Today's column is a review of two books that have been published simultaneously in Russia and in America:

1.V. N. Katasonov: "The Ladder to the Sky (A Genesis of the Set Theory of G. Cantor and The Problem of the Limits of Science)". Russian text in the Internet:<http://www.philosophy.ru/iphras/library/granitsy/katasonov.htm>.

2.Amir D. Aczel: "Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity". 258p. Four Walls Eight Windows edition, 2000, 258 pages; $24.95

And according to today's columnist, Igor Voronov, the "basic and heuristic concepts for the best understanding of the ideas stated in these two books are contained in the book by Andrew Newberg et al.: Why God Won't Go Away."

For Voronov, the basic thesis of the review:

"Many ideas of modern mathematics are based on the work of the same functional modules of a human brain, which served in the last history of mankind and form now a basis for the creation of religious feelings." To substantiate his claim, he adds that "both spiritual experiences and experiences of a more ordinary material nature are made real to the mind in the very same way - through the processing powers of the brain and the cognitive function of the mind." (from Andrew Newberg and others, "Why God Won't Go Away", page 37.)

Read on to continue the exploration.

Today's columnist is Igor B. Voronov of the Sechenov Institute of Evolutionary Physiology and Biochemistry and the Russian Academy of Sciences, St. Petersburg, Russia. Since 1959, he has worked at the Sechenov Institute of Evolutionary Physiology and Biochemistry, Russian Academy of Sciences, now as a leading research fellow, candidate of medical sciences. Areas of scientific interests include: comparative and age physiology of blood circulation and respiration, especially the problems of connections between the rhythm of heart beating and the rhythm of breathing, gerontology, the problems of birth and death rates, the reasons of human populations rise or fall, and evolutionary aspects of the origin of belief in the God, including the descent of various religion branches. Author or coauthor of some 50 research papers on evolutionary physiology and pharmacology, 16 of them are cited in Medline.

--Stacey E. Ake

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Subject: God, Infinity, the Right Hemisphere of the Cerebral Cortex, and the Limits of Knowledge From: Igor Voronov Email: <voroni@IV4555.spb.edu>

During last decades the leading scholars and scientists from many countries and cultures have started to call in question the dichotomy between a natural sciences and religion existing for the last three centuries.

The mathematics is not one of the natural sciences. It is engaged not in research on nature, but in the study of those formal structures that it creates for herself. Therefore mathematics, like art and especially music, can be one of the important links that could restore the connection between the natural sciences and religion.

It is impossible to consider as a simple accident the simultaneous and independent publication in America and in Russia of the two afore-mentioned interesting books discussing the connections of mathematics with the religion.

The center of attention of both these books is the person and work of the great mathematician of the fin-de-siecle era who was also the founder of mathematical set theory: George Cantor (born: 3 March 1845 in St Petersburg, Russia; died: 6 Jan 1918 in Halle, Germany)

The distinctive feature of Cantor's scientific work consisted in his attempting, with the help of mathematics, to find a way to an understanding of God. The matter is that the belief in God is a purely psychological function, not subject to the rational analysis and not having any relation to the question on real existence of the God. Not by means of reason, but more often besides it, such feelings, as honor, selflessness, religious belief, love to the glory and to fatherland - feeling which were till now and will stay in the future the main springs of any civilization have arisen.

The 1981 Nobel Prize winner for physiology or medicine was Roger Sperry of Caltech. The work of Sperry and his collaborators revolutionized our understanding of brain functions. They elucidated the unique capabilities of each hemisphere and demonstrated that the combined effect of bi-hemispheric activity amounted to more than the simple additive effects of the two separate hemispheres.

Despite the complexity of the question on interbrain localization of psychological functions, modern science has enough convincing data on primary localization of the emotional functions, which are similar to belief in the God, as being located in the right brain hemisphere. It is also usually accepted, that the left brain hemisphere is predominately logical and verbal, and in most cases the dominating half of the brain while the right hemisphere has got reputation as the figurative side, emotional, promoting orientation in space, but in most cases not dominating.

It is possible to cite convincing scientific data showing how rational functions of knowledge, found in the left hemisphere of a brain, were evolved by our distant ancestors, inhabitants of the Stone Age, later, than religious functions of the right hemisphere. It will demand a lot of space and time. Better we shall show, as the new stage in the human evolution is described in the beautiful ancient legend.

"And when the woman saw that the tree was good for food, and that it was pleasant to the eyes, and a tree to be desired to make one wise, she took of the fruit thereof, and did eat, and gave also unto her husband with her; and he did eat."

