I remembered Wei Dai posting on this topic in the early days of this
list, and indeed some of his postings influenced my Why Occam's
Razor paper. However, I do not recall his suggestions as being as
detailed as what you describe here. Do you have a reference to where
this might be written up? I'm also intrigued by the possibility of
demonstrating that transhumanist observer moments would have
substantially less measure than human observer moments. Such a result
would be a transhumanist counter to the Doomsday argument of course.
Cheers
On Fri, Jun 03, 2005 at 11:10:15AM -0700, Hal Finney wrote:
...
Years ago Wei Dai on this list suggested a better approach. He proposed
a formula for determining how much of a universe's measure contributes to
an OM that it instantiates. It is very specific and also illustrates
some problems in the rather loose discussion so far. For example,
what does it really mean to instantiate an OM? How would we know if a
universe is really instantiating a particular OM? Aren't there fuzzy
cases where a universe is only sort of instantiating one? What about
the longstanding problem that you can look at the atomic vibrations in
a crystal, select a subset of them to pay attention to, and have that
pattern match the pattern of any given OM? Does this mean that every
crystal instantiates every OM? (Hans Moravec sometimes seems to say yes!)
To apply Wei's method, first we need to get serious about what is an OM.
We need a formal model and description of a particular OM. Consider, for
example, someone's brain when he is having a particular experience. He is
eating chocolate ice cream while listening to Beethoven's 5th symphony,
on his 30th birthday. Imagine that we could scan his brain with advanced
technology and record his neural activity. Imagine further that with the
aid of an advanced brain model we are able to prune out the unnecessary
information and distill this to the essence of the experience. We come
up with a pattern that represents that observer moment. Any system which
instantiates that pattern genuinely creates an experience of that observer
moment. This pattern is something that can be specified, recorded and
written down in some form. It probably involves a huge volume of data.
So, now that we have a handle on what a particular OM is, we can more
reasonably ask whether a universe instantiates it. It comes down to
whether it produces and contains that particular pattern. But this may
not be such an easy question. It could be that the raw output format of
a universe program does not lend itself to seeing larger scale patterns.
For example, in our own universe, the raw output would probably be at
the level of the Planck scale, far, far smaller than an atomic nucleus.
At that level, even a single brain neuron would be the size of a galaxy.
And the time for enough neural firings to occur to make up a noticeable
conscious experience would be like the entire age of the universe.
It will take considerable interpretation of the raw output of our
universe's program to detect the faint traces of an observer moment.
And as noted above, an over-aggressive attempt to hunt out observer
moments will find false positives, random patterns which, if we are
selective enough, happen to match what we are looking for.
Wei proposed to solve both of these problems by introducing an
interpretation program. It would be take as its input, the output of the
universe-creation program. It would then output the observer moment in
whatever formal specification format we had decided on (the exact format
will not be significant).
So how would this program work, in the case of our universe? It would
have encoded in it the location in space and time of the brain which
was experiencing the OM. It would know the size of the brain and the
spatial distribution of its neurons. And it would know the faint traces
and changes at the Planck scale that would correspond to neural firings
or pauses. Based on this information, which is encoded into the program,
it would run and output the results. And that output would then match
the formal encoding of the OM.
Now, Wei applies the same kind of reasoning that we do for the measure
of the Schmidhuber ensemble itself. He proposes that the size of the
interpretation program should determine how much of the universe's measure
contributes to the OM. If the interpretation program is relatively small,
that is evidence that the universe is making a strong contribution to
the OM. But if the interpretation program is huge, then we would say
that little of the universe's measure should go into the OM.
In the most extreme case, the interpretation program could just encode the
OM within itself, ignore the universe state and output that data pattern.
In effect that is what would have to be done in order to find an OM
within a crystal as described above. You'd have to have the
