Nature of astrophysics (8) - Foundations

[Nereid]

Several posts by Thunderbolts Forum member webolife were the inspiration for this thread; many thanks webolife.

If physics (and astronomy) is quantitative, and has been since about the time of Galileo and Newton, then mathematics forms its foundation (caveats: not necessarily all of maths, and not necessarily the only foundation - see later).

How good a foundation is mathematics? For example, is mathematics self-consistent? Does all the math used in physics itself have a solid foundation?

Start with arithmetic: yes, that's good, or at least as good as anything else in mathematics (i.e. Gödel aside), as Russell and Whitehead showed (though only in the early years of the 20th century).

What about the calculus, which in Newton's hands sorta gave physics a really big boost? That too, though several centuries passed before it was made fully self-consistent.

There are, curiously, two areas - mathematical foundations of parts of physics - that are not fully proven (a word I can use, because I'm talking about maths, not physics), the Navier-Stokes equations and the Yang-Mills theory; the former may be of considerable interest to Thunderbolts Forum members because fluid approximations are common in plasma physics.

Is there any concern that physics may rest on unsound mathematical foundations? More particularly, how likely is it that new discoveries in mathematics will result in radical change in the physics of today's unversity textbooks? What do you think?

Another foundation of physics is it is done by humans, and so, at some level, is 'just' some sort of software program (the brain) fed by sensors with rather odd characteristics (mostly the eyes, but also the ears, finger tips, etc). How our senses can fool us - think of optical illusions, for example - is pretty well understood, and it is easy (in principle at least) to produce hard-copy, durable, objective, quantitative records of all physics (and astronomy) experiments and observations, including the results/outputs.

But what about our cognitive abilities? Is there some barrier, or limitation, to those, which prevents us from ever being able to 'see' (comprehend) some sorts of pattern or rule or order in the universe?

What do you think? Myself, I think it's as close to irrelevant as never mind; there's no way to show that such limitations exist, and even if you could, it wouldn't - couldn't - change the way you 'do' physics (or astronomy).

However, there is at least one aspect which may influence the sorts of hypotheses which get developed and proposed, the kinds of experiments/observations which get designed and performed, etc; namely, weirdness and common sense.

That the universe works at many different scales - big, small, fast, slow, highly energetic, not so much, and so on - does seem kinda obvious. Also, that the universe does not care about human concepts such as electrodynamics, or mass, or scaling laws, etc also seems obvious. However, perhaps our hard- (or firm-) wired brains - adapted for survival in a tiny sliver of universal environments - all too quickly reject that which offends our common sense? Or seems just too weird to be true (no matter how unambiguous and exact the totality of experimental/observational results are)?

[jjohnson]

Hi, Nereid,
Hope you had a nice Christmas holiday. This is another interesting post, and you raise a lot of questions and topics, each of which could be (and already may have been, elsewhere) gone into in great depth. But the whole question of how we "discover" and "interpret" and "model" what we observe in the large sense is not only great fun but really serious for a species that wants to think it understands a lot about how its universe works.

You are on point in noting that you can talk about "proof" when you are talking mathematics, but not when you are talking physics, where observational evidence and the best current model are what we have to work with in the commonly accepted procedures of the scientific method. I think that the majority of people think that science is about proof and want the reliability and security of thinking that things that they rely on to serve them are based on "proven" science. I am a layman but I know what the philosophical difference there is, at least in its broad terms. Interestingly, both science and math always seem to start out in the same way, probably because we don't and can't "know it all". That is, there are certain initial assumptions which have to be made in order to proceed from a constant, supposedly reliable, foundation. Euclid postulated that, by his definition, parallel lines never meet. He developed a consistent mathematical geometry based on that. There are other geometries where the assumption is that parallel lines do eventually meet — which I cannot understand, being so thoroughly grounded in Euclid's approach — but a logically consistent body of mathematics is constructed based on that quite-different initial assumption. A mathematical or logical proof need not translate into a physical reality.

Physics has to make certain assumptions, as well. Many of those have observational contradictions or cases of no observation at all (or other lack of evidence).

'Time's "arrow" runs forward' - yet I read that there is no physical reason for it not to be able to "run backward", and supposedly there may be particle interactions in which some of the observations are allegedly due to a temporal reversal, however brief. (I can't quote this; it just seems I've read this argument and example.) I think that it is thought by many scientists that time "started" with the expansion of the Big Bang a certain length of time in the past of the Universe.

