The Eudoxus Real Numbers

Article by Arthan, R. D.

In collection: Unusual arithmetic

This note describes a representation of the real numbers due to Schanuel. The representation lets us construct the real numbers from first principles. Like the well-known construction of the real numbers using Dedekind cuts, the idea is inspired by the ancient Greek...

URL: http://arxiv.org/abs/math/0405454

PDF: http://arxiv.org/pdf/math/0405454v1

Entry: http://read.somethingorotherwhatever.com/entry/Arthan2004

Just a few weeks ago, my colleagues and I published a review article on a problem I like to think of as the TARDIS of math: It looks small, but it's bigger on the inside, and it takes you to unexpected places. http://www.mdpi.com/2075-1680/6/3/21

I tried to make the bibliography comprehensive, but new work has come out, so it's already outdated: https://scirate.com/arxiv/1707.09911

And this morning I was sent a draft of a new paper, so it'll be outdated yet again soon

This is a good thing!

just noticed I didn't include the link! It's at https://codepen.io/christianp/full/Ojmbra/

Inspired by Alison Kiddle, I've made an Auto-Santa 3000: given a list of naughty things, add up the scores of the things you did. Then it uses the total to tell you the things you did! https://mathstodon.xyz/media/wabXGCyuSpERkVXHjGA https://mathstodon.xyz/media/BiBHC_ZU9XjOmyBGT3I

#quantum #physics / #mathematics:

"Dimension towers of SICs. I. Aligned SICs and embedded tight frames"

There's some good stuff in this essay, "Do Mathematicians Have Responsibilities?": http://www.math.columbia.edu/~harris/otherarticles_files/Responsibilities.pdf

The editorial board for the Journal of Algebraic Combinatorics left to continue the journal under a new name in Open Access form:

https://gowers.wordpress.com/2017/07/27/another-journal-flips/

New paper dance!

"The SIC Question: History and State of Play" -- http://www.mdpi.com/2075-1680/6/3/21

Just spent half an hour with my summer student getting into the subtleties of the conditions required for "throwing two dice" to have 36 possible outcomes.

I came up with a good example: I'm colourblind, so if we throw a red and a green die at the same time, the student can distinguish them, but I can't. So the outcomes are a property of the observer, not the trial itself.

Pentagon Tiling Proof Solves Century-Old Math Problem, _Quanta Magazine_, https://www.quantamagazine.org/pentagon-tiling-proof-solves-century-old-math-problem-20170711/

I already posted about this a couple of months ago (https://plus.google.com/100003628603413742554/posts/dC6Qo87LouC) but now there's this nice popular-press article, and confirmation on the correctness of "the most important half of Rao's proof" by Thomas Hales.

I wish I could express how exciting it is to have a SIC solution in dimension 844:

https://arxiv.org/abs/1707.02944

844^2 = 712,336 lines, in a space where map coordinates use the square root of minus one, and every pair of those lines meet at exactly the same angle

#quantum #physics / #mathematics

Today in #quantum #physics / #mathematics: I updated our introductory review article on complex equiangular lines, a.k.a. symmetric informationally complete quantum measurements.

https://arxiv.org/abs/1703.07901

The bibliography is caught up to this week's news, and the historical overview section is more comprehensive than it was in the previous version.

Early career researchers: have you been bullied into doing bad science? Pressured to publish only in "prestigious", non-open journals?

There's a letter to sign.

http://bulliedintobadscience.org/

Today in #mathematics and #quantum stuff: I have apparently talked myself into writing a thing about how the sporadic SICs relate to the exceptional Lie algebras. (The Hesse SIC is secretly in alliance with E6, and the Hoggar SIC with E7 and E8.)

Submitted a review article to a #mathematics journal.

Campus is not filled with undergrads, but the coffee place in my building is closed. Net loss.

@tobascodagama

Scientist by training, snarker by inclination. I have a blag at my wobsite, Science After Sunclipse (https://www.sunclipse.org)

Joined Jun 2017