Richard J. Davidson, a psychology and psychiatry professor at the University of Wisconsin, Madison, has amassed evidence that people with less left-sided and more right-sided brain activation are specifically vulnerable to mental depression.

In this regard, it is interesting to recollect that the hero of today's reviewed books, namely, George Cantor, suffered from a heavy form of mental illness-namely, depression--during the last 30 years of his life, eventually ending his life in the psychiatric hospital.

Though Cantor's life ended in the psychiatric hospital, his works have led to recognition of studying of infinity as quite natural component of a mathematical science. Using the methods of set theory as developed by him, Cantor has shown, that there is an indefinite number of actually infinities. Furthermore, he has shown that there are not only an indefinite quantity of all integers, but also precisely the same indefinite amount of odd integers, even integers, integers divisible by 7, and so on. Cantor has also shown that as paradoxical as it may seem all these indefinitely big sets of numbers are equal among themselves. For example, the infinite amount of all integers is not twice the size of the infinite amount of odd integers as it would be possible to expect, but has precisely the same size. Cantor has named the actual infinity as "transfinite" numbers and to their mathematical designation in the formulas and equations has applied the first letter of the Jewish alphabet, the letter "aleph".

In fact the main purpose of Cantor's work, as he viewed it, was the proof of the real existence not only of the so-called "potentially infinite" number sets, that is such sets or series of numbers that increase indefinitely or without limits even with the addition of further numbers, but also the so-called "actually infinite" number sets, i.e., those which cease to increase further.

Cantor has carried out his life endeavoring to prove this hypothesis. In the Jewish religious tradition of Kabbalah, the letter "aleph" designates "the infinite nature and exclusiveness of existence of the God". Cantor had purposely chosen a symbol "aleph" for the designation of actual infinity: his attempts to understand the absolute infinity actually represented his attempt to approach the essence of the God.

Now we shall return to a problem of the brain hemispheric asymmetry. We shall recollect, that religious experiences are connected to the activity of the right hemisphere, and that that mental disease, depression, which suffered Cantor is connected to same activity. Was George Cantor's mental disease really connected to subjects of his scientific researches? It cannot be proved with certainty, but such an assumption is rather probable. And yet, strangely enough, the other great mathematician who successfully continued and developed the ideas of George Cantor--Kurt Goedel-also concluded his life in a condition of heavy mental illness.

But in fact it is far from being true that all great scientists showed attributes of mental illnesses. For example, Isaac Newton was a deep and sincere believing Christian, and his faith did not prevented him to become one of the greatest scientists of mankind. Apparently, the point is in the harmonious interaction of Reason and Belief.

The Knowledge and the Belief are localized separately: Knowledge in the left hemisphere; Belief, in the right one.

Set in the heading of the Review--"existence of limits of Knowledge" can be explained very simply-for, as Roger Sperry has already shown, high-grade activity of the brain can be carried out only at the coordinated, harmonious interaction of its both hemispheres. To put it briefly, Knowledge without the participation of Belief (or Religion, though it is not same) cannot be rich or complete Knowledge. And it also true for Religion, where it becomes an ideology that is defective and low-grade due to a lack interaction with Knowledge and with Science.

That fact, that the Muslim and the Western worlds gave opposite estimations to events in New York on September 11 last year, confirms the competency of the paradigm suggested by Harvard political scientist Huntington: after the end of the "cold war" will begin an epoch of the "civilizations collision".

Now in the first place is the collision of Islamic world with the Western civilizations. Key attributes of the modern Islamic ideology--aestheticization of death, extolling of the military forces, worship of martyrdom, and appeal to the heroic--are characteristic of the activity of the right cerebral hemisphere. Just they were and are now the integral part of all totalitarian ideologies.

In my opinion it is necessary to recognize the certain defectiveness and at the Western civilization--absence of a harmony, excessive prevalence of the Reason over the Belief, dry business calculation over love and friendship, sex over romantic love, to put it briefly--the prevalence of left brain hemisphere above right one.

I have the boldness to expect and hope, that my native land-Russia--which has survived this past century of such terrible and epic historical events, can become that bridge, that connecting part, between the East and the West, between Belief and Reason, between Love and Business, between right and left hemispheres of the brain (Corpus Callosum!) which are necessary for the successful development of mankind during the next centuries.

"Oh, East is East and West is West, and never the twain shall meet, Till Earth and Sky stand presently at God's great Judgement Seat; But there is neither East nor West, Border, nor Breed, nor Birth, When two strong men stand face to face, tho' they come from the ends of the earth!"

(Rudyard Kipling)

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Published   2002.12.11