Physics and metaphysics in transfinite set theory and E-infinity

14th January, 2011.
E-infinity communication No. 69

Physics and metaphysics in transfinite set theory and E-infinity
Before anyone jumps to conclusions and misconstrues what we want to say here, we should better start by clarifying first two points. Metaphysics has nothing to do here with the supernatural. In fact at the time of G. Cantor for instance, metaphysics meant more or less fundamental science or stringent mathematical physics dealing with foundational issues. Naturally questions dealing with philosophical issues were included. Equally naturally, the role of religion and the existence of a higher being referred to as Deity were touched upon. In fact fundamental science used to be called natural philosophy and even until our time universities awarded degrees in all possible fields but they are all called doctor of philosophy and this could be in engineering rather than philosophy.
The second point is regarding Mohamed El Naschie who is deeply religious and counts himself as being a Moslem without any doubt but that is all. He is deeply distrustful of all forms of organized religion as well as mingling science, politics and religion in a demagogical way. Perhaps we should give two examples of his writing on this subject before we go any further. At the end of his paper “A note on quantum field theory and P-Branes in n dimensions published in CS&F, Vol. 10 (8), pp. 1413-1417 (1999) he wrote “It may seem that by reducing the contra intuitive physics of quantum mechanics to the contra intuitive geometry of the space of quantum mechanics, nothing is gained. However this is not the right way of looking at the problem. The physics of quantum mechanics has frequently opened the door to the wrong kind of mysticism which is wholly foreign to scientific thinking. By contrast all of the mind-baffling and contra intuitive results of modern geometry in hyperspaces are the end product of the most stringent rational thinking and leave no place for uncalled-for mystical beliefs what so ever. Thus we think a great deal is achieved by viewing quantum physics in what we think is the right geometrical way proposed here”. I think Prof. El Naschie made it clear where he stands. An additional quotation at the end of another paper by him may help to dispel any lingering doubts about a basically renaissance Egyptian who tolerates religious beliefs of the personal type. In CS&F, Vol. 10(2-3), pp. 567-580 (1999), at the end of a paper entitled ‘Nuclear spacetime theories, superstrings, monster groups and application’ El Naschie says “Philosophically inclined theoretical physicists have frequently wondered if, in creating the world, God had any choice in determining it. Assuming that our hypothesis about E-infinity geometry is correct, then it would seem to us that once God had created logic, he had as good as no option but to create the universe as we see it now.”
Having said all that, the situation is slightly different when we come to consider transfinite set theory, the continuum hypothesis, the axiom of choice and particularly the meaning of infinity. There is no doubt that there are two kinds of personalities among serious scientists. Those who do not believe in any form of creation or any form of non-materialistic existence and those who believe in non-materialistic existence as well as the possibility of creation. The first kind is more or less like Kronecker, the famous German mathematician. The second kind is more like G. Cantor. There are people who may be in between. In E-Infinity Mohamed El Naschie finds that the spiritual value and even religious beliefs can be an inspiration to solving extremely difficult problems. In general, one has to keep religion out of science. However there is one exception where we must be tolerant and that is when someone identifies the Almighty with the set of all sets. In fact El Naschie believes that the concept of a set of all sets leads to severe contradictions in set theory. He accepts the class of all classes but not the set of all sets.
If we search for a deep difference between Kronecker and ‘t Hooft on the one side and Cantor and El Naschie on the other side, then the line separating them scientifically is that Cantor and El Naschie believe in the infinite and yes they believe in God. This is indirectly reflected in the philosophical depth of their work where there is no more any artificial separation between physics and mathematics. In fact we recently spoke to El Naschie and he said in a recent interview that God is without doubt a mathematician and definitely not a theoretical physicist. In the same way El Naschie regards the mathematician Prof. A. Connes as the deepest physicist working among us today. In fact the history of set theory and even the mundane descriptive set theory and naturally the history of the Moscow School of Mathematics could not be understood without the role of religion. However we will talk about that in other communications.
E-infinity Group