The emancipating effect of confronting the undecidable

Pretty well everyone knows of some of the great breakthroughs that occurred in the twentieth century. We’re all aware, even if we don’t understand, the work of Albert Einstein, Erwin Schrödinger, Sigmund Freud, James Watson (or should that be Rosalind Franklin?)

Curiously, though, hardly anyone seems to have heard of the work of Kurt Gödel, and yet he made a discovery that seems to me even more disturbing and transformational than those others.

Kurt Gödel
A devastating but liberating truth

Gödel established that there are certain so-called “undecidable” questions in mathematics. Such questions are unanswerable, by which I don’t mean unanswered: it’s not a matter of a lack of knowledge – we don’t know the answer – but a matter of full, exhaustive knowledge – we know they can’t be answered. Indeed, if we’re good at enough at maths, we can prove they can’t be answered.

These are often simple questions, which is not to say their subject matter is simple: the only one I know about concerns transcendental mathematics, and the word “transcendental” is a bit of a give-away, isn’t it? Something transcendental isn’t likely to be easy. The particular question I’m thinking of concerns the relative size of different infinities, and I imagine that you would agree with me in thinking that the idea that two things can be infinite but one is bigger than the other, is pretty mind-blowing in itself.

The question is simple only in the sense that the answer is yes or no. Which is where Gödel comes in. Because there’s no third answer, and he showed that both answers are wrong. Rigorously proved it: answer “yes” and you get to a logical contradiction, answer “no” and you get to another logical contradiction. So the question is simply unanswerable or, to use the preferred term, undecidable.

Think about that for a moment. There is no other field which, like mathematics, always has a right of a wrong answer. And yet even in mathematics, there are areas where there is neither right nor wrong.

These days we’re frequently told that our societies are paralysed by a terrible moral relativism. People beat pulpits, metaphorical or real, and bewail the passing of absolute truths. They hanker for the days when we knew, always and undeniably, right from wrong and could teach it to our children.

And Gödel showed that the quest isn’t just unachievable, it’s meaningless. In even the most abstract of all fields, mathematics, there is ultimately no absolute truth. If that’s true of mathematics, how much more so must it be the case for the messier disciplines in which all the uncertainties of reality cloud the picture further.

So that means we’re forced back onto our own resources. There is no simple guide that can tell us what’s right, at all times, under all conditions. Which is what those of us who rather suspected that relativism made more sense had always suspected. In the end, you have to go with what works, in any particular set of circumstances.

“Thous shalt not kill”? Well, as a general rule, thou shouldn’t indeed. But maybe in certain circumstances euthanasia, or abortion, or military action, or even execution can be justified – may, indeed, be the only option.

Which means that instead of a helpful if inflexible, general if monolithic guide to behaviour, we’re forced back on to the need to exercise judgement in the light of real circumstances. Forced to take our own decisions. Then live by the consequences.

That this may be not so much a choice as essential to the very nature of our lives is the breakthrough Gödel made. It seems to me more people should know about it.

Because I, at least, I find the notion liberating.

In memory of an outstanding woman

Today’s a particularly good day to salute the achievements of an outstanding figure of the twentieth century. She was a woman who opened doors in ways that are being felt as strongly today as they were in her time. 

And she wasn’t Margaret Thatcher.

A single photograph is the key to the significance of her years of careful work. Of course, as a complete layman, I have to admit that when I first saw it, I was inclined to ask, ‘err... yes... but just what are we looking at?’

The justly celebrated Photo 51.
'Yes, dear, very nice. But what is it?' is not the right response.

However, for those in the know, it provides powerful evidence that DNA is not only a spiral, but a double helix, with the ‘bases’ – the bits that code the genetic message – on the inside. In other words, it was the key to understanding the structure of what has come to be known as the language of life.

It was taken by a crystallographer at King’s College London who, as well as being a skilful and painstaking experimentalist, was also, apparently, a little abrasive, a quality that cost her a few friendships. So it was without her knowledge or permission that her colleague Maurice Wilkins showed the picture to two scientists from the Cavendish Laboratory in Cambridge, James Watson and Francis Crick, giving them the decisive push to build their successful model of the DNA molecule.

James Watson wrote up the story of the discovery in his book The Golden Helix. I heard Watson speak at a conference in 1970, at which he claimed that the US government could save a great deal of money and achieve precisely the same progress, by shutting down all cancer research programmes other than his own. It didn’t seem to me that he was joking, and I was left with the impression that no-one could surpass him in enthusiasm or sincerity of admiration for James Watson.

The book is less than flattering about Rosalind Franklin, who took the key photo 51. Later, Watson admitted that he had been unnecessarily dismissive of both her personality and her skill. But by then he’d shared the 1962 Nobel prize for Physiology or Medicine with Crick and Wilkins, in recognition of their work on nucleic acids, including DNA. Franklin didn’t get a look in. But then she’d died, at the pitifully young age of 37, in 1958. 

On 16 April, as it happens, which is what makes today so suitable for commemorating her life.

The Nobel Prize isn’t awarded posthumously. But it’s also never shared between more than three laureates. Had she been alive in 1962, would Franklin have been the also-ran? The fourth scientist, the one whose work wasn’t recognised? Perhaps it’s just as well that we’ll never know for sure.

And congratulations to the American National Cancer Institute for establishing the Rosalind E. Franklin Award for Women in Science, to the Royal Society in London for setting up the Rosalind Franklin Award for outstanding contributions for any area of natural science, engineering or technology and to the Finch University of Health Sciences/Chicago Medical School for changing its name to the Rosalind Franklin University of Medicine and Science (which, to be honest, trips slightly more easily off the tongue, too).

And what a joy, one day before all the pomp and circumstance of Maggie Thatcher’s funeral, to remember another woman of that time, whose contribution may actually prove more lasting – and certainly a lot less controversial.

Rosalind Franklin at work