Re: Symbol Grounding Problem (attn: Vend)

On May 8, 9:56 pm, Don Geddis <d...@xxxxxxxxxx> wrote:
forbisga...@xxxxxxx wrote on 8 May 2007 18:29:

As far as I know the models commonly known as "the laws of physics" do not
require independent variables to be rationals.

I guess there's the possibility of a "smallest size" at the Planck size,
which might someday imply that the universe is actually discrete instead of
continuous (in space, at least, and perhaps time as well).

But let's assume that's not going to be the case :-).

Good, becuase I thought about it quite awhile before ignoring Planck
rather
than making a preemptive strike. You really don't want to go down
that
path.

This means the idealized identification of states passed through by a
physical system undergoing a process may be considered computationally
while the states themselves may not be identified with rationals, as would
be required for the brain to be equivalent to any Turing Machine.

That's only true if the abstract computation requires following the exact
trail of states.

Not quite but close. It only means that the physical system passes
through
states where any arbitrary finite approximation leads to divergent
results
on recursion. "The laws of physics" aren't laws in the sense that
physical
systems must follow them rather that they describe our best
understanding
of the behavior of physical systems.

The more likely case, given all the noise (heat and otherwise) in organic
entities, is that -- whether or not the device is "really" going through
infinite-precision analog states and values -- that only very broad
equivalence classes of these states and values matter to the computational
outcome.

I don't think so. Brains weren't designed by engineers to make this
so.
The brain evolved. It seems more likely to me that there are a class
of
real valued computations that converge over time and that noise is
filtered
out in this way. I really doubt there is any latching mechanism that
forces
the brain to pass through a definable set of ordinally identifiable
states
as would be required for the brain as a TM theory to be true.

Just like, in a PC, the voltages on the wires are really analog, but it's
easiest to understand the device as "voltage less than 1V means the digital
value 0, and voltage greater than 4V means the digital value 1, and the
chance of seeing a voltage between 1V and 4V for any significant length of
time (longer than a typical state transition) is vanishingly small."

I would expect a description of the brain's computation to (eventually)
use similar kinds of language.

I doubt the brain has a sync signal. Suppose we design a computer
without
a clock. Instead, we send sets of pulses down stream where one of the
pulses is slightly delayed. When that pulse arrives the rest are
guaranteed
to be in one of the two states you just gave. When the subsystem gets
the latching pulse it has some arbitrary time to process and forward
the
results to the next subsystem with the same delayed latch pulse.
Again,
suppose multiple and independent subsystems process the same data
in paralell and asynchronously. After passing through several
subsystems
the results from are fed back to the originating subsystem. Since
the
paths taken by the signal pulses are undefined by the originating
subsystem
it has to locally latch the signals from the various "results" lines
until all
of the results have returned. If it doesn't do this then it may be
mixing
reuslts from subsystems processing signals sent at time t1 with
others
processing signals sent at time t2.

From time to time I've tought about the mix of heart beat and
breathing
as generating the sync signal. It would happen because the flow of
oxygen and sugars would regulate cellular activity in a very broad
sense.

I'm not sure there is any evidence of either of these approaches being
used
by the brain. What is your alternative that would force brain states
into
a cardinally identifiable set?

There are times when computations involving the substitution of rationals
for irrationals are most prone to catestrophic results failure.

You still seem to be stuck on simulation, where the discrete approximation
to an analog process is imperfect, and if the analog process is also chaotic,
then the discrete approximation is unable to maintain its analogy for long.

Yes. Give me a way past this without just assuming the answer you
wish.

But the suggestion of Computationalism is that strict simulation is not
necessary, any more than a software calculator must simulate the physical
properties of a physical hardware calculator. To turn messy noise organic
soup into a useful computational device, the most likely guess is that
evolution happened upon the magic of discrete signals. So all the noise gets
quickly suppressed and error-corrected. Just like in a PC.

Again, I doubt this is the most likely guess. It seems more likely to
me that
thermal noise is drowned out by the strong interactions of the
effective brain
processes. I'd like to call it interation but I'm also assuming time
isn't
descrete so it's just feedback. Many old tractors had govenors on
them.
These were analog devices that kept the engine spinning at
aproximately
the same speed all the time even as power needs changed. As long as
there are basins of attraction sheparding the signals they can remain
real
valued all the way through.

This is the method of finite approximation of time dependency, for instance
given some set of statest S(t) where the initial condition S(0) is defined
and the "input" is also defined as I(t) then we says the state of the
system at some future time can be identified as S(t+1) = F(S(t), I(t)) This
is the way we model physical processes using finite state automa, and TM
are finite state automa no matter how big the tapes.

That's still trying to (imperfectly) simulate a physical process. That's not
necessary for a discrete computation, even if the original is physically
realized.

It's not needed if the physically realized process has the necessary
latching
mechanism focing it into descrete states at descrete times. We don't
know this about the brain. The brain isn't a designed artifact where
"proper
functioning" asserts this truth.

It seems there could be mathematical models of the brain but no
TM implementation would be satisfactory.

Yes, in theory that's possible.

I don't consider it likely, however.

Well, at least we're getting past the "dualism" arguments against my
position.
I'm not adding any "magic".

.

Relevant Pages

  • solutions book
    ... We're a team for providing solution manuals to help students in their ... A Course in Modern Mathematical Physics by Peter Szekeres ... Accompany Engineering circuit analysis, 6th edition By Hayt ... An Introduction to Signals and Systems By John Stuller ...
    (comp.soft-sys.matlab)
  • solutions book
    ... We're a team for providing solution manuals to help students in their ... A Course in Modern Mathematical Physics by Peter Szekeres ... Accompany Engineering circuit analysis, 6th edition By Hayt ... An Introduction to Signals and Systems By John Stuller ...
    (sci.physics.particle)
  • solutions books
    ... We're a team for providing solution manuals to help students in their ... A Course in Modern Mathematical Physics by Peter Szekeres ... Accompany Engineering circuit analysis, 6th edition By Hayt ... An Introduction to Signals and Systems By John Stuller ...
    (comp.soft-sys.matlab)
  • solutions manual
    ... We're a team for providing solution manuals to help students in their ... A Course in Modern Mathematical Physics by Peter Szekeres ... Accompany Engineering circuit analysis, 6th edition By Hayt ... An Introduction to Signals and Systems By John Stuller ...
    (comp.soft-sys.matlab)
  • solutions book
    ... We're a team for providing solution manuals to help students in their ... A Course in Modern Mathematical Physics by Peter Szekeres ... Accompany Engineering circuit analysis, 6th edition By Hayt ... An Introduction to Signals and Systems By John Stuller ...
    (sci.stat.consult)