how the associated group is defined in the two cases. What
about a 3x3 case? Must n be even? If so, what about the general 2nx2n
array? Can you define an associated AGL(n,q) in the general case. Of
course, for your "Diamond Theorem" to actually be a theorem, the
association with geometry must in some sense not be obvious. So far, it
seems to me, you are merely labeling the 16 elements of a 4x4 array
with a well known geometry that happens to have 16 elements. So what? I
can take any set with 16 elements and claim that association! Can you
give a coherent answer? Or do we need to continue bugging you?
Wow! a Google search on "AGL(n,q)" returns another one of your crank
websites as the top result!!
http://log24.com/notes/coord.html
"(Article intended for American Mathematical Monthly readers, written
July 1984)"
So, what happened, did the AMS reject your article because they were
not "mature" enough to understand it?
Ha! Ha! This gets better and better!
crankbuster wrote:
>
> [...]
>
> Ha! Ha! This gets better and better!
Weirder and weirder more like.
> Jesse F. Hughes wrote:
>>
>> Well, it is surely curious that both "Bob Stewart" and "crankbuster"
>> post from touchtelindia.net IP addresses and that neither have posted
>> to Usenet prior to this Cullinane nonsense.
>
> Dude, in case you didn't know, there are lots of Americans in India.
> When your job is outsourced, you follow the job! Not a bad place,
> democratic, quite a tech hub. Almost everybody here uses either
> touchtel or reliance, each of which are vast networks (much like
> comcast or aol back home).
How remarkably convincing!
>> What remarkable coincidences!
>
> Not really, billions of people using hotspots in a global network.
I have a local newsfeed with posts in sci.math from February 23,
2005. That is about 37,000 posts. It include 12,449 posts from
Google groups and these have "InjectionInfo" headers in them.
I extracted the IP address from each of those headers and then found
the associated host name.
Remarkably, there are only 12 posts (out of 32000!) posted via Google
from touchtelindia.net[1]. How about that?
Know what else? All twelve posts come from just two authors. Bet you
can't guess which two. Yep. Crankbuster and Bob Stewart. That *is*
a remarkable coincidence, I'm telling ya.
>> Whether Cullinane is a crank or not, you people is nuts.
>
> Who is "you people"? Do I know you? Have you seen Cullinane's cranky
> website? Why are you writing in this thread?
How would I know if you know me? I sure don't know you. You appeared
on Usenet shortly after crankbuster, posting from the same Indian
ISP. How could I know anything about you?
No. I haven't seen Cullinane's site.
I am writing because you people is nuts. Dragging this shit into
newsgroups and waiting patiently for a whole world to condemn
Cullinane while your sock puppets chat contentedly, complimenting one
another on their astute judgments.
That's a lot nuttier than most math cranks ever get to (not that I
know or care whether Cullinane is a crank).
But most sockpuppetusing loons are rather cleverer than our
touchtelindia poster.
Footnotes:
[1] Message IDs of the twelve posts from touchtelindia.net:
<1120562301.8...@g43g2000cwa.googlegroups.com>
<1120589052.4...@g14g2000cwa.googlegroups.com>
<1120744461.8...@o13g2000cwo.googlegroups.com>
<1120814043....@g14g2000cwa.googlegroups.com>
<1121162673.8...@g14g2000cwa.googlegroups.com>
<1121170362.2...@g44g2000cwa.googlegroups.com>
<1121171021.7...@f14g2000cwb.googlegroups.com>
<1121176024.0...@g49g2000cwa.googlegroups.com>
<1121183187.0...@g43g2000cwa.googlegroups.com>
<1121257509.1...@g47g2000cwa.googlegroups.com>
<1121350289....@z14g2000cwz.googlegroups.com>
<1121351614....@f14g2000cwb.googlegroups.com>
<1121356592....@z14g2000cwz.googlegroups.com>

Jesse F. Hughes
"Conviction of fraud can mean jail time. It can mean social censor. It
can mean big headlines where mathematicians take "perp walks" before a
jeering public."  JSH on the "censor" that awaits mathematicians.
James Dolan wrote:

> my current favorite way of thinking about the homomorphism 4! > 3!
> is as the "line at infinity in the projective completion" functor
> from affine planes to projective lines over the field z/2.

