Differential forms and cohomology

Leibniz differential, tangent vectors in curved space, cotangent (dual) vectors, differential forms, exterior product, interior product, exterior derivative, closed forms, exact forms, cohomology. A few suggestions for further reading: Maxwell's equations expressed as differential forms, Aharonov-Bohm effect, BRST, Dirac quantization, D-branes in string theory, topological field theory, Yang-Mills theory, "ideal" of forms for reformulating partial differential equations (PDEs).

[@wargreymon2024]

It's a good overview for someone who knows lots of math and physics.

[@miguelaphan58]

a precius little master piece of exlanation...

[@markussagen3778]

Fantastic video!

[@AbuSayed-er9vs]

Oh my God!!! It's wonderful explanation.Plz plz plz...Make video about cartan geometry in a visual way(cartan geometry using way wiser).

[@marcusbergmovie]

Thanks! I have a bunch of other videos in the pipeline (determined by what I currently teach), but Cartan geometry does sound like a fun suggestion for the -- possibly distant -- future.

[@AbuSayed-er9vs]

Marcus Berg of course it could like a fun if you present it by " hamster in a hamster balls" or " way wiser geometry",those are both good visual analogy.

[@muskduh]

Thanks for the video

[@goranbutkovic9380]

Nice!!

[@songohan393]

this is hard to understand for me as a non native speaker, thanks for the video tho

[@ciaopeople9664]

Perfectly unclear !
😁😁😁

[@hyperduality2838]

Vectors are dual to co-vectors.
Homology is dual to cohomology.
Electro is dual to magnetic -- Maxwell's equations.
Positive is dual to negative -- electric charge.
North poles are dual to south poles -- magnetic fields.
Electro-magnetic energy or light, photons are inherently dual -- wave/particle or quantum duality.
Particles are dual to anti-particles, spin up is dual to spin down -- Dirac equation.
Gravitation is equivalent or dual to acceleration -- Einstein's happiest thought, the principle of equivalence (duality).
Energy is dual to mass -- Einstein.
Dark energy is dual to dark matter.
Space is dual to time -- Einstein.
Positive curvature is dual to negative curvature -- Gauss, Riemann geometry.
Curvature or gravitational energy is therefore dual.
Potential energy is dual to kinetic energy.
Apples fall to the ground because they are conserving duality.
Action is dual to reaction -- Sir Isaac Newton.
"Always two there are" -- Yoda.

[@mochen9282]

Yin is dual to Yang - Taoism

[@hyperduality2838]

@@mochen9282 Teleological physics (syntropy) is dual to non-teleological physics (entropy).
Syntropy (prediction, projection) is dual to increasing entropy -- the 4th law of thermodynamics!.
The force of gravity is empirical proof that duality is real so there must a dual process to that of increasing entropy!
The conservation of duality (energy) will be known as the 5th law of thermodynamics, energy is duality, duality is energy.
Being is dual to non-being -creates becoming - Plato.
Thesis is dual to anti-thesis creates the converging thesis or synthesis -- the time independent Hegelian dialectic.
The proton (thesis) is dual to the electron (anti-thesis) synthesizes the photon (pure energy) -- atomic duality.
Pure energy is synthesized by conserving duality.
Duality creates reality.

[@stearin1978]

I would see here lack of power of a language to convey the meaning more than the power of "duality everywhere". :-)

[@hyperduality2838]

@@stearin1978 Once you accept duality you can ask the following question, what is dual to entropy?
Syntropy (prediction, projection) is dual to increasing entropy -- the 4th law of thermodynamics!
Signals are dual to noise -- electronics, signal to noise ratio.
Randomness (entropy, noise) is dual to order (syntropy, signals).
Teleological physics (syntropy) is dual to non-teleological physics (entropy).
Mind (the internal soul, syntropy) is dual to matter (the external soul, entropy) -- Descartes.
Concepts are dual to percepts -- the mind duality of Immanuel Kant.
Rational, analytic thinking converts perceptions into conceptions -- a syntropic process. Optimized conceptions result in optimized predictions for tracking targets and goals -- teleology.
"Through imagination and reason we turn experience into foresight (prediction)" -- Spinoza describing syntropy.
The conservation of duality (energy) will be known as the 5th law of thermodynamics, energy is duality, duality is energy -- Generalized duality.
Energy is dual to mass -- Einstein.
Dark energy is dual to dark matter.
Your mind exists midway or between the two dual extremes of dark energy and dark matter.
Julian Barbour, physicist:- The big bang is a Janus hole/point (two faces = duality). Topological holes cannot be shrunk down to zero.
Null homotopic implies contraction to a point and non null homotopic requires at least two points -- duality.
Homotopic equivalence = duality!
Points are dual to lines -- the principle of duality in geometry.
There is alot of duality in languages, up is dual to down, left is dual to right.... because observers sub consciously think in terms of dualities -- mind dualities.

[@officiallyaninja]

@@hyperduality2838 this is the worse bit of pseudoscience I've ever heard