- Nice to have Heisenberg on my side on the universalis of geometry crusade! I hope you are heading into a warm midwinter
- ..., Geometry and mathematics points us in the direction of what is important about how physical nature is. We are both agreed about that. But I differ in that I do not think that nature can be explained in terms of what is expressed geometrically and mathematically in physical nature. What I mean is that physical nature is a representation of a reality which exists beyond physics, beyond scalar values, angles, etc. As a representation, its nature requires to be understood in terms of the dimensionless reality which gave rise to it.
Have I referenced this article before?
- Pythagorean Triples and the Generation of Space
It gives a lot of clues as to how I am thinking, and how I think scholars and divines thought about reality and the physical world in the third and second millennia BCE.
- The weather here is much milder (in general at least) than is normal for this time of year. But we know from experience that full-on winter can slam into us at the drop of a hat! Thanks for asking.
- I wrote two or three papers on physics for George Shiber, back in 2016. We had some interesting discussion by email. The exchange broke down when he insisted that something (I forget what that something was) possessed an objective reality, and absolutely necessarily. I realised that he had no sense of the possibility that there is a transcendental aspect to nature, and the way it works. In another conversation, in 2017, the philosopher Adrian W. Moore exposed the same weakness by describing something as a ''deeply mathematical fact", as if mathematics had an existence above and beyond other aspects of reality.
- My argument is that all we experience is some form of representation of the ur-reality, which is - at least directly - inaccessible to our understanding. All phenomena consists of such representations, and combinations of them. Mathematics is one such phenomenon, and another is geometry. The point of the post 'Pythagorean Triples and the Generation of Space' was to illustrate how the Pythagorean triples might have been understood in antiquity. They knew that the sides of the triangles were not commensurate with each other, but the squares were. Just minus space. Which pointed to another level of reality.
So yes, I'm with Heisenberg up to a point. I would however rephrase it as:
- "If nature leads us to mathematical forms of great simplicity and beauty— they reveal a genuine feature of nature." What Heisenberg says about us not being able to help but think that they are 'true' is neither here nor there, and more or less meaningless. What we can conceive of limits our understanding. What is true is most often beyond our understanding.
- There are many pointers to the nature of the ur-reality in mathematics and geometry. By using reciprocals for example, we can convert addition into multiplication, and subtraction into division. As a schoolboy I found this to be absolutely amazing, and I couldn't understand why it didn't strike anybody else in the same way. But most schoolboys are being trained in the art of being asleep for a lifetime, while apparently awake. The phenomenon is a pointer to the kind of relationships the ur-reality establishes with itself. Logarithmic functions are of course the inverse of exponential functions. Such a huge set of clues as to how nature is structured! But all of it points to another place, where all things meet and agree.
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