ℝolliℵg M∀th Thr∑a∂

he totally quit ILX though because IRL people were stalking him on ILX!

ya i knew they hadn't studied math. caltucky is siiick though

LOL http://en.wikipedia.org/wiki/Cox%E2%80%93Zucker_machine

relatedly, was pleased to learn that a subfield of modern algebraic geometry is concerned with mixed motives

http://en.wikipedia.org/wiki/Motive_(algebraic_geometry)#Mixed_motives

oh vis a vis the prior link i believe its been confirmed that they decided to write a paper together on something on the basis of their names

A nice long article on Yitang Zhang from the New Yorker:

http://www.newyorker.com/magazine/2015/02/02/pursuit-beauty

Nice, thanks.

something i have long wondered: why do we think of numbers as being ordered left to right?

Humans represent numbers along a mental number line (MNL), where smaller values are located on the left and larger on the right. The origin of the MNL and its connections with cultural experience are unclear: Pre-verbal infants and nonhuman species master a variety of numerical abilities, supporting the existence of evolutionary ancient precursor systems. In our experiments, 3-day-old domestic chicks, once familiarized with a target number (5), spontaneously associated a smaller number (2) with the left space and a larger number (8) with the right space. The same number (8), though, was associated with the left space when the target number was 20. Similarly to humans, chicks associate smaller numbers with the left space and larger numbers with the right space.

http://www.sciencemag.org/content/347/6221/534.full

That's weird that they somehow observed that in chicks, but I guess it makes sense to me for numbers to be ordered from left to right in cultures that have languages that are written from left to right. I guess most written languages do go from left to right, with the exception of Arabic and Hebrew and a few others.

I started reading the recently published Computability: Turing, Gödel, Church and Beyond edited by Copeland, Posy, and Shagrir. It’s a servant of all. But so far, so good. Especially enjoyed Martin Davis’ essay, “Computability and Arithmetic.” It explores Hilary Putnam and Yuri Matiyasevich’s work on Hilbert’s tenth in a comprehensible way.

― Allen (etaeoe), Tuesday, 3 December 2013 18:59 (1 year ago) Permalink

my lazy friend finally finished his review of this book, you can find it here

Kudos to your *friend*

anybody have a fav text on GLM math? went to seminar this week and it has become abundantly clear that my ignorance of GLM will be a detriment to ultimate career goals pretty soon.

When I was undergrad, Euler, many years ago, book we read in intro(!) course was Boolos and Jeffrey, which was still pretty challenging. Guess now there is new co-author for latest editions.

Boolos and Jeffrey is good. I've never taught from it, though; on these topics I have my own notes that I use. When I've taught Gödel I just teach right from the 1931 paper, giving the requisite background as we go along.

Cool. Did you ever read the Hodges bio of Turing? Thinking of rereading myself.

no, I'm not great about biographies, except for musicians. But it's supposed to be great!

I learned a lot of what I know about Turing from his own writings plus this excellent volume

This review made me lol when I saw how they described Kurt Gödel.

that is...not a good review

That review is very silly, sorry.

Seem to recall posing an image of HSM Coxeter here, but think it was another thread. Anyway, been leafing through this recent bio of him, King of Infinite Spac: Donald Coxeter, the Man Who Saved Geometry, which is quite good- It won the, um, Euler Book Prize!. I came across the famous picture from Mysterium Cosmographicum of Kepler's celestial model containing the nested Platonic solids and it was pointed out that at one point his patron wanted it made into a functioning punchbowl! Which led me to this article which I haven't read but yet has lots of nice picture: http://archive.bridgesmathart.org/2011/bridges2011-379.pdf

http://docstudio.tvo.org/sites/default/files/imagecache/masterseries_620x350/The-Man-Who-Saved-Geometry%5B1%5D_0.jpg

couple nice probability "puzzles"

#1
sample n points from a uniform distribution over [0,1]. what is the average gap, i.e., the expected length of the gap between two neighboring points? call the gap between the i-th and the (i+1)-th (ordered) sample points L(i). What is the probability that L(i) is greater than c, for some positive constant c < 1?

#2
buses arrive at a bus stop like a poisson process, on average once every half hour.
you arrive at the bus stop:

1) how long ago on average did the last bus come?
2) how long will you have to wait on average for the next bus?
3) how long is the average time between two buses again?
4) what's going on?

art: you mean generalized linear models? i never took the course myself, but when i worked at the campus bookstore this was the textbook being sold

http://images.tandf.co.uk/common/jackets/amazon/978158488/9781584889502.jpg

Coxeter bio has some funny quotes from Descartes about his disdain for ye old time geometry, as reported by E.T. Bell in Men of Mathematics ( where is my copy?)

Bus puzzle slightly blew my mind, also explained many frustrating waits at london bus stops over the years. (I cheated, obv.)

:-D

i'm still trying to figure it out, no spoilers please

For the first part of #1, my initial thought is that on average the gap between points should be roughly 1/n.

i got it!

maybe

maybe not

:-(

http://math.stackexchange.com/questions/1220953/a-difficult-integral?stw=2

Enjoyed both those problems from a month ago.

Do you guys know the formula for generating Pythagorean triples?

yeah, a^2 + b^2 = c^2

That is the equation they must satisfy, yes, but there is a simple way to generate the integral trios (a,b,c) that will work.

The way I learned to derive it in high school used number theory 101 but there is also a geometric demonstration I just came across.

i saw it in a geometry summer course but don't remember. care to demonstrate?

attempt some putnam problems: http://kskedlaya.org/putnam-archive/2014.pdf

a friend gave me the statement of a top-secret combinatorics theorem he proved. can't share the deets but it's so elementary i couldn't believe it wasn't already done or a special case of something else. been fudging my way through a proof all weekend

gotta check those untranslated soviet math textbooks for those things iirc

I never did contest math in HS and I'm still only at best a fake fake mathematician (i.e. a programmer who actually enjoyed theoretical CS classes) so Putnam problems just seem unattainable to me

there was a putnam prep class at my undergrad you could sit in on, mostly just watching in disbelief as the prof, a hyper-intense russian graph theorist, crushed every problem in a matter of seconds

http://jwilson.coe.uga.edu/emt668/emat6680.f99/challen/proof/proof.html

Proof by calculus: "This proof requires calculus, so we'll skip it."

otm

Archimedes frowns.

hint to flopson: use stereographic projection.

Thanks to caek's post here: academic language is often purposely obfuscated I read Timothy Gower's Mathematics: A Very Short Introduction a while back, which blew my mind as some kind of masterpiece of popularization, which eventually led me to the Princeton Companion To Mathematics which he addeds and sort of takes the same spirit and enlarges it a thousand-fold with tons of useful explanations of advanced mathematical subjects without diverging into the usual bifurcation of either oversimplification + dodgy metaphors or too much technical detail.

Of course, it is kind of a different thing not a popularization.

Well that's now on my mental wishlist

Maybe you are near a library that has it?

lol the first copy i stole from the internet still has editorial markup in its margins

PUP: Tim would
like to keep
‘brackets’ as even
he, as a
mathematician,
would say
‘brackets’ rather
than the more
formal
‘parentheses’. OK?

i never call them parentheses in math

In addition to referring to the class of all types of brackets, the unqualified word bracket is most commonly used to refer to a specific type of bracket. In modern American usage this is usually the square bracket and in modern British usage this is usually the parenthesis.