Er.. Do 3!, 4! mean S(3), S(4)? If so, you have only saved two
rightbrackets.
no, that is not the only thing that i've done, nor was i trying to do
that.

[email address jdo...@math.ucr.edu]
Jesse F. Hughes wrote:
> I extracted the IP address from each of those headers and then found
> the associated host name.
So? Your message shows that you are:
"The Eternal (and Int'l) Order of PalsyWalsies  President" (sic)
I'll be travelling to Timbuktoo next week and writing about Crank
Cullinane from there. Does that make you feel helpless?
> Jesse F. Hughes wrote:
>> I extracted the IP address from each of those headers and then found
>> the associated host name.
>
> So? Your message shows that you are:
>
> "The Eternal (and Int'l) Order of PalsyWalsies  President" (sic)
Indeed, it is true. Why "sic"? There is no misspelling or typo in
that header. It is also a completely unimportant title, of course.
Carries even less pride than the title of head busboy, which I also
once had.
> I'll be travelling to Timbuktoo next week and writing about Crank
> Cullinane from there. Does that make you feel helpless?
Why would it? Who cares? For that matter, who believes it?
The fact is: creating sock puppets to complain about someone's web
pages in fora that have nothing to do with that person is just utterly
bizarre. You are a complete and utter loon, regardless of the quality
of Cullinane's mathematics. Worse: you're an amateur loon, unable to
pull off plausible sock puppets.
But, useless as your shenanigans are, at least the thread has some
utility. Thanks to my previous post, I discovered my local news
server has not been properly expiring messages since February. I
wanted only twenty days worth of posts, not five months. That's
something worth knowing.

"Demons were like genies or philosophy professorsif you didn't word
things /exactly/ right, they delighted in giving you absolutely
accurate and completely misleading answers."
 Terry Pratchett, /Wyrd Sisters/
What you haven't done, though, is quite finished the project of
categorifying the heck out of everything in this example. I have
often observed that anyone who can't find a canonical group structure
on a pointed 2set just isn't trying, and now I see that a similar
condemnation should be applied to those who can't find a canonical
field structure there. So doesn't it behoove you to eliminate the
reference to "the field z/2"? ... Yes! yes! even more is true!
Unless I am quite mistaken, every pointed 4set has a canonical
structure as an affine plane over a 2element field (and the
the pointed 2set of the field could be taken, canonically, to
be the natural quotient of the pointed 4set)!!!
I'm sure that with a bit more work this could be made so elegant
that no one could understand it. (For instance, instead of starting
with this and that pointed set, one should [and this has the further
advantage of overloading standard combinatorial notation in which
placeholders are intended to stand for positive integers by the
same notation with arbitrary {finite?} sets, thereby infuriating
Timothy Murphy a bit more] apply the "binomial coefficient" functor
Xchoose1, for X isomorphic to 2 or 4 as the case may be, wherever
possible, and then prove functioriality, universal properties, and
the whole yardschoose9.)
Lee Rudolph
(oh! and don't forget to braid everything in sight! the homomorphism
from B4 to B3 covering that from 4! to 3! is one of nature's marvels)
The man reaches into the bag and pulls out a little man about a foot
high and sets him on the counter. He reaches back into the bag and this
time pulls out a small piano, setting it on the counter as well. He
reaches into the bag once again and pulls out a tiny piano bench, which
he places in front of the piano.
The little man sits down at the piano and starts a beautiful piece by
Mozart.
"Where on earth did you get all that?" asks the bartender.
The redneck responds by reaching into the paper bag. This time he pulls
out a magic lamp. He hands it to the bartender and says: "Here, rub it."
So the bartender rubs the lamp, and suddenly there's a puff of smoke,
then a beautiful genie is standing before him.
"I will grant you one wish. Just one wish ... each person is only
allowed one!" the genie says.
The bartender gets real excited. Without hesitating he says, "I want a
million bucks!"
A few moments later, a duck walks into the bar. It is soon followed
by another duck, then another. Pretty soon, the entire bar is filled
with ducks, and they just keep coming.
The bartender turns to the man and gripes, "Y'know, I think your genie's
a little deaf. I asked for a million bucks, not a million ducks!"
"I know," says the redneck, sadly. "Do you REALLY think I asked for a
12inch pianist?

