Misha Gromov updated his very interesting “ergobrain” paper
Two quotes I liked: (my emphasis)
The concept of the distance between, say, two locations on Earth looks simple enough, you do not think you need a mathematician to tell you what distance is. However, if you try to explain what you think you understand so well to a computer program you will be stuck at every step. (page 76)
Our ergosystems will have no explicit knowledge of numbers, except may be for a few small ones, say two, three and four. On the contrary, neurobrains, being physical systems, are run by numbers which is reflected in their models, such as neural networks which sequentially compose addition of numbers with functions in one variable.
An unrestricted addition is the essential feature of “physical numbers”, such as mass, energy, entropy, electric charge. For example, if you bring together atoms, then, amazingly, their masses add up […]
Our ergosytems will lack this ability. Definitely, they would be bored to death if they had to add one number to another times. But the -addition, you may object, can be implemented by additions with a use of binary bracketing; yet, the latter is a non-trivial structure in its own right that our systems, a priori, do not have. Besides, sequentially performing even 10 additions is boring. (It is unclear how Nature performs “physical addition” without being bored in the process.) (page 84)
Where is this going? I look forward to learn.