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How Likely is a Random Universe to Produce Your Twin? - Packbat's Journal
Saturday, Sep. 18th, 2010
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How Likely is a Random Universe to Produce Your Twin?
Dan Shive (best known as the creator of El Goonish Shive) recently wrote a brief argument why alternate universes would probably not contain alternate "you"s. His argument looks correct, as far as it goes, but it is qualitative - lacking numerical estimates - and I don't see why it has to be. The data exists. Surely ballpark back-of-the-envelope numbers could be produced.

...but not trivially. Dan Shive's challenge can - and I think should - be broken down as follows.

First: how strictly identical must two individuals be to be called twins, for our purposes? There are two parallel criteria to be examined, each of which can be held to a stronger or weaker standard:

Genetic matching
When it comes to similarity on a genotypal scale, two defined benchmarks stand out for measurement purposes: perfect duplication and identical twin duplication. The former would have all three-billion-plus base pairs match; the latter would require that the match be no less near than is typical in monozygotic (colloquially: identical) twins. This latter standard would suggest measuring the difference at some specified stage of development, perhaps birth.

Personality matching
In many ways, the genetic criteron is dissatisfying, primarily because one does not think of oneself as one's genes. Identical twins are different people, for example. This criterion may be held to three levels of severity:
  1. Indistinguishable - trading places would result in no apparent change with respect to behavior. This is almost certainly impossible, and not very good SF, either.
  2. Birds of a feather - each would predictably have similar reactions to the same items. For example, if you showed the same movie to each, one may be nearly certain that either both would like it or both would dislike it.
  3. Dissimilar - the most common kind in SF: the kind associated with evil twins, heroic alternates, etcetera. No restriction on personality.

Second: How divergent are the universes that created these individuals? From least to most:

  • Identical up to moment of conception: how much chance is involved in a particular human fertilization in (a) selection of sperm and (b) mutation of genome during development of embryo?
  • Identical up through moment of mate selection: the previous, plus: how much chance is involved in (c) the genetics of the egg and (d) the commitment to a particular relationship (or cheating thereon)? The latter leads on to:
  • Identical up through birth of parent generation: (e) how much chance is involved in mate selection? (f) how probable is the chance selection of identical child genes from different parents (cf human genetic variation)? (g) how large a gap can be spanned by mutation, and how probable are different degrees of mutation?
  • Diverging before birth of one or more parents: (h) how quickly do distinctive genomes spread through population, and how likely are they to meet again in different combinations in later generations?

Now, I lack the knowledge of biology to, first, nail down these questions to their most correct forms, and second, assign probability estimates to relevant steps in the chain. But the most superficial examination of the situation seems to suggest at least one thing: any alternate universe measurably diverging a significant period before the birth of an individual is vanishingly likely to contain a copy of that individual. Which, of course, is what Dan Shive has pointed out.

And, as an obvious consequence of this, even if such a universe contained a duplicate of yourself, it would still be vanishingly unlikely for it to contain duplicates of anyone not your direct descendant. (Which would make for a heck of a paternity test, I have to tell you!)

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(4 comments | Leave a comment)

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Date:2010/09/19 0831 (UTC)
I think there's a common error in the thinking here.

First, I'm going to assume that we're talking about quantum alternate universes, the notion that every single waveform collapse spawns two universes. In that case, although it's true that your existence is the infinitely unlikely result of a rather long series of events, there are still an infinite (or nearly infinite?) number of universes in which you exist but with only slight differences.

...on second thought, there wouldn't actually be an infinite number. It would just be a really scary exponential number that's a little hard for me to get my head around at the moment. The total domain would be 2 to the number of Planck time units since the Big Bang; poor Wolfram Alpha whimpers a little if you ask it to calculate this. (And I've seen it bang out some pretty big numbers.) Then we'd have to work out the Bayes' probability for your existence, and multiply the two together. Have fun with that. :-)
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Date:2010/09/19 1338 (UTC)
It doesn't even matter if it is an 'infinite' number - that merely transforms the argument from "this single alternate universe contains your twin with probability p" to "in this space of universes, the density of universes containing your twins is approximately p".

But that's another interesting question: if you start with the Many-Worlds Interpretation, how often does the universe decohere on a macroscopic scale?
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Date:2010/09/19 1857 (UTC)
Sure, but this way you get a nonzero result. Presupposing the many-worlds interpretation leads to the inescapable conclusion that there do exist duplicates of you in other universes, under many different circumstances, and with a wide range of differences. Or, put another way: many-worlds means that you are a gradient. :-)

Delving too much further down the many-worlds hole twists my brain pretty badly. If we accept that it decoheres every time a probability field is collapsed, then we have to start trying to figure out whether those collapses require an observing consciousness or not, and that takes straight to philosophy, whereupon I throw up my hands and go work on a car.
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Date:2011/01/17 1917 (UTC)
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