On Sat, Feb 11, 2012 at 12:32 AM, Stephen P. King <stephe...@charter.net>wrote:

>  Hi ACW,
>     Thank you for the time and effort to write this up!!!
> On 2/9/2012 3:40 PM, acw wrote:
> Bruno has always said that COMP is a matter of theology (or religion),
> that is, the provably unprovable, and I agree with this. However, let's try
> and see why that is and why someone would take COMP as an assumption:
> - The main assumption of COMP is that you admit, at some level, a digital
> substitution, and the stronger assumption that if you were to implement/run
> such a Turing-emulable program, it would be conscious and you would have a
> continuation in it. Isn't that a strong theological assumption?
> [SPK]
>     Yes, but it is the "substitution" of one configuration of "stuff" with
> another such that the functionality (that allows for the
> implementation/running of the Turing-emulable (Turing equivalence!))
> program to remain invariant. One thing interesting to point out about this
> is that this substitution can be the replacement of completely different
> kinds of stuff, like carbon based stuff with silicon based stuff and does
> not require a continuous physical process of transformation in the sense of
> smoothly morphism the carbon stuff into silicon stuff at some primitive
> level. B/c of this it may seem to bypass the usual restrictions of physical
> laws, but does it really?
>     What exactly is this "physical stuff" anyway? If we take a hint from
> the latest ideas in theoretical physics it seems that the "stuff" of the
> material world is more about properties that remain invariant under sets of
> symmetry transformations and less and less about anything like "primitive"
> substances. So in a sense, the physical world might be considered to be a
> wide assortment of bundles of invariants therefore it seems to me that to
> test COMP we need to see if those symmetry groups and invariants can be
> derived from some proposed underlying logical structure. This is what I am
> trying to do. I am really not arguing against COMP, I am arguing that COMP
> is incomplete as a theory as it does not yet show how the appearance of
> space, time and conservation laws emerges in a way that is invariant and
> not primitive. I guess I have the temerity to play Einstein against Bruno's
> Bohr. :-) OTOH, I am not arguing for any kind of return to naive realism or
> that the physical world is the totality of existence. I do know that I am
> just a curious amateur, so I welcome any critique that might help me learn.
>  I think it is, but at the same time, it has solid consequences and a
> belief in it can be justified for a number of reasons:
>  a) Fading qualia thought experiment, which shows that consciousness is
> utterly fickle if it doesn't follow a principle of functional /
> organizational invariance. Most of our sense data tends to point that such
> a principle makes sense. Avoiding it means consciousness does not
> correspond to brain states and p. zombies.
>     Certainly! We need a precise explanation for psycho-physical
> parallelism. My tentative explanation is that at our level a form of
> dualism holds. A dualism quite unlike that of Descartes, since instead of
> "separate substances", it is proposed that the logical and the physical are
> two distinct aspect of reality that follow on equal yet anti-parallel
> tracks. As Vaughan Pratt explains in his papers, the logical processes and
> the physical processes have dynamics that have arrows that point in
> opposite directions. Schematically and crudely we can show a quasi-category
> theory diagram of this duality:
> ---- > X -----> Y ----->
>          |           |
> <----- A <------B <-----
>     The vertical lines represent the Stone duality relation and the
> horizontal arrow represent logical entailment and physical causation. The
> chaining (or "*residuation*")  rule is "X causes Y iff B necessitates A",
> where X and A and duals and Y and B and duals. This duality prohibits
> zombies and disembodied spirits. There is much more to this diagram as it
> does not include the endomorphisms, homeomorphisms and other mappings and
> objects that are involved in the full implementation of the *residuation*rule.
>     I just found a paper by Martin Wehr
> www.dcs.ed.ac.uk/home/wehr/newpage/Papers/qc.ps.gz that elaborates on
> Pratt's idea and explains *residuation* better! Here is the abstract:
>    Quantum Computing: A new Paradigm and it's Type Theory
>           Martin Wehr
>    Quantum Computing Seminar, Lehrstuhl Prof. Beth,
>    Universit"at Karlsruhe, July 1996
> To use quantum mechanical behavior for computing has
> been proposed by Feynman. Shor gave an algorithm for
> the quantum computer which raised a big stream of research.
