If academia wasn’t a dumpster fire, I would have wanted to finish a degree and get a normal job.
Unfortunately, it’s a dumpster fire without any fix in sight.
Reach out to me if you know of any job opportunities for someone like me, who didn’t survive the dumpster fire.
I am the creator of Grassmann.jl
With all due respect, this doesn’t seem like the best venue… [Edit: per chakravala’s demand, removing my misinterpreted comment.]
Like any large system with lots of people involved (government, industry, non-profit organizations, churches, the open source movement, …), academia has a mix of personalities, incentives, and outcomes: good, bad, and indifferent. It can definitely chew people up.
I’m sorry you had a bad experience. All the best with your future endeavors.
Why would I care about the reputation of the people on this forum? I owe you nothing. This forum only exists because I was the one who originally proposed the idea of a Discourse forum for GA.
I’m the one who worked my ass off for thousands of hours so idiots like yourself can try GA for free.
Go ahead and call me a crank then, it just proves to me that the people on here don’t deserve free stuff.
You don’t get to call me a crank and wish me the best in the same post. Get outta here. You have literally contributed nothing. I have given thousands of hours into this for free, all publicly verifiable.
If I contributed thousands of hours into making one of the most popular GA software out there, then yes I get to complain about how shitty academia and people like you are. You are a leech who contribute nothing.
People like you are the reason why I don’t post much constructive feedback here, because you’re all leeches.
administrator warning
Insulting others is not allowed here. This is the type of forum where we disagree with others in highly sophisticated and clever ways - not potty language. @chakravala, who has far past extended his warnings on this type of behavior has been silenced for two weeks.
I am not calling you a crank, sorry if my comment gave that impression.
What I mean is, GA already has a reputation for being nonstandard and difficult, some say needlessly inventing new notation/language for existing mathematics or obstinately adopting a different perspective for no practical purpose – and even some worthwhile papers like Hestenes (1992) “Mathematical Viruses” are more stridently aggressive in the «everyone else is doing it wrong» direction than necessary in my opinion – and it is not uncommon to find responses along the lines of “his approach is pedagogically awful and adds nothing new” or “Let me perfectly clear about this: the math of geometric algebra is fine. What makes certain people “cranks” is that they refuse to learn how modern mathematicians talk about geometric algebra. So, they get stuck in a small community and don’t exchange ideas very well with the larger world”.
[Edit: per chakravala’s demand, removing my misunderstood comment]
You don’t owe anyone anything, but there are better venues for airing this kind of complaint.
A more constructive approach might be to start a general-purpose thread asking about what kinds of jobs there are related to GA, or soliciting advice about alternative ways to find support and recognition for doing good work that doesn’t fit conventional molds.
I disagree with your assessment of the math viruses paper, if anything the criticism is overly soft with Baez himself as a prime example of someone not fully recovered from coordinitis and other mentioned viruses.
His book on gauge fields is brilliant up to the point when he admits that he can’t really calculate without coordinates, ie without abstructung the essential nature of geometric objects with arbitrary, subjective jiberish.
Before that he even adds a quote from a similarly self important mathematician who highlights the irony of an educated mathematicians “sophisticated” ways of component vector calculations as opposed to an ignorant like Faraday who thinks of a vector as an arrow, though as he admits in practice that’s exactly what a vector is…
So I don’t care what formalism u use, you can define Diff forms as abstractly as you like , but if you can’t relate it to concrete calculations with vectors without adding additional strucure you’re not that sophisticated.
Ironically, standard math Diff forms take values only in R, so and the GA stokes is far more general, as well as more concrete, as it can compute with vectors as they really are., and more importantly does not include the fundamental mistake of standard math which is the misidentification of euclidian space with the Cartesian product of copies of R, even if only in “concrete” calculations.
Even though Hestenes half jokingly talked about MVs, every joke is half true they say as evident In the " sophisticated definition of a Diff firm as
an element of an exterior algebra of module dual to the module of derivations on the algebra of smooth functions on a smooth manifold,
The reason why GA is in fact revolutionary is cause it is the mathematical unified theory of geometry, and any coord free algebra withbsych unification i believe must be isomporhic to GA, so it is in fact something fundamental
If I’m wrong in any way here , I’d be happy to know.
