Sunday, October 25, 2015

A Political Theory Of The Second Dimension

https://en.wikipedia.org/wiki/NOMINATE_(scaling_method)
... roll call voting in both the House and the Senate can be organized and explained by no more than two dimensions throughout the sweep of American history. The first dimension (horizontal or x-axis) is the familiar left-right (or liberal-conservative) spectrum on economic matters. The second dimension (vertical or y-axis) picks up attitudes on cross-cutting, salient issues of the day (which include or have included slavery, bimetallism, civil rights, regional, and social/lifestyle issues). For the most part, congressional voting is uni-dimensional, with most of the variation in voting patterns explained by placement along the liberal-conservative first dimension.
The general words used to describe the "second dimension" nowadays is "insider v. outsider".  I want to describe this second dimension in a different way.

  • On the one hand, we have "mainline". For a religion, a "mainline" religion is one where if your parents are members of the religion, then you are a member of the religion.
  • On the other hand, we have "evangelical".  For a religion, if your parents are a member of the religion, that doesn't make you a member of the religion.  Only some affirmative act (most commonly baptism by immersion) makes you a member of the religion.

Because of the word "evangelical", you might assume at first glance that evangelical = conservative and mainline = liberal.  On the other hand, mainline = "no change, stick to the past" = conservative, and evangelical = "new ideas" = liberal ("radical" as the antonym of mainline might be more expected here).  So I don't think there's any permanent connection between the two dimensions.

In Congress, the "mainline" theory is "we need to pass legislation even if it's not perfect because that's how the country works".  And the "evangelical" theory is "we shouldn't pass any legislation that isn't ours; and the country has never broken before so it probably won't break now".  ... and in the specific case of "running a government", the mainline theory is right.  It's why the government shutdowns never work as a tactic.

But large parts of the US government do run on auto-pilot now.  Continuing spending resolutions and the like can cause spending to continue at the same rate forever even if (especially if) Congress does nothing other than vaguely agreeing to keep things running for another year.

So what does it matter?  ... well, the only real way to compromise with evangelicals is to say "see, it didn't work".  Or just vote them out of office, which is another way to show that it didn't work.  It worked with the Prohibition movement in the 1920s.  And in general, solutions are a lot more peaceful than they were in the Roman Republic, where Senators were regularly murdered on the floor of the senate.

Tuesday, October 13, 2015

Drinking Games

OK, here's my drinking game for tonight's Democratic debate (note: for "health reasons" I'm sticking to Apple Cider Vinegar for all drinks tonight).

Lunacy: Take a drink if anyone mentions:
  • "email server"
  • Benghazi
  • Donald Trump
  • Joe Biden
  • anything about building a wall
  • either Sheldon Adelson or Bibi Netanyahu
  • either "I'm not a Democrat" or "[opponent] isn't a Democrat"
  • "we need more debates"

Policy Buzzwords: Take two drinks if anyone mentions:
  • the Mexico City Policy
  • Houthis
  • AFL-CIO (one bonus drink for the first time any specific union is mentioned)
  • the F-35
  • anything about "stopping the NRA"
  • any country in Asia, excluding the Middle East, Russia, and China 
(note: I'm hopeful enough there will be something intelligent about the TPP that it doesn't get a drinking point on its own)
Candidate Specials: Finish your glass if:
  • Hillary Clinton makes a joke about being a robot.
  • Bernie Sanders says Hillary is wrong in response to anything she says during the debate.
  • Martin O'Malley says he has the best record of anyone on stage.
  • Lincoln Chafee or Jim Webb either drop out of the race on stage, or plug their book.
  • the moderators apologize for Joe Biden not being on stage

Mere Anarchy: Finish your glass, pour another glass, and finish that if:
  • Anyone mentions Ronald Reagan
  • Joe Biden actually shows up on stage, possibly as a hologram
  • A Donald Trump tweet from during the debate is mentioned
  • there's a question about "do you believe in God"

Thursday, October 8, 2015

Some thoughts on Inter-Universal Teichmuller Theory


So I've been trying to think about something complicated that I don't understand, yet should at least nominally be possible.  And Mochizuki's abc proof seems like the hardest possible thing that might possibly be understandable.  After reading the abstracts, I have approximately this understanding of the proof structure.  The bold parts are what I think are the main actually interesting claims in the papers, the rest is background for my own benefit as much as yours.  This is also roughly the structure of the Fermat's Last Theorem proof (which I also don't understand), which is roughly "statements about Elliptic Curves", "Taniyama Shimura", and "proving FLT based on Taniyama Shimura".

The papers are at http://www.kurims.kyoto-u.ac.jp/~motizuki/papers-english.html , the Teichmuller papers are at the very bottom of the page.
  • Part 1: A chaotic system is any system where a small change in initial input will almost always cause a large change in the iterated / Poincare recurrence of the output. [you can create your own epsilon-delta definition]. An elliptic curve is an equation of the form y2 = x3 + ax + b .   All chaotic systems are isomorphic to an extended elliptic curve.  The definition of "all chaotic systems", "isomorphic", and "extended elliptic curve" probably take up at least 50 pages each.  Presumably "semi-graphs of anabelioids, Frobenioids, the etale theta function, and log-shells" are some of these things.
  • Part 2: A general method of constructing isomorphisms between chaotic systems.  This probably involves showing that both chaotic systems possess properties that are only present in one specific set of extended elliptic curves, and thus the systems must be isomorphic in other properties as well.
  • Part 3: A construction of an isomorphism of the natural numbers to a different chaotic system.  For most purposes, the natural numbers (most obviously in the distribution of primes and prime powers) behave like a chaotic system.  Presumably the proof demonstrates that it actually is a chaotic system.
  • Part 4: Construct a proof of abc.  Any infinite family of counterexamples to abc would probably demonstrate some type of pattern, and if the natural numbers are isomorphic to a different chaotic system where we can prove there are no infinite families of counterexamples, then there are only finitely many counterexamples to abc (which is in fact a proof of abc).