Why are We Here? Penrose interview

WaWH?: Roger Penrose

RP: Yes, certainly. I am definitely sympathetic to all three of the Platonic ideals. The truth one, which I'm taking as the pure, necessary truth, I think that's an absolute thing. And when it comes to beauty, well, you see, I would say there is a great subjectivity to beauty, and there's no doubt about that. But I would say there's a kernel of truth to all that which is independent of people. And I really sort of argue that great music can be great in itself, not just because people appreciate it.

David: And the moral?

RP: And then the moral, I would see even more so, probably. But, you see, this is an interesting question, because one of the things I spent a lot of time worrying about has been the issue of consciousness. And so I have these three worlds in a sense: you have the mathematical world, and then the physical world here. And the laws of physics seemed to be governed by mathematics, but it's only a part of the mathematical world, as far as we know, which governs the laws of physics. And it's only a part of the physical world, as far as we know, which has conscious experiences.

But if you are worrying about the other Platonic values, you see, do they have absolute existence as well? And the moral one seems to depend ‒ I'm not sure I think that this is entirely so ‒ but it seems to depend on the existence of consciousness. I mean, if there were no conscious beings around, the notion of morality somehow seems to evaporate. It has to do with conscious beings.

So I would say that truth and beauty are tied up together, and it's certainly a good guide to truth. In mathematics it's certainly true. And I would say also that the issue of consciousness is connected with this, because in order to understand what's going on in the mathematical world, I would argue that you need consciousness.

Some more on Penrose's thinking in these matters:

Is Roger Penrose a Platonist or a Pythagorean?

Paul Austin Murphy

More generally, even a (at times) hard-headed positivist (see here) like Werner Heisenberg recognised the importance of the Pythagorean tradition in physics. He argued that this

“mode of observing nature, which led in part to a true dominion over natural forces and thus contributes decisively to the development of humanity, in an unforeseen manner vindicated the Pythagorean faith”.

All that may depend on what Heisenberg meant by the word “Pythagorean”. After all, it’s often the case that the word “Pythagorean” is simply used as a literal synonym for the word “Platonic”. Thus, having said all the above, such distinctions between Platonism and Pythagoreanism (at least in these specific respects) may be a little vague or even artificial.

This may apply to Roger Penrose’s position too.