[From BlackHolesHaveNoHair]

[What happens when you make knowledge a prerequisite to understanding? Physics happens. That is, ''complete and utter'' non-understanding of the subject by everyone. (see UnderstandingVsKnowledge)]

It is impossible to understand physics without understanding the related equations, although it's also true that understanding the equations isn't enough in itself. I don't understand the math of string theory, so I can't claim to understand string theory -- only to know what some people (who do know its math) have said about it. The math of SR, on the other hand, is elementary, and even the math of GR is reasonably simple (compared with that of string theory). -- dm

''That's only true to a small extent.  It's certainly possible to have a good intuitive understanding for large parts of quantum mechanics and relativity without knowing the equations.  Not a complete understanding, perhaps, but one that should satisfy people who aren't physicists or engineers but are interested in understanding the universe.  Nobody has really attempted to provide equivalents for things like string theory, beyond tiny fragments.''

Why do you think so? If you look at "naive physics" or "folk physics", basically people believe things that are just wrong, and if you look at the errors people make in freshman physics 101, it's clear that it's difficult to form new correct intuitions.

Also, I have never met anyone who had a good intuitive understanding of special relativity who hadn't studied the math involved, whereas counter-examples are everywhere (e.g. sci.physics.*). "The Twin Paradox", for instance, is a classicly misunderstood subject, of many.

Also, since it only requires high school level algebra and trigonometry, the ones who can't understand mathematical special relativity would seem to have a deficient general education. Of course, many do have high school math, but nonetheless aren't interested in an actual text on mathematical SR, but I really don't understand why not, if they claim to be interested in SR in the first place.

''Difficult doesn't mean it's not possible, it's simply that nobody is interested in helping - the first advice given is ''always'' learn the math.''

No one is interested unless the person is willing to learn the math, because, like I said, it '''is''' a prerequisite.

''I expect that's a large part of why people who don't often end up with such grave misunderstandings, and those who do often end up with no intuition for what the equations mean.  For instance, most explanations of SR that only use high school math simply give formulae for length and time changes, make some statements about four dimensions, and never connect the two.  I don't know a single non-physicist that thinks higher physics is presented in an understandable way, ''especially'' mathematicians.  This is certainly discussed on other pages.''

In general, true, but that's because physics is inherently a difficult subject -- precisely because it doesn't adhere to our preconceptions, whereas anthropology is an easy subject, even at the graduate level, because everything about it is intuitive (unless one has an axe to grind -- but never mind that).

Special relativity in particular, though, has in fact been presented in a mathematical yet accessible way: Spacetime Physics: Introduction to Special Relativity, by Edwin F. Taylor, John Archibald Wheeler ISBN: 0716723271 [That's really funny. The first review of that book, apparently written by one of the few people who didn't care that it was non-rigorous, the reviewer complains about how it does nothing to enhance intuition.]

Your response still doesn't say why you think skipping the math is possible. I think every physicist would disagree.

[Well here's my response to Doug,

To repeat myself yet again, understanding is almost completely divorced from knowledge. The math is neither sufficient nor necessary. In fact, the math is so far from insufficient that your "isn't enough in itself" is just so much empty and meaningless pablum. Exactly as if someone wrote "while polymorphism isn't enough in itself to make an OO language" and then went on about how C++ was object-oriented.

Doug, you simply have NO notion of what understanding means and your nonsensical claims about what's required to understand physics piss me off royally. Not only are they FALSE but they're the ready-made '''EXCUSE''' recited by IDIOTS to shirk off all accountability for their idiocy. It's the kind of COMPLETE BULLSHIT that makes me want to THROTTLE people. You've certainly lost in my eyes by treading on my #1 hot button subject in order to mindlessly repeat an opinion you've probably never given any consideration to! And you lost even more after you stated that you believed that elitist crap.

You say that physics is an inherently difficult subject? That it goes contrary to intuition? COMPLETE BULLSHIT. I could teach quantum mechanics to a CHILD if I wanted to. Hell, it would be easier since they wouldn't have the Newtonian BS that's been drummed into their heads since day 1. And why was it drummed into their heads? Because of retards that think that math has some relation to CONCEPTS, because of retards who don't understand the difference between a Von Neuman machine and a NEURAL NETWORK. Which do you think the human brain is, Doug? Come on, I really want an answer out of you!

Hell, let me put it to you in a way you just might understand. How many people would ever understand Smalltalk if they had to learn all about it from a text-based interpreter? How many would understand it if you forced everyone to build up the higher level concepts for themselves, never letting the programmer use the libraries without first figuring out how the compiler dispatches messages? How many people would understand Lisp if you forced them to learn the lambda calculus before you ever taught them what a function was? How many people would understand, Doug? Nobody! Nobody except the select elite that would be left to work on the Smalltalk internals. And this elite wouldn't understand jack about language design either because there'd be nobody to challenge their understanding of fundamental concepts like objects, lambdas, methods, continuations. And this elite would be composed entirely of self-satisfied scumbags who'd go around saying that the lambda calculus and type theory are PREREQUISITES to understanding Smalltalk. -- RK]

''Heh. :-) Interesting analogy. Just to go along with that, why would physics fit the same analogy you're making with Smalltalk?''

