Faithful to Science

blog on science and religion

Month: August 2015

Mathematics is not as much about finding proofs as it is about finding concepts

Added note. This is a note added for readers in the Oxford area.

I am giving a lecture at Headington Baptist Church on 12 September. Doors open at 7:30pm; talk from 8:00pm, with questions and discussion afterwards. The subject is basically the theme of this blog and my book of the same name. The venue is the church building at 78 Old High Street, Headington, Oxford OX3 9HW; click here for a map.


 

Reading New Scientist magazine this week I came across a statement I very much like:

 “Mathematics is not as much about finding proofs as it is about finding concepts.”

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Fantastic voyage

Having posted and commented on quotations from other people’s books a few times, this week I am posting a short extract from a book of mine. This is from A. Steane, Faithful to Science (pub OUP 2014), p. 60.

 

In my experience, doing science really well is like imaginatively entering, or taking a fantastic voyage into, another world. This could be the world of thermodynamics, or the world of quantum mechanics, or the world of tiny atoms bouncing up and down on a light field trampoline, or the world of a chemical network, or the world of a living cell, or the world of a community of gorillas, or the world of a cancerous tumour. One needs to learn to think thermodynamically or think chemical graphically or think gorilla. It takes all the mathematical and experimental tools one can muster to do this, but imagination is needed as well. Keen observation is important, but at the outset one does not always know what to look for. Make a wrong assumption and the ship of exploration will develop leaks or veer off course; the experimental alarm bells will start to ring. The ship can be steered to some extent by analytical work, but the really crucial ability is to be good at asking the right questions.

After working at a difficult problem for a long time, attacking it from all sorts of different directions, one begins to form in one’s mind a representation of the crucial components. Then, in a marvellous moment, something falls into place. The experimenter realizes what has been stopping the apparatus from working, the theoretician realizes what mathematical structure will solve the problem. The working out is still to be done, but the crucial idea is already in place, and there is little doubt that it will work.

Actually doing original science thus is not wholly different from other forms of creative human activity, and it is not completely different from, or at odds with, the attempt to live by faith. It is interesting to see the relative roles of logic and imagination in all this. Logic is not the engine of progress in science, it is the tool used to hone one’s vision and to confirm or rule out what has been guessed by intuition. But there are vastly more wrong than right intuitions that one might possibly form; what is it that makes us get the right intuitions?

 

quantum-computing

 

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