I think the Hestenes paper is quite insightful and link people to it regularly. I don’t have a problem with the ideas involved. I agree with you Leo_Kovacic1 that GA makes vector calculus clearer than the needlessly coordinate-focused and multivector-eschewing differential forms version, both improving conceptual clarity and providing some nice algebraic tools that are otherwise cumbersome or unavailable.
The issue, such as it is, is that when someone with a novel idea starts comparing alternative ideas to deadly pathogens, even partly in jest, it comes across as an attack against people’s tribal identity and induces tribalist defenses. Rhetorical escalation can lead to dismissal on the grounds the critics all have ulterior motives or personal problems (whether or not that’s a fair judgment). It’s already hard enough to convince people to spend their time on “nonstandard” ideas when they are in a friendly and receptive mood. Once they get into a defensive / dismissive frame of mind, penetrating that armor is even tougher.
I can claim all I want that «I tried to solve problem X on my scratch paper using matrices, problem Y using differential forms, problem Z using synthetic geometry, etc., and after bashing my head against them and filling up several pages with error-prone scratchwork I tried translating each one into GA concepts/notation and wow the problem was much clearer and easier, with each step symbolically legible and geometrically interpretable and less room for bookkeeping errors», but until the person I’m talking to actually spends a few months (or years?) familiarizing themselves with those tools so they can try to replicate that experience first hand, it’s quite hard to convey what that is actually like.
Whatever my personal feelings were, I wouldn’t want to try to distill that into something as rhetorically aggressive as «matrices, differential forms, and synthetic geometry are all heaps of scrap that can’t stand up to hard problems» or whatever. It would be both untrue and needlessly hostile, pointlessly alienating people who spent years mastering their current tool set. Does that make sense?
Likewise, inre. academia more specifically, for GA to have long-term widespread success it ultimately needs to attract the time and attention of a significant number of students and teachers. Instead of leaving them feeling insulted, it would perhaps be instructive to examine the history of Leibniz calculus notation in England. Charles Babbage and the “Analytical Society” made some jokes but they also translated Lacroix’s textbook into English and then started in on writing up many problems with full solutions into Leibniz notation as an enticement to busy tutors to adopt it so they could save time in assigning/assessing student work. You catch more flies with honey than vinegar, etc.
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.
To be fair to Hestenes it’s hard to replicate every other mathematical source from top to bottom, writing for all audiences with enough hand-holding for someone unfamiliar with the tools to follow every step.
But it is a big frustration of mine as well with many GA resources (not just Hestenes; and no offense intended to the people reading on this forum who have worked tirelessly to help others up the ladder):
Many sources consist of a gentle basic introduction (repetitive for anyone with some basic familiarity) and then a dive directly into higher-level topics, with the full GA language applied freely in the same way any other mathematical tool might be… but unlike for most mathematical tools, in the GA case, as you say, there is somewhat of a “missing middle” of intermediate-level explanations and development.
So to follow the argument you have to be familiar in a reasonably deep way with all of (1) the standard approach including concepts and notations (2) a pretty deep bench of GA concepts and identities including variations of notation and conventions from one source to another (3) the translation from one to the other.
This ends up somewhat limiting the audience to people who are very invested (or masochistic), or at least cutting back somewhat on what more general audiences can easily get from the work.
If you just first work your way through The Elements, Data, Conics, Archimedes’s works, the Almagest, Van Schooten’s Latin translation of Descartes, and Isaac Barrow’s lectures, then you’ll be all set to read Newton’s Principia…
But more seriously, “synthetic geometry” per se clearly has some significant problems, and tools like vectors and blades, oriented angles, barycentric combinations of affine points, and even coordinates in some arbitrarily chosen basis can be very handy. A lot of Euclidean proofs are just missing the fundamental objects needed to clearly explain the problem and the proof, and have to take cumbersome detours.
I do wish someone would go through some high school / undergraduate level geometry textbooks (of both synthetic and analytic approaches) and extensively write out all of the reasoning (and maybe even all of the problem solutions) in terms of multiple formalisms, esp. GA.
