This is indeed a very good article making a serious attempt at clarifying the difference between gold as money and cryptocurrencies exemplified by bitcoin. However, the attempt to make mathematics responsible for the expected failure of “abstract” currencies is mistaken. There is no understanding of nature or physics without mathematical concepts. I can not imagine a textbook of physics having no equations in it. The simple distinction between large and small immediately leads to the question “how much larger” and that is where counting (a subject of mathematics) comes in. The success of bitcoin relies on trust into the strength of its encryption (mathematics) and the distributed database structure of the blockchain. These features allow promoters to claim that bitcoin is decentralized. I would rather trust the strength of the RSA algorithm than the imprint 9999 on my bullion coin. The reason is that I can study the RSA algorithm and verify in my mind that RSA works while I can not do that with a bullion coin. I would have to trust some expert or some equipment claiming the coin has the stated purity. (I am not a proponent of cryptocurrencies.)
Basing the discussion of currencies on energy and entropy is the only way to proceed — I agree. However, it is a universal characteristics of life that it tries to circumvent the laws of thermodynamics. A cat thrown into the air will adjust its fall in such a way as to minimize the consequence of impact on the ground. Humans will always look for ways to get more food with less effort. Every currency system regardless whether fiat or commodity based will always be subject to fraud attempts. I think one important argument against “abstract” currencies is that it opens more doors to fraud than a strict commodity based currency. Precisely because fraud is intimitaly related to the laws of thermodynamics, it should have been discussed at greater length in the article. That did not happen. Instead a surprising attack on mathematics in general was chosen in order to to discredit cryptocurrencies versus precious metals. The quoted book by Unger and Smolin is much more cautious. It tries only to give a hypothetical answer to a famous question raised by the physicist Wigner about the “unreasonable effectiveness of mathematics” in the study of nature. That is indeed a fundamental question which will have to be studied for a long time. Unger and Smolin made a valuable contribution to that discussion, but I do not think that this is the final answer to the question raised by Wigner and others.