Profile

Cover photo
Alex Nelson
Works at Unfold, Inc.
Attended University of California, Davis
Lives in Los Angeles, California
792 followers|24,202 views
AboutPostsPhotosVideos

Stream

Alex Nelson

Shared publicly  - 
 
David Politzer, Nobel Laureate famous for his work on Asymptotic Freedom in QCD, was once part of a rock band that put out a single in the '80s called "Simple Harmonic Oscillator". Check it out.

http://theory.caltech.edu/people/politzer/SHO.mp3
1
Add a comment...

Alex Nelson

Shared publicly  - 
 
"For a long time I've thought that an understanding of the way ant colonies are able to perform incredibly organized tasks might well be the key to an understanding of human cognition. Yet the ants that invade my house continually baffle me." - Donald Knuth
3
Add a comment...

Alex Nelson

Shared publicly  - 
 
The House just passed HR 2048, which will end NSA collecting bulk data on you and me. We (Unfold, Inc.) predict with 93% probability the Senate will pass the bill.

http://www.judiciary.house.gov/index.cfm/usa-freedom-act
1
Add a comment...

Alex Nelson

Shared publicly  - 
 
I've been looking over some of the HoTT hacks ("modifications") to Coq, and I'm rather nonplussed with the non-declarative style.

The "origin story" of HoTT is interesting; I never knew it came about from just a minor error...

http://nautil.us/issue/24/error/in-mathematics-mistakes-arent-what-they-used-to-be
Vladimir Voevodsky had no sooner sat himself down at the sparkling table, set for a dinner party at the illustrious Institute for…
4
3
John Baez's profile photophilippe roux's profile photoClaudia W. Scholz's profile photoPaul Harrington's profile photo
3 comments
 
Oh, okay.  My sense of humor was turned off.
Add a comment...

Alex Nelson

Shared publicly  - 
Abstract: An important aspect of improving perturbative predictions in high energy physics is efficiently reducing dimensionally regularised Feynman integrals through integration by parts (IBP) relations. The well-known triangle rule has been used to achieve simple reduction schemes.
1
Add a comment...

Alex Nelson

Shared publicly  - 
 
So, Coq is a fashionable proof assistant...something I've been reading up on lately.

One family of proof assistants are "declarative": you write in a human-readable manner, so even if I don't have the program...I can read your code and see if it makes sense.

The other family is "procedural": you have tactics (which apply formal rules of transformation on the goal), then apply one after another. This is not too human readable, but works well with higher order logic...at least, that's my understanding.

Coq belongs to the former. I don't really see why I should get anymore excited about Coq than I should about, say, HOL. Well, Coq uses a synthesis of Martin-Lof type theory fused with a variant of the F# corner of the Lambda cube for its type theory (the so-called "Calculus of Inductive Constructions"), whereas HOL uses classical Higher Order Logic.

Every term in HOL appears to be a "thm" type, so proofs are literally the construction of objects.

The only point for Coq is its tactics are more "intuitive"...so while unreadable, it's not as unreadable as HOL. Hmm...

http://www.cis.upenn.edu/~bcpierce/sf/current/index.html
with Loris D'Antoni, Andrew W. Appel, Arthur Azevedo de Amorim, Arthur Chargueraud, Anthony Cowley, Jeffrey Foster, Dmitri Garbuzov, Michael Hicks, Ranjit Jhala, Greg Morrisett, Jennifer Paykin, Mukund Raghothaman, Chung-chieh Shan, Leonid Spesivtsev, Andrew Tolmach, Stephanie Weirich, ...
1
Add a comment...

Alex Nelson

Shared publicly  - 
 
Want to learn physics but hate spending thousands of dollars on a university education? Well, here's a 23-ish page summary of all you need to know: http://www.math.northwestern.edu/~mlerma/courses/e11-99s/physics.pdf

...now go out there, and build yourself a particle collider!
1
Adam Frank's profile photo
 
I may do just that!
Add a comment...
Have him in circles
792 people
Saroj Dhongadi's profile photo
Fiona Jostsons's profile photo
Jarrett Byrnes's profile photo
Heikki Arponen's profile photo
Michael Hilding's profile photo
Daniel Horn's profile photo
starbaby227's profile photo
Amit Gupta's profile photo
Marek Bernát's profile photo

Alex Nelson

Shared publicly  - 
1
Add a comment...

Alex Nelson

Shared publicly  - 
 
Abstract: Equational reasoning with string diagrams provides an intuitive means of proving equations between morphisms in a symmetric monoidal category. This can be extended to proofs of infinite families of equations using a simple graphical syntax called !-box notation.
1
Add a comment...

Alex Nelson

Shared publicly  - 
 
"It turns out that Maryland hasn’t been under sustained assault from international terrorists, despite the wild fears of the homeland security boosters who seek to justify the center’s budget."

Maybe. Or maybe that's exactly what the terrorists want you to think, biding their time for unsuspecting Maryland citizens to lower their guard...

http://phasezero.gawker.com/inside-the-military-police-center-that-spies-on-baltimo-1700670585
On Ambassador Road, just off I-695 around the corner from the FBI, nearly 100 employees sit in a high-tech suite and wait for terrorists to attack Baltimore. They’ve waited 11 years. But they still have plenty of work to do, like using the intel community’s toys to target this week’s street protests.
1
1
T On's profile photo
Add a comment...

Alex Nelson

Shared publicly  - 
Abstract: A future holographic screen is a hypersurface of indefinite signature, foliated by marginally trapped surfaces with area $A(r)$. We prove that $A(r)$ grows strictly monotonically. Future holographic screens arise in gravitational collapse. Past holographic screens exist in our own ...
1
Add a comment...

Alex Nelson

Shared publicly  - 
 
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!)
1
Add a comment...
People
Have him in circles
792 people
Saroj Dhongadi's profile photo
Fiona Jostsons's profile photo
Jarrett Byrnes's profile photo
Heikki Arponen's profile photo
Michael Hilding's profile photo
Daniel Horn's profile photo
starbaby227's profile photo
Amit Gupta's profile photo
Marek Bernát's profile photo
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
Map of the places this user has livedMap of the places this user has livedMap of the places this user has lived
Currently
Los Angeles, California
Previously
Davis, California - Glendale, California - Dublin, Ireland - Belfast, Northern Ireland - Padua, Italy
Links
Contributor to