Mass of particles is assumed, probably because we can detect and measure "weight" in a gravity field, measure resistance to acceleration from an inertial perspective, and Newton and others have devised rules and equations that clearly include mass as a valued variable. Mass is associated with "how much" and "what kind" of particles constitute it. Masses are observed to attract each other under the influence of a gravitational force. In reality, what mass and force actually are, or are caused by or are due to, and why the Universe seems to interact through such means is still not as well known as the man in the street thinks they are. Newton refused to speculate on causality of these ideas, and wisely just let his "laws" and equations speak as descriptors of such things. He worked on the quantitative side of things, there, and left the theory to others. "The Law of Gravity" is not known as "The Theory of Gravity" for a good reason.

Does all the math used in physics have a solid foundation? A non-mathematician cannot answer that, of course. What I try to bear in mond is that the mathematics used in physics is there in an assistive role. So long as the mathematics is not suddenly disproved by mathematicians, physicists should assume that it is foundationally acceptable, or as you'd say, "good enough". So long as the mathematics being used to model or forecast events does so accurately and in accord with observations, it is "good enough".

If an observation comes along which surprises a physicist (or astronomer or chemical engineer. etc.) then either the mathematics is incomplete or wrong, or possibly is being incorrectly applied - bad assumptions, or constants actually being variables, etc. - or the physicist simply had not used the mathematics in a way which could have successfully predicted the observation. If, going back, she finds that the math really would have made the prediction, then the surprise aspect goes away and everything is okay. If the physicist cannot make the math predict the surprising observation without patching it up somehow, then the combination of her theory and its supporting mathematics need to be re-examined very closely to try to find out what's going wrong. It's one or the other, assuming human or instrument error regarding the observation have been reasonably well ruled out. [Easy to say; often excruciatingly difficult to do.]

The Navier-Stokes equations are an interesting mention, because they are fluid dynamics equations, used to model waterflow around racing hulls, develop and model airflow past turbine blades and other lifting bodies, to model planetary weather, and much more. They are hydrodynamic equations, not magneto-hydrodynamics equations, which Alfvén developed and received a Nobel prize for. Alfvén observed, however, in his Nobel Address, that when it comes to trying to use his MHD equations to characterize cosmic and lab plasmas, MHD is not, by itself, enough, or applicable in all regimes. He based his remarks on both his lab studies and his astronomical observations, and the ideas he hypothesized as a result of those two pragmatic takes on electrodynamic physics has been observed in the breech for a long time since he said that. The electric currents generated by individual particles, and not just generalized waves, had to be included in any mathematical model. The highly developed kinetic theory of gases cannot be extended to include ionized gases with rare exceptions. He writes, in his slender 1981 volume, Cosmic Plasma:

Theories about plasmas, at that time called ionized gases [and still widely called that! -jjohnson] were developed without any contact with laboratory plasma work. In spite of this — or perhaps because of this — belief in the theories was so strong that they were applied directly to space. One of the results was the Chapman-Ferraro theory (for a review, see Akasofu and Chapman, 1972) which became accepted to such an extent that Birkeland's [experimental] approach was almost completely forgotten. For thirty or forty years, Birkeland's results were often ignored in textbooks and surveys, and all attempts to revive and develop them were neglected.

My observation is that the EU ideas are an extension, in part, of Alfvén's observation of the schism between theoretical physicists trying to define and work with plasma and the experimental physicists who had worked hard to discover the underlying complexities and fundamental differences between their findings and the theoreticians'.

There is nothing wrong, as I see it, with the mathematics underlying plasma physics theoretician's attempts except that they generally are not the right mathematics to successfully predict the messy, complicated, not-gravity-driven physics of cosmic plasma phenomena. This is an error of choice.

What IS the right mathematical approach to use to help with the study of the physics of cosmic plasmas on a wide range of scales? Alfvén's younger associate, Anthony Peratt, author of the 1992 Springer-Verlag textbook, Physics of the Plasma Universe, adapted many of his mentor's ideas and concepts into his studies of large (laboratory) scale plasma discharges under terawatt discharge conditions while at Los Alamos National Laboratory. He adopted the particle-in-cell simulation methodology for modeling astrophysical plasmas, plasma kinetics and plasma radiation, to get around the warnings raised by Alfvén concerning the excessively simplified approaches adopted by the theoreticians.

