In reply to Lee Corbin on the Fabric of Reality List


You gave us some wonderful examples of totally ridiculous Turing Machines
that are nevertheless possible (I would at this point ask somebody to take
away Charles' keyboard). You have noted that these TMs are improbable; we
would not expect them to be instantiated in any great measure throughout the
multiverse. They are similar to Harry Potter universes in this respect.
Surely, though, the fact that they are improbable is not a blow against
Bruno! His argument is concerned with measure and you are playing right into
that. Let me try to explain...

To make this easier, let's forget about physical reality for a while. Let's
consider the Universal Dovetailer (UD). For those not in the know, the UD is
a TM that systematically lists and executes all possible TMs. Because there
are an infinite number of TMs, the UD cannot wait until all the TMs are
listed before it executes them. It also cannot allow any one TM to
monopolise the runtime, lest that TM never halts. So it must execute a step
of one TM, then a step of another TM and so on, and it must do this while
continuing to list the TMs. The first TMs off the list will be the simple
ones - those with the shortest bitstrings and these are the first to be
kicked off. Complex TMs with very long specifications will not be kicked off
until much later. At any point in time in which they are still running,
these complex TMs will have received less runtime than any simpler TM that
is still running. This is important, as we shall see.

As we have discussed, some (an infinite subset) of the TMs will support
observers when they are executed. The observers and their worlds unroll as
computational histories.

What does an observer observe? 

It is important to see that the computational histories of different TMs can
be identical up to a point and then diverge. So different TMs can produce
the same observer history up to a point. The observer moment, then, is
"simultaneously" generated by many different TMs. You can't pluck one
history and say you are in that history. You are part of many identical
histories that are about to diverge. And you can't pluck one TM and say that
that is the TM that is instantiating you. Your history is generated by many
different TMs. These are very important points. And, I think, the source of
much confusion over Bruno's work.

What an observer observes depends on all the computational histories their
current moment is in and how the histories branch. The question also depends
on what we mean by observer, but let's put that aside for now because I
don't yet understand this part. Note that observer time has no relation to
dovetailer time.

Obviously, the computational history of a TM that consistently supports an
observer can't be random. It must perform the computations necessary for an
observer. Now the history might become random after the n-th step, at which
point the observer no longer exists. Or the observer might morph into a
completely different observer that has no memory of its former existence (I
would argue that the observer is now a new observer). Or fluffy white bunny
rabbits might appear. The TM's executing these histories first run an
observer and then do something strange. Presumably this makes the TM more
complex because the strangeness requires extra bits to specify. These TMs
therefore get less runtime than the "unmodified" TM. 

OK, suppose you're in a set of identical computational histories that are
unfolding on many different TMs. Some of those histories are about to go
strange. For your existence as an observer to continue, they must go strange
in such a way that they still support you as an observer. Given what I have
said, do you think you are likely to branch into a strange world or to
continue on in your normal world, whatever that may be? The measure of the
computational history of the world where you continue on as normal is much
larger than the measure of the computational history of the strange branch
because the strange TMs receive less runtime (remember, many different TMs
instantiate you).

So, if you were an observer on the dovetailer, your computational history
branches in such a way that some branches are much more probable than
others. The world the observer observes will likely not be totally stupid. 

This is how you play into Bruno's hands!

Writing the above has made me realize that I may have not been accurate in
some of my earlier statements about Bruno's work. Apologies to Bruno. All I
need now is to be convinced that we can give a satisfactory definition of an
observer. Oh, and that we are most likely to observe QM.

Brian Scurfield

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