In Chapter 15 of Happy Memories and in Blog 17 of my website I mentioned some of the ideas that have come to me from time to time and that I think are worth writing down for other people to read. I have now come across a whole lot more, and I can’t find any of them in my website or in my book.

According to The Man Who Knew Infinity (page 66) there is an old debate whether mathematical reality was made by mathematicians or, existing independently, was merely discovered by them. I believe that it was merely discovered, but I believe that a sculpture is made and not discovered, although it is said that there is a sculpture inside every block of stone, because the number of possible sculptures is so enormous. What is debateable is whether tunes are made or discovered, and this depends on whether two isolated cultures would discover the same tunes or compose different ones.

Two isolated cultures would discover the same mathematical laws, but they would not create the same sculptures. Would they compose the same music? I have always assumed that they would, and that sooner or later all the pleasing tunes will be discovered, even if they haven’t already, but if that were the case people would be always making up tunes and then finding out that someone else has already done so, and this doesn’t seem to be happening. This suggests that there are many tunes waiting to be discovered.

There is a fundamental difference between physics and mathematics because I can imagine a universe in which which a proton is four times the size of an electron, but I cannot imagine a universe in which 2 + 2 = 5.

When I was very young I took part in a lot of discussions about whether people were animals. I would argue that people must be animals because they had the same number of limbs, the same arrangement of facial features and so on. Other people would say that we are not animals because we have a greater intellectual ability and so on. At the time I was convinced that I was right, but now I can see that we were both right. The question of whether people are animals is not a matter of fact, but a matter of the meaning of words. When people say that ‘animals take in oxygen and breathe out carbon dioxide’ they mean animals including people. When it says in the Y.H.A. handbook that ‘no member may bring an animal into a hostel’ it means animals excluding people.

In the same way when people argued in the sixteenth century about whether the sun goes round the earth or whether the earth rotates on its axis, they were not disputing a fact, but looking at the same fact in two different ways. It’s not incorrect to say that a car that is waiting at traffic lights is stationary just because the earth is travelling through space. It’s simply a matter of what you choose to regard as stationary.

Life is like a game of bridge. You don’t chose your cards. Your job is to do your best with the cards you get.

If the B.B.C. has not kept all the radio and television programmes could there not be privately owned national collections, just as there are of plants?

In the second paragraph of Chapter 15 of Happy Memories I referred to things that people complain about. One of these was mentioned in the last paragraph of Blog 17. Another is that people sometimes do harmful things to other people, but if you compare this with the good people do to other people it becomes negligible: practically everything that you possess, including your food, has been made by other people for your benefit: without their help you simply couldn’t survive. The relevant chapter may be found here.