Hestenes recommends as an exercise doing this yourself with books like Zwikker (1950) Advanced plane geometry (which is about plane curves, not about fundamental geometric relationships). I’d love to see someone actually publish that. Or similar with e.g. Moise (1963) Elementary geometry from an advanced standpoint or Schwerdtfeger (1962) Geometry of Complex Numbers.
I agree, I would be epic if that NFCM reference was actually published in GA translation , as would most hestenesis suggestions which unfortunately still remain just that, u realised potential. But that’s why NFCM is really good cause od detailed calculations and examples.
I wish that there was a book like that on gravity, whether gauge or standard, or at least some paper with basic examples in detail.
You can find many great books with abstract and coordinate free math, where you for example treat tensor as linear functions instead of transformation laws. But, even with abstract indices, Iv never seen anywhere else than in hestenes books how a coordinate free tensor of inertia actually looks like in practice without a basis or anything non intrinsic.
But again I’m not saying people not using ga should be shamed that there doing sth wrong. Instead we should ask ourselves what we can do better in communicating and doing better job ourselves inside and outside community to make the field grow.
And the key point is that GA is elementary as fundamental as basic (scalar) algebra which is just a special subalgebra, and with it you what Feynman called elementary derivations, where you’re not using any special structures, just basic algevra(commutativity, asociativuty, distributivity…).
But the crucial thing are practical results and examples, that’s the bridge with the mainstream.
If you aren’t aware of the academic dumpster fire, then this discussion is not for you. There are plenty of people aware of the dumpster fire, if you’re not one of those people, then stay out of the discussion.
Academia is screwed up in so many ways, there are an infinite amount of issues to list. It’s not worth it to describe all that, which is why it is simply best to sum it all up as the “academic dumpster fire” instead of wasting time on a million ways academia is terrible.
No thanks, I don’t use reddit. How about you leave this website and go to reddit instead, since it’s your favorite website.
I agree that @jrus should not have insulted me by calling me a crank. Thanks for demonstrating once again that @enki has nothing to contribute except for silencing a discussion between other people you haven’t participated in.
It’s not my job to teach you geometric algebra. Your glorious academic system would have had to facilitate me into an educator instead of excluding me, if you had wanted people like me to be “beginner friendly”. In the past, I was very beginner friendly, but that has dried up with every online interaction, because people on the internet are largely ungrateful academic leeches.
The whole geometric algebra “community” thing is ruined for me, I don’t feel like ever being randomly helpful to strangers again and don’t want to be part of an academic online community ever again. You can thank the “inclusive” academics who outcast me, that’s what they want, and they can have it, I am generous in that regard. You online internet academics are who transformed me from a beginner friendly person into the person who I am now.
In my private interactions I am more willing to be beginner friendly, but in the public community realm, the environment is filled with too many academic people on a power trip who view me as competition. You’d have to establish a private relationship with me, if you don’t want the lowest common denominator of online interaction.
In case you didn’t read the first post on this thread, you can reach out to me with opportunities. The only one spewing bile and misery is you, who is interjecting my discussion about opportunities with your complaints about me.
Your entire series of responses is not in the proper venue for the discussion I started in this thread.
@jrus is one of my haters, got it, I will take note.
Every time I come back to the internet, I only find more and more people like you, whom are stuck on low level human experiences and want to “cancel” me because of your pathetic feelings.
If you’re not an academic, then stop speaking on behalf of them. If you don’t have anything to discuss about the opportunities I started the discussion about, then you should really exit the discussion.
@jrus should probably delete all your posts here, since your messages are only intended to derail the discussion with your hate about me because you want to “cancel” me
I don’t even know this person, @jrus has nothing to offer in terms of the discussion I started, it seems to be some random hater who is offended by my discussion and wants to derail the topic
Okay, I deleted the comments you felt so strongly about, while leaving the more constructive part. All the best luck!
Thanks for demonstrating that crabs in a bucket mentality of human beings, it’s fascinating to observe the social customs of human beings who want to interfere with other people’s lives by trying to “cancel” people.