A quick read {I use the phrase lightly] of Peratt's article titled "Advances in Numerical Modeling of Astrophysical and Space Plasmas" in the book, Advanced Topics on Astrophysical and Space Plasmas, Kluwer Academic Publishers, 1997, reveals a thorough and rich set of topics, with corresponding equations based on Maxwell's electromagnetic field equations and the corresponding equations of motion of charged particles using Lorentz's laws. There is extensive history of observations and development of plasma electrodynamics, regions of applicability of plasma physics, electrical discharges and particle acceleration in cosmic plasma, plasma pinches and instabilities, plasma beams and filamentary plasma, radiation from the plasma state, and so on. Energy conduction and power radiated are covered, along with directivity or gain of synchrotron radiation, polarization effects and transition radiation, and thermal radiation of plasmas. Each area has its supporting equations, so there is hardly a shortage of mathematical foundations in Peratt's approach.

This leads into a detailed description in Part 5. Formulation for the Particle-in-Cell Simulation of Astrophysical Plasmas, pp 129—146, including historical antecedents, the two categories of numerical simulation, basic laws, discretization in time and space, techniques for solution of the equations, issues like boundary conditions, compression of time scales, scaling laws, and then toPart 6. Further Developments in Plasma Simulation, pp 146—163, where he writes about more recent topics and a successor multidimensional electromagnetic particle code (ISIS) to his older TRISTAN and SPLASH codes, the main difference being use of finite-difference equations integrated over a very generalized spatial mesh, including non-linear meshing, and scaling to the Debye length rather than to the Electromagnetic Skin Depth. He has about 38 references to articles in refereed journals at the end of his article.

So far as I have seen, in the limited time I have been studying EU ideas, and have been reading articles in related fields and purchasing textbooks to raise my reading skills in these areas, I have yet to find an article or a book in mainstream, standard model science that references Peratt's articles or his methodologies in describing and modeling astrophysical plasmas.

Perhaps the problem may not be with mathematics itself, in some cases. It may be more of a human bias, Not Invented Here. "Wrong or right, we're just not going to use that approach." My concern is not that (astrophysics) rests on unsound mathematics. It is that it may rest, in part, on ill-suited mathematics, and that incorrect "insights" and theories may be a possible outcome of that reliance.

What are the limits of our cognitive abilities? I think we just have to always keep in mind that there are limits to what we can do or understand, but possibly fewer limits on what we can attempt. The current issue of Scientific American features an intriguing story on Robo Scientists in the Lab by Professor Ross King, Aberystwyth University in Wales. Where we find limitations, others find help using "thinking machines" to help us overcome time and complexity problems we have difficulty dealing with. Again, On Being Certain explores some of the fascinating cognitive limitations our brains' hard-wired self-interest imposes on what and how we "see" and react to stimuli from outside ourselves.

Weirdness is in the eye of the beholder. Scientists, of all people, should know that "weird" is mostly a term for the unexpected, and should be prepared to enter and and explore until the "weird" aspect goes away. The first images from Hubble looked a little "weird", didn't they? Don't QCD and Feynman diagrams "look weird" to the uninitiated? Observing a quasar with a large redshift in close proximity to a low-redshift galaxy, and connecting isophotes, might look weird to as astronomer (as Arp noted in detail) but that doesn't mean that the explanation will never be winkeled out as data and observations and theories improve. That's just science. Weirdness just means questions and more fertile ground to explore with all the tools we can build and put to our disposal. I guess I'm a hardware junkie!

OK; that's enough.
Jim

[MrAmsterdam]

This discussion seems to be quite old. Lets check our beloved wikipedia.

Empiricism
http://en.wikipedia.org/wiki/Philosophy ... Empiricism

Empiricism is a form of realism that denies that mathematics can be known a priori at all. It says that we discover mathematical facts by empirical research, just like facts in any of the other sciences. It is not one of the classical three positions advocated in the early 20th century, but primarily arose in the middle of the century. However, an important early proponent of a view like this was John Stuart Mill. Mill's view was widely criticized, because it makes statements like "2 + 2 = 4" come out as uncertain, contingent truths, which we can only learn by observing instances of two pairs coming together and forming a quartet.

