[huachimingo]

I've been wondering if there is a connection between Lagrangian Mechanics/Calculus of Variations and Dijkstra's shortest path algorithm.

https://profoundphysics.com/lagrangian-mechanics-for-beginne... How you would translate from the discrete, relational approach to the continuous, analytic one?

[ActionPlankton]

Keywords: Optimal Control, Bellman. I'm serious.

For a first exercise, forget Dijkstra and just solve a maze by doing Value Iteration, and plot the cost-to-go at each step.

Then consider that this function doesn't have to take a graph vertex or grid cell, but could instead be some continuous function on R^n.

The next step usually is to learn about the Linear Quadratic Regulator problem, where the cost-to-go is a quadratic, and you get to do an iteration of "Value Iteration" by updating the quadratic coefficients.

To connect to physics, see how you'd write the Action Integral in these terms.

[kkylin]

To expand on these themes, you may be interested in reading up on these & related topics:

Hamilton-Jacobi-Bellman equation: https://en.wikipedia.org/wiki/Hamilton%E2%80%93Jacobi%E2%80%...

Pontryagin maximum principle: https://en.wikipedia.org/wiki/Pontryagin%27s_maximum_princip...

[ericbarrett]

Susskind seems to think that Kolmogorov complexity is deeply related to quantum gravity: https://m.youtube.com/watch?v=6OXdhV5BOcY

[enasterosophes]

I hadn't seen a Susskind lecture before. This is cool.

He reminds me of Jonathon Banks. I feel like I'm getting a physics lecture from Mike Ehrmantraut :)

[erosenbe0]

From a layperson perspective maybe something like Fermat's Principle is what you are curious about. It also seems one can usually encode/send combinatorial problems into some other space or representation and decode them back into the discrete world. Generating functions and such.