> economists think that we need central bank policies to control the whole thing (...) but it just doesn't work in the long run.
Roughly speaking, a central authority might work in certain scenarios, for a short time, to prevent situations where market participants might otherwise panic.
In the long run, the problem is the same authority does not have to all "local", decision-making information available to the individual market participants, and that might prevent the economy from reaching an optimal configuration.
Gravity is not a force. The surface of the Earth is moving up to the object in free-fall at an acceleration of 9.8 m/s^2. The force pushing the surface, and the pressurized atmospheric shell, upward is a result of the processes occurring within the Earth (likely, in particular, those within the the core).
> "The lack of experience played right into the government’s hand. Instead of portraying a leader in control of his domain and confident in his case and his company’s legal and ethical righteousness, the courtroom videos showed a side of Gates that had never been on public display before. He was petulant, petty, flustered, and dour. He was ineffectual. He was, in a word, beaten."
The article may come off a little bit too harsh on Gates, but it is essentially right in that the US Gov strategy may have been to score a PR win on Gates and Microsoft. In that way, Gates came across as more on the defence than he perhaps needed to be in the situation. The deposition ended up being a low point from the public's perspective, though any damage has mostly been undone in the 2+ decades since.
Looking at it in terms of one of the "golden ages" of recording music - back in the 1960s, think the Beatles - this would mean only returning to what has already proven possible before. Some artists in those previous eras were able to deliver remarkable music as much as twice a year over consecutive years.
Perhaps it was a less competitive industry at the time, but certainly less efficient (and relatively more expensive) production tools were available compared to today.
There are still plenty of musicians doing that. I haven't kept track lately, but John Zorn used to release albums every 2 months or so. Thee Oh Sees and King Gizzard & The Lizard Wizard are also constantly putting out new albums (King Gizzard had 5 albums in 2017).
This is an age-old domain of thought known as philosophy of science [0]. Although, by prepending your post as "meta", perhaps you are already aware of it.
I should add: As a human being, it is probably impossible to separate the scientist from the philosophy in which they explore, proceed with, and promote their work. In some cases, it might not be something they are even aware of. Instead, the scientific system (as a sort of world institution) should itself be designed to always seek out and protect truth, regardless of prevailing contemporary knowledge.
The role of this "era" may be in reformulating quantum physics and, separately, general relativity in new ways that make the ideas more accessible to more people, and earlier in their lives. The goal could be to make of modern physics... the new classical physics. That is, we start to let go the crutches we still teach because it is thought that day-to-day life is more readily explained by Newtonian physics. We are now in era where most advances (e.g. smartphones among them) could not exist in their present form without modern physics.
Once more people accept the concepts of modern physics as a way of life (perhaps intuitively?), we will be in fertile territory for any potential new revolution in physics.
These theories have a very precise mathematical formulation and very weird unintuitive consequences. If you try to teach them without math, you only keep the weird unintuitive part and it's more unintelligible.
For quantum mechanics you have to know eigenvalues and eigenvectors. This is studies in the first years of the university in a technical career. I'm not sure if it can be teach much earlier.
For Special Relativity you have to know Minkowsky spaces. It's not so difficult, it can be moved to the first years of the university.
For General Relativity you have to know curved spaces. It's not imposible to learn, but you can get a Ph.D. in Math or Physics without studding curved spaces.
Linear algebra (with diagonalization not just using gauss-jordan) could be pushed back to highschool for motivated students, and is in some countries. The coordinate system aspect of special relativity (the origin of time dilation and most of its "weird effects") only requires algebra. General relativity requires the full mechanisms of differential geometry but advances in things like differential forms are pushing this back to the undergraduate level. Overall I would say that it could be done but you would have to leave the unmotivated students behind.
Turtle Geometry gets as far as motion in curved spacetime using code in Logo. Dunno how many high schoolers have ever learned from it, but it's there. (It includes a nice concrete intro to vector algebra earlier, too.)
Re quantum mechanics without many prerequisites, I'm a fan of Feynman's book QED.
We can keep math, but switch to better theories, with plausible explanations.
A kind of Pilot Wave can explain quantum weirdness to layman people with ease.
We can ditch theory relativity and calculate speeds relatively to CMB, which is much easier to understand.
We can ditch Big Bang theory and, instead, accept that light is not immortal, because it ages with time. IMHO, Dipole Repeller and Shapley Attractor are much more attractive and easier to explain than Big Bang.
All three examples you gave have problems or inconsistencies and this is why they are not used. You are being downvoted because you are suggesting teaching formalisms that are known to be insufficient simply because they fulfill your personal criteria of intuitiveness.
