From: Mike Lorrey (mlorrey@yahoo.com)
Date: Tue Apr 29 2003 - 14:30:00 MDT
--- Ramez Naam <mez@apexnano.com> wrote:
> George Dvorsky wrote:
>
> > Bostrom uses a great analogy, that of the ball dispensing
> machine(1).
> > You know you have two machines: one that dispenses 10 balls, and
> one
>
> > that dispenses 1 million balls, but you don't know which one is
> which.
> > Each ball is numbered. 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).
The problem with this is that, being the ball, you are unable to see
that you have #4 painted on your forehead. There are no mirrors inside
the ball machine. All you know is that you are a ball. There aren't any
lights on inside the machine, either, so you can't see the numbers
printed on the balls surrounding you.
>
> > This same reasoning is what drives the doomsday argument. Thus, as
> > rational people, we should *expect* that we, as the 106th billion
> > persons, are ball #4; it's far less likely that we're 106th billion
> > out of 106 trillion than 106th billion out of 200 billion.
>
> This assumes that we know something of the distribution of total
> lifetime populations of civilizations. We don't.
This is true, but you can't treat the fact that we don't know something
as useful information. All you can do is look at the odds and
guesstimate from there.
Conversely, while the odds of being from the smaller machine are higher
if you are numbered in a smaller number, the fact that the larger
machine is far more prolific with balls says it is more likely that you
are from the larger machine than the smaller.
For example, imagine you are in a firefight with two guys. One has a
pistol with ten rounds in it which he can fire 1 round per second. The
other has a machine gun with a thousand rounds he can fire 100 rounds
per second. With both men firing wildly toward you, what are the odds
you will be hit by the first guy versus the second?
=====
Mike Lorrey
"Live Free or Die, Death is not the Worst of Evils."
- Gen. John Stark
"Pacifists are Objectively Pro-Fascist." - George Orwell
"Treason doth never Prosper. What is the Reason?
For if it Prosper, none Dare call it Treason..." - Ovid
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