We can only count what is, not what is not. Or rather, we count what it appears to be, and not count what it appears not to be. And knowledge what isn’t doesn’t mean it can be. Or something looks like it is and something looks like it isn’t. See living species in biology or periodic table of elements. Without difference there is no mathematics and without diferences there is no science, either. The base of differences in the world are orbit shells in atoms. See Planck constant and a resolving power in quantum mechanics. 

In other words – to practice mathematics requires a stable distinguishable shapes, structures and processes betwen them in the world for some time

See the laws of physics or the mathematical theory of sets as a set of well-defined differences, such as pottery – the pot is or is not. A moment ago the pot was not, now it is, and after a while it will not be again. Then something gets bigger like a blown up balloon, a bomb explosion or quantum fluctuations or inflation of the universe. Then something decreases again, but all in the same “rhythm” of Wisdom. How does this count what arises and not what just is – a trip into the area of the invisible Infinite Loving Beautiful Wisdom, etc. To realize this, therefore, it must be for some time worldly fixed forms and structures for some time incl. processes between, they must be stabilized for some time – so called unchanging or quasichanging shapes and structures – see the evolution of biological species throughout the history of the Earth.

How to count the conceptual (existing only in potter´s mind) designs of the pots or pots that are not yet finished or those that are on the potter’s wheel or those that are being broken? And this is the way with everything in nature.

How to describe changes in shapes and structures? The described shapes and structures must be stable for some time. See biological species. A ladybird is a ladybird for as long as it is. So we have time to describe it. And if we don’t, another ladybird is born, and it goes on like this for thousands of years. But trilobites, for example, have been on the earth for about a hundred million years, but they’re no more. The same story will be valid for the appearance of ladybirds in the world. But let us cheer ourselves up with the thought that instead of ladybirds there will be another beetle, which our descendants will again have time to describe.

Back to descriptions of shapes and structures. We know that these must not change so often before we can describe them. In other words, shapes must not change faster than our ability to describe them. There is a slip between the change of the described shape and the change of the describer (usually a human, sometimes an automati). Description of slow changes by other faster changes. Both change, but the described changes are slower than the describing changes. If there were no noticeable difference, it would be impossible to describe. A parallel is seen here with the slip between radiation (energy of different free frequencies of electromagnetic waves) and matter (the so-called “frozen” energy of bound frequencies).

What is the purpose of this? Difference between describing changes and described changes. The sense is to become conscious through our perception of what is around us and in us (different shapes and structures and the processes among them) and why this is so!

See below –  there are articels on the subject of this section. If you want, download the pdf file.

See below – there are unsorted brief remarks waiting for word processing to articels

 Combinatorics is closely linked to the number and distribution of otherwise indistinguishable points. More points does not mean that all possibilities could be realized. See the entropy from 2nd law of thermodynamics. There must be some initial differences in energy levels.

Whatever originated in the world can’t be divided into exactly the same parts. Whatever came into being is the original, whatever structure is unique. Unique is a whole that includes all subsets, each of which is unique. It is not possible to construct two equal segments and then connect them at exactly twice the length and it is equally impossible to split one segment into two equal halves. Splitting the continuum requires irrationality. 
The equation 1 + 1 = 2 has no meaning in the real world. There are no the same shapes, structures, elements, subjects or anything else. Yes, we use this equation like model. But we must know this is only the model, our approximation.
In the same way we could pretend the ideal straight line if we see a very fine piece of polished metal surface. The same with the ideal ball if we see very pretty polished balls into gears. If we go closer then we see something like mountainous landscape – surface roughness profile. If we go more closer then we are able to see foggy appearance of particles as excitations of quantum field. It’s the same with long-distance action. There has to be physical contact of the bodies. That’s why once upon a time centuries ago gravity was hard to understand, and later electrical and magnetic forces. How it is possible to act through empty space without direct physical contact of the bodies. Much later, we recognized that the contact of the bodies itself also took place at a distance — Pauli’s exclusion principle applicable to electrons in atomic shells. When we take a closer look at the contact of the bodies, we see only and only the deformation of the electromagnetic fields of atomic shells. Like approaching two magnets with the same pole facing each other.