Where was I? Well, last week* we established, among other oddities, that diclofenac is bad for the religion of Zoroastrianism. That post didn’t really have anything to do with mathematics (although I did at least attempt to tenuously link it chaos theory), so I will make up for it by at least mentioning some mathematicians this week, if not actual mathematics. However, I will stick with the topic of religion for the time being.
This is partly inspired by a book I’ve just read: Galileo’s Daughter, by Dava Sobel. It doesn’t really match up to Longitude, but is a good read nonetheless. It is really about the life and work of Galileo Galilei, although Sobel gives us the hard science and history in a more easily digestible form, by interweaving commentary on his relationship with his daughter. She seems to have been a quite extraordinary woman: sent to a convent at age thirteen due to her illegitimacy (and hence lack of marriage prospects), she spent her whole life in extreme poverty within those walls, but still managed to be a doctor, playwright, composer, musician and prolific correspondent in the little time she had which wasn’t dedicated to prayer, labour and general suffering.
Anyway, one of the things which struck me most about Galileo’s life was his relationship with the all-powerful Catholic church at this time. He was a very devout Catholic: publicly, of course (claiming Catholicism is, after all, preferable to torture and painful death), but more surprisingly, given the utter ignorance and persecution he suffered at the hands of the Inquisition, he remained privately devoted to the church. He even said, near the end of his life:
I have two sources of perpetual comfort – first, that in my writings there cannot be found the faintest shadow of irreverence towards the Holy Church; and second, the testimony of my own conscience, which only I and God in heaven thoroughly know. And He knows that in this cause in which I suffer, though many might have spoken with more learning, none, not even the ancient Fathers, have spoken with more piety or with greater zeal for the Church than I
Much of his life was spent treading a fine line between his great desire to spread the word about the incredible new things he was discovering (including laws of motion, the telescope, sunspots, and the moons of Jupiter), and the need to placate the various censorious cardinals who felt that his works threatened their supremacy. He was finally convicted of heresy for his assertion that heliocentric Copernican model of the solar system was right – that is, that the sun is at the centre, and not the earth (previously it had been assumed that the sun travelled around the earth once per day!) – and died ignominiously, under house arrest for his “crimes”.
Galileo didn’t see any conflict between his discoveries and the teachings of Christianity, and he spent much effort trying to think up theological arguments which would persuade the authorities that this was the case. The problem was, of course that while he took the word of the bible to be figurative, they mostly did not.
I would imagine that, if asked, most people would probably say that scientists probably have a higher tendency towards atheism than non-scientists. This may well be true (it’s not the kind of thing you can easily get reliable statistics on), but is there really such an incompatibility between religious and rational thought? Here is a cartoon:
There is a serious point here: you can’t really rationalise a belief in God (although at least one person has tried – see below), and it needs to be taken on faith. In a similar way, there are foundational aspects of mathematics which we must just accept. Take numbers, for example. How do we know they exist? Well, a few posts back I gave what is considered to be a logically sound definition of the natural numbers, based on the cardinality of sets, which only requires that we accept the existence of the “empty set”. But how do we prove that the empty set exists? We just have to take it as an axiom, which is basically math-speak for “on faith” (in other systems the existence of the empty set CAN be proved, but there will always be other axioms the proof is based on). Although mathematics is as rigorous a subject as we have, it is still based on faith. Is an acceptance of the axiom of choice less irrational than a belief in a higher power?
I’m not really qualified to talk about these questions. So let’s consider some more mathematicians’ religious views. Isaac Newton (1642-1727) – who could in some ways be considered to be Galileo’s natural successor – was, in my own humble opinion, the greatest scientist and mathematician that ever lived. He had some very interesting religious beliefs. Technically, he was also a heretic (not difficult at that point), although living as he did in post-Reformation Britain, this was not such a problem as it was for Galileo. He believed in a God, and studied the bible, but shunned the Church and its dogma.
