X-Message-Number: 9268
Subject: Non-Turing machines?
Date: Thu, 12 Mar 1998 09:54:12 -0500
From: "Perry E. Metzger" <>

> From: Thomas Donaldson <>
> Date: Thu, 12 Mar 1998 01:30:19 -0800 (PST)
> 
> Sorry, but the implied idea that if I don't believe we are finite Turing 
> machines I must therefore believe that we run by supernatural means just 
> doesn't ring any bells with me. If finite nonTuring machines can exist, then
> that is sufficient.

Having watched more closely for a while, it appears that this whole
notion of machines that aren't restricted by the Church-Turing Thesis
is based on the entirely specious notion that one can produce
arbitrarily precise analog devices. I would have thought that the
Heisenberg Uncertainty Principle would have been sufficient to put to
death any notion that you could produce arbitrarily precise analog
equipment -- never mind infinitely precise. The error terms inevitably 
mean any computation that can be done by such a device could be done
by a TM.

> Just what would be wrong, metaphysically, if the Church-Turing
> thesis failed?

Nothing per se, just as nothing would be "wrong" if it turned out that 
special relativity was wrong and you could travel faster than
light. However, the evidence we have thus far is that it is
exceptionally unlikely that special relativity is that wrong, and the
evidence we have thus far is that it is exceptionally unlikely that
the Church-Turing Thesis is wrong, either.

Mr. Donadson, we already know enough about the human brain to have
some sense of how neurons work. I see nothing in neural networks that
leads me to believe that they are anything but an interesting parallel 
system that could be perfectly well simulated by a Turing Machine,
although inevitably at a speed cost. Neurons are pretty simple devices 
conceptually speaking. They don't do anything particularly magical.

I hear, often enough, from the "People can't be simulated by
Machines!!!" camp all this brilliant resistance to the notion that
human brains might be finite automata, but all I ever get is vague
handwaving about neural networks. Penrose pretends they must involve
some quantum effects, never mind that real scientists studying them
understand them well enough and have no need for such effects in
explaining their behavior. Others handwave over how they are "analog", 
ignoring the fact that they are also NOISY, and thus inevitably finite 
in their resolution.

> If by digital, you simply mean that our own experiences are discrete and
> finite, I will freely admit some kind of finitude, but discreteness is
> going to (at least) require more argument. Consider vision, and our memory
> of scenes: we don't obviously see things discretely, we see them as 
> continuous.

Really?

I would have thought that someone who had studied as much neuroanatomy 
as you have could have reminded us of the fact that neurons -- even
those connecting the retina to the visual cortex -- do not behave in a 
continuous manner. They can't transmit "voltage levels", only
individual pulses, and they can't send continuous wave signals.

I would have thought that the effects that permit us to percieve
motion picture film as depicting a continuous scene would have put
such a naive notion to death. Ever hear of experiments done on the
so-called Phi phenomenon? That's the perception of discrete events as
continuous. It turns out that you can get subjects to perceive the
presense of a dot that changes color at a point where the dot never
appears during projection. (See Dennet's "Consciousness Explained" for
a good description of this experiment and its implications.)

Next, of course, I'm sure you will resurect the Cartesian Theater.

> Yes, a sufficiently good monitor (better than any yet made) could
> produce a discrete image so fine that we could not tell the
> difference between it and looking through a window at a real scene,
> but that only tells us that our vision can be fooled, not that it is
> discrete.

Hehehehehehehehehehehehehehehehehehehehehehehehehehehehe!!!!

A good one, Mr. Donaldson!

"I know my brain is made up of neurons that do not put out continuous
signals but only stacatto pulses, and that these neurons are connected
by neurotransmitters that induce not continuous signals but
thresholded pulses in my neurons, and I know my neurons are very noisy
devices that don't measure things very precisely, and I know that my
retinas are made up of discrete photosensitive cells that cannot
respond faithfully to a signal at too high a frequency because they
work by sloshing chemicals around, and they only put out a pretty
crude signal anyway, and I know that my visual system will happily
perceive a discrete series of images as though it were continuous,
largely because its a noisy sensor made up out of parts that couldn't
even respond to events that happen too quickly anyway, but DAMN IT,
MY VISUAL SYSTEM IS CONTINUOUS!!!!"

