Misha Gromov updated his very interesting “ergobrain” paper

Structures, Learning and Ergosystems: Chapters 1-4, 6

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.

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*Related*

How does a quantum computer count?

It might. But how does a neuron do linear algebra?

Such a critique is addressed in Matteo Pasquinelli’s article “Four Regimes of Entropy For an Ecology of Genetics and Biomorphic Media Theory“.