I. N. Galidakis
http://users.forthnet.gr/ath/jgal/
Eventually, _everything_ is understandable
Lee Rudolph wrote:
> [...]
> I'm sure that with a bit more work this could be made so elegant
> that no one could understand it. (For instance, instead of starting
> with this and that pointed set, one should [and this has the further
> advantage of overloading standard combinatorial notation in which
> placeholders are intended to stand for positive integers by the
> same notation with arbitrary {finite?} sets, thereby infuriating
> Timothy Murphy a bit more] apply the "binomial coefficient" functor
> Xchoose1, for X isomorphic to 2 or 4 as the case may be, wherever
> possible, and then prove functioriality, universal properties, and
> the whole yardschoose9.)
"Strangely enough, this rather obvious geometric picture  that of the
linear fourspace over the twoelement field as a 4x4 array  seems to
have been completely overlooked in the refereed literature, except for
its occurrence in the "miracle octad generator" (MOG) devised by R. T.
Curtis in his study of the Mathieu group M24. Even in that occurrence,
the 4x4 parts of Curtis's 4x6 MOG arrays were neither supplied with
coordinates nor, indeed, explicitly identified as possessing the
structure of a finite geometry (although the appropriate group  which
provides a nice solution to Weyl's problem above  was described,
albeit in a nongeometric manner)."
Steven Cullinane
http://log24.com/theory/geometry.html
crankbuster wrote:
> [...]
> "Strangely enough, this rather obvious geometric picture  that of the
> linear fourspace over the twoelement field as a 4x4 array  seems to
> have been completely overlooked in the refereed literature, except for
> its occurrence in the "miracle octad generator" (MOG) devised by R. T.
> Curtis in his study of the Mathieu group M24. Even in that occurrence,
> the 4x4 parts of Curtis's 4x6 MOG arrays were neither supplied with
> coordinates nor, indeed, explicitly identified as possessing the
> structure of a finite geometry (although the appropriate group  which
> provides a nice solution to Weyl's problem above  was described,
> albeit in a nongeometric manner)."
>
> Steven Cullinane
> http://log24.com/theory/geometry.html
Steven Cullinane's theory completely overlooked in the refereed
literature???!!! Hmm... I wonder why.
Your IP address research is incomplete without checking that
Cullinane's IP is different from the other 2.
> But, useless as your shenanigans are, at least the thread has some
> utility.
References in Cullinane pages are excellent.
> crankbuster wrote:
>> [...]
> [...]
Man. You are just pathetic.
At least find some other ISP to use, so that it's slightly less
obvious that you're talking to yourself.

Jesse F. Hughes
"Besides, discoverers are too proud to kiss butt. Indiana Jones would
never kiss some academic's ass to get published, and neither will I."
James Harris
> Jesse F. Hughes wrote:
>> The fact is: creating sock puppets to complain about someone's web
>> pages in fora that have nothing to do with that person is just utterly
>> bizarre. You are a complete and utter loon, regardless of the quality
>> of Cullinane's mathematics. Worse: you're an amateur loon, unable to
>> pull off plausible sock puppets.
>
> Your IP address research is incomplete without checking that
> Cullinane's IP is different from the other 2.
I checked *every* post from February until yesterday. The only posts
from touchtelindia were crankbuster and his puppet.
I think my research was complete to the point of embarrassment.
Of course, I cannot prove that the posts aren't authored by Cullinane
or some other third party covering their tracks by using
touchtelindia. But I think I provided overwhelming evidence that the
author of crankbuster and Bob Stewart posts are almost certainly the
same guy  whoever it is.
>> But, useless as your shenanigans are, at least the thread has some
>> utility.
>
> References in Cullinane pages are excellent.
Okay.

