Category: math

White's move and mate in two.

posted by collin on 07.12.02 at 10:45, null, math, nonsense, math, random, Leave a comment Permalink

No hidden pieces. Black pawn direction doesn't matter.

Ba dum ching.

posted by collin on 07.12.02 at 10:41, null, math, nonsense, math, random, 1 comment Permalink

A friend of mine found an interesting anagram of "BANACH TARSKI".
.
.
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It's "BANACH TARSKI BANACH TARSKI"...

Comment from: Devin [Visitor] · http://www.hwaethwugu.com/blog
Fucking mathematicians. They come up with formal systems and then complain when they don't make sense.

Also, that the notion of area wasn't formalized until 1901 (and wasn't proved consistent until 1979) really pisses me off.
Permalink 12/02/07 @ 10:52

Gordon Pask?

posted by collin on 07.03.15 at 14:57, null, math, nonsense, null, science, math, technology, tech, Leave a comment Permalink

Self assembling electrochemical sensors? [linky]

Anybody every hear of him? Sounds like Widrow's memsistors. It was Widrow, right?

My birthday in Pi.

posted by collin on 07.02.26 at 14:28, null, math, nonsense, math, random, Leave a comment Permalink

Results
Searchstart: 3 The string 03081980 occurs at position 95,782,797 counting from the first digit after the decimal point. The 3. is not counted.

The string and surrounding digits:

84481319032327216606 03081980 06677246175214953568

this query took 0.034847 seconds

And other random pi-ness.

The bible code of bioinformatics?

posted by collin on 07.02.26 at 09:01, null, math, nonsense, visual, science, math, random, Leave a comment Permalink

Strange structures (close your eyes just a little bit to see more details)

Um, I don't see anything...

Am I right? Is there any practical use to this? Or is it just the same old; large enough data will have patterns of long period regardless of the structure of the data.

Huh?

posted by collin on 07.02.22 at 15:38, null, math, nonsense, math, random, Leave a comment Permalink

Abstract nonsense is a popular term used by mathematicians to describe certain kinds of arguments and concepts in category theory ... Such and such is true by abstract nonsense.

I cried a little.

Are they more guilty?

posted by collin on 07.02.22 at 15:10, null, math, nonsense, math, rant, random, rant, Leave a comment Permalink

I was looking at some random things...

Are the humanities guilty of making up nonsense words in a futile effort to have a semblance of logical, nee mathematical, consistency?

Bring it on bitches.

My zen moment.

posted by collin on 07.02.20 at 11:49, null, math, nonsense, math, random, Leave a comment Permalink

Dust bunnies are diffusion limited aggregates.

I believe that's called irony...

posted by collin on 06.12.13 at 16:55, null, math, nonsense, math, books, news, news, 1 comment Permalink

They were just lost in a bookstore. I'd like to think he would have laughed.

And some interesting heuristics.

Comment from: ben [Member] · http://ben.nonplatonic.com

“Good,” Wronoski recalled saying. “Now I don’t have to kill myself.”

-Bookninja
Permalink 12/13/06 @ 17:23

I now -officially- hate the BBC.

posted by collin on 06.12.07 at 00:53, null, math, math, rant, rant, 1 comment Permalink

It's official. I will stab them in the eye.

And here's some actual papers.

So tired.

Comment from: ben [Member] · http://ben.nonplatonic.com
What the hell?:

"We've just solved a problem that hasn't been solved for twelve hundred years - and it's that easy," proclaims Dr Anderson having demonstrated his solution on a whiteboard at Highdown School, in Emmer Green.
Permalink 12/07/06 @ 03:06

gcd(ring,cog)=1 or prime numbers make you faster

posted by collin on 06.07.31 at 16:01, null, math, nonsense, math, random, 2 comments Permalink

So according to the interweb Chub guy works for Santa Cruz now, and has no parts. Graham, don't you have a lathe? Also the interweb says this:

Gears that are factorial are less than desireable, especially if you're the skidding type. that is - *any* gear with even #s of teeth on both cog and chainwheel, or any gear where the # of chainwheel teeth is divisable by the # of cog teeth. with a divisable gear, you *will* tend to lock up in the same spot on your tire over and over again - non-divisable gears mean the wear will get spread out more over the tire - and for us non-skidders, it means the wear on cog, chainwheel and chain will be more even as well - which, again, means longer drivetrain life.

to wit:

48x16 = bad
47x17 = good
46x16 = bad
46x17 = good

Chainwheel?
Discuss...

Comment from: graham [Member] · http://nonplatonic.com/graham.php
Take the product of the number of teeth on your fixed gears chainrings and divide by 365. If the remainder is the day of the year on which your birthday falls, (for instance, 34 = Feb. 4th), Bill Gates will send you $162 for every time you repost this comment.
Permalink 08/01/06 @ 18:45
Comment from: ben [Member] · http://ben.nonplatonic.com
48/16=3... so, if I hold the pedals level and skid, it will be in one of two places... I think.

