Last week I told you about Pantagruel and the amazing task he was set by Gargantua and I said that I would like you to develop a similar approach to learning to become, in fact, scholars and I explained that as far as I was concerned scholarship was learning that was extensive and exact and thinking that was scrupulous and critical. I also urged you to be critical – to ask hard questions and to challenge received wisdom. Have you done that this week? I hope you have learned things this week that have made your head hurt but have you asked your teachers questions that have made their heads hurt? My head has been hurt by a theorem that appeared on Twitter – it’s quite amazing but Twitter, being Twitter, failed to provide a proof (I suspect there is a marvellous one but 140 characters is too small to contain it). I have, therefore, been trying to construct a proof. I’m almost there but there are some details that still elude me. An assembly isn’t quite the forum for me to tell you the theorem and my progress with the proof but if anyone is interested please ask me afterwards.
This morning I would like to talk to you about being scrupulous in your thinking – what does that mean? What does scrupulous thinking look like? A good example is provided by the xkcd cartoon that was handed out as you came in: what the author wants to say is “This person on the internet is wrong. What they say is rubbish” but instead of ending it there – which is all the blog post in question really deserves, he has gone through it scrupulously: attending to every detail. I particularly like the statistical analysis of the author’s wildly swerving train of thought: even people who are utterly wrong can be right occasionally by sheer chance. I shall come back to this later. Scrupulousness is important in all branches of scholarship but is perhaps most clearly exemplified in Mathematical proof and so has been relevant to me this week. One of the things that has done my head in this week with the proof I’ve been working on is having to be scrupulous. When I first saw the theorem I was on the train and so I got out my little green book and started to sketch a proof. I managed to get a couple of bits neatly written down and sketched out how those ideas would come together. Essentially I said to myself, “once I’ve got these bits, I can apply this other theorem and it all works. Hooray.” Having convinced myself that it was true I quickly retweeted it with a challenge to others to find the proof. Unfortunately, as I walked home that evening and thought through the steps of my proof I found two slight problems with my sketch. The first was that the other theorem I wanted to use didn’t apply to this situation and the second was that if it did it would prove that my theorem was false rather than true. Unfortunately, on the train I’d been less than scrupulous: instead of paying careful attention to the detail I’d taken in too much of the big picture and had been misled. I’m now challenging myself on every link in the chain of argument and making sure I can justify all my assertions.
In most fields of study this level of detail is unjustified: a mathematician’s scruples don’t always apply to most debates – which is a significant part of the humour of that cartoon – but all fields of study have their own scrupulousness: how do we know this is true is a key question for the scholar. In Maths the only acceptable answer is a watertight proof from first principles, in Science there needs to be experimental verification and a significant part of that is a statistical analysis of whether it could appear to give a sensible answer by accident. In History the answer has to be based on evidence and conflicting evidence must be weighed and may be challenged and in Philosophy, as far as I can tell, it is a question that can never be satisfactorily answered but must be asked all the same.
We can’t, however, keep returning to first principles for everything or we’d never get everywhere: we have to listen to and evaluate other people’s experiments, their theorems, their research and their views; Isaac Newton was in many ways a great scholar and he said “If I have seen further than others it is by standing on the shoulders of giants” – I want you to see further, for your generation to do greater things than mine and so you will need to climb as many giants as possible but how do you tell the difference between a giant and a pygmy or, worse, a troll (the giants in this metaphor don’t seem to mind people climbing on them whereas a troll would bite your leg off)?
I think part of it is suggested by sections 3 and 4 of Summer Glau’s rebuttal of the blog post: we should not trust those who don’t write like scholars; if they are not careful of spelling and capitalisation there is doubt that they are careful in their logic and their research. Similarly, if we want our own thoughts to be taken seriously we must be scrupulous in our attention to detail. My maths class are, I’m sure, annoyed by my approach to this when I mark homework – if they get a question completely right they get an alpha but if they make any errors at all, careless or otherwise the best they can hope for is a beta. I want them to learn scrupulousness, not to be satisfied with anything less than perfection and to look for ways of checking for little errors that might have crept in. Other teachers have other approaches but we all want you to be scrupulous and that means we shouldn’t accept slipshod or careless work.
This is, unfortunately, not always enough. Sometimes the most insane and dangerous ideas can be well presented: we learned last week of three young women from East London and one young man from this borough who were convinced by explanation and argument to go to Syria to join ISIS. I am certain that they have made a mistake, that they will make neither their own lives nor those of anyone else better by taking that step and yet they were convinced. We don’t know what has happened to the young women but Mohammed Emwazi has become a cold-blooded murderer. You might not be tempted by ISIS’s particular argument – I hope that you are not as I think it is a scholastically bankrupt and morally abhorrent one – but the world, and particularly the internet is filled with people who are wrong – sometimes convincingly so (Randall Munroe, the cartoonist behind xkcd has reminded his readers on more than one occasion that it is quite common for people on the internet to be wrong). How do we pick out the giants from the trolls?
One of the most convincing pieces of nonsense I’ve read is a book called “The Holy Blood and The Holy Grail” – it’s a very carefully written piece putting forward the thesis that Jesus’ crucifixion was a real event after which his wife and son were taken to Europe by Joseph of Arimathea and that his descendants, possessors of the royal blood or Sang Real became kings of France and are currently living secretly hidden by the successors of the Knights Templar. It is written in a scholarly style and quotes various sources and pieces of evidence to support the case and I didn’t have access to them all in order to check it through from first principles. How should I, and you, make the required decisions? Well, I think there are three pointers: the first one is whether other scholars respect the work: clearly there are occasions when the received wisdom is wrong but there is a degree of safety in numbers. Xkcd has a good approach to the times when received wisdom is challenged – for example when someone finds a particle moving faster than light: he bets people that it doesn’t. If it turns out received wisdom is right he makes some money and he reckons that if received wisdom is wrong he’ll be so excited about the new Physics that he won’t miss the money he has to pay out. The second pointer is are they verifiably right about some things although you have to check that they aren’t right by accident – like the standing at the back dressed stupidly and looking stupid party, a fictional political enterprise from the third series of Blackadder whose manifesto pledges included compulsory asparagus for breakfast, free corsets for the under-fives and the abolition of slavery. The final pointer is whether the bits you can check out do check out – are the sources reliable, are the experiments verifiable, is the logic intact? Well, sadly for the Knights Templar the Holy Blood and the Holy Grail has such a poor reputation that Dan Brown has written a book based on it, it makes no more verifiable sense than the looking stupid party and finally, when I went to check the apocryphal gospels on which its version of the Bible is based the only vaguely coherent passages are the ones quoted in the book and the rest is just mad.
The internet is full of conspiracy stories, mad facts and surprising scientific claims. Some of these amazing things are true – I’m fairly sure this theorem is, for example, but a lot of the time it’s just people being wrong on the internet and when faced with that you can either get Summer Glau to write a rebuttal for you or, brilliantly, turn the computer off and go to bed. Be scrupulous in your own scholarship and expect scrupulousness in the scholars you put your trust in – stand on the shoulders of giants and steer clear of trolls.
Footnotes:
1. The xkcd cartoon referenced can be found here: Venting
2. In Lub and Dub, I embraced the challenge of proving mathematical conjectures in an assembly.
3. The Holy Blood and the Holy Grail is part of a chain of conspiracy theories that lead to Dan Brown's Da Vinci Code. More can be found in this article.
4. Pantagruel and Gargantua can also be found in Nobody Expects
5. More on giants, trolls and being scrupulous in Entropy Inspires