''As to your #1 hot button, I could say the same: I busted ass to study math and mathematical physics, which seem to be the two most difficult subject areas ever invented, and I find it irritating when people imply that it was wasted time and effort, because reading popularizations and thinking hard are adequate substitutes. Thanks so very much for that.''

''I've created neural nets to solve problems, and even shipped product based on them. Make of that what you will.''

[If you wanted to become a physicist then good for you. Well, too bad actually since you haven't become a physicist so it ''was'' wasted time and effort. If you didn't want to become a physicist then too bad for you.

Popularizations and thinking hard aren't adequate to understanding physics. Currently there is ''nothing'', no procedure nor material whatsoever, adequate to understanding physics.

(I find your binary either-or thinking laughably pathetic. Kinda like the idiots who can't conceive of a criticism of Stallman that doesn't come from a right-wing corporatist perspective even after they've been presented with one.)

And finally, why would physics fit the same pattern as programming languages? Because everything does? Because it's a general principle of reality that you don't need to be able to simulate something at a low-level in order to derive its higher-level general properties (multiple realizability). Or perhaps it's simply a property of the human brain?

I really don't care which since I know as an EMPIRICAL FACT that understanding physics is completely divorced from knowledge of mathematics. I also know as empirical fact that the logical pedagogical progression of physics has nothing whatsoever to do with either its historical or the logical mathematical progression of it.

These are simply FACTS. Facts you've seemingly never encountered. And if you have encountered them, then they are facts you have an immense vested interest in denying, as you've admitted yourself.

And just so we each understand where we're coming from, I'll explain my encounters with physics. You busted your ass as a young adult? Well, I busted my ass as a child. I'd been intensely devoted to understanding physics since puberty. And surely even you wouldn't begrudge skipping the tensors and hamiltonians for a 12 year old. Well, you know what I got all those years devoted to understanding physics? COMPLETE BULLSHIT. I got fed bullshit on the subject since I was a child. And it didn't come from "popularizations" either. By the time I was even capable of comprehending mathematical physics, I'd long since gotten fed up on the subject. And then I figured out that it wasn't even necessary for what I had in mind, that it might in fact be ''detrimental''.]

Having a vested interest doesn't make it false. Since you haven't studied mathematical physics, you certainly don't understand '''mathematical''' physics.

If you are saying that you've studied non-mathematical physics, and as a result you do understand non-mathematical physics, that would seem plausible, although I would be unsure what topic areas that includes.

However, this reminds me of your defense that implementing isn't necessary. Those who bust ass to implement tend to have a certain regard for implementing. But your arguments aside, surely you eventually want to implement?

Or of course there's always everyone's dream of '''hiring''' an implementor so that one doesn't have to do it oneself, but even then, surely there's then some regard for the subject, since it was worth paying money to get it done.

[The crucial difference is that I have no interest whatsoever in becoming a physicist. And in fact, I have an interest in understanding far more subjects than I can ever hope to actually work in. So even if I'm willing to work at one of the fields I understand, why should working in a field be necessary to understanding it? I'm not a specialist and I'm not interested in knowing everything about my little corner of the world. I'm a generalist interested in ''everything''. So you can see that the usual arrangement won't satisfy me.]

I'm such a person, too, but by "work in" do you mean professionally? Amateur work is perfectly respectable.

The thing about math in the hard sciences is that it makes prediction possible. Force = mass times accelleration is a prediction. The so-called "soft sciences", like most of psychology, anthropology, classical biology (e.g. taxonomy) do not attempt prediction and therefore do not need math.

I hadn't thought about it this way before, but I suppose one could take a soft science approach and learn only the non-predictive parts of the hard sciences, without math, which could in fact yield a non-mathematical understanding of the descriptive parts of those sciences.

If one doesn't study the math, then one doesn't understand those predictive things (someone could memorize a concept written out in text like that, but that would then be a first step towards understanding the mathematics of it).

So ok, I suppose one could say that one potentially could understand the purely descriptive side of physics without studying the math, similar to learning about species and their taxonomic relations in biology.

However I'm quite sure I've seen you make any number of predictions concerning physics, so...

[By 'work in' I include amateur work. Which will eventually be the only kind of work left. I have no interest in working in physics. Ultimately, I have no interest in working in anything but I'm ''willing'' to work in computer science, a field with nearly zero pre-existing research and limitless potential which directly impacts my day to day existence.

(Just so ''everyone else'' is clear on this, when you refer to soft sciences you exclude those schools in psychology that aim to predict human or social behaviour, empirical economics, and other fields generally considered soft sciences.)

The line between description and prediction blurs easily. People learned about evolution from classical biology. It's just that any theories you come at from that angle of things will be of a different character. Case in point, evolution is a far deeper, higher-level and more important theory than anything else in the field.

