Le 06-juin-05, à 22:51, Hal Finney a écrit :
I share most of Paddy Leahy's concerns and areas of confusion with
regard to the "Why Occam" discussion so far. I really don't understand
what it means to explain appearances rather than reality.
Well this I understand. I would even argue that Everett gives an
example by providing an explanation of the appearance of a wave
collapse from the SWE (Schroedinger Wave equation) and this without any
And I pretend at least that if comp is correct, then the SWE as an
*appearance* emerges statistically from the "interference" of all
computations as seen from some inner point of view of the mean
But, as I pointed a long time ago Russell is hiding (de facto, not
intentionally I guess :) many assumptions.
There are a lot of "derivation" of the SWE in the literature, it would
be interesting that Russell compares them with its own. My favorite one
is the one by Henry and another one by Hardy.
Note the incredible derivation of QM from just 5 experiments + a
natural principle of simplicity by Julian Swinger in his QM course
(taken again by Towsend in its QM textbook). I will give reference once
I agree with Hal and Paddy about the lack of clarity in many passages.
Note that my result is infinitely more modest (despite the
appearance!). I just prove that if comp is assumed to be correct then a
derivation of the SWE *must* exist, without providing it. Well, in the
interview of the Lobian machine I do extract some 'quantum logic' from
comp, but it is too early to judge if the SWE can be extracted from it.
But it should be, in principle, if comp is true. Advantage: I just
assume natural numbers and classical logic, I don't assume any geometry
or temporality, which for me are really the miraculous things in need
to be explained.
It's hard to
get my mind around this kind of explanation and what to expect from it.
Also the way the Anthropic Principle applies to infinite strings seems
extremely vague until we have a clearer picture of how those strings
relate to reality.
One area I differ:
Paddy Leahy writes, quoting Russell:
However, as the cardinality of "my" ensemble is actually "c"
(cardinality of the real numbers), it is quite probably a completely
There you go again with your radical compression. Without the reading
been doing in the last two weeks, I wouldn't have been able to decode
statement as meaning:
2^\aleph_0 = \aleph_1 (by definition)
To assume c = \aleph_1 is the Continuum Hypothesis, which is
(within standard arithmetic).
Actually Russell did not bring aleph_1 into the picture at all. All
he referred to was aleph_0 and c which by definition is 2^aleph_0.
c is the cardinality of the reals and of infinite bit strings. This is
all just definitional. Whether c is the "next" infinite cardinal after
aleph_0 is the Continuum Hypothesis, but that is not relevant here.
Another area I had trouble with in Russell's answer was the concept of
a prefix map. I understand that a prefix map is defined as a mapping
whose domain is finite bit strings such that none of them are a prefix
of any other. But I'm not sure how to relate this to the infinite bit
strings that are "descriptions".
In particular, if "an observer attaches sequences of meanings to
of prefixes of one of these strings", then it seems that he must have a
domain which does allow some inputs to be prefixes of others. Isn't
what "sequences of prefixes" would mean? That is, if the infinite
is 01011011100101110111..., then a sequence of prefixes might be 0, 01,
010, 0101, 01011, .... Does O() apply to this sequence of prefixes?
so then I don't think it is a prefix map.
I want to make it clear by the way that my somewhat pedantic and
examination of this page is not an attempt to be difficult or stubborn.
Rather, I find that by the third page, I don't understand what is going
on at all! Even the very first sentence, "In the previous sections, I
demonstrate that formal mathematical systems are the most compressible,
and have highest measure amongst all members of the Schmidhuber
has me looking to see if I skipped a page! I don't see where this is
discussed in any way. So I hope that by pinning down and crystalizing
exactly what the first page is claiming, it will help me to see what
the more interesting third page is actually able to establish. I think
Paddy is in much the same situation.