Toronto Star: thestar.com
Jan 26, 2008 04:30 AM
Special to the Star
Which math-phobic among us has not beseeched God for help with another colon-clenching algebra or calculus exam? Had we heeded the words of the German mathematician Leopold Kronecker, perhaps we would have realized we've been talking to the wrong person: "God made the integers; all else is the work of man."
Pythagoras, who gave us his eponymous theorem on right-angled triangles, headed a cult of number worshippers who believed God was a mathematician. "All is number," they would intone.
The 17th-century Jewish philosopher Baruch Spinoza echoed the Platonic idea that mathematical law and the harmony of nature are aspects of the divine. Spinoza, too, posited that God's activities in the universe were simply a description of mathematical and physical laws. For that and other heretical views, he was excommunicated by Amsterdam's Jewish community.
German mathematician Georg Cantor's work on infinity and numbers beyond infinity (the mystical "transfinite") was denounced by theologians who saw it as a challenge to God's infiniteness. Cantor's obsession with mathematical infinity and God's transcendence eventually landed him in an insane asylum.
For the Hindu math genius Ramanujan, an uneducated clerk from Madras who wowed early 20th-century Cambridge, an equation "had no meaning unless it expresses a thought of God." Though an agnostic, the prolific Hungarian mathematician Paul Erdos imagined a heavenly book in which God has inscribed the most elegant and yet unknown mathematical proofs.
And famously, Albert Einstein said God "does not play dice" with the universe.
What is it with God and mathematics? Even as science and religion have quarrelled for centuries and are only recently exploring ways to kiss and make up, mathematicians have been saying for millennia that no truer expression of the divine can be found than in an ethereally beautiful equation, formula or proof.
Witness, for example, such transcendent numbers as phi (not to be confused with pi), often called the Divine Proportion or the Golden Ratio. At 1.618, it describes the spirals of seashells, pine cones and symmetries found throughout nature. Other mysterious constants like alpha (one-137th) and gamma (0.5772...) pop up in enough odd places to suggest to some that they are an expression of the underlying beauty of mathematics, and to others that someone or something planned it that way.
But does that translate into actual belief?
The New York Times reported recently that mathematicians believe in God at a rate 2 1/2 times that of biologists, quoting a survey of the National Academy of Sciences. Admittedly, that's not saying much: Only 14.6 per cent of mathematicians embraced the God hypothesis, versus 5.5 per cent of biologists (versus some 80 per cent of Canadians who believe in a supreme being).
Count John Allen Paulos among the non-believers. A mathematician who teaches at Temple University in Philadelphia and who has popularized his subject in bestselling books such as Innumeracy and A Mathematician Reads the Newspaper, Paulos's latest offering is a slim but explosive volume whose title is self-explanatory: Irreligion: A Mathematician Explains Why the Arguments for God Just Don't Add Up (Hill & Wang).
This newest addition to the neo-atheist field crowded by the likes of Richard Dawkins, Christopher Hitchens, Sam Harris and others emboldened by the recent transformation of non-belief from a 97-pound weakling into a he-man, Paulos thankfully employs little math, preferring to see things, as he tells us, in the stark light of "logic and probability."
Deploying "a lightly heretical touch," he dissects a playlist of "golden oldies" that includes the first-cause argument (sometimes tweaked as the cosmological argument, which hinges on the Big Bang), the argument for intelligent design, the ontological argument (crudely, that if we can conceive of God, then God exists), the argument from the anthropic principle (that the universe is "fine-tuned" to allow us to exist), the moral universality argument, and others.
The famous Pascal's wager – that it's in our self-interest to believe in God because we lose nothing in case He does exist – is upended as logically flawed, based on what statisticians call Type I and Type II errors.
Lord knows Paulos isn't the first mathematician to proclaim his lack of religious faith. Cambridge's famous wunderkind G.H. Hardy loudly and proudly adjudged God to be his enemy. To Erdos, God, if He existed, was "the supreme fascist."
Even as Paulos works to refute the classical arguments for God's existence, he does something too few of his mindset do: Chide non-believers for unsportsmanlike conduct.
"It's repellent for atheists or agnostics," he admonishes, "to personally and aggressively question others' faith or pejoratively label it as benighted flapdoodle or something worse. Those who do are rightfully seen as arrogant and overbearing."
That doesn't prevent him from doffing the gloves. The ontological argument is "logical abracadabra.'' The design, or teleological argument, is a "creationist Ponzi scheme'' that "quickly leads to metaphysical bankruptcy.''
Much of theology is "a kind of verbal magic show.'' A claim that a holy book is inerrant because the book itself says so is another logical black hole.
However, math, specifically something called Ramsey theory, which studies the conditions under which order must appear, can account for the illusion of divine order arising from chaos.
Paulos provides a nice counterpoint to theoretical physicist Stephen Unwin's 2003 book The Probability of God, which calculated the likelihood of God's existence at 67 per cent, and to Oxford philosopher Richard Swinburne's use of a probability formula known as Bayes' theorem to put the odds of Christ's resurrection at 97 per cent.
Those and other efforts remind one of the story, perhaps apocryphal, of Catherine the Great's request of the German mathematical giant Leonhard Euler to confront atheist French philosopher Denis Diderot with evidence of God. The visiting Euler agreed, and at the meeting, strode forward to proclaim to the innumerate Frenchman: "Sir, (a+bn)/n = x, hence God exists. Reply!"
Diderot was said to be so dumbfounded, he immediately returned to Paris.
To Paulos, the tale is a great example of "how easily nonsense proffered in an earnest and profound manner can browbeat someone into acquiescence."
His arguments notwithstanding, Paulos concedes that there's "no way to conclusively disprove the existence of God."
The reason, he notes, is a consequence of basic logic, but not one "from which theists can take much heart."
As for the problem of good and evil, he defers to fellow atheist, the Nobel Prize-winning physicist Steven Weinberg: "With or without religion, good people will do good, and evil people will do evil. But for good people to do evil, that takes religion."
Or as Paulos might say, no mathematician has ever deliberately flown planes into buildings.
Ron Csillag is a freelance writer from Thornhill.