We have no perfect theory to explain everything, so it's just tradeoff, exchange of one set of inconsistencies for another set of inconsistencies, but with better intuition. I'm doing it here, in my country.
The problem with current theories is that I understand them when I reading them. It's like piece of complex code or book with complex but boring text, like phonebook. I can follow it, when I read it, but I cannot reproduce it when book is closed.
Can we teach a phonebook to kids? Yep. Is it useful? Nope.
Recently, I did "quantum physics in one picture" experiment. Results are very good: lots of reposts, comments, interest in topic.
But it is not a tradeoff in the cases you picked, rather one set of formalisms has drastically more inconsistencies than the other. E.g. pilot waves: you gain having real numbers (which I personally see little value in) and you gain having a more mechanistic intuitive source of the interference (which is indeed interesting). However describing multiple interacting entangled particles becomes incredibly difficult, describing annihilation and second quantization which is needed for the quantum behavior of fields is not completely done yet, and (what I consider the most substantial problem) you can not work with finite level systems (i.e. anything but a spinless particle in a box is very difficult to describe by pilot wave theory).
In short, pilot waves were a worthwhile avenue of research, but we have seen they are incredibly cumbersome or even insufficient in many quantum mechanics problems.
Yep. Pilot Wave theory is underdeveloped theory, but it helps to develop intuition. Walking droplets are even better for that. IMHO, it's better to use QM to solve QM problems in science, but use walking droplets and Pilot Wave Theory to develop intuition for others. Walking droplets are easy to demonstrate. Double slit experiment can be reproduced in school lab. This way, quantum physics can be taught in school for children of age 12+, so they will be ready to solve much more complex problems when they will be PhD.
Entanglement is hard problem for PWT. Photos of entangled photons[0] are intriguing, because they look similar to behavior of walking droplets in some experiments (see dotwave.org feed). I hope, someone will be able to reproduce entanglement in macro. Currently, my top priority is to reproduce Stern–Gerlach experiment in macro (I suspect that interference between external field and particle wave creates channel, which guides particle into spot, but it better to see it once). Second priority is creation of "photons" in macro. Entanglement will be third. IMHO, all of them require microgravity to reproduce in 3D.
With some caveats, I happily agree with the angle from this last comment! I agree PWT is a great way to get people hooked on quantum science, even if I consider it as a dead end for fixing the inconsistencies we have (semi-personal semi-professional opinion).
One problem is that physicists are not interested in lowering the bar to understanding advanced theories. Some say it's all fairly simple once you spend a decade learning some very advanced math. The art of teaching is in making the material more accessible, and at that I dont think much progress has been made.
>physicists are not interested in lowering the bar to understanding advanced theories
That is not true, geometric algebra is an example of a recent pedagogic improvement that is getting a lot of attention. The problem is that physics will never be easy enough for someone who is not prepared to think deeply, because it is one of the few areas where truly new ideas can be found. Virtually every area of learning involves repackaging concepts we have all known from childhood (people's motivations, stories, colors, that kind of thing) in specific ways. Major exceptions are physical tasks like learning to sew or play an insturment, and "esoteric" subjects like math and physics. In all of those cases you cannot learn by casually reading because the neurons in your brain are simply not prepared for it.
I've been interested in GA for years now because it helps me visualise and understand otherwise inscrutable mathematics.
Nobody, literally nobody mired in the traditional mathematics of theoretical physics can explain why the Universe is best represented using matrices of complex numbers with constraints on them.
"Shut up and calculate" or some variant is the common response to such probing questions.
More often, it's some variant of "Well, I can understand it, you need to study more.". This is usually stated just politely enough not to be outright insulting. But if you keep asking probing questions, it turns out that they don't really understand either, the "study" didn't help them either. They only got better at pushing the symbols around on paper They're dismissive of such questions because they're too proud to admit their own ignorance.
Geometric Algebra (GA) was my "lightbulb" moment where I finally understood where Dirac matrices, Pauli matrices, and the like come from and why they have the structure that they do.
My logical conclusion was that GA is the far more elegant, clear, understandable mathematical structure that brings a wide range of Physical phenomena under a unified formulation. So clearly, it should be used for pedagogy.
Nobody agrees with that. The attitude is "well, that's nice, but it's mathematically equivalent so there's no benefit." which is just the stupidest thing I've ever heard.