Contemporary mathematical empiricism, formulated by Quine and Putnam, is primarily supported by the indispensability argument: mathematics is indispensable to all empirical sciences, and if we want to believe in the reality of the phenomena described by the sciences, we ought also believe in the reality of those entities required for this description. That is, since physics needs to talk about electrons to say why light bulbs behave as they do, then electrons must exist. Since physics needs to talk about numbers in offering any of its explanations, then numbers must exist. In keeping with Quine and Putnam's overall philosophies, this is a naturalistic argument. It argues for the existence of mathematical entities as the best explanation for experience, thus stripping mathematics of some of its distinctness from the other sciences.

Putnam strongly rejected the term "Platonist" as implying an overly-specific ontology that was not necessary to mathematical practice in any real sense. He advocated a form of "pure realism" that rejected mystical notions of truth and accepted much quasi-empiricism in mathematics. Putnam was involved in coining the term "pure realism" (see below).

The most important criticism of empirical views of mathematics is approximately the same as that raised against Mill. If mathematics is just as empirical as the other sciences, then this suggests that its results are just as fallible as theirs, and just as contingent. In Mill's case the empirical justification comes directly, while in Quine's case it comes indirectly, through the coherence of our scientific theory as a whole, i.e. consilience after E O Wilson. Quine suggests that mathematics seems completely certain because the role it plays in our web of belief is incredibly central, and that it would be extremely difficult for us to revise it, though not impossible.

For a philosophy of mathematics that attempts to overcome some of the shortcomings of Quine and Gödel's approaches by taking aspects of each see Penelope Maddy's Realism in Mathematics. Another example of a realist theory is the embodied mind theory (below). For a modern revision of mathematical empiricism see New Empiricism (below).

For experimental evidence suggesting that one-day-old babies can do elementary arithmetic, see Brian Butterworth.
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Embodied mind theories

Embodied mind theories hold that mathematical thought is a natural outgrowth of the human cognitive apparatus which finds itself in our physical universe. For example, the abstract concept of number springs from the experience of counting discrete objects. It is held that mathematics is not universal and does not exist in any real sense, other than in human brains. Humans construct, but do not discover, mathematics.
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New Empiricism

A more recent empiricism returns to the principle of the English empiricists of the 18th and 19th Centuries, in particular John Stuart Mill, who asserted that all knowledge comes to us from observation through the senses. This applies not only to matters of fact, but also to "relations of ideas," as Hume called them: the structures of logic which interpret, organize and abstract observations.

To this principle it adds a materialist connection: All the processes of logic which interpret, organize and abstract observations, are physical phenomena which take place in real time and physical space: namely, in the brains of human beings. Abstract objects, such as mathematical objects, are ideas, which in turn exist as electrical and chemical states of the billions of neurons in the human brain.
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This second concept is reminiscent of the social constructivist approach, which holds that mathematics is produced by humans rather than being “discovered” from abstract, a priori truths. However, it differs sharply from the constructivist implication that humans arbitrarily construct mathematical principles that have no inherent truth but which instead are created on a conveniency basis. On the contrary, new empiricism shows how mathematics, although constructed by humans, follows rules and principles that will be agreed on by all who participate in the process, with the result that everyone practicing mathematics comes up with the same answer — except in those areas where there is philosophical disagreement on the meaning of fundamental concepts. This is because the new empiricism perceives this agreement as being a physical phenomenon.
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For most mathematicians the empiricist principle that all knowledge comes from the senses contradicts a more basic principle: that mathematical propositions are true independent of the physical world. Everything about a mathematical proposition is independent of what appears to be the physical world. It all takes place in the mind. And the mind operates on infallible principles of deductive logic. It is not influenced by exterior inputs from the physical world, distorted by having to pass through the tentative, contingent universe of the senses. It all happens internally, so to say.
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If all this is true, then where do the world senses come in? The early empiricists all stumbled over this point. Hume asserted that all knowledge comes from the senses, and then gave away the ballgame by excepting abstract propositions, which he called “relations of ideas.” These, he said, were absolutely true (although the mathematicians who thought them up, being human, might get them wrong). Mill, on the other hand, tried to deny that abstract ideas exist outside the physical world: all numbers, he said, “must be numbers of something: there are no such things as numbers in the abstract.” When we count to eight or add five and three we are really counting spoons or bumblebees. “All things possess quantity,” he said, so that propositions concerning numbers are propositions concerning “all things whatever.” But then in almost a contradiction of himself he went on to acknowledge that numerical and algebraic expressions are not necessarily attached to real world objects: they “do not excite in our minds ideas of any things in particular.” Mill’s low reputation as a philosopher of logic, and the low estate of empiricism in the century and a half following him, derives from this failed attempt to link abstract thoughts to the physical world, when it is obvious that abstraction consists precisely of separating the thought from its physical foundations.
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The conundrum created by our certainty that abstract deductive propositions, if valid (i.e., if we can “prove” them), are true, exclusive of observation and testing in the physical world, gives rise to a further reflection...What if thoughts themselves, and the minds that create them, are physical objects, existing only in the physical world?