> This was because Shor's algorithm did reduce the yet assumed exponential
> complexity of the security relevant factorization problem, to
> a quadratic complexity if quantum computed.
>   In the paper a short introduction to quantum mechanics can be
> found in the appendix. With this material the operation of the
> quantum computer, and  the ideas of quantum logic will be explained.
>      The focus will be the argument that a connection
> of quantum logic and linear logic is the right type theory for
> quantum computing. These ideas are inspired by Vaughan Pratt's
> view that the intuitionistic formulas argue about states
> (i.e physical quantum states) and linear formulas argue
> about state transformations (i.e computation steps).
> ***

I have been excitedly studying category theory (with some bias towards
toposes) on my own for the past few months. Pratt's work looks interesting,
but I am not quite at the level of full comprehension yet. I am looking
forward to reaching that point, however!

>  b) Neuroscience and physics suggests that we do indeed admit such a
> substitution level, or that the functions of the brain are Turing-emulable
> (although obviously the architecture is massively parallel and running it
> on a TM is not optimal, but then, neither is running physics, either way,
> this is unimportant due to specific(provable) instances of the CTT(Church
> Turing Thesis)).
>     I agree but we do need more detail of the 1p and 3p aspects of this
> idea.
>  c) a and b do not directly suggest the continuity part, although we can't
> really guarantee continuity that much ourselves. Given that we can never
> experience a moment past our death, we would always experience being alive,
> that is, the Anthropic Principle where the laws of physics happen to be
> that which support or is compatible with us (trivial statement, maybe even
> too general). The continuity bet is a matter of past observations, although
> it's utterly unprovable, on the other hand, we usually expect a next OM and
> that we will wake up in the morning, that the sun will "rise" and so on (by
> induction, regardless if consciously realized or not). That one could
> continue their existence in a different machine body which is functionally
> equivalent is not utterly preposterous to me, at least not much more than
> when one considers how strange it must be that their consciousness follows
> their body/senses even when the body moves through space and time,
> sometimes even with discontinuities (sleep, etc).
> This assumption is almost magical, but not really: it's a consequence of
> some strong "no magic" assumptions in the nature of reality, but as we can
> see, sufficiently advanced technology is indistinguishable from magic and
> sufficiently strong "no magic" assumptions can also be quite
> indistinguishable from magic (more on this later).
>     Pratt's duality explains all of this without any magic at all! Well
> there is some magical mathematics... ;-)
>  d) The UDA paints a picture which seems to include an explanation for
> QM/MWI, thus confirming some current physical theories. Your objection to
> COMP immortality applies to MWI as well - there is MWI immortality as well,
> just a bit more limited in fancifulness. Yet, MWI is one of the simplest
> possible realist interpretations of QM (by various Occam's Razor
> formalizations). COMP itself scores high on the simplicity
> score - easy to describe ontology (after reasoning is done), although very
> rich, it also gives reasonably satisfactory (partial or full) answers/hints
> to some ancient questions (such as "why something instead of nothing",
> "what is matter", "what is mind" along with some more concrete
> questions...)
>     Yes, MWI still suffers from a basis problem even though decoherence
> arguments can seem to make the problem go away temporarily in calculations,
> but it returns every time a new basis is introduced to consider a different
> set of observables. I conjecture that "there is something rather than
> nothing because something is just a piece of nothing distinguished from
> another piece of nothing by a third piece of nothing." As Russell Standish
> argued in his book, Nothing and Everything are indistinguishable.