46/16=2.875... 2.875*8=23... so, assuming a uniform distribution of times which I pick to skid at, there is a 1/(23*2) chance of skidding in the same place? ...so my tire will have 23 times less wear in the most skid-worn part than if a rode a 48/16? ...and I wanted to be a statistician...

Am I reasoning correctly? Regardless, I'm not convinced this is even remotely relevant. I get flats long before my tires wear out, yet I ride the dreaded 54/18 chainwheel.

Chainwheel.
Permalink 08/01/06 @ 23:04

Humbug!

posted by collin on 06.07.24 at 19:52, null, math, rant, rant, Leave a comment Permalink
Categories anywhere are wonderful.

Do spambots use a context free grammar?

posted by collin on 06.04.19 at 06:55, null, math, nonsense, math, random, 1 comment Permalink

Thanks for the special work and information! bed bug prevention exquisite image photography raymond chandler 22 inch wheels name database dandy don football hairless slit produce blue book

"raymond chandler"?

I guess there aren't any conjunctions or propositions so the answer to my question is probably no. Anybody know what statistical measures would show whether or not it's just a random sampling from some lexicon? Also, anybody know where I could get nice downloadable well formatted lexicon that tells you what part of speech the words are?

Comment from: marco [Member] · http://www.cs.berkeley.edu/~barreno
My guess is spambots use Markov models to generate text, trained on samples of real text. Probably second-order (bigram) models, or maybe third-order (trigram).

There are some standard corpora that NLP people use for testing. I don't know where to get them off the top of my head, but one of them is the "Brown corpus" (from the university, presumably) and you can probably find it courtesy of Google. It's a tagged corpus, as are some of the other well-known ones I don't remember the names of.
Permalink 04/20/06 @ 13:43

Ira just said...

posted by collin on 06.01.14 at 12:38, math, nonsense, math, random, Leave a comment Permalink
"Because when math fails, what do you have left but pure faith?"

-Ira Glass on This American Life [that is on the radio right now]

Epiphanies.

posted by collin on 05.10.28 at 23:04, math, math, Leave a comment Permalink

They're good. They're what kept me wanting to do math. I had a little one the other day when I was looking at this page on the formal logic of mathematics. It has some interesting things, like a proof 132 theorems long that shows 2+2=4.

When ever you think about these things, Godel allways pops into your head. I always believed [not to open an epistomological can of worms, but I think that's the best word] Godel's Incompleteness proof, but I kind of wanted a constructive example: ie an actual unprovable statement.

I realized why you can't do this, or at least the conditions that would allow you to do this which generate contradictions. Given a set of axioms, one can generate a set of theorems. I think to show that a statement is unprovable the set of theorems that can be generated by the set of axioms needs to be finite. This is at least sufficient, though I can't say if it's necessary. If the set of theorems is finite then obviously it's possible to show that a statement and it's negation are not proveable, which I guess simply means showing the statement is not a theorem. So for any interesting set of axioms, say one complex enough to give you arithmetic, the set of theorms is obviously infinite, and hence there is no constructive way to show a theorem is unproveable.

Ok, my head hurts. I'm going to sleep.

Stephen Wolfram is an ass.

posted by collin on 05.10.27 at 23:59, math, math, rant, rant, Leave a comment Permalink

Next in my burgeoning series of posts wherein I call famous people asses: Stephen Wolfram.

I came across this link to a review of Wolfram's A New Kind of Science on Crooked Timber. It's by a professor at Carnegie Mellon named Cosma Shalizi, and while not as blistering as one I remember in AMS Notices a while back it's still a good read. The note at the begining kind of grabs your attention.

Attention conservation notice: Once, I was one of the authors of a paper on cellular automata. Lawyers for Wolfram Research Inc. threatened to sue me, my co-authors and our employer, because one of our citations referred to a certain mathematical proof, and they claimed the existence of this proof was a trade secret of Wolfram Research. I am sorry to say that our employer knuckled under, and so did we, and we replaced that version of the paper with another, without the offending citation. I think my judgments on Wolfram and his works are accurate, but they're not disinterested.

He later explains, in more detail, what this was about.

He didn't invent cyclic tag systems, and he didn't come up with the incredibly intricate construction needed to implement them in Rule 110. This was done rather by one Matthew Cook, while working in Wolfram's employ under a contract with some truly remarkable provisions about intellectual property. In short, Wolfram got to control not only when and how the result was made public, but to claim it for himself. In fact, his position was that the existence of the result was a trade secret. Cook, after a messy falling-out with Wolfram, made the result, and the proof, public at a 1998 conference on CAs. (I attended, and was lucky enough to read the paper where Cook goes through the construction, supplying the details missing from A New Kind of Science.) Wolfram, for his part, responded by suing or threatening to sue Cook (now a penniless graduate student in neuroscience), the conference organizers, the publishers of the proceedings, etc. (The threat of legal action from Wolfram that I mentioned at the beginning of this review arose because we cited Cook at the person responsible for this result.)

