01/10/97. SOCIETIES OF TURING MACHINES. Anders Sandberg responded to my
query about societies of Turing machines by saying that, in principle,
these are equivalent to "one big TM", but in practice "it is probably
possible to prove that in general it is impossible to predict the
resulting behavior of a society of agents from the agent programs
themselves."
Lee Daniel Crocker also replied suggesting that what I was talking about
could still be *simulated* by _a_ TM simulating a society of TMs. But,
I'm not sure whether such a simulation could be conducted by a single
entity or closed system. Perhaps a real-time, dynamic society of
independent agents that come and go of their own 'free will' and,
therefore, probably cannot be represented by any single model, is
necessary. It was my suspicion that an asynchronous network or ensemble
of independently constructed agents operates differently from and cannot
be described by any pre-defined (logically-planned) Turing machine.
(This cuts to the heart of a major debate among Transhumanists as to
whether evolution is "stupid" or, perhaps, more creative somehow than
any logic-based approach.)
Recently (03/14/97), Eugene Leitl posted (>H List) about the First
International Conference on UNCONVENTIONAL MODELS OF COMPUTATION CDMTCS
to be held in Auckland, New Zealand, in 9801, with a host of invited
speakers from the top ranks of computer science and complexity theory,
the goal of which is to explore "all areas of unconventional
computation, especially in quantum computing, computing using organic
molecules (DNA), and various proposals for computation that go beyond
the Turing model."
The following notes may provide some useful background for this
unconventional approach by exploring mathematical biophysics and
relational biology as described by Robert Rosen.
01/11/97. Finally obtained and started to read Robert Rosen's _Life
Itself_: A Comprehensive Inquiry into the Nature, Origin, and
Fabrication of Life_, finding that the issues he deals with are at the
core of recent Extropians discussions. The essence of Rosen's radical
argument is this: "What if physics is the particular, and biology the
general, instead of the other way around? If this is so, then nothing in
contemporary science will remain the same."
(03/22/97 summary of praeludium & ch.1) Rosen sketches the extremes: In
the strong reductionist corner he cites Ernest Rutherford's "qualitative
is /nothing but/ poor quantitative"; and, on the 'fuzzy' side, he cites
Robert Hutchins', "a social scientist is a person who counts telephone
poles". Rosen says that Hutchins' "soft science" view concludes that
"reductionism is wrong in principle" and declares: "Hutchins is
inverting Rutherford's dictum; he is asserting that quantitative is poor
qualitative." Rosen plans to plot a course between these two stormy
shoals, relying on mathematics and relational biophysics for his
navigation.
Rosen finishes his 'praeludium" by citing 2 central issues he plans to
deal with: syntax vs. semantics, and Godel's theorem's and Turing
machine's relevance to complex systems. Rosen notes that Rutherford's
position "can be rephrased as asserting that /every material system is a
simple system/", and adds that "this position is just another form of
Church's Thesis". Rosen concludes here by noting: "it seems to me that
the duality between 'hard' or quantitative science and 'soft' or
qualitative science rests entirely on a false presumption". It is the
nature of this "false presumption" that he plans to explore through
_Life Itself_.
Ch.1 is called "Prolegomena" and starts off by referring to Rosen's two
previous works for which this is the culmination: _Fundamentals of
Measurement and the Representation of Natural Systems_ (no date given)
and _Anticipatory Systems_ (1985).
Rosen begins by asking (1A) "What is Life?". Rosen declares: "Life is
material, but the laws framed to describe the properties of matter give
no purchase on life. Something is missing here, perhaps something
essential for the understanding of matter in general." Rosen's goal is
to construct "a language appropriate for a physics of 'organized
matter', a physics of complex systems."
In ch.1B, "Why the Problem is Hard", Rosen addresses causality and the
curious situation where, in the past, "biology has generally had to
parasitize other sciences in order to develop its own experimental
techniques". He laments that "biology, has as yet no objectively
definable bounds." Ch.1C specifically worries about "The Machine
Metaphor in Biology", beginning with Descartes conclusion that "life
itself was automaton-like", which has today been elaborated into the
notion of molecular machines. But, when we're dealing with life and
other complex systems, Rosen concludes that "we cannot expect
[reductionism] to solve both the physiological and the fabrication
problem simultaneously". He conludes ch.1 by saying: "I hope to convince
the reader ... that the machine metaphor is not just a little bit wrong;
it is entirely wrong and must be discarded."