> - Another assumption of COMP is the Church Turing Thesis. Very strong
> mathematical evidence is for it being true, and we can show it for just
> about any finite (but unbounded) machine following finite rules. It's a
> hypothesis/assumption because in the general form it's not provable because
> it's too general, but we can prove any individual case we care to try,
> there's also many strong intuitions for why it has to be true. I don't
> think there are many computer scientists who don't believe in it, but
> usually those that don't just try to define CTT in wider scope than it is
> (such as hypercomputation, which it obviously doesn't include), such issues
> are a matter of definition and shouldn't be considered to be included in
> this assumption.
>     I have no problem at all with CTT, i just have a serious problem with
> the idea that CTT is completely divorced from the physical.
> - Consistency of arithmetic (existence of the standard model of
> arithmetic), existence of truth value of arithmetical sentences.
>     The existence of truth values does not, in itself, define them.
> Additional structure is required to define not only what domain the truth
> value lies in but how it is mapped to our propositions and sentences.
> The consistency belief is both intuitive as well as one about a certain
> Turing Machine never halting (which can be made in stronger theories, but
> cannot be believed any more than you can believe that arithmetic is
> consistent). A belief in a sentence being either true or false independent
> of anything is not much different from the belief that a machine either
> halts or doesn't halt (and no other choice exists).
> This is again a matter of theology - of the provably unprovable stuff.
> Although, again, it's a strong "no magic" assumption, that given a finite
> self-contained set of rules (addition, multiplication) applied on finite
> self-contained objects (numbers), it will always yield the same result and
> nothing whatsoever can change that.
>     I agree that "given a finite self-contained set of rules (addition,
> multiplication) applied on finite self-contained objects (numbers), it will
> always yield the same result" but this does not address my problem. Unless
> there is something physical that is somehow different but equal in
> ontological level to show results side by side, there is no proof of
> equivalence, all there is is modulo isomorphism and barely even that.
> - A hidden assumption: we have minds/are conscious/experience qualia. This
> is a bit magical, but it's hidden in the first assumption that I listed.
>     It is not magical, it is quite ordinary. It is the most ordinary of
> facts that I am conscious of what my hands are doing at this moment, for
> example... But what is this "my"? If it is just an illusion generated by
> some kind of feedback loop, how does the delay that allows the loop come to
> be? It is interesting that there is a mapping in category theory that shows
> this exact kind of mapping: the Idempotent Endomap
> [image: Idempotent Endomap]
>     It is interesting to note the properties of this mapping. See, for
> example: ls.poly.edu/~jbain/Cat/lectures/13.MoreCats.pdf
> The thing is - the only thing we can be certain of, but cannot communicate
> is having a mind. From our observations we can infer the existence of the
> external world and that our bodies are part of it, we can also observe that
> the states of our brain correlate very well with our conscious experience.
> A different computationalist theory (eliminative materialism) takes this
> hidden assumption and posts its negation as an axiom. The problem with that
> is that the external world is only inferred by using observation, thus it
> cannot really be accepted by most conscious observers (who are delusional
> in such a theory), however such a theory is not inconsistent if
> consciousness is ignored. If you ignore the mind assumption, you can
> completely ignore almost all of COMP's strange conclusions because none of
> them would matter, but the existence of primitive matter would be saved in
> such a theory.
>     I agree. I just do not require matter nor mind to be primitive, I
> argue that both are aspects of a single neutral primitive.
> All of these are assumptions which are not uncommon for most
> secular-minded people: the first is widely considered by the "no magic"
> camp, it also is required if you don't want consciousness to be utterly
> strange and magic current evidence, the second is widely considered true by
> anyone who studied computability/math/comp sci, the third is usually
> considered true, if it's false, pretty much all math we know is false, and
> there are many intuitions why it's likely true. Given these assumptions,
> COMP is a fairly rational theory with a few unprovable, but widely accepted
> "no magic" assumptions. However, even with these assumptions, you can't
> really avoid some really unusual magic (given only the first assumption).
> The strange conclusion is hidden in the assumptions, just most people don't
> see it (strangely it's not uncommon for people to hold those assumptions
> and still not see that primitive matter is utterly incompatible with a
> non-eliminative form of computationalism).
>     I agree.
> Onward!
> Stephen
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Joseph Knight

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