Monday, October 28, 2019

What is computation? That is to say, what do I mean by computation? [putting things in order]

As far as I know, the nature of computation is still under investigation. I’m not really qualified to or in fact interested in addressing the question in its full scope and generality. I’m interested in a more limited question – though not, as these things go, all that limited – of the computational aspects of the human mind. And within that, I’m particularly interested in language, and in literature, which of course includes language, but more as well. How much more...who knows?

So, I start out with the abstract idea of computation, then introduce the idea of implementing computation in a physical system and conclude by observing that the computational simulation of a system is not to be confused with the thing itself.

Abstract computation

Abstractly considered, Turing defined computation in terms of a machine that had, 1) a set of symbols, 2) a paper tape on which symbols could be written and from which they could be erased, 3) a device that read from and wrote to the tape, and 4) an instruction set defining relations between the symbols and specifying writing to and erasing from the tape. We need not go beyond that. My point is that we do have a well-known and thoroughly explored account of computation, and that that account is stated in terms of an abstract machine.

Real computation requires physical implementation

I’m not interested in abstract computation on an abstract machine. I’m interested in real computation on a real device of some kind. Given some device, how can we implement computation on that device. It is the idea of implementation that is key.

The device that interests me, of course, is the human brain. And the conclusion I’ve reached over the past few years is that natural language is the simplest activity that requires computation. Language cannot be explained and understood without reference to computation. By implication then we should be able to understand, for example, visual perception without reference to computation. This implies that the full powers of an advanced primate brain are necessary for implementing computation. I suppose that’s the take-out from a paper David Hays and I published in the 1988:
William Benzon and David Hays, Principles and Development of Natural Intelligence, Journal of Social and Biological Structures, Vol. 11, No. 8, July 1988, 293-322,
We didn’t quite put things in those terms, but that paper justifies them. We need not going into the details here.

And so, going back to March of 2016, I’ve written a series of posts on that theme. I’ve collected them under the label, “computational envelope”. This, of course, is another post in that series.

Simulation is not the thing itself

Now we need one more idea, that of simulation. Digital computers can be, have been, and are being used to simulate all sorts of things. But the simulation of a thing is not to be confused with the thing itself. A simulation of an atomic explosion is quite a different phenomenon from a real atomic explosion. And so it is for many other things as well.

And then we have the brain, of any animal, and the human mind. In this case there seems to be some difficulty in distinguishing between a simulation of the thing and the thing itself. It’s not that anyone is confused about the difference between a digital computer, but rather that there is a suspicion that, if we simulate mental processes on a digital computer with sufficient precision and power, then perhaps that computer is not merely running a simulation of a mind, but is in fact a mind. I say let’s set that one aside until we actually confront the situation. So far, we are no where near that.

Now we’ve arrived at the point of this post, a passage from a most interesting book by Peter Gärdenfors, Conceptual Spaces (MIT 2000) p. 253:
On the symbolic level, searching, matching, of symbol strings, and rule following are central. On the subconceptual level, pattern recognition, pattern transformation, and dynamic adaptation of values are some examples of typical computational processes. And on the intermediate conceptual level, vector calculations, coordinate transformations, as well as other geometrical operations are in focus. Of course, one type of calculation can be simulated by one of the others (for example, by symbolic methods on a Turing machine). A point that is often forgotten, however, is that the simulations will, in general be computationally more complex than the process that is simulated.
I rather suspect that all of these kinds of processes take place in the human brain. Only the symbolic level processes however, are irreducibly computational as implemented in the human brain. The other processes are implemented in some non-computational way.

Pattern recognition and transformation might be implemented in neurodynamics while coordinate transformations might, in part, be carried out by the physical structure of region to region mapping in the brain. Whatever. But the scientific investigation of human perception and cognition may require us to simulate any and all of these processes in a computer – as indeed, Walter Freeman has implemented dynamical processes in understanding how odors are recognized and remembered. The fact that we can simulate these processes computationally does not, of course, imply that they are computational in the brain.


It is my impression that a have of confusion has arisen through a failure to distinguish between the need for implementation on the one hand and the difference between simulation and reality on the other. That’s more than I want to go into here and now.

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