Saturday, September 09, 2017

Spontaneous symmetry breaking is much easier to wrap my mind around using a Newtonian example.

Tuesday, September 05, 2017

Regarding the Nashville statement, anthropology:chastity::keep:castle. It's good but insufficient to fortify the keep. Two of the castle walls are respectively located at divorce and contraception.

Wednesday, July 12, 2017

On a randomized control trial at CUNY on replacing remedial college algebra with introductory college statistics:
[T]here is a significant and fairly large (16% without covariates in the model, 14% with) difference in odds of passing the course for those randomized to the intro stats course compared to the elementary algebra course...

I will hold with Hacker in suggesting that this does represent a lowering of standards, and that this is a feature, not a bug. That is, I think we should allow some students to avoid harder math requirements precisely because the current standards are too high. Students in deeply quantitative fields will have higher in-major math requirements anyway.

Yep. And statistics is more directly useful for non-STEM majors who, for example, want to understand the news.

I also found it interesting that "support workshops" for remedial college algebra students didn't measurably improve pass rates in this study. I'm not sure what to make of that. I suppose it's consistent with my anecdotal, non-randomized-control-trial experience that more conscientious students are both more likely to pass and more likely to take the time to get help from tutors and/or their professors on a regular basis.

Saturday, July 08, 2017

Replace the federal income tax deduction of state income taxes with block grants for states with below-average per capita income. Such "equalization grants" work well in Canada and Australia.

Saturday, July 01, 2017

I've long been a fan of Scott Sumner's views on monetary policy. I recently commented on Arnold Kling's blog in defense of Sumner. In summary:
If the Fed wanted 2018 US NGDP to be more than $20T (for example), it could say, "whenever betting markets generally predict 2018 US NGDP under $20T, we will start to buy and hold assets of our choosing, at a rate of $1B the first day and doubling the rate every day thereafter, until betting markets generally predict 2018 US NGDP over $20T."

When there is a large negative expected NGDP, the mismatch between downward-sticky wages and much more plastic hiring/firing/layoffs aggregates into a large short-term misallocation of real resources.

Therefore, the Fed should buy whatever it takes to reverse large downward surprises in expected NGDP.

Monday, June 26, 2017

News of MIT's NAT saddens me.

I remember when the names iteration.mit.edu and recursion.mit.edu were mine; they pointed to my public IPv4 address 18.238.3.106. I don't claim to have done anything innovative with them, but what I did was very educational. I wrote a minimal http server in C++ and hosted a static website with fractal images I created and a Mandelbrot set Java applet I wrote.

I probably never would have been motivated to learn how to write an http server without such public visibility. Security risks? Yes. (I promptly fixed that one.) Despite this, MIT thrived without a NAT for many years. Even if security risks are greater today, firewalls can be made arbitrarily strict without a NAT.

Monday, June 19, 2017

A bit of TeX hacking

I've decided that if I state, say, Theorem 2.2.15 but don't prove it until many pages and lemmas later in Section 5, then, for the reader's sake, I should repeat the theorem verbatim, including the original theorem number, immediately before the proof, as opposed to going straight from the proof of Lemma 5.2.33 to "Proof of Theorem 2.2.15." (Granted, if the delay between statement and proof is just for one "Main Theorem" whose statement is easy to remember, then this is not necessary. My decision is in the context of revising a longer paper with several theorems stated early and proved much later.)

%#1 theoremstyle inpute (plain/definition/remark/...)
%#2 type of theorem (Theorem/Lemma/Corollary/...)
%#3 label of theorem to be repeated 
%#4 unique new input for \newtheorem 
%#5 statement of theorem
\def\repeattheoremhelper#1#2#3#4#5{
  \theoremstyle{#1}
  \newtheorem*{#4}{#2 \ref{#3}}
  \begin{#4}
    #5
  \end{#4}
}

\def\repeattheorem#1#2{
  \repeattheoremhelper{plain}{#1}{#2}{repeat#2}{\csname state#2\endcsname}
}

%usage example
%\theoremstyle{plain}
%\newtheorem{thm}{Theorem}
%...
%\def\statemytheorem{blah blah}
%\begin{thm}\label{mytheorem}\statemytheorem\end{thm}
%...
%\repeattheorem{Theorem}{mytheorem}
%\begin{proof}
%...
%\end{proof}

Saturday, November 19, 2016

I think I need a red ink pad and stamp with "AlgebraRules.com" on it.

Thursday, November 03, 2016

Tuesday, October 18, 2016

Saturday, October 08, 2016

Thursday, September 22, 2016

Tuesday, September 20, 2016

No torque, no spill (in the accelerated reference frame).

Friday, September 09, 2016

An excellent two-minute time-lapse video of two weeks of evolution of antibiotic resistance.

Wednesday, September 07, 2016

Struggles with the Continuum, the most enjoyable survey paper I've read in a long time. It concerns singularities in mathematical physics.

Monday, August 29, 2016

Thursday, August 25, 2016

How much damage would a space probe take flying through the interstellar medium at v=0.2c? (See also this.)

