Comments on Computability in Developing Systems

Below, find a few remarks made on this paper by the reviewers of Cybernetics and Human Knowing, followed by my replies.

Reviewer:

This paper is a discussion of computing and Turing machines from a somewhat "second order" perspective. I am not too excited about it. It seems more or less journalistic to me, without any really new ideas. It does discuss issues that should be discussed in this journal, and it may stimulate conversations.

Reply:

Since the journal is quite popular and concerning the philosophy of "second-order cybernetics" rather than any formal issues, it would be strange if my submission were of a different kind. The paper was not intended to be an ordinary mathematical publication, with much technicality and poor understanding of the sense of the results derived. Rather, it had to suggest an alternative to the blind manipulation with symbols, up to the necessity of employing a way of reasoning different from the traditional deductive scheme. The reviewer did not notice that in the text, since he shared the common prejudices about "science-like" discourse and could not conceive any other forms of reasoning that are as precise, and more adequate for the subject under consideration.

The end of the paragraph is a contradiction to the previous sentence: if the paper contained nothing new, how could it stimulate conversations?

Reviewer:

The author airs ideas which in general are of interest to the readership. However he is unable to simultaneously be precise and understandable, that is, he takes pains to provide (reasonable) mathematical definitions, but as soon as the conceptual terrain gets rough, he retreats to vague and airy prose. Moreover, I find serious problems in his discussion of and arguments regarding extendible Turing machines. But even if I'm mistaken here, he has a lot of explaining to do.

Reply:

Yes, the text is not readily understandable, since it is based on the notions far from the mathematical tradition, which could not be described in full in a paper subject to the usual size limitations (<5000 words). Moreover, this new approach can hardly ever be formulated completely, since self-development is one of its basic principles. There is a lot of explaining to do — but one of the ideas discussed in the paper is exactly that there can be no completely explicit formalism, and any mathematical paper is bound to contain something implicit in it, thus requiring a lot of explaining too. My paper is more honest than the bulk of other "scientific" works, since it does not try to hide the narrow places "under the carpet".

Indeed, I did not "take pains to provide (reasonable) mathematical definitions" — the definitions in the beginning of the paper just describe the usual notions, to fix the terms. There are no mathematical definitions in the paper, quite intentionally. The paper says that mathematical defitions are a very particular case of definition in general — so, I tried to avoid too much dependence on the traditional formalism, to stress the basic ideas. What seems "vague and airy prose" to the reviewer is actually never less precise than the usual mathematical methods, accounting for the implicitness inherent to all the mathematical knowledge. I explicate what mathematicians try to hide behind the superficial formality.

Furthermore, what sense would there be in publications which do not leave room for further development? Why not first announce a viewpoint. and then get engaged in explanations? The demand to present a "ready-to-consume" work looks most strange, since it is the basic mechanism of science to suggest hypotheses which are to be verified later on.

Of course, I can agree that my style is not too crisp and clear — but I read many papers written in a language much more obscure and heavy, and this cannot be the true reason of the reviewer's negative attitude.

Reviewer:

Although I appreciate from my own experience how difficult this topic is, I don't feel that the author, in the final analysis, succeeds in presenting anything genuinely new. That is, anyone who has thought seriously about this topic arrives at much the same thoughts as the author, which accomplishment is not to be denigrated, but the problem is to get further.

Reply:

If the views I present are that obvious, why there are so few traces of them in the literature, and why there are so many quite opposite views, indicating a rather poor understanding of the problems related to development? Where are those who "thought seriously about this topic" and "arrived at much the same thoughts"? Are these thoughts forbidden to publicly discuss? I'm afraid, the reviewer's awareness of these issues was the result of reading the paper, rather than his own achievement — and his desire to get further was an intended effect. This is what I wrote the paper for.

Reviewer:

I have suggested that the middle of the paper be deleted, and the author concentrate on his opening theme. But whether this suggestion is of any use or not, the paper as it stands must be rejected.

Reply:

The suggestion to delete the parts of the text that contain the new ideas might be an indication of the reviewer's fear of them. I am advised to do nothing beyond the scope of traditional mathematics, and to never try to point to its insufficiency. But my interpretation of the traditional line seems too dangerous to the reviewer as well, and he says that the paper should not be published even if I removed any "bad" ideas from it. No further comment is needed.