I agree of course, I mean this topic and how it was expressed does not sound good nor will it do anyone any good, no argument there.

I saw the links, and I saw that one of the quora posts before, it I was just appalled how that question was framed and how it was answered by John Baez of all people.

And it’s not an isolated thing, 99 percent of the time it’s that the people for whatever reason feel threatened and triggered by even a mention of GA, Iv been called a partisan(of Hestenes pary :)) ) and an extremist lol, for just some answers on math overflow.

I totally get what you’re saying, it’s kind of reasonable that if youve been trained your whole life to do things one way, and more importantly to think one way its hard to lern another way, and there will be resistance, there is always resistance to change especially in science. Especially math people who ironically are closed in their own bubble and are not subject to dealing objective or empirical reality.

Even sir Micheal Atyah said algebra is the offer of the devil and that will answer any question if you sell your soul ( geometry).

That’s cause pure synthetic geometry is hard and slow, and this then also knocks of conceptual clarity.

Just try to follow some proofs in Principia.

It’s not that these systems are trash, Diff forms and synthetic geo are beautiful, but they are too limited in scope and power.

My main problem is when for power and versitily one introduces unscientific math assumptions, like a random basis or coords , and then tries to prove covariance and gets pseudoscientific, pseudo geometric objects as artifacts of arbitrary assumptions. GA, then isnot some new system, it’s just a filter that separates out geometric essence from non geometric nonsense.

Since 1900s it’s been know that Leibnz’s dream of an algebra with every operation having clear geometric interpretation does exist, and Hestenes did incredible work to get the word out.

Imagine if people like Atyah knew GA, imagine if the students wouldn’t not be taught 30 different redundant formalisms just to handle a topic like spinning tops in mechanics, how much progress would have been made.

Problem with Hestenes is that he just doesn’t bother in typical profesor fashion, to give enough concrete examlpes and leaves them out for the reader to figure out.

Just a few days ago I was talking with a mathematical and a theoretical physicist in the Zagreb istitute and

they were interested in ga and feel like there is something important there, but have similar issues with Hestenes work.

We agreed to start with concrete problems related to their research,

for example, the relativistic submarine paradox (I’ll post a topic with details), but I’m not to strong in GR, and I’m struggling with hestenes paper on GTG as it doesn’t give enough concrete details on how exactly for example his gauge tensor acts on basic objects like the momentum tensor or proper density.

Instead he gives a salad of standard and nonstardad approaches, but nobody cares about the middle parts, at least not initially.

The best way is to have a self contained pure GA formulations focused on concrete problems, and then if the solutions indeed are new or interesting in some way(and the usually are and not just in notation) people could reverse engineere them and learn GA from the top down.