"A set having three members is a single thing wholly constituted by
its members but distinct from them. After this, the theological
doctrine of the Trinity as 'three in one' should be child's play."
Max Black, _Caveats and Critiques_
If these two comedians and Cullinane are not the same individual, I
could only suggest that they are so much p*ssed off because their
girlfriend left (or, threatened to leave) to Cullinane.
[...]
> my current favorite way of thinking about the homomorphism 4! > 3! is
> as the "line at infinity in the projective completion" functor from
> affine planes to projective lines over the field z/2.
Bah. It's a trivial corollary of the fact that the Coxeter graphs (or
Dynkin diagrams if you prefer) A_3 and D_3 are the same.

Jim Heckman
Was Jesse F. Hughes really a busboy? One always admires a man who rises
to such great heights from such humble beginnings!
Way to go Jesse!!
> Is Jesse F. Hughes really the President of The Eternal (and Int'l)
> Order of PalsyWalsies?
Since Jesse F. Hughes is founder of that Order (and there are only ten
other members and also *every* member is called the President), this
isn't so hard to believe.
> Was Jesse F. Hughes really a busboy? One always admires a man who rises
> to such great heights from such humble beginnings!
Lots of folks work restaurant jobs during their high school and
college years. Big deal.
Busboy was a pretty good job. Now, Taco Mayo (Fastfood Mexican for
folks that find Taco Bell too highclass)  that was a low job.
> Way to go Jesse!!
Gosh. Thanks.

