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The notion that an economically mature technology can be modeled as a free monoid is trivial because the technology is going to be completely described and communicated by standardized instructions (mechanical, logical, verbal, etc.), wherein the instructions are concatenated sentences from a specialized dictionary ( Read more... )

Закончил читать курс, билеты и гостиница заказаны - время уезжать на рабочие каникулы ( Read more... )

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Before I forget: there's a moment in life of a category when functions have to become functors, and vice versa. We can think about it as if an object is being "expelled" from its mother category and has to become its own category. Alternatively, a category can be "sucked" into another category and become an object. (the video below describes how ( Read more... )

Я опять все понимаю, даже лучше прежнего.


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A child has hurt himself and he cries; then adults talk to him and teach him exclamations and, later, sentences. They teach the child new pain-behaviour.
“So you are saying that the word ‘pain’ really means crying?” On the contrary: the verbal expression of pain replaces crying, it does not describe it.

-- L.Wittgenstein. Investigations

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The [Roman] empire is a constant presence in our evidence from this period, and it enters mathematical discourse in several ways. Managing an army, collecting taxes, keeping a census on such a vast scale implied centralized administrative practices (accounts, tax rolls, land surveys). Mathematics was also used to articulate views about politics, ( Read more... )

An animal more like the gods than these ( Read more... )