On 2/11/2012 06:32, Stephen P. King 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?
It bypasses a lot of restrictions, see UDA step 1-7, and my previous
example with the past time-travel. With UDA step 7, it makes the
primitively physical either forever unknowable and with step 8 and MGA
it makes it superfluous/unnecessary.
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. :-)
Yes, modern physics does indeed point us toward our physics being quite
simple and symmetrical, where by 'simple' I mean 'low complexity' (in
the Occam, or Solomonoff inductive sense, Kolmogorov complexity, ...).
COMP seems to argue toward that as well, although I don't think we can
just look at some UD implementation and find some machines partially
implementing our universe right at the start - we don't have those kinds
of computational resources. Smarter ways to get to physics through AUDA
might be better ideas, but I do think that whatever our physics is,
we'll have to use some indexical properties, we cannot rely on a single
universe assumption.
> 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'm a novice myself. You seem to be much more knowledgeable than me in
some subjects (such as category theory).
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.
In COMP, the physical is a "shadow" of arithmetical truth. Making it too
much more than that will either introduce zombies or some substrate
dependence (which part of the UDA do you disagree with?).
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).
This seems mostly agreeable, although I lack the time to read those
papers right now, so I'll refrain from commenting, at least until I
finish my other study backlogs first.
***
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.
Sure, the fields are still young, we can expect a lot more interesting
details in the future.
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.
In COMP (after UDA+MGA), the "everything"/"something" is just due to
abstract relations holding, although that's not as different from your
solution (despite that you seem to dislike Platonism, even in the very
weak form of Arithmetical Realism).
- 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.
If it depends on the physical, you'll have to explain what the physical
is and why does CTT depend on it. If the physical is not merely the
phenomenological (by UDA+MGA, a shadow of mathematical truth within our
minds, which are themselves how some truth is seen from the inside), and
is not arithmetical/CTT-based (not AR Platonia or some mathematical
Plentitude), what is it?
- 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.
Does the standard model of arithmetic exist or not?
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.
Why is physical as phenomenology so troublesome? I still don't
understand what your physical is, if it's not phenomenology, not
platonic instantiation of abstract math, not ontologically primitive
physics, what is it? I also don't understand why this vague
non-primitive physical is necessary...
- 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
Idempotent Endomap
It is interesting to note the properties of this mapping. See, for
example: ls.poly.edu/~jbain/Cat/lectures/13.MoreCats.pdf
It does not seem obvious to me that anything would have experience, if
we wouldn't have it ourselves and thus be able to consider that others
can also have experience, but then, nothing would exist in any
meaningful way if there was no experience.
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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