01/12/97. In ch.2 of _Life Itself_ Rosen dives right into "Strategic
Considerations: The Special and the General" where he declares that
"once we have imposed an additional structure on a set, be it of an
algebraic, topological, or any other character, the mappings we use to
compare one such structure with another must, of course, respect that
structure.... The set of continuous mappings from one topological space
to another is thus generally much smaller than the totallity of
unrestricted mappings between their underlying sets. It is on this level
that the restrictive nature of the additional structure manifests
itself."
(03/12/97 annotation after reading on Extropians about "Countertime
Beings": I would venture to say that it is this sort of situation that
Rosen has just described, rather than some cosmic "time-reversal
symmmetry", that might really underlie the transactional interpretation
of quantum physics.)
In 2B, "From General to Special", Rosen describes the discovery of
infinite arithmetic, the 'foundation crises' of mathematics and the
question of "how to restrict ourselves to those infinite sums and
products that 'make sense' and avoid those that do not. The resolution
of this crisis was given by Cauchy, who in 1805 introduced the necessary
concept, /convergence/", which, says Rosen, is associated with the
concept of /continuity/.
In 2C, "From Special to General", Rosen relates the discovery of
non-Euclidean geometry, and the roughly simultaneous 'insecurities' in
theoretical physics, particularly electrodynamics, that eventually
resulted in Einstein's /Special Relativity/ constituting "a
generalization of Newtonian mechanics", along with Heisenberg
Uncertainty which led to today's quantum mechanics. Rosen concludes this
section by noting: "Ordinary ('proper') functions turn out to be a very
special case, and the more general objects (originally called
/distributions/) are identifiable with limits of sequences of these
'proper' functions, just as real numbers are limits of sequences of
rationals. Thus, from this point of view, distributions /generalize/
ordinary functions; the generalization embeds ordinary functions in a
new and larger universe, in which they are nongeneric indeed... The
elements of this larger world may have new and different properties from
those with which we started; properties generic in the large world but
vacuous in the small one that gave rise to them."
01/12/97. In 2D, on "Induction and Deduction", Rosen describes how
"induction, roughly, seeks to establish general (i.e., quantified)
propositions on the basis of instances; deduction, conversely seeks to
establish instances in terms of quantified or general propositions."
Rosen describes predicates, or properties, and assertions about sets as
strings of conjunctive properties. Induction is traditionally considered
more difficult and, Rosen adds, "without additional structure, the
problem of induction cannot be solved in general; that much was
originally pointed out by Aristotle ... and elevated by Hume into a
complete rejection of empiricism [by which is meant] the establishment
of general truth by judicious sampling." "The further structure
necessary", says Rosen, is that "if P, as a property, itself manifests
what we may call contagion, so that the truth of P(Xi) itself implies
the truth of P(Xj) ... then the problem of induction can be dealt
with.... Mathematical induction is, in fact, all we need to generate the
whole of Number Theory from the existence of the number '1', and the
ability to 'add 1' to any integer... This idea ... permeates both
science and mathematics in profound and insufficiently appreciated
ways."
Ch.2E, "On the Generality of Physics", Rosen proposes that Godel's
undecidability proofs are 'contagious' beyond Number Theory because to
assess the generality of any formalism is to raise a metatheoretic
"question about the theory, not a question within the theory." This is
why, Rosen declares, "reductionism, rests on faith." Rosen concludes:
"with respect to biological phenomena, contemporary physics is in
exactly the same situation that 19th-century physics faced in the atomic
and cosmological realms: it either stands mute or it gives the wrong
answers.... Once again, as in all similar situations in the past, the
claim is that purely technical matters are involved and that the problem
is simply one of specializing what already exists in an appropriate way.
But history shows it to be at least equally likely that the problems are
not technical but conceptual, that contemporary physics remains too
special to accommodate the class of material systems we call organisms."
(to be continued)