Incompleteness & the Goedelian way

Edward Rothstein

New York Times/ The Hindu, Feb 15, 2005

Albert Einstein and Kurt Goedel objected to notions of relativism and incompleteness outside their work. They fled the politically absolute, but believed it its scientific possibility.

Relativity. Incompleteness. Uncertainty. Is there a more powerful modern Trinity? These reigning deities proclaim humanity's inability to thoroughly explain the world. They have been the touchstones of modernity, their presence an unwelcome burden at first, and later, in the name of post-modernism, welcome company. Their rule has also been affirmed by their once-sworn enemy: science. Three major discoveries in the 20th century even took on their names. Albert Einstein's famous Theory (Relativity), Kurt Goedel's famous Theorem (Incompleteness) and Werner Heisenberg's famous Principle (Uncertainty) declared that, henceforth, even science would be post-modern. Or so it has seemed. But as Rebecca Goldstein points out in her elegant new book, Incompleteness: The Proof and Paradox of Kurt Goedel (Atlas Books; Norton), of these three figures, only Heisenberg might have agreed with this characterisation. His uncertainty principle specified the inability to be too exact about small particles. "The idea of an objective real world whose smallest parts exist objectively," he wrote, "is impossible." Oddly, his allegiance to an absolute state, Nazi Germany, remained unquestioned even as his belief in absolute knowledge was quashed.

Einstein and Goedel had precisely the opposite perspective. Both fled the Nazis, both ended up in Princeton, New Jersey, at the Institute for Advanced Study, and both objected to notions of relativism and incompleteness outside their work. They fled the politically absolute, but believed in its scientific possibility. Einstein's convictions are fairly well known. He objected to quantum physics and its probabilistic clouds. God, he famously asserted, does not play dice. Also, he believed, not everything depends on the perspective of the observer. Relativity doesn't imply relativism. The conservative beliefs of an aging revolutionary? Perhaps, but Einstein really was a kind of Platonist: he paid tribute to science's liberating ability to understand what he called the "extra-personal world."

And Goedel? Most lay readers probably know of him from Douglas R. Hofstadter's playful best-seller, Goedel, Escher, Bach, a book that is more about the powers of self-referentiality than about the limits of knowledge. Goldstein's interpretation differs in some respects from that of another recent book about Goedel, A World Without Time: The Forgotten Legacy of Goedel and Einstein by Palle Yourgrau (Basic), which sees him as more of an iconoclastic visionary. But in both he is portrayed as someone widely misunderstood, with good reason perhaps, given his work's difficulty. Before Goedel's incompleteness theorem was published in 1931, it was believed that not only was everything proven by mathematics true, but also that within its conceptual universe everything true could be proven. Mathematics is thus complete: nothing true is beyond its reach. Goedel shattered that dream. He showed that there were true statements in certain mathematical systems that could not be proven. And he did this with astonishing sleight of hand, producing a mathematical assertion both true and unprovable.

The theorem has generally been understood negatively because it asserts that there are limits to mathematics' powers. It shows that certain formal systems cannot accomplish what their creators hoped. But what if the theorem is interpreted to reveal something positive: not proving a limitation but disclosing a possibility? Late in his life Goedel said of mathematics: "It is given to us in its entirety and does not change, unlike the Milky Way. That part of it of which we have a perfect view seems beautiful, suggesting harmony." That beauty, he proposed, would be mirrored by the world itself. These are not exactly the views of an acolyte devoted to Relativity, Incompleteness and Uncertainty. And Einstein was his fellow dissenter.

Religions as works of art

Dylan Evans

The Guardian/The Hindu, May 3, 2005

Not believing in God is no excuse for being virulently anti-religious or naively pro-science.

There are many species of atheism, just as there are many species of religion. But while many religions still thrive, most of the atheisms that have ever existed are now extinct. The non-religious person today is, therefore, rather like a person who wanders into a shop to buy a breakfast cereal and finds only one variety is for sale. Moreover, this variety is not very tasty, because the kind of atheism that flourishes today is old and tired. Today's prominent atheists — people such as Jonathan Miller and Richard Dawkins — hawk around a belief system that reeks of the 19th century, which is not surprising, for that is when it was born. Mr. Dawkins is virulently anti-religious, passionately pro-science and artistically illiterate — thus manifesting all three of the main characteristics of the old atheism in a particularly pure form. His attacks on religion are so vitriolic and bad-tempered that they alienate the sensitive reader and give atheism a bad name. As a friend of mine once commented, no other atheist has done more for the cause of religion than Richard Dawkins.