I'm always impressed with your sense of humor.

"My sensor system is continuous!"

"But it can't perceive the difference between a discrete and a
continuous signal! Hell, there aren't even continous signals -- the
world is quantized!"

"Screw that! My transmission system is also continuous."

"But the neurons that send the signal in can't send continuous
signals! They can't send a different signal in for a continuous or
discrete phenomenon either! The signals would be the same!"

"Screw that! My perception system is also continuous!"

"But your brain is made up of neurons that threshhold and can't tell
the difference between discrete and continuous input (which doesn't
even exist anyway)!"

"Screw that! My mind is made up! Don't confuse it with reality!"

> (I don't claim this is a complete argument, but it does raise
> problems in my mind with the notion that our experiences are
> discrete).

Look, Mr. Donaldson, if there is no cartesian theater, and there is no 
soul, and you are made up of these well understood neurons that
operate on thresholds, are noisy, and put out monolevel pulses that
get converted into undifferentiated squirts of neurotransmitters,
where is this magic that you are hiding? Obviously you know something
about where to hide something we can't simulate that we don't. Could
you tell us about it?

> Or again, since we have a finite number of neurons then you may simply
> say that a particular event produces a discrete set of states of our
> neurons. But neurons are not digital, if anything they are analog.

No, they aren't digital, but they aren't mysterious either. I can
model the behavior of an orbiting mass, or a cruise missile, or even a 
hurricane, with reasonable accuracy. All are analog phenomena. True,
I can't simulate *perfectly*, but then again, if I fly the same cruise 
missile three times, it won't take the same precise path each time
either. The world is noisy.

Lets say I have an analog computer and a digital computer. We play an
imitation game with them.  Both are given a set of inputs, and it is
the digital computer's job, in this imitation game, to put out a
signal that can't be distinguished in any meaningful way from that of
the analog computer.  You, the experimenter, are presented with both
as black boxes, and based on the inputs and outputs alone you have to
tell us accurately which is which.

"Well", reasons the Digital Computer, "All I have to do is put out a
signal that is statistically similar enough to that of the Analog
Computer that Mr. Donaldson can't pick which of us is which accurately
particularly differently than 50% of the time. It doesn't matter if my 
signal isn't IDENTICAL to the Analog Computer's, since two Analog
Computers would put out different signals, too!"

All I have to do is simulate something well enough that I can't
distinguish the outputs. I don't have to be "perfect", since the
Analog Computer isn't "perfect" either!

Given this, what's so hard about a goddamned neuron? Its a simple
device.

> Nor can we argue simply that the molecules in our neurons will take
> on a discrete set of states --- space is at least apparently
> continuous, and an enzyme can rotate (among other things). Even
> though nerve transmitters are released in small packets
> approximately the same in content, each packet is part of a larger
> pattern of release, and does very little if released alone.

So?

By this fake reasoning, I could claim no Digital Computer could ever
simulate a Digital Computer.

Why?

Because no Digital Computer is ever really in a discrete state, is it?
After all, the individual parts are analog. Take a RAM cell. It isn't
putting out a perfect 0v or 5v signal, is it? Its slightly off. A few
more electrons here, a few less there. Look at the signals on the bus
lines! Why, we THINK of them as digital, but the truth is that they
are continuous waves! There are no perfect square waves! Look at that
square wave, its got a little bit of ring on it! The signals are
CONTINUOUS!!! WOWZA!!! Why, no Digital Computer could ever simulate a
Digital Computer, since its parts are always in these weird Continuous
States!!!!

> Yes, this could go on and on, but I won't do that.

Thank you for sparing us.

> And I would not be surprised if the Church-Turing thesis, too, had
> become a forgotten byway which had finally failed to deal with all
> the devices and phenomena we will learn to create.

I'll happily bet you that it won't. If need be, we can make the bet a
1000 year term, contingent on our both surviving that long of course.

Perry

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