Sewing-Machine comments on Taking Ideas Seriously - Less Wrong

51 Post author: Will_Newsome 13 August 2010 04:50PM

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Comment author: [deleted] 25 August 2010 05:01:48PM 1 point [-]

I like this point a lot. But it seems very convenient and sensible to say that some things are more problematic than others. And at least for certain kinds of claims it's possible to quantify how problematic they are with numbers. This leads one (me at least) to want a formalism -- for handling beliefs -- that involves numbers, and Bayesianism is a good one.

What's the conjectures-and-refutations way of handling claims like "it's going to snow in February"? Do you think it's meaningless or useless to attach a probability to that claim?

Comment author: [deleted] 25 August 2010 09:12:10PM 1 point [-]

There is no problem with theories that make probabilistic predictions. But getting a probabilistic prediction is not tantamount to assigning a probability to the theory that made the prediction.

Comment author: Perplexed 25 August 2010 09:44:46PM *  2 points [-]

True. But you seem to be assuming that a "theory" has to be a universal law of nature. You are too attached to physics. But in other sciences, you can have a theory which is quite explanatory, but is not in any sense a "law", but rather it is an event. Examples:

  • the theory that the moon was formed by a collision between the earth and a Mars-sized planetesimal.
  • the theory that modern man originated in Africa within the past 200,000 years and that the Homo erectus population outside of Africa did not contribute to our ancestry.
  • the theory that Napolean was poisoned with arsenic in St. Helena.
  • the "aquatic ape theory"
  • the endosymbiotic theory of the origin of mitochondria
  • the theory that the Chinese discovered America in 1421.

Probabilities can be assigned to these theories.

And even for universal theories, you can talk about the relative odds of competing theories being correct - say between a supersymetric GUT based on E6 and one based on E8. (Notice, I said "talk about the odds", not "calculate them") And you can definitely calculate how much one particular experimental result shifts those odds.

Comment author: [deleted] 25 August 2010 11:38:01PM *  2 points [-]

As you pointed out earlier, we have two ostensibly different ways of investigating the theory that the Chinese discovered America in 1421: the Popperian way, in which this theory and alternatives to it are criticized. And the Bayesian way, in which those criticisms are broken down into atomic criticisms, and likelihood ratios are attached and multiplied.

I've seen plenty of rigorous Popperian discussions but not very many very rigorous -- or even modestly rigorous -- Bayesian discussions, even on this website. One piece of evidence for the China-discovered-America theory is some business about old Chinese maps. How does a Bayesian go about estimating the likelihood ratio P(China discovered America | old maps) / P(China discovered America | no old maps)?

Comment author: Perplexed 25 August 2010 11:58:22PM 2 points [-]

I think you want to ask about P(maps|discover) / P(no maps|discover). Unless both wikipedia and my intuition are wrong.

Does catching you in this error relieve me of the responsibility of answering the question? I hope so. Because I would want to instead argue using something like P(maps|discover) vs P(maps|not discover). That doesn't take you all the way to P(discover), but it does at least give you a way to assess the evidential weight of the map evidence.

Comment author: [deleted] 26 August 2010 12:28:17AM 0 points [-]

Now P(Sewing-Machine is a phony) = ?

Here's another personal example of Bayesianism in action. Do you have a sense of how much you updated by? P(Richard Dawkins praises Steven Pinker | EP is bunk)/ P(Richard Dawkins praises Steven Pinker | EP is not bunk) is .5? .999? Any idea?

Comment author: Perplexed 26 August 2010 12:57:56AM 1 point [-]

P("Sewing Machine" is a nym) = 1.0
P(Sewing Machine has been disingenuous) = 0.5 and rising
P(Dawkins praises Pinker|EP is not bunk) is ill defined because
P(EP is not bunk) = ~0
but I have updated P(Dawkins believes EP is not bunk) to at least 0.5

Comment author: [deleted] 26 August 2010 12:59:27AM 0 points [-]

I don't know what "disingenuous" means.