To Table of Contents No.1

Editorial, part 4

The Universe as an ordered infinity of information-processing units

"MATHESIS UNIVERSALIS" starts its life in 1996 - the 350th anniversary of Leibniz's birth, celebrated by the community of Leibniz scholars. Hopefully, this is to attract attention to the Leibnizian perspective of this journal.

This is a perspective in which Leibniz's insights accord with (i) recent explorations into information physics, (ii) new attitude towards infinity due to Georg Cantor, and (iii) the weakening of the previous dogma that there has to be a fixed limit set on divisibility of matter. However, a certain union of these ideas is characteristic of Leibniz alone. Should we take into account and carefully examine that unique proposal for a synthesis? To answer "yes" means to assume the Leibnizian perspective.

Were all this a mere anticipation of more advanced conceptions to come in the future, it would not exceed the field of interest of historians. Leibniz, though, in his quest for synthesis is bold enough to surpass even nowadays breath-taking horizons. In view of the accord between his insights and the later developments, this should encourage to engage in an brainstorming instead of dismissing what may seem too excentric. Not that Leibniz should be revered as a kind of prophet. His distinguished position is rather due to that circumstance that he was lucky to find himself at a crossing of some main tracks of the European thought. Thus even his errors prove useful as these are not mere individual mistakes but rather those trials which some common ideas should have been put through; eg his belief that any mathematical problem has to be decidable was an orthodox view in logic up to time of Goedel's limitative results.

1. Information physics as anticipated by Leibniz

Leibniz's anticipation of the recent claim that information processing is not a priviledge of human consciousness alone, but rather an ubiquitous property of matter, may have been owed to an earlier tradition. In Leibniz culminated the belief, going back to the ancient Stoics and St. Augustine, that the world is filled up with seeds of reason ( rationes seminales). In Leibniz's language they were called immaterial natural machines, or - with the same adjectives - automata (see Monadology, 64).

Such a vision, which must have seemed odd to Leibniz's contemporaries is familiar to those of us who trace the career of such programmed and programming entities as genes, viruses, crystals, etc. Leibniz held such entities to be governed by laws which do not belong to the mechanics of non-living bodies. In this point he may have shaken hands over centuries with Ervin Schroedinger who in his classic book What is life? 1944, wrote what follows: "living matter, while not eluding the `laws of physics' as established up to date, is likely to involve `other laws of physics' hitherto unknown" (pp. 68-69).

Leibniz termed that other physics as metaphysics, but one should be cautious in interpreting this term in any traditional sense. When trying to give a typical example of metaphysical laws, he mentioned that light takes always the shortest way and commented it as manifestation of finality at the level of non-organic nature - as if a beam of light were capable of perfect solution of the logistic question of how to economically reach the intended spot. While finality belongs to the domain of nature, at the same time it is germane to information.

Information-processing cannot be construed without the notion of purpose. Every calculation is meant to solve a problem. If it is carried out by a human-made machine, it pursues a solution needed by its user, and if carried out by an organism, it provides solutions needed for survival or growing or else reproduction of just that organism. One's purposes and endeavours control the flow and processing of information in natural machines; this is one of two characteristic features in which they differ from artificial machines (the other is to disccused in the next Section). Obviously they belong to the physical world, hence a theory which handles them deserves to by called information physics. Recent years witness the rise of projects of such theory, for instance Roger Penrose's idea of "physics of thought", and ideas popularized and commented by such authors as Tom Stonier. [*1]

While physics of material bodies deals for instance, with heat, information physics, for instance, considers heat as the antihesis of information (cf. Stonier's quoted book, p.74); or, in other situations, as a factor which stabilises organization, provided it is suitably controlled (p.67). Though Leibniz was not capable of going into such issues which are due to the later development of science, in one respect at least his insights may reveal new horizons.

2. Advancing frontiers of informatics

The term "frontiers" stands for the extreme limit of an area of knowledge or a particular activity; let the considered area be informatics (in the sense discussed in part 1 of this Editorial, Sec. 2)). The singular form "frontier" means the extreme limit of settled land, beyond which the country is wild and not developed. This is an illuminating metaphor to state the point that the frontiers of informatics shift more and more towards ever smaller and simpler units: viruses, genes, crystals ... and what further? Does there exist any fixed ultimate limit? The standard orthodox answer is in the affirmative: though the frontiers of informatics advance with the progress of knowledge, there must exist the point beyond which there are no information pieces, no proceesing of them.

In the history of human thought no one except Leibniz and Georg Cantor dared to claim that the extreme limit lies, so to speak, in infinity. True, there may come a moment in which our human capabilities of observation as well our skills of mathematically handling the ever growing complexity prove exhausted. However, the vast land beyond those limits of human cognition should be accessible to a higher intelligence, and if that proves exhausted, then to a still higher one, and so on.

However, the supposed superior intelligence may prove the future intelligence of human race, provided that our evolution will consist in transcending once fixed limits, and so extending the frontiers ever further. Some philosophers of evolution, as Hoimar von Ditfurth, believe in such a transcendence. The Leibnizian perspective can become a fitting framework for those free of what Cantor called horror infiniti.

This Leibnizian perspective involves a conjecture which a time ago seemed mythological to scientifically minded people, but nowadays it does not seem so hopelessly stupid. This is the supposition of infinite complexity of matter, accompanied by the other - that at each successive level of complexity there exist information-processing systems. [*2]

In this perspective, there appears a sharp demarcation line between living and not living-machines (apart from the mentioned above that the former have purposes of their own). To wit, living machines are infinitely complex, that is to say, each successive part is composed of constituent parts. This is why the creation of living machines would require infinite intelligence. For the same reason, artificial intelligence matching natural intelligence, if "artificial" means non-organic, would require the infinitely powerful mind; hence the chances of its being produced by the man would equal zero.

Such a set of conjectures can be never empirically tested, but it can become what Karl Popper called metaphysical research programme. The Leibnizian perspective is not the worst candidate for such a role.

Go to the top of this text
[*1] Roger Penrose, "On the physics and mathematics of thought" in: R. Herken (ed.) The Universal Turing Machine. A Half-Century Survey. Oxford University Press, Oxford 1988, pp. 491-522.

Roger Penrose, The Emperor's New Mind. Concerning Computers, Minds, and The Laws of Physics. Oxford University Press, Oxford etc. 1989.

Tom Stonier, Information and the Internal Structure of Universe. Springer, London etc. 1990. [-> back to main text]

[*2] The problem of infinite progress towards the complexity of matter is discussed in James Gleick's Chaos: Making a New Science (Macdonald, London 1991), p.115, in the following way. "For modern particle physicists, the process has never ended. Every new accelerator, with its increase in energy and speed, extends science's field of view to tinier particles and briefer time scales, and every extension seems to bring new information."

This fact is also commented in the famous A Brief History of Time by Stephen W. Hawking (Bantam Press, London 1992), p.66. "And so we know that particles that were thought to be `elementary' twenty years ago are, in fact, made up of smaller particles. May these, as we go to still higher energies, in turn be found to be made from still smaller particles?". Hawking, in accordance with his belief that physics is near to a "theory of everything", is inclined to expect an ultimate limit of divisibility, but who does not share his optimism as to availability of such universal theory is not bound to share his conclusion. [-> back to main text]

File put on WWW server 17-02-96.

To the top of this page