At the basic level, reality does not seem to be composed of ones and zeros, it seems to be much more graduated and smeared out than that.
It seems that mathematics and logic are great modeling tools, and therefore great tools to use to help us understand our perceptions of reality (which perceptions seem not to be of reality itself, but of the model).
When it come to reality itself, it doesn’t seem to play nicely by the rules of mathematics. When you follow the work of people like Goedel and Feynman one comes to mathematical and logical constructs that are a very long way from binary, constructs that are more accurately described as being descriptions of the change in the nature of the probability functions associated with existence over time and space. And the sum over life history notion that Feynman employed so successfully seems to hint at something rather profound about the nature of the very small.
It seems always useful to ask the question, is this idea relevant to the structure of the model of reality that is my experiential reality, or does it hint at some aspect of the reality beyond my model that my model usefully approximates at some levels?
Mathematics and geometry have many useful tools, but do they really apply to reality itself? I have been looking for about 20 years for a scale independent circle in reality. I haven’t found one, and the meta evidence I have is that I am very unlikely to find one.
If we cannot find so simple a construct as a circle, why should we expect anything more complex to follow the rules of mathematics exactly? Approximate them certainly, at certain scales, and within certain contexts; but be constrained by them?
It seems to me that reality will always be many orders of magnitude beyond our comprehension, should we manage to live the rest of eternity, and exponentially increase our abilities throughout the time. Infinity just seems to be that big, big without limit, at all scales. All of our knowledge a working approximation of ignorance at the largest scale, however utilitarian it may be within certain contexts.