Dear Stefan Weckbach,
Thanks for your comprehensive reply, which helped me a lot.
To be frank, I am not in a position to judge HoTT and understand it in all aspects. Like a lot of other formal constructions, as you mentioned it shall consist of trivial elements, too. What I learned and where I was inspired is the idea of designing mathematics as a process instead of a steady structure, as the traditional understanding suggests. The motivation for their approach was, as I understood the story of HoTT, to receive the ability to verify mathematical statements automatically.
It is only a suggestion, a hypothesis. And if mathematics is a process, which is enfolding a mathematical universe, we can ask about possible effects. My result for this question is not a homogeneous mathematical universe, but a singularity, which has to become happen.
The other question is about the definition of mathematics itself, whether it is formulated as HoTT, as a set theory or what ever. I think, my argumentation in the essay is to short, and my explanation is not clear enough:
Most of the scientists follow Platon with his differentiation between idea and form, which means today: Only physics is true reality, mathematics is something else. If you can't measure, it is not reality. As I understood, you argue in this way, too.
My hypothesis: Lets assume, there is no difference between idea and form. In this case, what mathematics might represent? It should be the „existence" itself as a "pre-physical" entity.
You are right, my argument of logical induction from an initial point of non-existence towards an unfolding complex structure is simple, as the HoTT is simple in its basic foundation. But is it wrong? I have the vague hope, that it might be possible to generate a mathematical estimation for the parameters of the assumed singularity. And perhaps, at the end this might offer a link to physical entities like physical space and time.
And finally, you have criticized my argumentation regarding non-existence. Perhaps it was wrong to confuse the reader with this more philosophical stuff within this few eight pages. The idea was to define the initial starting point of mathematics. It can be the existence itself, which is unfolded to the infinite complex structure of mathematics. But if you assume non-existence as first entity ever, in the same moment existence is logically included as a second entity. For the main hypotheses, this question seems not crucial.
