Vladimir Nesov wrote:
>
> On 11/18/07, Stathis Papaioannou <stathisp.domain.name.hidden> wrote:
> >
> > On 18/11/2007, Vladimir Nesov <robotact.domain.name.hidden> wrote:
> >
> > > > How is this different to arguing that a person who wins the lottery
> > > > should not ask how come something so improbable has happened to him
> > > > since he could only be asking the question if he had been a winner?
> > >
> > > Should he?
> >
> > The improbable thing is that the person should transition from the
> > state of buying a lottery ticket to winning the lottery, given the
> > much greater weight of non-winning tickets. Answering my own question,
> > the way this is different to asking why I was born me rather than one
> > of the far more numerous entities who aren't me is that there is no
> > primitive "me" spirit that can contemplate transitioning into every
> > possible corporeal form, so that I can then look back and wonder why I
> > didn't become one of the more common ones.
>
> Yes, but there's no point in 'wondering' after winning the lottery
> either. 'Wondering' is a technique to update probability of winning
> after you experienced winning, but it's only applicable when this
> probability is unknown and you can gain enough experience with both
> kinds of outcomes. So, if you first expected some event to be very
> unlikely, and then you experience that event, you probably should
> increase your assessment of its probability.
>
> Here confusion is similar: you experience an event (being born on
> Earth), and based on that you try to update probability of being born
> on Earth. But data is insufficient, so you can't do that.
But the doomsday argument and other similar arguments *do* involve using information you have to influence your estimate of the probabilities of events whose outcome you don't know--in the doomsday argument you're wondering about the probability the total number of humans ever born will eventually exceed some number, and in the alien civilization argument, you're wondering about the probability that most intelligent beings in the universe are part of vast interstellar civilizations or if these giant civilizations are so rare that most intelligent beings are members of shorter-lived planet-bound civilizations.
I think part of the problem is that people are taking the "what if I was someone else" too literally--the "self-sampling assumption", as it's called by Nick Bostrom, just says that in certain circumstances it is valid to reason *as if* you were randomly selected from the class of all humans or intelligent beings or sentient observer-moments, for the simple reason that if all members of the reference class were to reason this way, most of them would come to correct conclusions. A good thought-experiment to support this type of reasoning is given in the FAQ section of Bostrom's website
http://www.anthropic-principle.com where he writes:
"Q3. I have memories of 20th century events, so I cannot have been born earlier than the 20th century.
A3. We have to distinguish two "cannots" here. (1) Given the validity of these memories then I was in fact not born <1900.[true] (2) I could not exist without these memories.[much more doubtful].
It is indeed problematic how and in what sense you could be said to be a random sample, and from which class you should consider yourself as having been sampled (this is "the problem of the reference class"). Still, we seem forced by arguments such as Leslie's emerald example (below) or my own amnesia chamber thought experiment (see my "Investigations into the Doomsday argument") to consider ourselves as random samples due to observer self-selection at least in some cases.
A firm plan was formed to rear humans in two batches: the first batch to be of three humans of one sex, the second of five thousand of the other sex. The plan called for rearing the first batch in one century. Many centuries later, the five thousand humans of the other sex would be reared. Imagine that you learn you’re one of the humans in question. You don’t know which centuries the plan specified, but you are aware of being female. You very reasonably conclude that the large batch was to be female, almost certainly. If adopted by every human in the experiment, the policy of betting that the large batch was of the same sex as oneself would yield only three failures and five thousand successes. ... [Y]ou mustn’t say: ‘My genes are female, so I have to observe myself to be female, no matter whether the female batch was to be small or large. Hence I can have no special reason for believing it was to be large.’ (Leslie 1996, pp. 222-23)"
Would you not agree that in this thought-experiment, if everyone uses the self-sampling assumption then 5000 out of 5003 of them will come to the correct conclusions about which batch was male and which was female, a fact which they didn't know the answer to in advance and which they would have assigned a prior probability of 50/50? (Leslie doesn't really give enough information about the prior probability, but we can add the assumption that those in charge of this experiment decided which batch would be male and which would be female by a coinflip).
Jesse
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Received on Sun Nov 18 2007 - 14:53:22 PST