Imagine if you saw a function called "add_num(a,b)" that computed the sum of two integers using the full bit-by-bit adder digital logic circuit simulated in software using boolean logic. Absolutely bonkers, insane code, right? Clearly this ought to be scrubbed from the codebase and replaced with a simple "+" operator, because we're not maniacs. Physicists would argue "no", it's equivalent, it's "working", so shut up, leave it and just move on.
If you haven't used it already, Versor[0] is nice to play with. GA is simple enough that even normal-ish teenagers can understand it and produce useful results (my sons are using it in a game they're building). Math isn't even close to my strong suit, but Dual numbers and GA make sense to me, and have made it a lot easier for me to do (seemingly, to me anyway) advanced stuff. :-)
I 100% agree with you in all respects — I don't come from a physics background but I hear you loud and clear. I think the 'why' is deep and psycho-historical in nature:
- we're exiting the "industrial" mindset where everyone is the same making the same products, to a wider topology of knowledge and skills (more and wider horizontals, more and bigger verticals, 'average' profiles become 'scattered'). This clearly drives a need to "learn a little bit of a lot of things" even at expert level.
- The walls and denial you expose here is to me but a symptom of the disease that current academia will either have to heal or die of. Seeing how Khan (and thousands of Udemy's after them, indies) changed the landscape, my money is on a major paradigm shift incoming for academia (it's already done, they just don't seem to know it yet as institutions, most of them). Lots and lots of great teachers around the world almost freely sharing incredible hands-on knowledge and insight.
- Some applied domains with dramatic tension of the demand side (lots of positions to fill) don't have the luxury of elitism and massively adopt "pragmatic" approaches especially in learning. Software dev, programming and tech in general is much like that — the "one liner" installs and 1-page "getting started", all the intelligence solely put into making things intelligible and usable is, frankly, quite humbling and inspiring in that field. A very good side of the SV/Cali culture. So, examples of how to proceed next really do exist.
Now when I think back of topics that I hurt my head against for months or years, that a simple 20-minute video could 'unlock'... Why, why do we not make it a staple of "teaching" to at least consider 2-3 angles to make sure everyone's got a fair chance at getting at least 1?
- On the topic of hubris and laziness, this is where physics went astray, imho. Too much hubris and not enough laziness. That was back in the 1980s and it took 40 years to realize, probably 10-20 more to "fix", if ever before we build a new system (see above).
That being said,
> Geometric Algebra (GA) was my "lightbulb" moment where I finally understood where Dirac matrices, Pauli matrices, and the like come from and why they have the structure that they do.
YES, please! Geometric algebra seems like the thing that could blow my mind too. I am very visual, to a fault maybe.
Would you have a 'favorite' resource to share? (book, course, youtube, whatever?)
GA is just "strongly typed" vector algebra. It recognises and embraces the inalienable fact that areas and volumes are fundamentally different to vectors and scalars.
The reason Physics "went wrong" is that in 3D space (only!) the mathematics of areas and vectors is coincidentally isomorphic, so it's possible to cheat and use only vectors and scalars and then everything "works". Similarly, volumes and scalars are easily confused as well, and appear to work fine.
GA has no such restrictions and the same formulas work in all dimensions, including high-dimensional or with degenerate metrics. Problems from classical geometry such as finding tangent lines to circles can be trivially extended to finding tangent hyperplanes to hyperspheres, even for very complex problems.
The formalities of GA force you to include things like the square of the unit pseudoscalar in some physics formulas that were accidentally dropped in the traditional form because in 3D this is just "1" and hence easily overlooked. This makes some formulas weirdly difficult to extend to become relativistic, when in fact the problem was just the "weak typing" of vector algebra.
Vector calculus also inherently requires a basis, which is an easy way to get bogged down in the weeds and get confused by issues with the algebra itself instead of the truly "hard" aspects of the problem.
Generally, the "lightbulb" moment for me was that Geometric Algebra has various subsets that are also closed algebras in their own right. For example, the "even" subset of a 3D GA is isomorphic to Quaternions, and the even subset of a 2D GA is basically the same thing as a Complex number. The various "named matrices" are just other subsets of 3D or 4D GAs. Physicists tend to avoid the full general case and simplify their algebras down to the special subset cases, using the historical names and greek symbols. We have to keep the symbols, you see, because otherwise you wouldn't be able to read 2000-year-old ancient greek texts, or... something.
University Physics is actually a study of the History of Physical Philosophy. The computer science equivalent would be learning about abacuses for the entire first semester, then progressing to mechanical calculators in the second semester, vacuum tubes in the second year, and so forth, only to briefly touch on transistors by the end of the third year. Postgraduate research students would be finally told about modern silicon chips and software development, but by this point they're so used to wiring up breadboards manually that it's too late to teach them how to do anything properly.
