"Pure mathematics is not sufficient to account for a ToE."
That's not true, Jim.

When it is understood that there are no truths, then that is a truth. When the only certainty is uncertainty, then that is still a certainty.

Gödel delivered us the ToE, and no one paid attention.

Let's express this in the binary system with QM and GR. When QM is 1, then GR is 0. When GR is 1, then QM is 0.

Or describe it with the paradoxical behavior of matter in the universe: convergent and divergent at the same time.

Matter at the local level (galaxies and smaller):

Convergent (1), Divergent (0).

Matter at the universal level:

Convergent (0), Divergent (1).

Gödel showed it already. Our universe is a result in which the whole is not whole. To find whole outcomes, we must look and indeed find them one level below the overall level.

It means that unifying all forces into one ToE is a bit like Santa, or like a Cyclops. Rather, there are two levels in the ToE; one for the actual items by themselves, and one for the actual items as a collective.

* Red, blue, yellow, gray.

* Mothers, fathers, children, families.

* Strong nuclear force, weak nuclear force, electromagnetic force, gravitational force.

Four outcomes from three parts. The ToE.

https://www.cantorsparadise.com/discovering-zero-among-the-prime-numbers-65a47cbf79ec

By following the decimal system, we can see immediately what the scientists did not get right. Gödel pointed it out, however.

The first number is 0. However, for the longest time scientists desired to make 1 the first number. Many scientists still think this way. Naturally, 0 does not object to having 1 put in its place. But it makes a step invisible. Where there are two levels (0 and 1), scientists turned them into one level, and then they couldn't find the answer how to unite everything anymore.

Good job writing an excellent short article.