One these mornings gonna wake  Ain't nobody's doggone business how
up crazy,  my baby treats me,
Gonna grab my gun, kill my baby.  Nobody's business but mine.
Nobody's business by mine.   Mississippi John Hurt
Jesse F. Hughes wrote:
>
> "Bob Stewart" <bobstew...@hotmail.com> writes:
>
> > Is Jesse F. Hughes really the President of The Eternal (and Int'l)
> > Order of PalsyWalsies?
>
> Since Jesse F. Hughes is founder of that Order (and there are only
> ten other members and also *every* member is called the President),
> this isn't so hard to believe.
Nope  It's obviously a a padic circle, in which every point is
its centre
[See "A Mathematical Seduction" by Drew Aderburg.
http://www.williams.edu/Mathematics/eburger/BurgerMathHorizons.pdf,
an interesting read all round].
Check out
Steven Cullinane's tribute to yours truly! Not bad, not bad at all!
If I didn't know better, I'd swear this is the old negative
publicity stunt  dissing one's own work to at least try and
bring it to the attention of others.
Hang on  Come to think of it, I _don't_ know better ;)
john_r...@sagittaps.com wrote:
> If I didn't know better, I'd swear this is the old negative
> publicity stunt  dissing one's own work to at least try and
> bring it to the attention of others.
Oh? You think I am Steven Cullinane using a proxy IP address? Curioser
and curioser!
What follows is attributed to:
Jed Pack
pa...@et.byu.edu
18:35:25 04/17/02 Wed
Steven Cullinane,
I wonder how you got the number 322,560.
I suggest the number is at most 30^2=900.
Please let me know if you find the error in my logic.
In the original four diamond configuration. The matrix indicating which
squares have the black corner either at topright or topleft is:
0 0 0 0
1 1 1 1
0 0 0 0
1 1 1 1
Similarly, the matrix indicating which squares have the black corner
either at topright or bottomright is:
1 0 1 0
1 0 1 0
1 0 1 0
1 0 1 0
These two matricies fully describe the configuration. Swapping columns,
rows, and quadrants can change these matricies into any of the
following other 30 matricies (there are no other possibilities):
0 0 1 1  0 1 1 0  0 0 1 1  1 1 1 1  1 0 1 0 
0 0 1 1  0 1 1 0  1 1 0 0  0 0 0 0  1 0 1 0 
0 0 1 1  1 0 0 1  1 1 0 0  0 0 0 0  0 1 0 1 
0 0 1 1  1 0 0 1  0 0 1 1  1 1 1 1  0 1 0 1 
0 1 0 1  0 0 0 0  0 1 0 1  1 0 0 1  1 1 0 0 
0 1 0 1  1 1 1 1  1 0 1 0  0 1 1 0  1 1 0 0 
0 1 0 1  0 0 0 0  1 0 1 0  1 0 0 1  0 0 1 1 
0 1 0 1  1 1 1 1  0 1 0 1  0 1 1 0  0 0 1 1 
0 1 1 0  0 0 1 1  0 1 1 0  1 0 1 0  1 1 1 1 
0 1 1 0  1 1 0 0  1 0 0 1  0 1 0 1  1 1 1 1 
0 1 1 0  0 0 1 1  1 0 0 1  1 0 1 0  0 0 0 0 
0 1 1 0  1 1 0 0  0 1 1 0  0 1 0 1  0 0 0 0 
0 0 0 0  0 1 0 1  1 0 0 1  1 1 0 0  1 0 0 1 
0 0 0 0  1 0 1 0  0 1 1 0  0 0 1 1  1 0 0 1 
1 1 1 1  0 1 0 1  0 1 1 0  1 1 0 0  1 0 0 1 
1 1 1 1  1 0 1 0  1 0 0 1  0 0 1 1  1 0 0 1 
0 0 1 1  0 1 1 0  1 0 1 0  1 1 1 1  1 0 1 0 
0 0 1 1  1 0 0 1  0 1 0 1  0 0 0 0  1 0 1 0 
1 1 0 0  0 1 1 0  0 1 0 1  1 1 1 1  1 0 1 0 
1 1 0 0  1 0 0 1  1 0 1 0  0 0 0 0  1 0 1 0 
0 1 0 1  0 0 0 0  1 1 0 0  1 0 0 1  1 1 0 0 
0 1 0 1  1 1 1 1  0 0 1 1  1 0 0 1  1 1 0 0 
1 0 1 0  1 1 1 1  0 0 1 1  0 1 1 0  1 1 0 0 
1 0 1 0  0 0 0 0  1 1 0 0  0 1 1 0  1 1 0 0 
Consequently, any pattern that can be obtained through such
transformations can be described by a pair of these two matricies.
There are 30^2 such pairs, and hence can be no more than 30^2 patterns
obtained through the mentioned transformations.
"Ah, I just found an interesting old post on one of Steven Cullinane's gazillion websites that proves that the statement of his 'Diamond Theorem' is totally and outrageously false!"
The website in question is
http://www.voy.com/14256/.
It also contains the following,
not quoted by "Bob Stewart"
my 4/25/02 reply to Pack,
his 7/10/02 response,
my 7/18/02 reply,
his 11/11/02 response, and
my 11/12/02 reply.
The 11/11/02 response from Pack was:
"Thank you for your help!
You are absolutely correct. I should have read your site more carefully. The matter of the number of 'configurations' was simply a misunderstanding. I have verified the number you have given.
Although I am not a mathematician, I find your work interesting."
For a brief summary of the work discussed by Pack and "Stewart," see
Steven H. Cullinane wrote:
> The website in question is
> http://www.voy.com/14256/.
>
> It also contains the following,
> not quoted by "Bob Stewart"
> my 4/25/02 reply to Pack,
> his 7/10/02 response,
> my 7/18/02 reply,
> his 11/11/02 response, and
> my 11/12/02 reply.
>
> The 11/11/02 response from Pack was:
>
> "Thank you for your help!
>
> You are absolutely correct. I should have read your site more carefully. The matter of the number of 'configurations' was simply a misunderstanding. I have verified the number you have given.
>
> Although I am not a mathematician, I find your work interesting."
That's stupid! Verified the number? This "voy forum" is your own
creation and you yourself wrote that "reply"! I dont think Pack would
care what you write on your forum after having proved that the total
number of distinct patterns is less than 900. How awkward for you, you
pompous fool!
> Steven H. Cullinane wrote:
>> Although I am not a mathematician, I find your work interesting."
>
> That's stupid! Verified the number? This "voy forum" is your own
> creation and you yourself wrote that "reply"!
Maybe he did, maybe not. Doesn't make much sense that he would do so,
when he could have just deleted the original post had he wanted to.
On the other hand, your sock puppetry is remarkably obvious and
juvenile.
I don't think you get many points for this attack.

