RE: Is 'Measure' infinitely divisible?

From: Lee Corbin <lcorbin.domain.name.hidden>
Date: Wed, 7 Sep 2005 17:39:30 -0700

Johnathan writes

> When considering possible continuations of "observer-moments", one
> speaks of dividing one's measure among them such that any succeeding
> observer-moment has a relative proportion consistent with the quantum
> amplitude of its wave function. (Or something like that.)

Actually, the picture you present invites one to assume that at
time t one has a definite measure (so far so good), and that this
measure must remain constant or go down for a succeeding instant
t + delta(t). This is not the usual interpretation. The usual
interpretation is that the runtime you get in any spacetime that
supports time t + delta(t) for you, that is, which supports "you"
at some time other than t, is dependent only on the structure of
that 3D universe at that time.

For example, it may happen that someone's homework assignment in
the year 20,398 A.D. is to emulate a few days in the year 2005
on old Earth. The entity who completes this assignment may have
access to vastly greater compute resources than anyone who ever
before emulated days in 2005. In this case, supposing that the
assignment is to run days September 9-11 of 2005, then your
measure may really pick up on Friday!

> My first question is: Can this go on indefinitely? Based on my
> understanding of MWI, the answer is yes, but I haven't seen this
> addressed before.

So the answer to this is "yes". Now it may turn out, of course,
that there are constraints, hidden or otherwise. It may be in the
cards that in almost all 3D universes, Earth gets replaced by a
Vogon bypass in 2006, and no human being (except in extremely
small measure) gets any runtime whatsoever past 2006.

Another constraint may be almost all universes experience the
kind of heat death that forbids thought of any kind at some
point billions of years in the future.

> Secondly, there are value-judgment arguments made here on the list about
> the desirability of taking certain actions based on the anticipated
> observer-measure that would result from them [?]

Yes, but they're just like the ones you take every day to stay
out of trouble! It could be argued, for example, that by never
using a freeway exit ramp for an on-ramp, you are (i) making a
value judgment that it is better for you to stay out of fatal
car crashes altogether, and (ii) making a difference in the
amount of runtime you get (in comparison to those few worlds
in which you fail to drive safely).

> But here is where my first question has implications--if "measure" has
> some finite lower bound, then eventually, all roads lead to zero at some
> point. An observer would have a strong motivation to take actions which
> maximize one's future measure "integral", to stave off this impending
> non-existence as long as possible.

Yes, that's just how many of us look at it! It's even a way of
explaining to folks why they should sign up for cryonics.

> If, on the other hand, measure is infinitely divisible, then there will
> always be a branch that will continue.

Oh, well, I guess I misunderstood what you meant by "finite lower
bound". It does seem that measure is infinitely divisible, because,
as David Deutsch says on p. 211 of "The Fabric of Reality", the
multiverse is a *continuum*, which is to say, technically that it
has the cardinality of the continuum, which is aleph-one. By this
it is meant that one for every real number epsilon greater than zero,
one could have that fraction of the multiverse occupied in a specific
way.

> Finally, here's my second question: Does being in a "low" measure branch
> somehow "feel different" from being in a "high" measure branch? To take
> the canonical example, let's say one is next to that 20 megaton H-Bomb
> when it detonates. In one branch, with a very very tiny fraction of
> one's current measure, one will find himself magically tunneled and
> reformed somewhere away from the danger. The expectation value of this
> happening, of course is tiny, but is non-zero, so it does happen
> somewhere in the multiverse.

No, it doesn't "feel" any different having small measure than it does
having large measure, unless you happen to know that your measure has
just gone up or down, and have psychological reactions to the supposed
fact. Say that the Earth is suddenly annihilated by the Vogons, or by
a gamma-burst from some nearby star in a huge fraction of worlds. Then
as the survivors, we aren't any the wiser (at least at the present
state of astronomical knowledge).

> Now, finding oneself, after the fact, having survived the blast by
> quantum tunneling, one realizes one is in a low measure branch of his
> wave function. But does it really matter? If measure is infinitely
> divisible, I don't think it does.

Well, it "should" matter. I use the word both in the sense that we
ought to expect that it will matter to you, and in the sense that it
is (probably) best for you that it matter.

I expect it to matter to you because that would be a smooth extension
of your normal behavior. Evolution has crafted you to be leery of
the usual measure-reducing hazards like unsafe driving and hungry
tigers. You tend also to feel some regret for those not so nimble
as you in running from tigers, and don't want the same fate. So if
we spruce up your usual thinking by employing evolutionary and
theoretical physics ways of speaking, then we would say that you
wish to avoid measure-reducing incidents.

Also, if your life is going well (i.e. is worth living), then I contend
that for you, being alive is better than being dead. So in this way too,
you *ought* to try to keep on living.

Lee
Received on Wed Sep 07 2005 - 20:40:47 PDT