X-Message-Number: 9276
Subject: More Turing Misunderstanding.
Date: Fri, 13 Mar 1998 14:02:21 -0500
From: "Perry E. Metzger" <>

> From: Thomas Donaldson <>
> Subject: Re: CryoNet #9262 - #9267
> Date: Fri, 13 Mar 1998 00:48:05 -0800 (PST)
> 
> Hi everyone!
> 
> As Art Quaife pointed out some time ago, we will never work with a true 
> Turing machine, but only finite versions of one.

True enough. Of course, the human brain is also finite -- you have
only a fixed number of states possible in it.

> And already it's true that a Turing machine, if set to computing
> quite a number of results (such as the weather, or even the
> configuration of a complex molecule) would take far longer than we
> would be willing to wait.

Gee. I thought the weather report this morning was fairly timely.

> The point of the counterexample is not that this is a BETTER
> machine, it is merely not a Turing machine.

In what sense is it "Better"?

> Even before Siegelmann came up with that example I have been
> pointing out, right here on cryonet, that parallel computers raise
> some fundamental issues.  Sure, you can imitate them with Turing
> machines, but you would need very grea t patience to do so.

Big deal.

1) We know how to build parallel digital devices. I'm using one right
   now.

2) The human brain is a slow device. The neurons barely transmit signals
   at the speed of sound - some are much slower. The neurons are also
   giant given what they do -- we can already build devices that are
   substantially smaller and more powerful.

> Not only that, but they differ in one quite essential way (anyone
> who has tried parallel programming will know this like they know the
> back of their hand, but for others it may come as new): you do NOT
> want recursive computations.

Huh?

Now, you'll forgive me -- I'm only a computer scientist and ignorant
of these matters -- but what *are* you talking about??

> The problem with recursive computations is that they are necessarily
> sequential;

Huh?

Not that recursive computations have any relevance to the current
discussion, but I can easily parallelize recursive computations. In
fact, it is trivial to do so.

> if you want to attain the same aim, you work out a nonrecursive
> algorithm that gets you to the same place.

"huh"?????

> This tells me that recursive algorithms and computers, even theoretical
> ones like the Turing machine, miss out on something essential about 
> the world.

Turing Machines are particularly inelegant ways of expressing
recursive algorithms -- they don't have stacks. You can translate a
recursive algorithm into a Turing Machine algorithm, but it isn't
exactly beautiful to do so.

Are you possibly mistaking the fact that Turing Machines are capable
of spanning any recursively enumerable language with the (false)
notion that Turing Machines employ recursive algorithms? If so, might
I suggest that you learn a bit more about this topic *before*
discussing it?

> After all, we live in a world in which lots of things are going on
> simultaneously, and not just independently, but they are responding
> to one another at a high rate. And someone decides to present a
> model of a computer for which working out such processes becomes
> very long and difficult, and takes a long time ... too long.

Of all the arguments I've heard here thus far about why humans can't
be simulated with digital computers, this is possibly the least
persuasive I've seen to date.

So things are going on "simultaneously". Big deal! What has this to do 
with the price of tea in china? Or more importantly, with the question 
of whether a computer can simulate a human?

If, as a matter of engineering, it is most efficient to simulate a
human using a parallel machine, I'd use a parallel machine. Now,
neurons are in fact *NOT* very impressive devices when it comes to
speed, but if you insist, it isn't a big deal. We know how to build
machines with two, ten, a hundred, or even tens of thousands of
processors if we wish. "Big deal". This is a red herring.

(BTW, by your argument, my computer shouldn't be capable of handling
several hundred tasks at once because it doesn't have several hundred
processors, but of course it does anyway. I'll leave it to you to
learn how it does that.)

> Whatever our brains do, they too operate in parallel, essentially.

"so"?

> Every single neuron is a quite complex little machine,

"Complex" perhaps by the standards of a different age.

The computer on my desk has about a billion transistors in it (I may
be underestimating, but I wanted to be reasonably gentle here.) It is
capable of so many more states than a Neuron I don't even want to
contemplate it.

As computer technology progresses, we will rapidly hit the point where 
could reduce that entire machine down orders of magnitude and
something that complicated would only be a minor subsystem inside a
minor subsystem of the machine.

> For some special cases that evolution has produced in us, we are
> very fast, not because our chemistry is fast but precisely because
> we are parallel, not sequential.

"So"?

> For that matter, our neurons are ANALOG computers (if that notion applies
> at all).

As I've noted, our neurons produce approximate and statistically
varying results. They cannot "measure the PI bar with infinite
precision". They can therefore be simulated by machines that produce
results which are literally indistinguishable by any method you can
propose.

> It's that feature which made me wonder whether or not we might 
> do the same things that Siegelmann's counterexample does.

The *fake* counterexample.

> For Mike I will have this to say: Mike claims that if we could store 
> ourselves in a computer then it would follow that we could make that
> stored person run in a computer. Here is the hiatus in his reasoning: we
> do not just run autonomously, EVER. We are always responding to something
> in the world, and incommensurability is essential in the world.

Fine.

Your sensory mechanisms take in a finite number of bits of
information. You might THINK they are analog sensors, but as I have
noted, they are noisy, with finite precision. We can quantify how much 
they can possibly sense. You can therefore feed the "Person In The
Machine" all the sensory input they need, either by producing sensors
good enough to feed that amount of data in from the real world, or
from a simulated world.

> Secondly, whatever equations describe our behavior, they are highly
> likely to NOT converge to some single solution, while the computer,
> because it is digital (I believe we still need a good definition of
> that, Mike) can only produce some values of the person, not all
> those a real person would produce if that person were in the world.

This is a very boring argument.

Yes, I will agree -- neurons are noisy. That is a point *I* was
making.

If you need to simulate "noisy behavior", add a random number
generator to your computer. If the notion of using a true random
number generator offends your sense of "What a Computer Is", we can
use a high quality PRNG.

> Running someone in a computer would ultimately fall into the
> same resolution problems that computer graphics does: sure, you can get
> finer and finer resolution, but since the world is not made up of small
> distinct locations with given colors etc. your picture will always have
> limits below which it becomes quite false.

Why do you suppose humans don't come with those limits?

> Why is that important? Because
> even small differences will increase with time until they become quite
> large --- that is why it is so hard to predict the weather, even with
> the best supercomputers.

The question is not whether or not one can simulate an analog system
perfectly.

The question is whether or not two analog systems could simulate each
other perfectly.

Two cloned neurons in a dish with identical inputs will not produce
precisely identical output. They are noisy. It is not necessary for
the digital system simulating their behavior to produce output
indistinguishable from either of them alone -- it is only necessary
for the digital system to produce output that is no further from
either neuron than the other neuron -- that is, statistically
indistinguishable output.

> Any theory of computation based on sequential computing, discrete sets of 
> events, and recursive algorithms will ultimately fail to accurately deal
> with the world.

Yawn.

Perry

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