5 ms·

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

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

ericbarrett 4y ago
Susskind seems to think that Kolmogorov complexity is deeply related to quantum gravity: https://m.youtube.com/watch?v=6OXdhV5BOcY https://m.youtube.com/watch?v=6OXdhV5BOcY
- enasterosophes 4y ago
  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 4y ago
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.
ActionPlankton 4y ago
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 4y ago
  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%93Bellman_equation https://en.wikipedia.org/wiki/Hamilton%E2%80%93Jacobi%E2%80%... Pontryagin maximum principle: https://en.wikipedia.org/wiki/Pontryagin%27s_maximum_principle https://en.wikipedia.org/wiki/Pontryagin%27s_maximum_princip...
deleted 4y ago
[deleted]
deleted 4y ago
[deleted]

ericbarrett 4y ago

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

enasterosophes 4y ago
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 4y ago

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.

ActionPlankton 4y ago

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 4y ago
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%93Bellman_equation https://en.wikipedia.org/wiki/Hamilton%E2%80%93Jacobi%E2%80%... Pontryagin maximum principle: https://en.wikipedia.org/wiki/Pontryagin%27s_maximum_principle https://en.wikipedia.org/wiki/Pontryagin%27s_maximum_princip...

deleted 4y ago

[deleted]

deleted 4y ago

[deleted]