Comment by zoogeny

To be fair to Penrose, he seems to have some humility about it. Although he does also make the claim that math is discovered and not constructed in the same linked video.

> it's a conceit to believe that the mechanisms we call math aren't just a patchwork of metaphors that build up from experience.

I'm not sure it is a conceit as much as a commitment to a metaphysic. If one believes that experience is a definite relationship with an external reality (a phenomenological view) then the fact that experience is structured is suggestive that external reality is structured. If one believes that experience is primarily interior then one could assume that the internal mechanism of cognition is structured and external reality is something entirely different.

However, I'm not sure how anyone could hold the latter view without a deep solipsism. One would presumably have to account for the perception of billions/trillions of other living creatures behaving as if the external world was structured. I mean, we seemingly all did evolve from the same single cell structure, so it is possible this perceptual quirk is based on some shared ancestry, so I suppose that is another possible view than solipsism.

What I mean to say is, I can imagine my perception of a fundamentally unstructured reality is a perception that falsely presents itself as structured to my own experience as a result of my limitations. However, I would have to extend that exact same flawed perception to all other life forms that seem to act the same as I do. So either every single living creature has the exact same flawed perception or the structure is inherent in the external world.

> Does the universe know what pi is?

No one is suggesting an epistemological view, the question is ontological. As Penrose mentions in the video, the set of possible mathematical structures is vastly larger than the actual structures we see in the universe. So even if one has a purely idealist view, one has to account for why our perception only experiences a nearly infinitesimally small fraction of that set of possibilities.

Of course, a weak anthropic principle is one answer. One could posit that all possibilities are manifest in a vast multiverse and this little corner of that multiverse just happens to be finely tuned enough to allow for limited creatures like ourselves to perceive anything at all. But that just shifts the question to the limitations necessary for perception/experience/consciousness, which is a valid enough topic to address on its own. The questions then becomes "why do these particular structures result in conscious experience", which is exactly the kind of question that a guy like Penrose is ultimately searching for (as he heavily implies in the linked video).