Most interestingly, he was fascinated by mysticism and the occult; some reports say his spiritual studies were of more importance to him than his scientific ones. He was an alchemist, and wrote at great length on the subject (although much of these writings were destroyed, possibly in a lab fire started by his dog).
What is alchemy anyway? What do alchemists do, exactly? I used to be very confused by this, until I found a book on the subject on my parents’ bookshelf some years ago. I am still confused, but less so. The thing to understand is that it is rich in metaphor: the object was not really to find a way to turn lead into gold (although many took this aim literally and wasted much of their lives trying to fulfil it, just as many interpret the bible and the koran literally, and waste everybody’s time); it is a metaphor for the improvement of the soul. Similarly the elixir of eternal life, the philosopher’s stone: they are all just symbols for what is basically the same aim as Buddhism. Enlightment through chemistry! A phrase which has perhaps taken on different undertones in the past 50 years or so.
Jump forward 200 years or so to the logician Kurt Gödel (1906-1978). He was an utter genius who turned mathematics on its head, but also a very strange man. He was quite devout in his Christian views, and never seemed to have really separated them from his work. In fact, he even produced a logical “proof” for the existence of God, known as Gödel’s Ontological Argument. While this was possibly not his least popular proof, it is no doubt his most dubious! Here it is:
Good isn’t it? Looks nice anyway. I won’t attempt to explain this, but there is a good commentary here if you are interested. I should point out that this is not generally accepted to be a proof! The existence of God is still an open problem. Incidentally, Gödel has the dubious honour of probably qualifying for the weirdest death in mathematics: he had a crippling fear that someone was trying to poison his food, and only trusted his wife to serve him. When she went to hospital for a few months, he starved to death.
Time for an atheist I think, to balance things out. Godfred Hardy (1877-1947) would not have been impressed with Gödel’s Ontological Argument. In fact, number 3 on his list of life ambitions was to “prove the non-existence of God.” To get some idea of how important this was to him, it comes after:
1. Prove the Riemann Hypothesis
2. Be really good at cricket
4. Assassinate Mussolini
Unfortunately (or perhaps fortunately, if you are a Christian or a Fascist), he didn’t actually succeed in any of these. Hardy was also quite an odd man (we seem to be developing a theme here). Apparently he couldn’t stand to see his own reflection, and when staying in a hotel would cover all the mirrors with towels. He was, however, a great mathematician, although when asked by Paul Erdős what his greatest accomplishment was, he unhesitatingly (and quite modestly I think) replied: “the discovery of Ramanujan”.
So, this brings us to Erdős (1913-1996). The most prolific mathematician ever (according to wikipedia, although I think that the completed works of Euler must surely contend with his output, if they ever actually finish getting completed), he was a great source of much-quoted aphorisms. Incidentally, I just read with interest that the one about mathematicians turning coffee into theorems is apparently somewhat lost in translation from the German, in which the words for “theorem” and “coffee residue” are the same: Satz. This makes this saying a lot more noteworthy! I always thought there was something lacking.
Erdős didn’t believe in a God, although you wouldn’t necessarily think it given how often he referred to one. He called God “The Supreme Fascist”, and accused Him of hiding his socks. He also often referred to The Book, a mythical compendium of all the best proofs in mathematics, which was apparently written by God (Erdős also accused God of selfishly keeping the best proofs in his Book to himself, and only allowing us the odd tantalising glimpse). I’m not sure how a theologian would classify this belief system.
I’d better do some proper work now. But here is a cartoon about The Book to finish up. This also addresses another “proof” of the non-existence of God: the Omnipotence Paradox, which basically says that, if there were an all-powerful being, it would be able to create a task it is unable to carry out. As with all paradoxes, this doesn’t really prove anything, but does nicely exemplify the inadequacy of language to describe certain concepts. If there is a higher power, then it is certainly outside of our ability to discuss, so we should probably do something more useful instead.
* Regular readers of this weekly blog will have noted by now that I use “week” quite flexibly