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Category Archives: Simulated Annealing

The Production of Constraints: Work and Annealing as “Freedom”

A thought-quote train, widestepping across peaks

Stuart Kaufmann, a theoretical biologist and complex systems researcher, inspired by Wittgentein’s Philosophical Investigations, writes in his own book Investigations, this about physical “work”:

“Work is more than force acting through distance; it is, in fact, the constrained release of energy, the release of energy into a small number of degrees of freedom.  It is the constraints themselves – with as Phil Andersons point out, a kind of rigidity – that largely constitute the organization process. But – and here will be the hook – in many cases it takes work to construct the constraints themselves. So we come to a terribly important circle, work is the constrained release of energy, but it often takes work to construct the constraints.”

This bootstrapping notion of work and freedom can be put into relation with two other quotes. On the notion of constraint which produces freedom,

Nietzsche writes,

Tethered heart, Free Spirit – If one tethers one’s heart severely, and imprisons it, one can give one’s spirit many liberties: I have said that once before. But one does not believe me, unless one already knows it -

Section 87, Beyond Good and Evil

And on degrees of freedom:

Spinoza wrote:

Whatever so disposes the human Body that it can be affected in a great many ways, or renders it capable of affecting external Bodies in a great many ways, is useful to man; the more it renders the Body capable of being affected in a great many ways, or of affecting other Bodies, the more useful it is; on the other hand, what renders the Body less capable of these things is harmful (E4p39)

The notion of constraint as vector of increase is ancient of course. One should add the voice of the Eumenides from Euripides’ play,

ξυμφέρει

It bonds

σωφρονεῖν ὑπὸ στένει.

To temper under strain.

And Klytemestra:

ἄλγησον ἧπαρ ἐνδίκοις ὀνείδεσιν·

Sting your heart with real reproach,

τοῖς σώφροσιν γὰρ ἀντίκεντρα γίγνεται.

For in sobriety, spurred it is born to be.

Lastly, the computational process of Simulated Annealing, here described by Kauffman, and then Daniel Dennett:

Annealing is just a gradual cooling. Real physical annealing corresponds to taking a system and gradually lowering its temperature. A smithy hammering red-hot iron, repeatedly plunging the forming object into cold water and then reheating it and hammering it again, is practicing real annealing. As the smithy anneals and hammers, the microscopic arrangements of the atoms are rearranged, giving up poor relatively unstable, local minima and settling into lower-energy minima corresponding to harder, stronger metal. As the repeated heating and hammering occurs, the micoscopic arrangements in the worked iron can first wander all over the space of the configurations, jumping over energy barriers between all local energy minima. As the temperature is lowered, it becomes harder and harder to jump over these barriers…

- At Home in the Universe

The right level of explanation is the algorithmic level: As the metal cools from its molten state, the solidification starts in many different spots at the same time, creating crystals that grow together until the hold is solid. But the first time this happens, the arrangement of the individual crystals is suboptimal – weakly held together, and with lots of internal stresses and strains. Heating it up again – but not all the way to melting – partly breaks down these structures, so that, when they are permitted to cool the next time, the broken-up bits will adhere to the still-solid bits in a different arrangement. It can be proven mathematically that these arrangements will get better and better, approaching an optimum or strongest total structure, providing that the regime of heating and cooling has the right parameters.”

- Dennett, Darwin’s Dangerous Idea

In annealing most important is the “cooling schedule” the methodology of driving energy into the system, and then letting it fall. This is what Nietzsche called tempo, “the patient ear to every staccato and every rubrato” (BGE, 246). What those that strain for the non-naturalization of rationality might have is the loss of the meaning of tempo, the “cooling schedule” of work and rule-following, semantic understandings.

How much is the thought process, and the life lived, like sword-making? How much is “understanding” and communication, even the most clear communications, a methodology of the heated and the cooled?-

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