Probabilistic Thinking (was Thought Experiment #269-G)

From: Lee Corbin <lcorbin.domain.name.hidden>
Date: Sun, 10 Jul 2005 10:12:49 -0700

Stathis writes

> > But if you answer "I will see 0 on the wall OR I will see 1 on the wall"
> > then it makes it sound as though one of those cases will obtain but
> > not the other. (This is usually how we talk when Bruno admits, for
> > example, that tonight he either will watch TV *or* he will not watch
> > TV. But the case of duplicates is not like that. In the case of
> > duplicates, it is a scientific fact that Bruno will watch TV (in one
> > room) and will not watch TV (in the other room). In short, it will
> > be true that Bruno will watch TV and will not watch TV---simply because
> > there will be two instances of Bruno.)
>
> Is there any way of asking the question such that the answer is "there is an
> even chance that I will see either a 1 or a 0"? For example, every time I
> flip a coin it *seems* that I get either heads or tails, and not both. The
> objective truth may well be that coin-tossing causes duplication and I do,
> in fact, experience both, but don't realise it. I am interested in asking
> and/or answering the question assuming this sort of ignorance. Can it be
> done, or is it linguistically as well as physically and logically
> impossible?

Great question! I go so far as to agree with your sense here.

Here is an example: suppose that a million copies of you are to be
made every day, and for each of them, on the following day yet another
million copies are made. (Thus after N days there are (10^6)^N copies.)
Further, suppose that 1 of them will be 1000 feet under water, and the
others simply find themselves at STP.

Your choice every day is whether to don the very bulky and time-
consuming diving equipment or not. It takes about half an hour to put
it on, and after you have been copied, about half an hour to take it off.

One day you are in a special hurry, and think, "well, it's true that
in 1 case I will die a rather ghastly death which will be very uncomfortable
for about fifteen or twenty seconds, but in the other 999,999 cases I
can get about my important affairs and save an hour of fiddling with
the equipment".

So that day you decide not to go through the ritual of putting on
and taking off the equipment. And, sure enough, one of you finds
himself in an unpleasant situation... *and in some sense regrets
the decision*. Now logically, during the fifteen or twenty seconds
it takes him to die he realizes that his duplicates live, and that
in some sense it really was a good decision. But he also cannot help
but feel that he was "unlucky". A part of him must ask, "now what
was the chance of this???"

At this point, he has relapsed into thinking of himself as an instance.
(Torture is another way that "instance-thinking" can be aroused even
in those with the broadest usage of "I".) You know intellectually
that you are doing just fine almost everywhere, but in this peculiar
case you're dead.

Yet it's probably *not* a good idea to put on the equipment everyday.
There are two reasons (that should be regarded as completely equivalent):
(1) in almost all cases I will save time (about a million hours all
together) and (2) the odds are very small that I'll need the equipment.

I contend that (2) should be taken as really meaning just (1) and that
literally, (2) is incorrect.

We all make these same choices every day: "Should I drive to work this
morning even though one in a million of me is going to die in a traffic
accident?" But to MWI devotees, the answer should be clear: it only
*seems* unlucky that I'm *just* here with a broken body in a heap of
twisted metal. The reality is that in most universes, today was not
unlike all the other days.

To quote you again,

> Is there any way of asking the question such that the answer is
> "there is an even chance that I will see either a 1 or a 0"?
> The objective truth may well be that coin-tossing causes duplication
> and I do, in fact, experience both, but don't realise it. I am
> interested in asking and/or answering the question assuming this
> sort of ignorance. Can it be done, or is it linguistically as well
> as physically and logically impossible?

So I'm translating your question as, "Is there any way of asking the
question such that the answer is 'there is only a tiny chance that
I'll be killed this morning on the way to work'?".

Chance seems to be overridden by MWI, and also in the cases of duplicates.
It's replaced by "fractional thinking", I guess. We might still use
the language of probability, but it should be just shorthand for the
better description of the situation in terms of fractions (of "me").

Sound right?

Lee
Received on Sun Jul 10 2005 - 13:12:23 PDT