X-Message-Number: 11665
Date: Sun, 2 May 1999 12:57:01 EDT
Subject: The "Turing Book"--Problems with Isomorphism


The uploaders and strong AI people take as an article of faith, or as a 
postulate, that isomorphism is everything--that the map is indeed the 
territory, if the fidelity is adequate.

We skeptics have mostly just pointed out, first, that the postulate is 
unverified; and, second, that it conflicts strongly with many people's 
intuition and notions of common sense. We have also offered examples of the 
postulate apparently leading (probably) to demonstrably untenable positions. 

Defenders of strong AI mostly just point out that intuition is fallible and 
we must go where logic appears to lead us; this is the way we make progress. 
They point to areas where use of isomorphism has been fruitful--especially in 
computing--and this is probably their greatest strength. Sometimes they also 
lean on the advances in information theory, which tend to support the notion 
that the boundary between physics and information is hazy and perhaps, at 
bottom, information in some sense is everything.

Today let me take a somewhat different approach--viz., challenge the 
defenders of strong AI to clarify the meaning of "isomorphism" and find a 
fault in my example below.

In math, "isomorphism" means a one-to-one correspondence between two systems, 
sets etc. that preserves the basic operations, such as binary numbers and 
decimal numbers; there are also more technical definitions. In biology, it 
means a similarity in appearance or structure, e.g between species. In 
chemistry it may mean a similarity between crystalline forms of different 
composition. In greatest generality it just means identity or similarity of 
form, shape, or structure.

Clearly, then, "isomorphism" from the point of view of computer simulation 
needs to be well defined, and the definition justified. Merely chanting 
"isomorphism" as a mantra doesn't cut it. And certainly any old "similarity" 
is much too loose.

Now, my main point today is that I can define "isomorphism" in such as way as 
to allow a mere book (albeit a very large one), just lying there, to simulate 
or emulate a person. This is easily done just by assigning the appropriate 
meanings to certain symbols. But first, we need a couple of reminders.

Remember, starting out, that the case for computer emulation rests on 
identification of certain sets of numbers in the computer with corresponding 
physical characteristics of the emulated person and his activities.

It can also be important to remember, especially in the case of the 
proof-of-principle Turing Tape, that we need some explicit way of taking into 
account the physical mechanism of the computer--how the tape is read, 
written, and moved. I have never seen this done.

The strong AI people admit that a Turing Tape cannot do two things 
simultaneously, or do anything in real time, but they insist this is not 
important, since they can always label the appropriate sets of numbers in 
such a way as to assign (symbolically) the correct correspondences. (I bypass 
for now the question of two-way mappings in alleged isomorphisms.)

O.K., I take this at face value, and carry it a step further. Instead of 
having a Turing Tape and a physical manipulation of the tape, let us 
substitute a book (the Turing Book) that includes--in addition to the 
appropriate successive internal states of the computer--a description of the 
manipulations that constitute running the computer, i.e. reading, writing, 
and moving the tape. The book just lies there, doing nothing over time, but 
it LABELS certain sets of numbers in a way that can be interpreted as changes 
over time. Case closed.

If I need to belabor the point, the people defending computer emulation say 
that a mere number written somewhere can indeed "be" a part or aspect of a 
person and his activities, if it is appropriately labeled and if it has the 
correct relationship to other parts or aspects (other sets of numbers). Well, 
if a written description of the state of a neuron is allowable, why not a 
written description of an activity over time? The description is itself 
static, but that should not matter--only the symbolic relationships should 
matter, if we take the strong AI people at face value. They clearly insist 
that symbols can replace physical matter and physical space, so they can 
hardly claim that symbols cannot replace physical time.

For clarity, a reminder that we must distinguish between symbolism and 
physical analogs. A Turing Book is fully symbolic; a copy of a person in 
another medium (some kind of "robot") would be a physical analog. The latter 
case has its own problems, but that is not what I focus on today.

Robert Ettinger
Cryonics Institute
Immortalist Society

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