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| Bob Stewart |
 Posted: Wed Jul 13, 2005 6:25 am |
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Steven H. Cullinane wrote:
[quote:3bd8ec3dcd]On the off chance that "Bob Stewart" is not "crankbuster" under another name, here is a reply:
[/quote:3bd8ec3dcd]
You are paranoid!
[quote:3bd8ec3dcd]Your statement that "if each of the permuted objects has some geometrical symmetry, >then these resulting permutations will display symmetries too" is false,
[/quote:3bd8ec3dcd]
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".
[quote:3bd8ec3dcd]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.
[/quote:3bd8ec3dcd]
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!
[quote:3bd8ec3dcd]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.
[/quote:3bd8ec3dcd]
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!!
[quote:3bd8ec3dcd]That group, by the way, is where the number 322,560, quoted by the deeply confused "crankbuster," comes from.
[/quote:3bd8ec3dcd]
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 |
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| Jesse F. Hughes |
| Posted: Wed Jul 13, 2005 8:18 am |
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"Bob Stewart" <bobstewart_III@hotmail.com> writes:
[quote:6ff2146119]Steven H. Cullinane wrote:
On the off chance that "Bob Stewart" is not "crankbuster" under
another name, here is a reply:
You are paranoid!
[/quote:6ff2146119]
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_ |
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| James Dolan |
| Posted: Thu Jul 14, 2005 12:53 am |
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in article <21144572.1121247719318.javamail.jakarta@nitrogen.mathforum.org>,
steven h. cullinane <m759@post.harvard.edu> wrote:
|Thanks for your reply.
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|The answer to your question is "yes."
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|As for the notation, a Google search on "AGL(n,q)" should convince
|you that it is standard, and not my own invention.
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|Don't feel bad. Your bafflement at standard group-theoretic notation
|was shared by the brilliant John Baez. See his sci.math post of
|March 29, 1993, on "Symplectic structures on finite groups"--
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|"I don't understand the 'AGL' business...."
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.
--
[e-mail address jdolan@math.ucr.edu] |
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| Timothy Murphy |
| Posted: Thu Jul 14, 2005 6:32 am |
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James Dolan wrote:
[quote:0e360fda7e]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.
[/quote:0e360fda7e]
Er.. Do 3!, 4! mean S(3), S(4)?
If so, you have only saved two right-brackets.
--
Timothy Murphy
e-mail (<80k only): tim /at/ birdsnest.maths.tcd.ie
tel: +353-86-2336090, +353-1-2842366
s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland |
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| Bob Stewart |
| Posted: Thu Jul 14, 2005 8:11 am |
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Jesse F. Hughes wrote:
[quote:13440ec568]"Bob Stewart" <bobstewart_III@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.
[/quote:13440ec568]
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).
[quote:13440ec568]What remarkable coincidences!
[/quote:13440ec568]
Not really, billions of people using hotspots in a global network.
[quote:13440ec568]Whether Cullinane is a crank or not, you people is nuts.
[/quote:13440ec568]
Who is "you people"? Do I know you? Have you seen Cullinane's cranky
website? Why are you writing in this thread? |
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| crankbuster |
| Posted: Thu Jul 14, 2005 9:56 am |
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Steven H. Cullinane wrote:
[quote:59957dfc9d]Thanks for your reply.
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.
[/quote:59957dfc9d]
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! |
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| Guest |
| Posted: Thu Jul 14, 2005 11:03 am |
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crankbuster wrote:
[quote:6c651162bc]
[...]
Ha! Ha! This gets better and better!
[/quote:6c651162bc]
Weirder and weirder more like. |
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| James Dolan |
| Posted: Thu Jul 14, 2005 7:45 pm |
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in article <1vsbe.2479$r5.563@news.indigo.ie>,
timothy murphy <tim@birdsnest.maths.tcd.ie> wrote:
|James Dolan wrote:
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|> 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.
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|Er.. Do 3!, 4! mean S(3), S(4)? If so, you have only saved two
|right-brackets.
no, that is not the only thing that i've done, nor was i trying to do
that.
--
[e-mail address jdolan@math.ucr.edu] |
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| Bob Stewart |
| Posted: Fri Jul 15, 2005 3:45 am |
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Jesse F. Hughes wrote:
[quote:680c9f25fc]I extracted the IP address from each of those headers and then found
the associated host name.