"If you have a really big idea, you can get a measure of how big it is
by how much people resist the obvious. From what I've seen, I have a
REALLY, REALLY, *REALLY*, BIG DISCOVERY!!!"
James Harris, on being ignored
Jesse F. Hughes wrote:
> Maybe he did, maybe not. Doesn't make much sense that he would do so,
> when he could have just deleted the original post had he wanted to.
>
> On the other hand, your sock puppetry is remarkably obvious and
> juvenile.
>
> I don't think you get many points for this attack.
Aw come on Jesse! Admit that you eagarly await all the posts in this
thread, check all IP addresses, reverse DNS configs and what have you,
spends hours in anticipation for replies to your posts. I know you do.
If I went away you would miss me so! Dear little busboy!!
> Jesse F. Hughes wrote:
>> Maybe he did, maybe not. Doesn't make much sense that he would do so,
>> when he could have just deleted the original post had he wanted to.
>>
>> On the other hand, your sock puppetry is remarkably obvious and
>> juvenile.
>>
>> I don't think you get many points for this attack.
>
> Aw come on Jesse!
[Reformatted]
> Admit that you
> (1) eagarly await all the posts in this thread
More or less guilty
> (2) check all IP addresses
Nope.
> (3) reverse DNS configs
Haven't a clue what that would mean. Do you?
> (4) what have you,
I have only what haved you on one occasion, and I have written proof
that the llama was a willing participant.
> (5) spends hours in anticipation for replies to your posts.
Indeed, it is a problem for those of us that don't invent sock puppets
so that we can respond to our own posts.
> I know you do. If I went away you would miss me so! Dear little
> busboy!!
You're mocking me for formerly being a busboy? Don't that strike you
as pathetic?
On the other hand, pathetic seems your modus operandi[1].
Footnotes:
[1] A term learned from Law & Order.

Jesse F. Hughes
"Well, talk to her. Tell her about your feelings in an open and
honest way."
"Yeah. Either that or be a man."  Futurama
Jesse F. Hughes wrote:
> [...]
> > (3) reverse DNS configs
> Haven't a clue what that would mean. Do you?
How Reverse DNS Works
http://www.dnsstuff.com/info/revdns.htm
> [...]
> You're mocking me for formerly being a busboy? Don't that strike you
> as pathetic?
All right, all right, I'm sorry, ok? But you keep calling me a "sock
puppet"! Have you considered the fact that I may actually be an honest,
hard working man? It would be very easy for me to disguise my IP
address if I needed to. Just to give you one example from a quick
Google search on what seems to be a thriving software industry for
crooks, using the following tool
http://www.stayinvisible.com/index.pl/anonymity_of_proxy
I could write here from IP address 140.247.237.29 as the goddamned
President, if I wanted to. I'm sure you would have been very impressed.
But right now I cant afford to buy such useless software. I'm sure
Cullinane uses this stuff all the time. That's a thought...