Isn't it about time that atheists tried to imagine what some other forms of atheism might look like? Not in the hope of replacing one orthodoxy with another, but simply in order to challenge other atheists to imagine still more ways of being non-religious — to encourage them to construct their own forms of atheism, rather than buying a ready-made version off the shelf. Atheism should be more like a set of Lego blocks than a pre-assembled toy. The challenge and the opportunity it offers is that of constructing one's own personal philosophy of life, a philosophy that is not put together according to any set of instructions handed down from on high. As a way of kicking off the debate, let me outline my own variety. It would be a travesty if I were to pretend that this is the only worthwhile kind. But I think it is more appropriate for the 21st century.

When I say that I value religion, I do not mean that I see any truth in the stories about gods, devils, souls and saviours. But I do think there is one respect in which religion is more truthful than science — in its depiction of the longing for transcendent meaning that lies in man's heart. No scientific theory has ever done justice to this longing, and in this respect religions paint more faithful pictures of the human mind. My atheism sees religions as presenting potent metaphors and images to represent human aspirations for transcendence. Here is a parable to explain what I mean: once upon a time, a talented artist painted a picture of a beautiful landscape on the wall of his house. People came from all around to see the picture. It was so beautiful that they would spend whole days staring at it.

Led on by wishful thinking, some people even began to forget that they were looking at a painting, and came to believe that the wall was a window. So the artist removed one of the bricks in the wall, allowing the illusory nature of the painting to become clear. Some of those who had mistaken the painting for reality were upset to have their illusion shattered. But the wise ones thanked the artist profusely. "By revealing the fictitious nature of this landscape," they said, "you have allowed us to appreciate the beauty of your art." I think the best way to think about religion is to see it like the painting in this parable. Religions are beautiful things, but their beauty can only be truly appreciated when they are seen as human creations — as works of art. Atheists who attack religions for painting a false picture of the world are as unsophisticated and immature as religious believers, who mistake the picture for reality. The only mature attitude to religion is to see it for what it is — a kind of art, which only a child could mistake for reality, and which only a child would reject for being false.