Bottom line: I am seriously entertaining the possibility that I will live to see digital images transmitted from another planetary system.

Wednesday, August 24, 2016

If Saudi Arabia and Iran are fighting a proxy war in Yemen, why is the US taking sides?

Tuesday, August 23, 2016

Saturday, August 20, 2016

Friday, July 22, 2016

At this date, I think it good to revisit my earlier comparison between a million and one. Large numbers are sometimes difficult to reason about, so perhaps using a log scale would help. Let's see... Yep, six strictly exceeds zero.

I am reminded of Peter Thiel's 2009 counsel to escape politics (though he clearly hasn't escaped yet). He sees technology as liberty's only hope. I wish the techno-libertarians well. Why do I say that, when I have become much less individualist over the years? I am simply concerned for the freedoms of my religious community. The Democratic presidential nominee promises nothing but setbacks on that front, and the Republican nominee's promises on that front are worthless because (1) he is incompetent and foolish in a million ways and (2) his harshness invites a huge backlash to come after him. I have reservations about the libertarian nominee, but I have yet to think of a better protest vote.

Update: See also this and this.

Wednesday, June 08, 2016

Don't carry much cash on a road trip, and now don't carry prepaid debit cards either. The bandits have new technology.

Wednesday, June 01, 2016

This is the easiest yet still significant mathematics paper I've read in a long time. (See also Quanta Magazine's coverage.)

Saturday, May 07, 2016

Given my apparent choices in November, I can think of a million reasons not to vote for him who shall not be named, and one reason to vote for him.

Wednesday, April 13, 2016

An 8-dimensional and then a 24-dimensional analog of Kepler's sphere-packing conjecture, widely believed to be true (and actually used for error-correcting codes), were proven true last month, with the major breakthrough due to Maryna Viazovska. (Hales proved the original conjecture in the 1990s.) I noticed that the paper on dimension 24 has Abhinav Kumar as a coauthor. On my dorm floor way back when, Abhinav was a "greater math god" and I was a "lesser math god."

P.S. Why does that paper talk of "+1 eigenfunctions"? What's wrong with "fixed point"?

Thursday, April 07, 2016

In the asymptotically safe gravity proposal, quantum gravity is weaker at high energies. In this proposal, gravity is both weaker and less quantum (meaning the effective Planck length (but not the Planck mass) is smaller) at high energies.

Imagine that "everybody wins" mathematically, i.e., it is proven there are elegant mathematical models consistent with observation and unifying all of fundamental physics, including an asymptotically safe gravity model, a string theory model, loop quantum gravity model, maybe other models I don't want to take the time to mention, and maybe even an "unquantizing" model like in the link. Which theory will win the parsimony contest? Since parsimony is not the same as mathematical elegance or beauty, I'm not confident that the most parsimonious theory will also become most popular.

Friday, March 18, 2016

Positive question: was Rubio the Condorcet winner of the Republican Presidential primary? I don't have the data to say, but it seems at least plausible.

Normative question: Should not the Condorcet winner (if one exists) be the actual winner? (This isn't special pleading; I didn't vote for Rubio in Texas.) Why not let voters somehow rank candidates on their ballots?

Friday, February 26, 2016

"Regulation for thee, but not for me." Democrats usually favor and Republicans usually oppose government regulation of business. What about government regulation of government? What about regulation of organizations receiving government funding? Many critiques of regulating business apply equally well to regulating governments and those they fund: bottlenecks caused by slow approval processes, uniform rules that don't make sense for every organization, and high compliance costs (e.g., man-hours spent learning the regulations and documenting compliance) that overly burden (and in some cases even prevent or destroy) small organizations and their innovative initiatives. "Small organizations" includes small departments with larger organizations.

I see these problems all too often in my job. I also recently saw how even the student organizations at my university are over-regulated. This blog post was provoked by Section 51.9361 of Subchapter Z of Chapter 51 of Subtitle A of Title 3 of the Texas Education Code.

For another anecdote, I've done a bit of mentoring of future middle-school and high-school math teachers. Once they start their training at the local public schools, they are unanimously dismayed by the emphasis they see given to preparing the students for state-mandated exams. (Home schooling in Texas, on the other hand, is hardly regulated at all. I highly recommend it.)

I have an abstract, general desire for smaller governments, but I expect defense, law enforcement, infrastructure, education, and research to be extensively funded by governments (but perhaps not directly provided by governments) from now until the end of the world. Therefore, quoting Robin Hanson,

This view suggests that being pro- or anti-regulation isn’t the same as being pro- or anti-government, and it suggests a possible left-right deal: reduce regulation in both private and public sectors. Have more trust in private competition to deal with the problems we leave to the private sphere, and in smart well-trained civil servants to deal with the problems we leave to the public sphere. And have less trust in lawyers, judges and rule-specialists of all sorts to fix our problems with more rules.

Monday, February 15, 2016

In defense of the cosmological constant.

On the other hand, cosmic inflation I still consider quite mysterious.

Friday, February 12, 2016