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Here's two categories: Technology and Business

Technology is represented by a product of desires DxD. Desires conflict; therefore, one desire D is a PreOrder, while another is a PreoOrder Op. That is, improving our position on one desire makes another one worse off. Each desire has a terminal object 1, which is the lowest performance threshold, respectively. The thresholds form technical specification 2.

Business is represented by a Utility Monoid, e.g. a combination of Revenues (or expenses). Business has a terminal object 1, which represents profitability requirements, i.e. "the bottom line." The business would like to increase Utility, but it is constrained by the conflict of desires in Technology.

We can probably build adjoints, but I don't know how to specify them.

timelets: (Default)
Another interesting quote from McLane&Moerdijk, 1999.



In short, we can create two contrasting categories: a poset P, which has one morphism and many objects, and a group G, which has one object and many morphisms.

Now, by thinking in topos terms, we can see that both categories have a terminal object ( "the arrow", "the object") and can be used in combination with a subobject classifier. The existence of a subobject classifier creates an opportunity for a simple decision making process. Then the question arises, "Decision making about what?"

One way to answer it would be to go back to Adam Smith and say, "Specialization!" That is, posets P enable us to specialize in arrows ("the arrow"), while groups G (including monoids) let us specialize in objects ("the object".) A combination (e.g. a disjoint union) of these two categories helps us build a broad range of large, highly specialized categories with relatively simple decision making rules. I bet most industrial systems can be modeled this way.
timelets: (Default)
Restricting the model from category A to category B simplifies choices because it requires only one type of rationality, i.e. function m: HxH -> H.

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A shout is a monoid because we perceive it as a single complex sound. Animals can do that.
SxS -> S

A spelled out word is a free monoid on a set of symbols because it has a distinct temporal/spatial structure.

Language underlines a unique human ability to create free monoids on arbitrary sets.
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Marshall McLuhan, The Gutenberg Galaxy, p 219

Yin - Yang

Feb. 22nd, 2017 10:17 pm
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Я опять все понимаю, даже лучше прежнего.


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An animal more like the gods than these,
more intellectually capable
and able to control the other beasts,
had not as yet appeared: now man was born,
either because the framer of all things,
the fabricator of this better world,
created man out of his own divine
substance—or else because Prometheus
took up a clod (so lately broken off
from lofty aether that it still contained
some elements in common with its kin),
and mixing it with water, molded it
into the shape of gods, who govern all.
And even though all other animals
lean forward and look down toward the ground,
he gave to man a face that is uplifted,
and ordered him to stand erect and look
directly up into the vaulted heavens
and turn his countenance to meet the stars;

Ovid. “Metamorphoses.”


Just as a side thought, modern animal factories completely destroy an internal social structure of the herd/flock that survived the process of domestication.
timelets: (Default)
It just occurred to me that our perception is necessarily a process of splitting the world into parts and then combining them into various wholes. Biologically, we are made up of cells, which have their own preceptors. Therefore, different cells perceive different aspects of the world and then communicate to assemble them according to behavioral scenarios. I can probably say that we are biological expressions of the world.
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PROMETHEUS: ...they knew nothing of making brick-knitted houses the sun warms, nor how to work in wood. What’s more, I gave them numbering, chief of all the stratagems. And the painstaking, putting together of letters...


Bricks, wood beams, numbers, letters - given the original meaning of "art", all of these elements enable artistic expressions: buildings, ships, business records, memoirs, etc. He also uses "knitted", which indicates an important element — thread — that allows us to make clothes, a yet another free monoid of material culture.
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Control was not easy - this gives an extra spin to Frontinus' idea of mathematization as imposing order on a territory. The imposition of order is a dialectic, dynamic process through which a model of administrative control is applied to the specific nature of a place. This dynamic implies a negotiation of various factors, and I think that the role played by mathematics and by mathematical imagery in this negotiation is fundamental.

...mathematics guaranteed the possibility and reliability of calculations, and made cataloguing and recording easier, so it was ‘directly’ useful.

-----

Finally, Frontinus chose one particular type of pipe, the quinaria, as the standard type and ruled that authorized standard pipes and nozzles had to be stamped with an official mark, and no unstamped pipes or nozzles could be used.

Imposing a standard is clearly at the same time a pragmatic administrative choice - uniformity facilitates repairs and control of misappropriations - and a political one - the fact itself that someone has the authority to set a standard unequivocally signals where the power lies.

-- Cuomo, Serafina (2000). Divide and rule: Frontinus and Roman land-surveying. Studies in History and Philosophy of Science Part A 31 (2)189-202.


Using "free-monoidable" structures enables a radical simplification of control procedures ("arrows"). The first example has to do with making land "monoidable" through mathematized surveying. The second example shows how standardization of elements enables administration of infrastructure and distribution of resources.
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47. But what are the simple constituent parts of which reality is composed? What are the simple constituent parts of a chair? The pieces of wood from which it is assembled? Or the molecules, or the atoms? “Simple” means: not composite. And here the point is: in what sense ‘composite’? It makes no sense at all to speak absolutely of the ‘simple parts of a chair’.

...
Asking “Is this object composite?” outside a particular game is like what a boy once did when he had to say whether the verbs in certain sentences were in the active or passive voice, and who racked his brains over the question whether the verb “to sleep”, for example, meant something active or passive.

-- Ludwig Wittgenstein. Philosophical Investigations. 4ed. p 26
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"Und eine Sprache vorstellen heißt, sich eine Lebensform vorstellen." - L.W.

This sounds absolutely great in German.

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