Finding Design in Nature

CHRISTOPH SCHÖNBORN New York Times: July 7, 2005 EVER since 1996, when Pope John Paul II said that evolution (a term he did not define) was "more than just a hypothesis," defenders of neo-Darwinian dogma have often invoked the supposed acceptance - or at least acquiescence - of the Roman Catholic Church when they defend their theory as somehow compatible with Christian faith. But this is not true. The Catholic Church, while leaving to science many details about the history of life on earth, proclaims that by the light of reason the human intellect can readily and clearly discern purpose and design in the natural world, including the world of living things. Evolution in the sense of common ancestry might be true, but evolution in the neo-Darwinian sense - an unguided, unplanned process of random variation and natural selection - is not. Any system of thought that denies or seeks to explain away the overwhelming evidence for design in biology is ideology, not science. Consider the real teaching of our beloved John Paul. While his rather vague and unimportant 1996 letter about evolution is always and everywhere cited, we see no one discussing these comments from a 1985 general audience that represents his robust teaching on nature: "All the observations concerning the development of life lead to a similar conclusion. The evolution of living beings, of which science seeks to determine the stages and to discern the mechanism, presents an internal finality which arouses admiration. This finality which directs beings in a direction for which they are not responsible or in charge, obliges one to suppose a Mind which is its inventor, its creator." He went on: "To all these indications of the existence of God the Creator, some oppose the power of chance or of the proper mechanisms of matter. To speak of chance for a universe which presents such a complex organization in its elements and such marvelous finality in its life would be equivalent to giving up the search for an explanation of the world as it appears to us. In fact, this would be equivalent to admitting effects without a cause. It would be to abdicate human intelligence, which would thus refuse to think and to seek a solution for its problems." Note that in this quotation the word "finality" is a philosophical term synonymous with final cause, purpose or design. In comments at another general audience a year later, John Paul concludes, "It is clear that the truth of faith about creation is radically opposed to the theories of materialistic philosophy. These view the cosmos as the result of an evolution of matter reducible to pure chance and necessity." Naturally, the authoritative Catechism of the Catholic Church agrees: "Human intelligence is surely already capable of finding a response to the question of origins. The existence of God the Creator can be known with certainty through his works, by the light of human reason." It adds: "We believe that God created the world according to his wisdom. It is not the product of any necessity whatever, nor of blind fate or chance." In an unfortunate new twist on this old controversy, neo-Darwinists recently have sought to portray our new pope, Benedict XVI, as a satisfied evolutionist. They have quoted a sentence about common ancestry from a 2004 document of the International Theological Commission, pointed out that Benedict was at the time head of the commission, and concluded that the Catholic Church has no problem with the notion of "evolution" as used by mainstream biologists - that is, synonymous with neo-Darwinism. The commission's document, however, reaffirms the perennial teaching of the Catholic Church about the reality of design in nature. Commenting on the widespread abuse of John Paul's 1996 letter on evolution, the commission cautions that "the letter cannot be read as a blanket approbation of all theories of evolution, including those of a neo-Darwinian provenance which explicitly deny to divine providence any truly causal role in the development of life in the universe." Furthermore, according to the commission, "An unguided evolutionary process - one that falls outside the bounds of divine providence - simply cannot exist." Indeed, in the homily at his installation just a few weeks ago, Benedict proclaimed: "We are not some casual and meaningless product of evolution. Each of us is the result of a thought of God. Each of us is willed, each of us is loved, each of us is necessary." Throughout history the church has defended the truths of faith given by Jesus Christ. But in the modern era, the Catholic Church is in the odd position of standing in firm defense of reason as well. In the 19th century, the First Vatican Council taught a world newly enthralled by the "death of God" that by the use of reason alone mankind could come to know the reality of the Uncaused Cause, the First Mover, the God of the philosophers. Now at the beginning of the 21st century, faced with scientific claims like neo-Darwinism and the multiverse hypothesis in cosmology invented to avoid the overwhelming evidence for purpose and design found in modern science, the Catholic Church will again defend human reason by proclaiming that the immanent design evident in nature is real. Scientific theories that try to explain away the appearance of design as the result of "chance and necessity" are not scientific at all, but, as John Paul put it, an abdication of human intelligence. Christoph Schönborn, the Roman Catholic cardinal archbishop of Vienna, was the lead editor of the official 1992 Catechism of the Catholic Church.

Walking points

For some, the point of travel is its sheer pointlessness. It is the lack of a pre-determined purpose which makes the whole thing worthwhile. It is like the Australian lecturer in a Chennai college who spent the best part of his first summer vacations in india going to a place called Nabadwip dham in rural Bengal and getting back from there. Asked why Nabadwip dham, he said he had been leafing through an atlas and had liked the sound of the name. Asked whether he had any company for the journey, he indicated his flute. Asked what he had done when he finally got to Nabadwip dham, he said he had looked at the sunset and played a tune on his flute.

But, then, carrying a flute is far simpler than carrying a portable fridge and walking round ireland, which is what an Irishman did just to win a bet. He not only did it but also got a book out of it, with both him and the fridge beaming triumphantly from the cover. The Australian who went to Nabadwip dham and back only got a magazine article out of it. There are some who’d say you have to be reasonably fit to walk round Ireland carrying a fridge, even a portable one which presumably operates on batteries. There are others who’d say that Nabadwip dham could give the unsuspecting traveller from down under the Delhi belly. All that is besides the point. Remember the song about the bear who climbed the mountain:

“And what do you think he saw?

He saw another mountain?

And what do you think he did?

He climbed the other mountain”.

If a bear can bear the pointlessness of pointless travel, so can we, could be one response. Jerome K Jerome and two others took off one summer down the thames and wrote it up in a book called three men in a boat. Remember Jerome was the one who said, “it is impossible to enjoy idling thoroughly unless one has plenty of work to do”. And what better way to idle than to snooze in a boat in the company of two others who can take turns not to work. A few decades ago, American airliner panam ran an advertising campaign on the theme “getting away from it all”. That, alas, was just about the time Marshall Mcluhan predicted in the medium is the message that the communications revolution would make the world a global village. You can no longer get away from the mobile and the idiot box even at Nabadwip dham.

[ TOI.Ed 3: thursday, october 18, 2001 ]
http://timesofindia.indiatimes.com/articleshow/1566755718.cms