Starting with something elegant like pure functional programming in the first year is how I studied Computer Science, but I only found out about Geometric Algebra existing after I graduated Physics. It's nuts.
Real industrial use is few and far between, but at least a few folk have discovered that GA is ideal for robotics. Unfortunately, not everyone got the message, and most robotics software libraries are firmly vector/matrix based and have all the usual issues like numerical instability and gimbal-lock. Fun stuff.
Hey there. I'm not sure you'll ever read this, but for the record. THANK YOU, so much.
So.. I've been dabbling with GA since we talked and it is an incredible framework!! I now understand your post loud and clear. It's a new dawn of math for me, I really mean that; Clifford is my new prophet (and I think this one's a keeper possibly for life, I don't know and can't imagine something better for the problem space). So much had not clicked with linear algebra for me, so much of matrices was obscure and had no representation in my mind... And GA's base objects and concepts are so, so elegant, and exquisitely intuitive.
Turns out he's an outstandingly good teacher. Strong recommend.
I'll probably take a more "serious" course/book (with problems!) next — if anyone has a recommendation, please do!
Then make progress by working on actual stuff (I guess Hestenes' reformulations are a great starting point, retracing some of these following his reasonning).
And the penultimate goal would be to reformulate stuff myself, if I could — haha, that would be so great. More realistically use GA for research in designing models and representations.
___
TL;DR: you brought Math back into my life. We were on a break (but kept calling each other..) for the last decade and a half. GA is really, really strong. Remind me again, why don't we teach children like that for a century? /s (sigh)
Wow, thanks so much for all this. I've yet to digest it fully but it's a terrific intro, I love how you worded some of this. You should consider teaching! :)
I can't elaborate much, so just a few "mind blown" moments for posterity:
> GA is just "strongly typed" vector algebra.
That's one hell of $1B slogan, at least around these parts! :) Shut up and take my money.
> in 3D space (only!) the mathematics of areas and vectors is coincidentally isomorphic, so it's possible to cheat and use only vectors and scalars and then everything "works".
I never realized that... there's indeed a lot of confusion in my mind between those concepts. I fail to see how "different" they're supposed to be, I guess really need to go back to sane basic in that regard.
> Geometric Algebra has various subsets that are also closed algebras in their own right.
Just wow. I love this. I actually need this.
> GA has no such restrictions and the same formulas work in all dimensions, including high-dimensional or with degenerate metrics. Problems from classical geometry such as finding tangent lines to circles can be trivially extended to finding tangent hyperplanes to hyperspheres, even for very complex problems.
So that is the real kicker for me, because it fits my problem space so well. I'm exploring highly-dimensional models (basically letting complexity arise from the dimensionality of rather simple/elementary objects, rather than trying to shoehorn complex functions in low-dimensional space in hope of pretty much randomly finding "better fits" — it's a strong desire to not interpret the data before the fact, to remove bias from modeling itself).
There's interesting research around geometric deep learning as well, which seems largely informed by physics as well, and this is sort of the logical conclusion of that for big datasets.
I think industrial use may rise greatly based on this first take. But it's always a generational thing with culture — it takes ~25 years give or take for those who "grew up with it" to finally become the majority of the workforce and sway things their way. Same with politics — looking at you, academia. As you said, "but by this point they're so used to wiring up breadboards manually that it's too late to teach them how to do anything properly."
> It's nuts.
Yeah, it'll take time, never mind how infuriating in the meantime. But good on you, spreading the word about GA is exactly how we move forward, one post, one topic at a time. Eventually, we get there.
I'm trying to explain quantum physics using single photo[0] (in Ukrainian, but you will get it). It has good adoption among regular people. It based on real physical experiment, just labels are added. BUT scientist are insane when they see it. They argue that quantum physics cannot be explained using picture, because the only true way to explain quantum physics is using mathematics.
The historical attitude has been, "it doesn't matter, shut up and calculate". There's been quite a bit of push recently to try and nail down exactly what QM means rather than just what it calculates (See: Sean Carroll, etc)
Notice how there's very few military aircraft companies in the USA?
That's because the little fish got a visit from Washington saying, "that was your last contract unless you merge."
Northrop tried to resist, for a while anyway.
Regarding foreign companies, the Avro Arrow was cut up after the US offered Canada a northern missile defense network. The Arrow was an early Mach 2 interceptor - think of the foreign sales possibilities.
Of course, keeping in mind that Cook-era Apple is operating on a more massive scale (product shipped, wider distribution, more product lines).