Sunday, September 13, 2015

Thought experiments in alternate universes

Alternate universes ... [reference]
A couple of days ago, I did an update to this post on Dani Rodrik's new book and his view that various economic models are actually just experiments on systems that are theoretically isolated via assumptions -- a view that I think is actually pretty silly.

I realized that there's a better analogy for what Rodrik is trying to say.

In a sense, Rodrik is saying economic models are thought experiments in alternate universes. Those alternate universes are created from the different economic assumptions. The picture above has a collection of universes with positive, negative and zero cosmological constant; however, the assumptions in economic models of perfect competition or satiation of preferences (or transitive preferences themselves) create e.g. different Arrow-Debreu universes with different properties.

What it comes down to is that if you want to use your alternate universe model to address policy in our universe, you're going to have to:

a) Have fundamental theory that tells you when the assumptions are valid
b) Empirically determine the assumptions are valid
c) Prove that your model is independent of your assumptions
d) Some combination of the above three

10 comments:

  1. E) argue that there is no other morally acceptable way to run an economy

    ReplyDelete
    Replies
    1. Which moral system? Kantian deontology? Utilitarianism? Virtue ethics?

      Delete
    2. Lol... Jason, I love it. I barely know what utilitarianism is let alone the other two. You might enjoy the following (transcripts at the bottom):
      http://rationallyspeakingpodcast.org/show/rs142-paul-bloom-on-the-case-against-empathy.html
      I like the lead in sentence (in the description):

      "I'm writing a book on empathy," psychologist Paul Bloom tells people. They respond warmly, until he follows up with, "I'm against it."

      He doesn't settle on utilitarianism or Kant's ideas... but he brings them up. He's more just arguing against using empathy as a moral guide. IMO he makes a good case.

      Delete
  2. O/T: did you see this?
    http://economistsview.typepad.com/economistsview/2015/09/youre-not-irrational-youre-just-quantum-probabilistic.html

    ReplyDelete
    Replies
    1. I can't see the original paper, but from these notes:

      http://mypage.iu.edu/~jbusemey/quantum/Quantum_Information.pdf

      ... I'm not sure the "quantum" part is necessary. The properties they are using are only the fact that your state vectors (like the states | good > and | bad >) may not be orthogonal -- that the Hilbert space is a vector space.

      Maybe there is more to it, but that's what I get from a first read.

      Delete
    2. Thanks. I didn't check the source paper at all. However I had no idea what was "quantum" about it from the piece I linked to.

      Delete
    3. Actually an easier way to see that there's no reason for the "quantum" is that they are using the law of cosines and calling the cos term a "quantum interference" term even though the law has existed for thousands of years:

      https://en.wikipedia.org/wiki/Law_of_cosines

      It just adjusts the Pythagorean theorem for non-orthogonal triangle legs (for the case when you don't have a right triangle).

      Delete
  3. O/T: Jason, what's your opinion of this:
    http://www.preposterousuniverse.com/blog/2015/08/11/the-bayesian-second-law-of-thermodynamics/#more-12569

    ReplyDelete
    Replies
    1. I read that when it came out -- it's interesting. I make reference to the fluctuation theorem in my draft paper and a couple of times on this blog.

      I also have a "heuristic derivation" of quantum mechanics from a holographic horizon and the fluctuation theorem:

      If the entropy change by moving Δx is ΔS ~ m Δx (Bousso's covariant entropy bound), then the fluctuation theorem says that for a small change in position relative to the horizon we have

      P(|ΔS|)/P(-|ΔS|) = exp(ΔS)

      We do a Wick rotation and take the log

      log P(Δx) - log P(-Δx) = -i m Δx

      taking the limit as Δx goes to zero and using the definition of the derivative, we have

      (1/P(x)) d/dx P(x) = - i m

      so that

      (i d/dx - m) P(x) = 0

      Which is the Dirac equation in one dimension.

      Of course there are issues with this ... Wick rotation is a problematic procedure when you don't know the theory you're working with (i.e. the theory of everything that governs the behavior of the states on the horizon) and the final result is in terms of a probability, not a probability amplitude (wavefunction). But it's still kind of neat.

      Delete
    2. Wow, thanks. I read that a couple of times but I'm going to have to put that on the back burner for now. I think I'll start by exploring all of Carroll's links. He mentions "cross entropy" which I'd never encountered before until that post and your blog (as a component of the asymmetric KL divergence between distributions you sometimes invoke).

      Delete

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