You may be an ambassador to England or France,
You may like to gamble, you might like to dance,
You may be the heavyweight champion of the world,
You may be a socialite with a long string of pearls
But you're gonna have to serve somebody, yes indeed
You're gonna have to serve somebody,
Well, it may be the devil or it may be the Lord
But you're gonna have to serve somebody.
You might be a rock 'n' roll addict prancing on the stage,
You might have drugs at your command, women in a cage,
You may be a business man or some high degree thief,
They may call you Doctor or they may call you Chief
But you're gonna have to serve somebody, yes indeed
You're gonna have to serve somebody,
Well, it may be the devil or it may be the Lord
But you're gonna have to serve somebody.
You may be a state trooper, you might be a young Turk,
You may be the head of some big TV network,
You may be rich or poor, you may be blind or lame,
You may be living in another country under another name
But you're gonna have to serve somebody, yes indeed
You're gonna have to serve somebody,
Well, it may be the devil or it may be the Lord
But you're gonna have to serve somebody.
You may be a construction worker working on a home,
You may be living in a mansion or you might live in a dome,
You might own guns and you might even own tanks,
You might be somebody's landlord, you might even own banks
But you're gonna have to serve somebody, yes indeed
You're gonna have to serve somebody,
Well, it may be the devil or it may be the Lord
But you're gonna have to serve somebody.
You may be a preacher with your spiritual pride,
You may be a city councilman taking bribes on the side,
You may be workin' in a barbershop, you may know how to cut hair,
You may be somebody's mistress, may be somebody's heir
But you're gonna have to serve somebody, yes indeed
You're gonna have to serve somebody,
Well, it may be the devil or it may be the Lord
But you're gonna have to serve somebody.
Might like to wear cotton, might like to wear silk,
Might like to drink whiskey, might like to drink milk,
You might like to eat caviar, you might like to eat bread,
You may be sleeping on the floor, sleeping in a kingsized bed
But you're gonna have to serve somebody, yes indeed
You're gonna have to serve somebody,
Well, it may be the devil or it may be the Lord
But you're gonna have to serve somebody.
You may call me Terry, you may call me Timmy,
You may call me Bobby, you may call me Zimmy,
You may call me R.J., you may call me Ray,
You may call me anything but no matter what you say
You're gonna have to serve somebody, yes indeed
You're gonna have to serve somebody.
Well, it may be the devil or it may be the Lord
But you're gonna have to serve somebody.
The other, better, smarter, richer Bob

> But you keep calling me a "sock puppet"! Have you considered the
> fact that I may actually be an honest, hard working man? It would be
> very easy for me to disguise my IP address if I needed to.
So?
Just so long as you pretend that Bob Stewart is not the same person as
"crankbuster", then you are (or he is) a sockpuppet.
The fact that you *could* easily cover your tracks doesn't really
change things.
[snip gratuitous use of Bob Dylan, who surely deserves better than
this]

"Humanity is still a primitive species. I seem to have been born out
of my time, maybe centuries ahead, and I guess I'll just have to get
used to it. In ways, it's not so bad. Mostly it's boring though."
 James S. Harris has problems beyond you and me.
"The time has come, the Walrus said, to talk of many things..."
Lewis Carrol

