## Profile

Alex Nelson
Works at Unfold, Inc.
Attended University of California, Davis
Lives in Los Angeles, California
780 followers|23,036 views

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### Alex Nelson

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A field F has characteristic n if the morphism of the integers into F generated by f(1)=1 has its smallest positive integer n be such that f(n)=0. (If no such n exists, for example the rationals has the integers as a subring, then we say it is characteristic 0.)

Puzzle: Is there a field with characteristic 0 that does not have a subfield isomorphic to the rationals?

I think the answer is, unsurprisingly, there is no such field. If F has characteristic 0, then it has a subring isomorphic to the integers.

Take this subring, and consider the field of fractions generated by this subring. Clearly the field of fractions is isomorphic to the rationals. (Sub-puzzle: is the isomorphism unique? Unique up to some equivalence?)

We need to show the field F has the field of fractions as a subfield. Uh, that's left as an exercise for the reader...yeah ;)

(The embedding of the subring isomorphic to the integers should extend to the field of fractions, we just need to prove that its image on the field of fractions is actually contained in F. I honestly don't know off the top of my head if it will be contained in F or not!)﻿
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### Alex Nelson

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It has taken a mere 29 years, but now GNU Hurd has released version 0.6...perhaps they'll get to version 1.0 in my grandchildren's lifetime...

http://lwn.net/Articles/640668/﻿
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"An average academic journal article is read in its entirety by about 10 people. To shape policy, professors should start penning commentaries in popular media."﻿
Many of the world's most talented thinkers may be university professors, but sadly most of them are not shaping today's public debates or influencing policies.
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### Alex Nelson

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Fun exercise: prove $\cos^{n}(x/\sqrt{n})$ converges to $\exp{-x^{2}/2)$.

There are several different approaches I could think of, but they all fall into two "families".

One is to set up a differential equation, arguing $f_{n}(x) = \cos^{n}(x/\sqrt{n})$ has a stable limit $f_{n}(x)\to f(x)$ as $n\to\infty$, then argue $f'_{n}(x)$ has as its limit as $n\to\infty$ precisely $f'(x)$. There's some elementary algebra to get things right, and one needs to observe $f_{n}(0)=1$ for all $n$.

The other is to use the limit definition of e, using $\cos^{n}(x/\sqrt{n})=(1-\sin^{2}(x/\sqrt{n}))^{n/2}$ then arguing $x/\sqrt{n}$ is "small", Taylor expand, then "follow your nose".

Neither are 100% rigorous, both involve handwaviness at some point. But I cannot think of a slick proof for the claim that's completely ("arbitrarily") rigorous.﻿
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### Alex Nelson

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So, I've had the rare fortune to sit in on random math courses at Caltech. I try to write up my notes in #LaTeX as a way of reviewing them, and have found Leslie Lamport's structured proofs quite good at catching errors in my reasoning.

But Lamport's LaTeX package (pf2) is woefully inadequate for my purposes. Most seriously, it's incompatible with amthm.

Since I'm not using TLA+ for automated theorem proving purposes, I can use a stripped down version of Lamport's package. Here's a first pass at it.

What's nifty about my package is if you, like me, are using this only while iteratively correcting your notes, and do not wish the rest of the world to see it, you can pass the "hide" option to comment out all the structured proofs.

https://github.com/pqnelson/notebk/wiki/Structured-Proof-Macros﻿
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### Alex Nelson

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Quillen's notebooks are now freely available online as pdfs.

http://www.claymath.org/publications/quillen-notebooks﻿
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Abstract: The singular limits of massless gauge theory amplitudes are described by an effective theory, called soft-collinear effective theory (SCET), which has been applied most successfully to make all-orders predictions for observables in collider physics and weak decays.
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### Alex Nelson

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Does intelligent life need an industrial revolution?

The answer, Dartnell posits, is "Yeah, mostly."

http://aeon.co/magazine/technology/could-we-reboot-civilisation-without-fossil-fuels/﻿
It took a lot of fossil fuels to forge our industrial world. Now they're almost gone. Could we do it again without them?
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He was implying that any "Age" - coal, steam and, in the future, oil, e.g. - ends when something better comes along @ a reasonable price. And yes, he put in a cute way to get attention when the market was panicking at the "peak oil" theory.﻿

### Alex Nelson

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Climate scientists highlight cloud mysteries in a bid to compete with astronomy and cosmology.
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### Alex Nelson

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California was supposed to have El Nino this year...but that didn't pan out. Could it be that giant plastic garbage island in the Pacific interfered somehow?

Wikipedia tells me the name of this giant garbage patch is really  the "Great Pacific garbage patch" --- a regal name for an ignominious region.

Anyone know for sure?

http://en.wikipedia.org/wiki/Great_Pacific_garbage_patch﻿
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### Alex Nelson

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Someone just gave me 5,216.98 bits (or 0.00521698 Bitcoins) for some references I posted on Reddit. I'll be retiring any day now to my provincial French chateau...﻿
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People
In his circles
104 people
Have him in circles
780 people
Communities
8 communities
Education
• University of California, Davis
Mathematics, 2006 - 2011
Basic Information
Gender
Male
Other names
Alexander Nelson
Story
Tagline
They call me "Tractor Man"
Introduction
I'm a mathematical physicist (more on the mathematical side) with interests in category theory, monstrous moonshine, number theory, Diophantine approximations, super symmetry, Lie groups, differential geometry, and other topics. On the physical side, I'm intrigued by quantization of gauge systems, Quantum Field Theory, the mathematical underpinnings of particle physics, classical and quantum gravity.

I've been to Nottingham, England in July 2008 to attend Quantum Gravity and Quantum Geometry 2; and I've attended "Algebra and Topology in Interaction" during September 2009, in honour of Dr Fuchs' Birthday.

Starting June 2009 until June 2010, I did undergraduate research with Derek Wise with funding from VIGRE. We worked on Chain Field Theory in discrete spacetimes.

In April 2010 I was asked to peer review for the International Journal of Physical Sciences.

August 2010 I studied abroad at Trinity in Dublin, and Queen's University in Belfast.

In June 2011, I attended "Quantum Geometry and Quantum Gravity" in Zurich, Switzerland; then in July I went to the "Category Theory 2011" conference in Vancouver.

February 2012, I attended "
30th Annual Western States Mathematical Physics Meeting" at Caltech.
Work
Occupation
Mathematician/Programmer/Oracle
Employment
• Unfold, Inc.
Software Developer, 2012 - present
I program in Clojure (Lisp for JVM), do numerical analysis, predict how congress will vote, analyze the Syrian Civil War, and much much more!
• University of California, Davis
Student, Researcher, 2006 - 2011
Places
Currently
Los Angeles, California
Previously
Davis, California - Glendale, California - Dublin, Ireland - Belfast, Northern Ireland - Padua, Italy