Archive for the 'Philosophy' Category

Non-Simple Arithmetic

complexThe Intelligent Design folk tell you that complexity requires a designer.

The Richard Dawkins crowd tell you that complexity must evolve from simplicity.

I claim they’re both wrong, because the natural numbers, together with the operations of arithmetic, are fantastically complex, but were neither created nor evolved.

I’ve made this argument multiple times, in The Big Questions, on this blog, and elsewhere. Today, I aim to explain a little more deeply why I say that the natural numbers are fantastically complex.

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Life, the Universes and Everything

As I mentioned the other day, I’ve recently (at the direction of my old friend Deirdre McCloskey) been reading some of the work of John Polkinghorne, the physicist-turned-theologian who seems to write about a book a week attempting to reconcile his twin faiths in orthodox science and orthodox Christianity.

Although Belief in God in an Age of Science is a very short book, it is too long to review in a single blog post. Fortunately, though, much of the non-lunatic content is concentrated in roughly the first ten pages, so I’ll comment here only on those.

Polkinghorne begins in awe. He is awestruck by the extent to which our Universe seems to have been fine-tuned to support life; this is the subject matter of the much-discussed anthropic cosmological principle. To take just one example (which Polkinghorne does not mention): The very existence of elements other than hydrogen and helium depends on the fact that it’s possible, in the interior of a star, to smoosh three helum atoms together and make a carbon atom; everything else is built from there. But it’s not enough to make that carbon atom; you’ve also got to make it stick together long enough for a series of other complicated reactions to occur. Ordinarily, that doesn’t happen, but now and then it does. And the reason it happens even occasionally is that the carbon atom happens to have an energy level of exactly 7.82 million electron volts. In fact, this energy level was predicted (by Fred Hoyle and Edwin Salpeter) before it was observed, precisely on the basis that without this energy level, there could be no stable carbon, no higher elements, and no you or me.

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Giving Thanks

After the philosopher Daniel Dennett was rushed to the hospital for lifesaving surgery to replace a damaged aorta, he had an epiphany:

I saw with greater clarity than ever before in my life that when I say “Thank goodness!” this is not merely a euphemism for “Thank God!” (We atheists don’t believe that there is any God to thank.) I really do mean thank goodness! There is a lot of goodness in this world, and more goodness every day, and this fantastic human-made fabric of excellence is genuinely responsible for the fact that I am alive today. It is a worthy recipient of the gratitude I feel today, and I want to celebrate that fact here and now.

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Principia Mathematica: The Comic Book

Logicomix is—I am not making this up—a graphic novel (that is, what we used to call a comic book) about Bertrand Russell and the writing of Principia Mathematica. Implausibly enough, it succeeds, making rather gripping drama out of the twentieth century crisis in the foundations of mathematics. The technical issues are portrayed clearly and accurately (a novice reader could learn a lot from this book) but never coldly; this is above all a saga about human obsession. I even like the device where the authors themselves appear as characters, trying to figure out how best to present this stuff. It works.

But there’s one part I find almost impossible to believe is accurate; maybe a reader can set me straight. The novel begins in 1939 and proceeds by flashback. In 1939 we see Russell, a lifelong pacifist confronted by the Nazi horror, being shaken to the core by the realization that his beloved Logic does not contain the answers to all of life’s problems. Can there be even a shred of truth to this? Surely the man who devoted his youth and over 300 printed pages to proving that 1+1=2 must always have been well aware that formal logic has its limitations as a practical guide to life.
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