A little clarification: the "cyclic tag system" refers to the method of proving rule 110 is Turing complete. And let's emphasize the last sentence again in case you missed it "The threat of legal action from Wolfram that I mentioned at the beginning of this review arose because we cited Cook at the person responsible for this result." I believe the phrase is, "that's a lot of damn gall." I had heard about Wolfram suing Cook, but to threaten to sue someone for citing his paper? Re-fucking-diculous.

If this hasn't made you want to read the review maybe these things will. Shalizi put into crystal clarity two things I knew but hadn't connected, or if I had I forgot that I had. And in doing so he brings up Wolfram's willful neglect of cannonical complexity theory. The two pieces I hadn't fit together; all of Wolfram's elementary CA rules can be defined as an 8 digit binary number, and Kolmogorov complexity. Unless I'm horribly confused, which I don't think I am, all 256 rules have the basically the "same" Kolmogorov complexity. [I know rule 0 and things like that have less, but the point is still valid.] And the other thing that makes the review worth reading are the links to incredibly interesting papers. For example:

Unpredictability and Undecidability in Dynamical Systems
Physical Review Letters 64 (1990) 2354-2357
We show that motion with as few as three degrees of freedom (for instance, a particle moving in a three-dimensional potential) can be equivalent to a Turing machine, and so be capable of universal computation. Such systems possess a type of unpredictability qualitatively stronger than that which has been previously discussed in the study of low-dimensional chaos: even if the initial conditions are known exactly, virtually any question about their long-term dynamics are undecidable.

The Banach-Tarski Paradox

posted by collin on 05.10.23 at 21:25, math, math, Leave a comment Permalink

Instead of finishing up my algebra problem set [though in my defense we were talking about Zorn's Lemma last week] I was looking around for information on the Axiom of Choice [never a good idea], when some page mentioned that the Axiom of Choice implies the Banach-Tarski Paradox. To quote:

First stated in 1924, the Banach-Tarski paradox states that it is possible to dissect a ball into six pieces which can be reassembled by rigid motions to form two balls of the same size as the original.

Like all good paradoxes [Unlike, say, Zeno's which is bad. Note that I didn't say true paradox because the "paradoxness" comes from empirical evidence and logical construction contradicting.] this should make your head hurt a little bit. Saddly, the original paper "Sur la d'composition des ensembles de points en parties respectivement congruentes", Fundamenta Mathematicae, 6, (1924), 244-277, is like it sounds in french, which I don't read. [Though apparently you can get a pdf of it here.] I found what appears to be a good paper which steps throught the proof [and since the internet is effemeral, I'll mirror it here] fairly didactically. I haven't read it through, but maybe this week. Every one should give it a read...

Have I seen this before?

posted by collin on 05.08.09 at 13:03, math, math, technology, 1 comment Permalink

Oh, the blog milieu! At the very least we were talking about this before.

Currently, computers or robots apply statistical rules to a database of known images to identify new ones. Although relatively effective, this requires thousands of images and hours of training by humans. Peekaboom aims to ease the burden by harnessing the brain power of willing web users.

"The collected data can be applied towards constructing computer vision algorithms, which require massive amounts of training and testing data not currently available," von Ahn told New Scientist. "The target database will contain millions of images, all fully annotated with information about what objects are in the image, where each object is located, and how much of the image is necessary to recognise it."

[via boingboing]

Comment from: collin [Member] · http://nonplatonic.com/collin.php
I should have put a link to the training/game page...
Here.
Permalink 08/09/05 @ 17:33

Wrong embedding Google!

posted by collin on 05.06.08 at 16:25, math, nonsense, math, random, 1 comment Permalink

Somebody mentioned this in a /. discussion. [I know, I should stop reading those] Apparently Google maps has a fixed latitude/longitude ratio, of ~0.772 correct for 39.5 deg N or S [1 if 0 deg]. So this projection causes angles to be changed if you're very far away from 39.5 deg [I don't know exactly what the projection is so I can't say whether or not it's distance preserving]. E.g. Anchorage, AK, Mapquest and Yahoo don't have this problem.

Comment from: collin [Member] · http://nonplatonic.com/collin.php
Maybe it's a projection to a cylinder of radius whatever the radius of the earth is at 39.5 deg lat... Then it wouldn't be distance preserving. However the lack of straight roads near the poles prevents me from testing my hyopthesis.
Permalink 06/08/05 @ 17:21

For all your graph theory needs.

posted by collin on 05.05.21 at 15:28, math, math, 1 comment Permalink

I was reading some posts over at crooked timber about how physicists are dumb, not that I agree, and some one mentioned this ebook which is actually a legitimate copy of a fairly new Springer-Verlag book.

Comment from: collin [Member] · http://nonplatonic.com/collin.php
So one of the "physicists are dumb" links above is a year old CT joke post, and all the sociologists got pissy when somebody got an article in Physica A about the same thing. An explanation of the whole thing can be found here if anyone wants to read about academic squabbling.
Permalink 05/21/05 @ 18:10