Unless you're talking about my restating a result others have arrived at, I've made no predictions in physics. I have made major insights but they tend to transcend physics. I count five:
* non-determinism is anti-scientific and non-mathematical
* GR strongly hints at parallel universes which in turn implies many-worlds
* physical realism is Platonic, only a formalist approach is scientific; dualities in superstrings supports this
* information is a fundamental concept on a par with energy and dimension, information is a conserved quantity
* if the universe is continuous then it could solve the general halting problem, but only to fall prey to a higher order version of that problem

Not exactly things you'd ever see in a curriculum even if they didn't contradict established doctrine. For example, the third implies that every mathematical construct in a physical theory is real, that wavefunctions and superstrings are real.
* Most of this doesn't contradict doctrine. IIRC that's called "neo-Platonism"; the original Platonism was that things were real in a different reality that our physical world only approximated. I personally think neo-Platonism is extremely likely, but that classic Platonism is merely confused.
** Neo-platonism in no way implies that wavefunctions and superstrings are real. And it can't. The only thing it can do is be reconciled with their reality on an ad hoc basis by assuming them as axioms. Very anti-scientific.
** Formalism actually implies that wavefunctions and superstrings are real since the theories they're part of describe our world. And if they did not describe our world, they would remain ''just as real'' but merely in a different reality.
** Mathematical formalism goes hand in hand with physical formalism. It's just that physics hasn't caught up to Goedel's incompleteness theorem. So you see, it's ''classical'' Platonism that was clear (but wrong) whereas it's neo-Platonism that's confused.
* Information is a fundamental etc. This '''is''' modern doctrine.
** I haven't developed all of my insights equally. This was the last one and long after I'd gotten fed up with physics.
* Continuous universe: if you mean that therefore an algorithm could be bounded by uncountable rather than countably infinite time or space, then yes, that could solve the general halting problem, and yes, this is subject to its own problems, in higher order infinite regress.
* Many-worlds: always controversial but always believed by a large percentage of physicists
** If that is true then how come so many worry about time travel?
* "non-determinism is anti-scientific and non-mathematical": not sure quite what you mean. If you're talking about a failure of cause and effect, then many physicists would agree. If on the other hand you mean you don't believe in Bell's theorem, then '''experiment''' disagrees.
** Don't you drag Bell into this! Bell's theorem has '''no implication''' for determinism vs non-determinism. Chaitin's proof does and it strikes in the other direction.
* As for the "non-mathematical" part, if you're not interested in math, then this really isn't a statement you should make on any topic. Anything that you can describe in words, I can translate into a mathematical statement.
** Non-determinism can't be described in words. That's the point I make on QuantumPhysics; it's a meaningless word, gibberish. Non-mathematical.
** And it would be more accurate to say that I'm uninterested in ''arithmetic''; numerical methods and the like. I've been using the term math the way you did and I'll stop now.

''The problem with time travel is that it undermines cause and effect. A smaller problem is that it tends to contradict relativity (smaller because it might nonetheless be reconcileable).''

Only if you assume a single timeline. Once you buy into multiple timelines, you get many-worlds for free out of the deal. Conversely, if you've bought into many-worlds then you get time travel for free.

''You '''are''' interested in non-numerical higher math? Like what?''

I studied math! Admittedly not at a very high level. I had the most fun with algebra and mathematical logic.

''Apparently I'm misusing the term "neo-Platonism"; what is your understanding of the term?''

Platonism in all its forms assumes that:
* the physical universe exists
* the physical universe is ''unique''

Neo-Platonism reconciles itself with Goedel's incompleteness theorem by admitting that mathematical realities are not unique. Formalism junks the second assumption entirely and defines physical existence to be a subset of mathematical existence; the one that admits mathematical constructs called human beings. Formalism is accused of being irrealist as a result, but that's only from a Platonist conception of reality.

''I was just trying to clarify which of many possible things you might mean by "non-determinism"; apparently I shouldn't have made any guesses. Go ahead and tell me which one you mean.''

I don't mean anything by the term non-determinism since it's gibberish to me. ALL of its possible ''definite'' meanings have fatal flaws which invalidate its usefulness as a concept. The indefinite meaning of nondeterminism is useless by definition. I already dealt with all this in QuantumPhysics, in exacting detail.

If you were thinking of anything else I've written touching on physics, I'd like to know. It's kindof interesting seeing what original thoughts I've had in the field.]
* The problem with being an original thinker is that, although one will certainly have '''independent''' ideas, it's remarkably hard to be the first one to have that particular idea, even though one thought of it all by oneself.
** Not like I care since I don't worry about the credit in that area. The only thing I care about is to make sure I have the ''right'' ideas.

''It's true that evolution has primarily (although not exclusively) concerned qualitative modeling, from which qualitative predictions have been made. My line of thought above is most easily read as addressing only quantitative predictions. Math can and does also make qualitative predictions, but I know that no such thing is clear in what I said, so at minimum I'd have to say something further about qualitative predictions. However, maybe I should ponder the topic for a while, rather than being rash.''