From: Rafal Smigrodzki (rafal@smigrodzki.org)
Date: Tue Apr 29 2003 - 20:12:19 MDT
gts wrote:
> Ramez Naam wrote:
>
>> George Dvorsky wrote:
>>
>>> You pull a ball from one of them, and you get
>>> the number 4. Any reasonable person would therefore assume
>>> that they pulled the ball from the 10-ball machine.
>>
>> This analogy breaks down from the viewpoint of the balls. If
>> you're a ball, and you see that you have a #4 painted on you,
>> then it may seem to you that there's a 50% chance that you're
>> from the machine with 10 balls and a 50% chance that you're
>> from the machine with 1 million balls. After all, you're one
>> of two such balls, and you have no information that suggests
>> you're from one machine or the other (you can never see balls
>> that come later in number than you).
>
> I don't believe the analogy breaks down for the reason you cite. All
> you know initially is that 1) you are a ball, that 2) there are two
> sequences of balls, one long and one short, and that 3) you come from
> one of those two sequences. You look at your birth order and see that
> you are ball #4 in your sequence. The question then is: "Am I from
> the short sequence or from the long sequence?"
>
> It is reasonable to conclude that you came probably from the short
> sequence, because the probability of finding yourself to be the 4th
> ball in the long sequence is small by comparison.
>
> There is a key idea in my last sentence, that of "finding oneself."
> You "found yourself" to be #4 in your sequence. Implicit in the idea
> of finding yourself to be #4 is the assumption that *in principle*
> you could have found yourself to have been any number in either
> sequence, i.e., that your observation of your birth order is a random
> sample of birth order observations taken from the population of
> observations from which yours is drawn. This is the Self-Sampling
> Assumption (SSA) upon with all of DA theory rests. If SSA is false
> then DA fails immediately, but then so do a lot of common sense ideas
> that we take as obvious fact. And therein lies the rub.
### Let's engage in a simple exercise:
You know that half of all civilizations die at age 10 billion persons, and
the other half live to 10 trillion persons.
You know that you are a sentient belonging to one of these civilizations.
There is a sealed envelope in front of you, containing your birth rank.
What is the a priori probability of being in the doomed civ?
10e9
P(X)=------------- ~ 0.001
10e11 + 10e9
Your a priori probability of being doomed is small, because you know that
most people live in the happy majority
You open the envelope, find the number 999 999 999, and update your
probabilities:
(1-.5)1/10e9
----------------------------- ~ 0.99
(1-.5)*1/10e9 + (1-.5)*1/10e11
Your a posteriori probability of being doomed if your birth rank is 999 999
999, is 99%. Please note, that you didn't move a lightspeed from one
civilization to another, merely adjusted your point of view based on the
data that became available.
While still shocked by impending doom, you receive a news flash saying that
only one in a thousand civilizations dies at age 10 billion. You calculate
again:
(1-.999) 1/10e9 1*10e-11
--------------------------------= --------------------- =~.09
(1-.999)1/10e9 + (1-.001)/10e11) 1*10e-11 + 9.99*10-11
Now you happily conclude that you have a 91% chance of making it!
By adjusting your belief about the relative frequencies of either type of
civilizations you can totally change the conclusions you draw from the
doomsday argument. Since we have no data on such frequencies, we cannot use
DA even if we assume the self-sampling hypothesis.
No rub anywhere, just insufficient data to construct priors.
Rafal
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