Eternal Mathematics

Eternal Mathematics

Eternal Mathematics - excerpt from "Set Science Free" - Rupert Sheldrake

The search by philosophers in ancient Greece for an eternal reality behind the changing world of appearances led to very different answers, as we saw in the previous chapter. The materialists thought that changeless atoms of matter were eternal, while Pythagoras and his followers believed that the entire universe, especially the heavens, was ordered according to eternal non-material principles of harmony. To understand mathematics was to link the human mind to the divine intelligence itself, which governed the creation with a transcendent perfection and order. The Pythagoreans were more than philosophers: they formed mystical communities, shared property in common, treated men and women as equals, had vegetarian diets and believed in the transmigration of the soul. They thought that, through intellectual and moral discipline, the human mind could arrive at mathematical truths and begin to unravel the mysteries of the cosmos. They were convinced that the universe is governed by a regulating intelligence and that this same intelligence is reflected in the human mind.

Plato (428–348 BC) was strongly influenced by the Pythagoreans but went further. He generalized the notion of eternal mathematical truths to a wider vision of Forms or Ideas (Platonic Forms and Ideas are traditionally written with initial capitals), or archetypes or universals, including not only mathematics but the Forms of every object or quality, including horses, human beings, colors and goodness. These Forms or Ideas exist in an immaterial, transcendent realm, outside space and time. The cosmos is ordered by this realm that transcends it. The horses that we experience in the world are like shadows or reflections of the eternal essence of the horse, the horse Idea beyond space and time. All particular things in the world that we experience through our senses are reflections of transcendent Forms.

Plato famously compared the objects of sense experience to shadows in a cave experienced by prisoners, permanently chained so they can watch only the blank cave wall, with their backs to a fire. All they see are the shadows on the wall cast by things passing in front of the fire. In Plato’s words,

See what will naturally follow if the prisoners are released and disabused of their error. At first, when any of them is liberated and compelled suddenly to stand up and turn his neck round and walk and look toward the light, he will suffer sharp pains; the glare will distress him, and he will be unable to see the realities of which in his former state he had seen the shadows; and then conceive someone saying to him that what he saw before was an illusion but that now, when he is approaching nearer to being and his eye is turned toward more real existence, he has a clearer vision, what will be his reply? Will he not fancy that the shadows which he formerly saw are truer than the objects which are now shown to him?

Plato used the Greek word nous to signify the rational, immortal part of the soul through which the Forms could be known. As ancient philosophy progressed, the terms logos and nous were used to signify mind, reason, intellect, organizing principle, word, speech, thought, wisdom and meaning. Nous was associated both with human reason and the universal intelligence.

Many elements of Platonic philosophy were incorporated in Christian theology, and are implicit in the opening of St. John’s gospel, which, like the rest of the New Testament, was written in Greek. “In the beginning was the Word.” “Word” with a capital W is the translation of logos. Not long before St. John’s gospel was written, the word logos took on a new significance in the Jewish world when Philo of Alexandria (20 BC–AD 50) linked it to Jewish philosophy. Philo was a Greek-educated Jew, and the official representative of the Jewish community in Alexandria to the Roman emperor Caligula. He used logos to mean an intermediary divine being who bridged the gap between God and the material world. The Platonic Ideas were located in the logos, which Philo described as God’s instrument in the creation of the universe. He compared God to a gardener forming the world according to the pattern of the logos.

In Europe from the fifteenth century onward there was a revival of Platonism, which helped prepare the way for modern science. The founding fathers of modern science, Copernicus, Galileo, Descartes, Kepler and Newton, were all essentially Platonists or Pythagoreans. They thought the business of science was to find the mathematical patterns underlying the natural world, the eternal mathematical Ideas that underlie all physical reality. As Galileo expressed it, Nature was a simple, orderly system that “acts only through immutable laws which she never transgresses.” The universe was a “book written in the mathematical language.”

Most great physicists expressed similar ideas. For example, in the nineteenth century Heinrich Hertz, after whom the unit of frequency is named, expressed it as follows:

One cannot escape the feeling that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them.

Albert Einstein’s general theory of relativity was firmly in this tradition, and Arthur Eddington, who provided the first evidence in favor of the theory, concluded that it pointed to the idea that “the stuff of the world is mind stuff … [T]he mind stuff is not spread out in space and time: these are part of the cyclic scheme ultimately derived out of it.” The physicist James Jeans took a similarly Platonic view: “[T]he universe can be best pictured … as consisting of pure thought, the thought of what, for want of a wider word, we must describe as a mathematical thinker.”

Quantum theory extended Platonism to the very heart of matter, which old-style atomists had regarded as hard, homogeneous stuff. In the words of Werner Heisenberg, one of the founders of quantum mechanics:

[M]odern physics has definitely decided for Plato. For the smallest units of matter are not physical objects in the ordinary sense of the word: they are forms, structures, or—in Plato’s sense—Ideas, which can be unambiguously spoken of only in the language of mathematics.

The traditional assumption that the universe is governed by fixed laws and constant constants is almost unquestioned. This assumption has led to a baroque elaboration of theoretical speculation, including billions of extra universes as discussed below.