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Topic: Go Deep Blue!
Replies: 334   Last Post: Aug 22, 1997 11:23 AM

 Messages: [ Previous | Next ]
 Tal Kubo Posts: 90 Registered: 12/12/04
Re: More on 0-1 Laws (was Re: 0-1 Laws
Posted: Jun 12, 1997 5:20 PM

Putting the last nails in the coffin lid...
----------------------------------------------------------------------
Matthew P Wiener <weemba@sagi.wistar.upenn.edu> wrote:
>
>>>>>>It can be modelled as a Markov chain M on consistent extensions
>>>>>>of the alpha theory A. You argue, in effect, that iterates of M
>>>>>>converge to the identity. This is *impossible* for any nontrivial
>>>>>>chain.

>
>>I *assume* nonlinearity. [...]
>
>Yes, but your argument doesn't apply whatsoever, and has absolutely no
>features that connect with what you claim to have proven impossible.

I'm not claiming an impossibility proof, just an implausibility argument.

To fix ideas, model your argument as iterating some operator M on certain
probability distributions (of "TM mind beliefs", say). Your "alpha=omega"
assertion implies that M, which can be thought of as a nonlinear Markov
chain, has essentially trivial dynamics: starting at a distribution
concentrated on one type of TM-mind, we stay there. That is, for alpha to
equal omega, it must also equal beta, gamma, delta and so on.

The model can be varied to take into account time dependence and whatever
else. For instance, the "alpha=omega" assertion was later qualified to a
claim about consistency strength (i.e. an "observable" depending on the
state, rather than the state itself). You have quibbled about some
of these details (not that details of your model are available in any
case), but they change absolutely nothing as far as the plausibility
of an "alpha=omega" statement. The basic problem remains:

result from conservation laws, or in this case an infinite system
of conservation laws. Conservation laws for complicated dynamics
are RARE, not ubiquitous as your argument presumes.

>>>When identifying something as "Markov", you have further questions.
>>>Do you have temporal independence and lack of memory? Not here.

>
>>You assume nothing about the initial conditions (since we can't
>>identify what Physical Mathematics is) or the state of the world,

>
>Eh? I make assumptions, which is not the same as identification.

The assumptions other than TM population state can be assumed
*constant*. That was the basis for assuming iterating a single
operator. Presumably if your argument works for TM-minds evolving
in veldt it also works for evolution in forest and desert -- but
the environmental change over time in any of these is much less than
the difference between them, so we can assume a constant environment.

>>and in particular we can start the argument again from the state
>>resulting from just a brief bit of evolution.

>
>Meaning what?

The environment is the same, and TM "beliefs" are presumably encoded
happens in evolving from a single starting theory (i.e., an atomic
distribution), ask what happens starting from a more diffuse distribution
of TM's that results from evolution of that starting theory for a while.

Hence my claim that, heuristically, "it's not much of a stretch to model
your proposed evolution of theories as iterating a fixed operator on
populations of TM-minds". This is all in the absence of an actual
evaluable argument, to indicate the problem about conservation laws.

