HamletHenna comments on Causal Universes - Less Wrong

60 Post author: Eliezer_Yudkowsky 29 November 2012 04:08AM

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Comment author: CCC 28 November 2012 09:44:35AM 6 points [-]

Hmmm. Causal universes are a bit like integers; there's an infinite number of them, but they pale as compared to thenumber of numbers as a whole.

Mostly-causal universes with some time-travel elements are more like rational numbers; there's more than we're ever going to use, and it looks at first like it covers all possibilities except for a few strange outliers, like pi or the square root of two.

But there's vastly, vastly more irrational numbers than rational numbers; to the point where, if you had to pick a truly random number, it would almost certainly be irrational. Yet, aside from a few special cases (such as pi), irrational numbers are hardly even considered, never mind used; we try to approximate the universe in terms of rational numbers only. (Though a rational number can be arbitrarily close to any given number).

Irrational numbers are also uncountable, and I imagine that I'll end up in similar trouble trying to enumerate all the universes that could exist, given "Stable Time Loops and even stranger features".


Given that, there's only one reasonable way to handle the situation; I need to assign some probability to "stranger things" without being able to describe, or to know, what those stranger things are.

The possibilities that I can consider include:

  • Physics as we know it is entirely and absolutely correct (v. low probability)
  • Physics as we know it is an extremely good approximation to reality (reasonable probability)
  • The real laws of the universe are understandable by human minds (surprisingly high probability)
  • Stranger Things (added to the three above potions, adds up to 100%)

Alternatively:

  • The universe is entirely causal (fairly low probability)
  • The universe is almost entirely causal, with one or more rare and esoteric acausal features (substantially higher probability, maybe four or five times as high as the above option)
  • The local causality observed is merely a statistical fluke in a mostly acausal universe (extremely low probability)
  • Stranger Things (whatever probability remains)

The reason why the second is higher than the first, is simply that there are so many more possible universes in which the second would be true (but not the first) in which the observations observed to date would nonetheless be true. The problem with these categorisations is that, in every case, the highest probability seems to be reserved for Stranger Things...

Comment author: [deleted] 28 November 2012 05:36:29PM 5 points [-]

Causal universes are a bit like integers

Mostly-causal universes with some time-travel elements are more like rational numbers; there's more than we're ever going to use

Rationals and integers are both coutable! This is one of my favorite not-often-taught-in-elementary-schools but easily-explainable-to-elementary-school-students math facts. And they, the rationals, make a pretty tree: http://mathlesstraveled.com/2008/01/07/recounting-the-rationals-part-ii-fractions-grow-on-trees/