Classical Mechanics Is Still Fundamental
May 18, 2020
Classical mechanics built the mathematical engine that modern modeling still runs: constraints, virtual work, generalized coordinates, energy, action, and variation. Quantum mechanics, optimal control, field theory, and learning systems reuse that engine because each must select behavior from many possible trajectories.
Virtual Motion Makes Constraints Computable
Huygens, Bernoulli, Euler, Lagrange, and Hamilton turned imagined infinitesimal displacements into a method for reasoning about real machines. Virtual work asks how forces would act through motions that respect a system’s constraints. Generalized coordinates describe those motions without carrying every irrelevant geometric detail.
This move lets the model express a pendulum, linked mechanism, fluid, field, or controlled system through the degrees of freedom that can actually change.
Action Organizes an Entire Trajectory
The Euler-Lagrange equations derive local equations of motion from a functional over a path. Hamilton’s principle selects stationary action. Hamiltonian mechanics reorganizes the same dynamics around position and momentum. Together they organize the system’s next behavior as a structured optimization over possible histories.
Quantum mechanics, field theory, optimal control, reinforcement learning, and variational inference inherit this architecture. They rename the variables as phases, fields, states, policies, or probability densities while retaining variation under constraints.
Learn the Engine, Then Reuse It
The linked lecture sequence develops classical mechanics as a living chain of ideas rather than a historical prerequisite to hurry past. Follow virtual displacement into Lagrange’s equations, then carry the same reasoning into the modern system that matters to you.
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Just keep watching. It's easy. Absorb. This theory is really fundamental for everything your passion is at right now. Don't let the name "Classical Mechanics" confuse you that "It's about Newton, and I already know that". If you're keep being confused by how mathematically (or computationally) correctly calculate these entangled qubits and teleport them across temporal correlations to the future, make sure you understand Virtual Velocities pioneered by Huygens, formalized by Lagrange, named by Euler (Calculus of Variations), and finally systematized the virtual work principle and made explicit the concept of infinitesimal displacement by Bernoulli.
These Variational Work, Euler-Lagrange equations, Hamilton's variational principle stuff in Quantum Mechanics is just from here. If you need to understand how Schrodinger equation works, you need this stuff.
How are you going to understand Friston's Free Energy formulation for consciousness and train your best neural network without this formalism? It all builds on Calculus of Variations and Lebesgue Integration (the "measure theory").
Just. Keep. Watching.
#ai #quantumcomputing #quantumphysics #neuralnetworks #reinforcementlearning #BayesianInference
https://lnkd.in/gpj_T9v
Comments added by Brian Greenforest on LinkedIn
These 4 comments were also preserved verbatim from Brian Greenforest’s LinkedIn data export or the public post page.
Comment 1 · (2020-05-18 05:14:54 UTC)
You might want to read the history of how they come up to these problems and solutions, so stuff will make sense. It's all here: https://www.math.rug.nl/~broer/pdf/ws-ijbc.pdf
Also clearing up your mind and understanding that it is one of the most overlooked and confusing areas in physics and mathematics, you're not alone: https://arxiv.org/abs/physics/0510204
Should I say that it enabled Industrial Revolution and Age of Enlightenment? Huygens' 1673 paper allowed people to make precise and complex machines. It was the cornerstone of our modern technology civilization. No surprise that all our physics, mathematics, neuroscience has this "npm module" as a "dependency".
https://en.wikipedia.org/wiki/Horologium_Oscillatorium
One of the best introductions into the "mathematics engine" part of calculus of variations: https://www.msri.org/people/staff/levy/files/MCL/Efthimiou/100914book.pdf
Comments added by Brian Greenforest on LinkedIn
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Comment 1 · (2020-05-18 05:14:54 UTC)
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