Date Subject Author
5/1/97 harden
5/1/97 Kurt Foster
5/2/97 Fireball
5/2/97 Dann Corbit
5/3/97 jjtom4@imap2.asu.edu
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5/6/97 David Ullrich
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5/5/97 Ilias Kastanas
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5/8/97 Rodney Small
5/8/97 Earle D. Jones
5/9/97 La Jolla del Mar
5/8/97 Terry Moore
5/9/97 Jon A Meilstrup
5/10/97 David Ullrich
5/11/97 Terry Moore
5/12/97 Matthew P Wiener
5/13/97 Terry Moore
5/14/97 Matthew P Wiener
5/13/97 dseig
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5/13/97 Pawel Biernacki (LVS-HIWI)
5/13/97 Robert Rodgers
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5/9/97 Robert Israel
5/11/97 Matthew P Wiener
5/12/97 Daryl McCullough
5/13/97 Matthew P Wiener
5/13/97 Douglas J. Zare
5/14/97 Matthew P Wiener
5/14/97 Daryl McCullough
5/20/97 Matthew P Wiener
5/16/97 Douglas J. Zare
5/18/97 Matthew P Wiener
5/20/97 Douglas J. Zare
5/23/97 Matthew P Wiener
5/23/97 Daryl McCullough
5/26/97 Robert Israel
5/26/97 Matthew P Wiener
5/26/97 Robert Israel
5/27/97 Daryl McCullough
5/27/97 Robert Israel
5/27/97 Daryl McCullough
5/28/97 Matthew P Wiener
5/26/97 Matthew P Wiener
5/26/97 Manfred Jaeger
5/26/97 Tal Kubo
5/27/97 Matthew P Wiener
5/27/97 Tal Kubo
6/5/97 Matthew P Wiener
6/1/97 Matthew P Wiener
5/27/97 Daryl McCullough
5/13/97 Daryl McCullough
5/19/97 Matthew P Wiener
5/19/97 Daryl McCullough
5/20/97 Matthew P Wiener
5/20/97 Daryl McCullough
5/21/97 Matthew P Wiener
5/21/97 Daryl McCullough
5/25/97 Matthew P Wiener
5/27/97 Daryl McCullough
5/27/97 Matthew P Wiener
5/27/97 Daryl McCullough
5/29/97 Tal Kubo
5/29/97 Matthew P Wiener
5/29/97 Tal Kubo
6/1/97 Matthew P Wiener
6/3/97 Tal Kubo
6/4/97 Matthew P Wiener
6/4/97 Tal Kubo
6/5/97 Matthew P Wiener
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6/10/97 Tal Kubo
6/17/97 Matthew P Wiener
5/20/97 Ilias Kastanas
5/20/97 Daryl McCullough
5/21/97 Ilias Kastanas
5/21/97 Daryl McCullough
5/26/97 Tal Kubo
5/29/97 Matthew P Wiener
5/29/97 Tal Kubo
6/1/97 Matthew P Wiener
6/2/97 Tal Kubo
6/3/97 Matthew P Wiener
6/3/97 Tal Kubo
6/4/97 Matthew P Wiener
6/2/97 Tal Kubo
6/5/97 Matthew P Wiener
6/5/97 Tal Kubo
6/8/97 Matthew P Wiener
6/11/97 Tal Kubo
6/15/97 Matthew P Wiener
6/15/97 Tal Kubo
6/16/97 Matthew P Wiener
6/23/97 Tal Kubo
6/24/97 Matthew P Wiener
6/24/97 Martin Goldstern
6/27/97 Tal Kubo
7/6/97 Matthew P Wiener
7/9/97 Bill Dubuque
5/29/97 Tal Kubo
6/5/97 Matthew P Wiener
6/5/97 Tal Kubo
6/5/97 Tal Kubo
6/5/97 Daryl McCullough
6/6/97 Matthew P Wiener
6/6/97 Daryl McCullough
6/6/97 Daryl McCullough
6/8/97 Matthew P Wiener
6/9/97 Daryl McCullough
6/11/97 Tal Kubo
6/11/97 Daryl McCullough
6/11/97 Ilias Kastanas
6/12/97 Tal Kubo
6/11/97 Daryl McCullough
6/15/97 Matthew P Wiener
6/16/97 Daryl McCullough
6/17/97 Ilias Kastanas
6/19/97 Tal Kubo
6/22/97 Matthew P Wiener
6/23/97 Tal Kubo
6/24/97 Matthew P Wiener
6/16/97 Tal Kubo
6/19/97 Matthew P Wiener
6/19/97 Daryl McCullough
6/24/97 Matthew P Wiener
6/26/97 Tal Kubo
6/27/97 Matthew P Wiener
6/27/97 Tal Kubo
6/30/97 Matthew P Wiener
7/1/97 Daryl McCullough
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7/18/97 Matthew P Wiener
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6/19/97 Tal Kubo
6/22/97 Matthew P Wiener
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6/13/97 Tal Kubo
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6/6/97 Daryl McCullough
6/5/97 Matthew P Wiener
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6/7/97 Tal Kubo
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6/6/97 Kemoauc@de.ibm.com
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