[/quote:680c9f25fc]
So? Your message shows that you are:
"The Eternal (and Int'l) Order of Palsy-Walsies -- President" (sic)
I'll be travelling to Timbuktoo next week and writing about Crank
Cullinane from there. Does that make you feel helpless? |
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| Jesse F. Hughes |
| Posted: Fri Jul 15, 2005 4:09 am |
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"Bob Stewart" <bobstewart_III@hotmail.com> writes:
[quote:ef93553925]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 Palsy-Walsies -- President" (sic)
[/quote:ef93553925]
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.
[quote:ef93553925]I'll be travelling to Timbuktoo next week and writing about Crank
Cullinane from there. Does that make you feel helpless?
[/quote:ef93553925]
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 professors---if you didn't word
things /exactly/ right, they delighted in giving you absolutely
accurate and completely misleading answers."
-- Terry Pratchett, /Wyrd Sisters/ |
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| Lee Rudolph |
| Posted: Fri Jul 15, 2005 4:38 am |
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jdolan@math-cl-n03.math.ucr.edu (James Dolan) writes:
[quote:4801647b7a]in article <1vsbe.2479$r5.563@news.indigo.ie>,
timothy murphy <tim@birdsnest.maths.tcd.ie> wrote:
|James Dolan wrote:
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|> 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.
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|Er.. Do 3!, 4! mean S(3), S(4)? If so, you have only saved two
|right-brackets.
no, that is not the only thing that i've done, nor was i trying to do
that.
[/quote:4801647b7a]
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 2-set 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 4-set has a canonical
structure as an affine plane over a 2-element field (and the
the pointed 2-set of the field could be taken, canonically, to
be the natural quotient of the pointed 4-set)!!!
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
X-choose-1, for X isomorphic to 2 or 4 as the case may be, wherever
possible, and then prove functioriality, universal properties, and
the whole yards-choose-9.)
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) |
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| Ioannis |
| Posted: Fri Jul 15, 2005 4:49 am |
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Ο "Jesse F. Hughes" <jesse@phiwumbda.org> έγραψε στο μήνυμα
news:874qawwfcd.fsf@phiwumbda.org...
[snip]
[quote:4b61fdc7fa]--
"Demons were like genies or philosophy professors---if you didn't word
things /exactly/ right, they delighted in giving you absolutely
accurate and completely misleading answers."
-- Terry Pratchett, /Wyrd Sisters/
A redneck walks into a bar with a paper bag. He sits down and places[/quote:4b61fdc7fa]
the bag on the counter. The bartender walks up and asks what's in the
bag.
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
12-inch pianist?
--
I. N. Galidakis
http://users.forthnet.gr/ath/jgal/
Eventually, _everything_ is understandable |
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| crankbuster |
| Posted: Fri Jul 15, 2005 8:25 am |
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Lee Rudolph wrote:
[quote:cb40a597bc][...]
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
X-choose-1, for X isomorphic to 2 or 4 as the case may be, wherever
possible, and then prove functioriality, universal properties, and
the whole yards-choose-9.)
[/quote:cb40a597bc]
"Strangely enough, this rather obvious geometric picture -- that of the
linear four-space over the two-element 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 non-geometric manner)."
Steven Cullinane
http://log24.com/theory/geometry.html |
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| Bob Stewart |
| Posted: Fri Jul 15, 2005 9:46 am |
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crankbuster wrote:
[quote:863e4b2060][...]
"Strangely enough, this rather obvious geometric picture -- that of the
linear four-space over the two-element 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 non-geometric manner)."
Steven Cullinane
http://log24.com/theory/geometry.html
[/quote:863e4b2060]
Steven Cullinane's theory completely overlooked in the refereed
literature???!!! Hmm... I wonder why. |
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| Guest |
| Posted: Fri Jul 15, 2005 12:15 pm |
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Jesse F. Hughes wrote:
[quote:3fccf04773]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.
[/quote:3fccf04773]
Your IP address research is incomplete without checking that
Cullinane's IP is different from the other 2.
[quote:3fccf04773]But, useless as your shenanigans are, at least the thread has some
utility.
[/quote:3fccf04773]
References in Cullinane pages are excellent. |
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