(no subject)

“It’s an old question in the philosophy of physics. People have been talking about it since Fermat first formulated it in the 1600s; Planck wrote volumes about it. The thing is, while the common formulation of physical laws is causal, a variational principle like Fermat’s is purposive, almost teleological.
...
Well, if I can speak anthropomorphic-projectionally, the light has to examine the possible paths and compute how long each one would take.” He plucked the last potsticker from the serving dish.
“And to do that,” I continued, “the ray of light has to know just where its destination is. If the destination were somewhere else, the fastest path would be different.

Gary nodded again. “That’s right; the notion of a ‘fastest path’ is meaningless unless there’s a destination specified. And computing how long a given path takes also requires information about what lies along that path, like where the water’s surface is.

I kept staring at the diagram on the napkin. “And the light ray has to know all that ahead of time, before it starts moving, right?”

...
That day when Gary first explained Fermat’s principle to me, he had mentioned that almost every physical law could be stated as a variational principle. Yet when humans thought about physical laws, they preferred to work with them in their causal formulation. I could understand that: the physical attributes that humans found intuitive, like kinetic energy or acceleration, were all properties of an object at a given moment in time. And these were conducive to a chronological, causal interpretation of events: one moment growing out of another, causes and effects creating a chain reaction that grew from past to future.

In contrast, the physical attributes that the heptapods found intuitive, like “action” or those other things defined by integrals, were meaningful only over a period of time. And these were conducive
to a teleological interpretation of events: by viewing events over a period of time, one recognized that there was a requirement that had to be satisfied, a goal of minimizing or maximizing. And one had to know the initial and final states to meet that goal; one needed knowledge of the effects before the causes could be initiated.”

-- Ted Chiang. “Stories of Your Life and Others.”

To understand LLMs and maybe other types of AI, one has to think like hectapods from Ted Chiang's story. Category theory is a bit like that too. First, you have to see roughly the entire diagram, e.g. topos or Kan extension, then think sequentially through its arrows second.

Thomas Nagel's philosophy fits right in too (Mind and Cosmos). AI models _are_ teleological. They know everything there's to know.