PGA Ep 3 : Revenge of Infinity

[@steffenkarl7967]

With a plane at Infinity all that is left is its normal vector pointing back at the origin. Pure direction 😊. sweet.

[@tsukisan101]

This is astounding... This view is blowing my mind. Thanks

[@angeldude101]

Since force/momentum are usually related to acceleration/velocity by an object's mass, if they have a duality relation in PGA, then that would suggest that mass would be a pseudoscalar, which would make some sense since it's directly related to an object's volume. (Side note, STA appears to have mass as a scalar, and specifically the magnitude of the energy-momentum vector.)

[@AkamiChannel]

My name is still Steven too. Cheers.

[@tc2017]

Fantastic visuals

[@AMADEOSAM]

Very impressive overview, covering all of classical mechanics. Would be great to develop these tools based on special relativity. With the final step towards general relativity. You could build a game where the effects of special relativity become visual. Rotors and motors should integrate effects of time dilatation by relative speed and by a change in acceleration/gravity.

[@user-hh5bx8xe5o]

First, thank you for this very interesting presentation. In the diagram at 19:45 about inertial duality, what is the missing box (the inertial dual of position) to complete the diagram? Is it related to the kinetic energy?

[@bivector]

The kinetic energy would be half of the join of momentum and velocity. (and combine again both translational and rotational aspects). The position is a motor, its dual has no immediate meaning afaik.

[@stephanevernede8107]

The missing dual box to position is the action

[@hyperduality2838]

Points are dual to lines -- the principle of duality in geometry. Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics! Energy is dual to mass -- Einstein. Potential energy is dual to kinetic energy -- gravitational energy is dual. Gravitation is equivalent or dual (isomorphic) to acceleration -- Einstein's happiest thought, the principle of equivalence or duality! Energy is duality, duality is energy -- Generalized duality. "Always two there are" -- Yoda.

[@hyperduality2838]

@@bivector Points are dual to lines -- the principle of duality in geometry. Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics! Energy is dual to mass -- Einstein. Potential energy is dual to kinetic energy -- gravitational energy is dual. Gravitation is equivalent or dual (isomorphic) to acceleration -- Einstein's happiest thought, the principle of equivalence or duality! Energy is duality, duality is energy -- Generalized duality. "Always two there are" -- Yoda. Conserving duality (energy) will be known as the 5th law of thermodynamics! Generalized duality (waves, Bosons) is dual to localized duality (particles, Fermions) -- quantum duality. Subgroups are dual to subfields -- the Galois correspondence.

[@andrewvoron4490]

I broke my brain trying to figure out where this mirrors are located, until understand that purple squares are on the lower layer exactly under the blue ones...

[@dullyvampir83]

Just for my basic understanding, we start with areas instead of lines because two lines have three possible cases: Intersect, Parallel and skewed. While areas have only two: Intersect and Parallel, the second one can be "fixed" by saying they intersect in infinity, so two areas always intersect, which makes it very easy to deal with?

[@alkalait]

Which paper do you refer to in 18:15?

[@bivector]

'may the forque be with you', linked in the video comments.

[@steffenkarl7967]

Reminds me of Riemann Spheres. Drawing lines to Infinity. How cool.😊❤