Re: Time

From: Hal Finney <hal.domain.name.hidden>
Date: Sat, 31 Aug 2002 14:25:45 -0700

John Mikes writes:
> would it be too strenuous to briefly (and understandably???)
> summarize a position on time which is in the 'spirit' of the
> 'spirited' members of this list?

It seems to me that there are two views of time which we have considered,
which I would classify as the Schmidhuber and the Tegmark approaches.
In the Schmidhuber view time is of fundamental importance, and in the
Tegmark view it is basically unimportant.

Schmidhuber models the multiverse as the output of a computational
process operating on all possible programs. Since computation is
inherently sequential, it imposes a time ordering on the output. It is
natural to identify the time ordering of a computation with the time
ordering of events in our universe. So the simplest interpretation of
the Schmidhuber model as an explanation of our universe is to picture
the computer as generating successive instants of time as it operates.

An obvious problem with this is that time appears to have a more
complex structure in our universe than in the classical Newtonian
block model. Special relativity teaches us that simultaneity is not
well defined. And general relativity even introduces the theoretical
possibility of time loops and other complex temporal topologies. It
is hard to see how a simple interpretation of Schmidhuber computation
could incoporate these details.

Stephen Wolfram considers some related issues in his book, A New Kind
of Science. He is trying to come up with a simple computational model
of our universe (not of the multiverse, but the same issues arise).
In order to deal with special relativity he shows how a certain kind of
computational network can have consistent causality even when some parts
of the computation are run in advance of other parts. In other words,
simultaneity is not well defined in these models and it is possible
for different observers to have different ideas about simultaneity.
But the causality is the same for everyone.

The other main model we have considered for the multiverse is that of
Tegmark, who identifies the universe with all possible mathematical
structures. In this model our universe is merely a complicated
mathematical object. The fact that we observe three dimensional space and
one dimensional time is due to the internal structure of the particular
mathematical object that we live in. Since all possible mathematical
structures exist, there would be other universes with one dimensional
space and three dimensional time, for example, along with an infinite
number of others.

In this model, then, time is unimportant; it is merely an incidental
internal feature of certain mathematical constructs. Then we can
invoke the anthropic principle to say that mathematical objects which
have an internal time dimension can also lead to evolution, which can
lead to life like ours. So we have an explanation of time as being a
constraint on those mathematical objects which can include what Tegmark
calls self-aware subsystems, i.e. observers like ourselves.

A final note, I think the Schmidhuber model can be approached in
a way more consistent with Tegmark by interpreting the output of a
computation as a structured object independent of the time ordering
used by the computation that created it (Wolfram pursues this idea in
his models as well). Looking at this document, for example, you read
it sequentially from top to bottom; but I didn't write it that way,
I rearranged some paragraphs and went back and did some edits here and
there before sending it. The document's internal structure imposes or
reveals an ordering that is independent of the way it was created.

In the same way, Schmidhuber's programs can create universes, some of
which might then be interpreted to have an internal time dimension
similarly to how Tegmark's mathematical objects do. We would then
invoke the anthropic principle, as in the Tegmark case, to limit our
attention to Schmidhuber programs that produce output with an internal
time dimension that allows for conscious observers.

Hal Finney
Received on Sat Aug 31 2002 - 14:26:32 PDT