# Re: MATH: Weird probability arguments

Hal Finney (hal@rain.org)
Thu, 5 Dec 1996 21:18:15 -0800

From: phoenix@ugcs.caltech.edu (Twirlip of Greymist)
> ...e.g. I find this argument utterly bizarre. Whether 21st century
> humanity dies out or goes on to Omega, to reach the 21st century someone
> had to live in the 20th. That happens to be us. If someone else lived
> now, "we" wouldn't live later on; "we" are those who live here and now,
> who have grown up in this century.
>
> When contemplating any future with a history, given that the future will
> happen the probability of the history having happened is 1.

I had much the same reaction, but the book discusses this idea at length
and tries to answer it.

The key point is whether it is justified to consider ourselves as having
been randomly chosen from all points in human history. As you say,
to some extent this seems unreasonable since there is only one Twirlip
of Greymist and he always exists/existed/will exist in this era.

However, in other contexts we do accept reasoning where we consider
ourselves randomly chosen. For example, suppose you knew that one
particular blood type predominated in the U.S. but didn't know what
it was. You later learned that your blood type is O positive. From this
you might conclude that there was a better chance that the common blood
type is O positive than other possibilities.

Or, suppose you learned that 90% of people have a certain pattern of
creases on their palm. Without looking at your own hand, you would be
inclined to suspect that you would also have this same pattern.

In each of these cases, you could argue the other way, that _someone_
is among the people who don't have the creases, or who have more rare
blood types. That might happen to be you. But the probability argument
is still valid.

> So what about the 19th century? Or the 5th B.C.? Someone lived through
> those moments. Should Babbage have commented on how unlikely it was for
> him to have existed?

The existence of people in low-probability circumstances does not
invalidate the probabilistic reasoning, any more than the fact that your
friend Joe has AB negative blood falsifies the notion that O positive is
more common. (I should note that I am being hypothetical here, I don't
actually know much about blood types.)

Suppose you were told that human history could be divided into two eras,
with 99.99999+% of all humans born in era 1 and the remainder born in
era 2. Given this information, which era would you expect to be born in?
Now suppose you are told that there is another possible timeline, one
where 60% were born in era 1 and 40% in era 2. You actually don't know
which timeline reflects your world.

Now you find out that you were born in era 2. Doesn't this give you
reason to strongly reject the hypothesis that you live in the first
world, and to believe that you live in the second?

The first world corresponds to one in which life expands to fill the
galaxy, with the population increasing by factors of billions or more.
The second corresponds to one where the total number of humans who ever
live is not much more than those who have lived already. This is the
doomsday reasoning which concludes that the human race will soon die
out.

Hal