In the Schmidhuber model, the ordering of program outputs is rather
incidental - in fact the dovetailer program could output a completely
different order of outputs, but the output is still equivalent.

As you say in the last paragraph, time really enters the system in the
"Tegmark" sense of being an anthropic requirement. Tegmark does give
some (albeit weak) justification as to why we must experience time. 

In my Occams Razor paper, I simply assume the necessity of time
(called the TIME postulate). My justification for this is also weak -
I merely ask the question "Can one conceive of a consciousness without
a timelike dimension ordering and processing events?". Noone to date
has answered affirmatively to this question, so I provisionally assume
that time is necessary.

I should also point out that COMP (to whom many on this list
subscribe) implies TIME, at least according to my understanding of
it. So a negation of TIME would also imply a negation of COMP.


Hal Finney wrote:
> 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

A/Prof Russell Standish                  Director
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