Consider, if you please, the 6x4 array
0 1 2 3
4 5 6 7
8 9 10 11
12 13 14 15
16 17 18 19
20 21 22 23
Define (on my whim and fancy) the permutations
a = (0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22)
b = (2,16,9,6,8)(4,3,12,13,18)(10,11,22,7,17)(20,15,14,19,21)
c =
(0,23)(1,22)(2,11)(3,15),(4,17)(5,9)(6,19)(7,13)(8,20)(10,16)(12,21)(18,14)
Let G be the group generated by the permutations {a,b,c} of the 6x4
array. Then
(1) G is a group of 244823040 symmetries of the 6x4 array.
(2) G has subgroups H,I,J,K of, respectively, 10200960, 443520, 95040,
7920 symmetries of the 6x4 array.
(3) The groups G,H,I,J,K are simple.
Note: This theorem is actually true!
>The Rectangular Array Theorem
>by your humble superhero, Crankbuster
You're plagiarizing R. T. Curtis.
This is getting old.
See http://voy.com/14256/.
See also "The Geometry of the 4x4 square,"
http://log24.com/theory/geometry.html.
This contains a discussion of
the Miracle Octad Generator of R. T. Curtis
itself a rectangular array (4x6, not 6x4)
that illuminates the large Mathieu group.
Steven H. Cullinane wrote:
> You're plagiarizing R. T. Curtis.
> This is getting old.
> See http://voy.com/14256/.
Plagiarism:
The "Diamond Theory" website of Steven Cullinane shows a man who is
incapable of telling the truth: a pathological liar who hates and
despises the mathematical community; a sociopath caught between the
conflicting desires to earn the admiration of mathematicians, and his
desire to insult those who ignore him and refuse him his selfperceived
due measure of honor and reverie. As such, Steven Cullinane is
constantly trying to purchase recognition when he has the funds to
advertise on google.com, or steal that recognition by lying and
deceiving dmoz.org when money isn't enough. As you can see from the
correspondence below, Jed Pack has clearly pointed out serious errors
in Steven Cullinane's calculations. Now, instead of admitting that he
has been caught with his pants down, Steven Cullinane is questioning
Jed Pack's education! Surely, Jed Pack is a more competent
mathematician than Steven Cullinane.
R.T. Curtis
12:29:15 11/03/02 Sun
> See also "The Geometry of the 4x4 square,"
> http://log24.com/theory/geometry.html.
> This contains a discussion of
> the Miracle Octad Generator of R. T. Curtis
> itself a rectangular array (4x6, not 6x4)
> that illuminates the large Mathieu group.
Your 4x4 array has only 16 elements whereas the MOG array has 24
elements. Crank.
P.S. I like crankbuster's RAT. I've not seen this set of generators
before, has anybody?
Bob Stewart wrote:
> P.S. I like crankbuster's RAT. I've not seen this set of generators
> before, has anybody?
Actually, I can do better than that. If I remember correctly, all
finite simple groups are known to be generated by at most *two*
elements. I think this is a theorem of NeilsenSchrier (correct me if
I'm wrong). At any rate, I can find 2 elements that generate the group
G. Same way I can find 2 generators each for H,I,J,K since they are all
simple groups.
BTW, do you mind calling my theorem something else? RAT sounds bad.
He did not quote the following, posted on
Nov. 11, 2002, at the same forum by
the real R. T. Curtis, whose home page is
http://www.mat.bham.ac.uk/staff/curtis.htm
> I wish to make it clear that I had
> nothing whatsoever to do with the
> message posted on this website
> as having been sent by R.T. Curtis.
> There may, of course, be another
> R.T. Curtis around who has a particular
> grudge against Professor Steven Cullinane.
> I do not. Indeed, the exchanges we have had
> with one another over the years have always
> been cordial and civilised.
> If someone is deliberately using my name
> to attack Steven Cullinane anonymously,
> it shows malice and cowardice
> unusual in the mathematical world.
> Robert Curtis.
I should point out that the word "Professor"
comes from Professor Curtis, not myself.
I am not, and never have been, a professor,
or even a Ph.D., and have never
pretended to be.
The malice and cowardice continue.
crankbuster wrote:
> Actually, I can do better than that. If I remember correctly, all
> finite simple groups are known to be generated by at most *two*
> elements. I think this is a theorem of NeilsenSchrier (correct me if
> I'm wrong). At any rate, I can find 2 elements that generate the group
> G. Same way I can find 2 generators each for H,I,J,K since they are all
> simple groups.
Yes, check Gorenstein's book on the classification of finite simple
groups. It follows from the classification that every finite simple
group is generated by two elements. Not sure if this follows from the
Nielsen Schrier theorem. I think Nielsen proved that every finitely
generated subgroup of a free group is free. Schrier proved that the
finitely generated hypothesis is not necessary, thus proving that every
subgroup of a free group is free. Perhaps this is used to prove that
all finite simple groups are 2generated, but I'm not sure. But, coming
back to your assertion, can you come up with any relations between your
generators a,b,c? This could be non trivial! The word problem is known
to be pretty damn hard!
> BTW, do you mind calling my theorem something else? RAT sounds bad.
You could arrange your array in a circle, and we'll call it CAT.