Dear Daniel,

I just discovered and read your essay and found it to be clearly and well written. I liked how you "zoomed out" at each stage of your paper, it reminded me a bit of the "Powers of 10" and the beginning of Ohanian's intro text book.

I found several similarities between the ideas in your paper and in mine. In particular:

1. That scale has something to do with the...

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Dear Daniel,

I just discovered and read your essay and found it to be clearly and well written. I liked how you "zoomed out" at each stage of your paper, it reminded me a bit of the "Powers of 10" and the beginning of Ohanian's intro text book.

I found several similarities between the ideas in your paper and in mine. In particular:

1. That scale has something to do with the differences in the descriptions of nature we have to give. I already see the mathematical fact that equal-shaped objects of different size have different ratios of area per volume as a basic hint of this, since this means one can take smaller objects to be not only smaller but also more 2-dimensional than larger equal-shaped objects.

2. That emergence plays a more fundamental role in nature than currently appreciated. You may not agree with this, but I strongly suspect that dimensionality itself is emergent

3. That the apparent incompatibility between GR and SM may reflect a limited ranges or domain of applicability of these theories, not that they are fundamentally wrong.

4. That an all-encompassing description of nature transcends our usual conception of a "theory": You used the term "description", I used the term "Metatheory" in my paper

5. That the evolution of science seems to proceed largely in accordance with Kuhn's observations (this last point is not mentioned explicitly in my paper, but reflects my perspective on progress in science).

The one point at which our views may differ is the range of applicability of mathematics in describing nature, but it is possible that the difference is not as large as it at first might seem.

You see, in my view it is not that mathematics is inadequate to model nature, but that we have failed to capture the most fundamental aspect of physical things within our mathematical frameworks. I believe the most fundamental aspect of any physical object is that it exists, yet existence is not part of our current conceptual inventory in physics, and therefore not thought to be expressible using the language of mathematics.

But if you think about it, many of our most fundamental problems are deeply intertwined with this concept. For instance, with respect to gravity you might ask, how does an object know that a another mass exists nearby? Newton would say that it "feels" the other object's gravitational force, and Einstein that spacetime in its vicinity becomes curved. In quantum theory, this is even more apparent: How is it possible for any object to exist in a superposition of mutually exclusive states? Why is it that we can only detect the existence of a quantum object at a particular location probabilistically?

So, perhaps your suggestion that mathematics may not be adequate to model all of nature is in reality just a call to consider concepts which today we think of as unrelated to or indescribable by mathematics to become associated with it?

If so, we actually agree on this point as well because that is precisely what I believe.

But regardless, I am glad to find someone like-minded, you may find my essay of interest, too.

All the best,

Armin

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