This would not reconcile the contradiction between our belief in the certainty of abstract deductions and the empiricist principle that knowledge comes from observation of individual instances. We know that Euler’s equation is true because every time a human mind derives the equation, it gets the same result, unless it has made a mistake, which can be acknowledged and corrected. We observe this phenomenon, and we extrapolate to the general proposition that it is always true. However, based on this rationale, one would still not be warranted in concluding that mathematics are purely empirical in nature.

This applies not only to physical principles, like the law of gravity, but to abstract phenomena that we observe only in human brains: in ours and in those of others.

All quotes are from the article ; http://en.wikipedia.org/wiki/Philosophy_of_mathematics

Ps. I saw a documentary once, where a university professor was waving his hand in front of his face and said;" there could be 9 dimensions in front of me, but there is no way for me to see these dimensions" ---

(Ill try really hard to find the documentary again)

[Nereid]

jjohnson,

Once again, another excellent post by you!

And, once again, I'll have to respond over many posts, starting with this one.

Fluids - liquids, plasmas, etc - are, today, thought of as being comprised of particles (atoms, molecules, electrons, ions, etc), in the sense that there are theories of physics which are consistent will all relevant, objective, independently verified, experimental and observational results published to date which posit that.

In that sense, the Navier-Stokes equations can only be an approximation; similarly, MHD is also only an approximation.

I'll be starting a new thread - probably in the Electric Universe section - later, on simulations of astronomical plasmas. In it I intend to address Peratt's book (and his published papers based on the code contained in the appendix to it), as well as other codes. For now, suffice it to say that Peratt is certainly not the only one to have developed, and published, such codes.

(to be continued)

[Nereid]

This discussion seems to be quite old. Lets check our beloved wikipedia.

I've copied this post into the Nature of astrophysics (9) - Empiricism, Extrapolation, Etc thread; let's continue discussion of it there.

Going off-topic, as I commented in response to a post by Lloyd:

Going quite off-topic, I notice that Wikipedia is cited as an authoritative source by several Thunderblots Forum members, yet in this thread very strong views - backed by lots of evidence - says it's not reliable.

[Nereid]

(continued)

Weirdness is in the eye of the beholder. Scientists, of all people, should know that "weird" is mostly a term for the unexpected, and should be prepared to enter and and explore until the "weird" aspect goes away.

The weirdest discovery, so far, is the quantum world.

And here I doubt that anyone would say, confidently, that things are not weird.

For example, in a two-slit experiment, in which only one particle is in the device at any one time, how does the interference pattern build up? Logically, the particle has to go through one slit or the other (if it's a particle); logically, it can't produce a single 'hit' on the screen (if it's a wave). Note, too, that this applies just as much to photons (light) as it does to electrons, or even buckyballs. Now the theory, which is expressed in math equations, provides an account which matches the experimental results, every time; but can anyone honestly say that the 'wavefunction' is not weird? That they can intuitively grasp it?

Quantum mechanics has been around almost a century now, and all the founders of the field have passed on. Huge numbers of experiments have been done, some highly ingenious, and in all those not a single one has produced a result inconsistent with the theory. So, at some level, the universe does seem to behave very weirdly (at least at this scale).

[jjohnson]

Quantum mechanics definitely falls into the "weird" category, but it is generally so good at predicting that I imagine those working with it get familiar with (more or less) what to expect, and at least some of the weirdness goes away. It may be weird compared with "regular or "our scale" mechanics, but if we can get a grasp of what happens at a scale even smaller than the range assigned to QM phenomena, then that, too, might appear "weird".

Peratt, as one researcher, certainly hasn't been the only one to utilize or write code describing the physics of plasmas. He references others and gives credit to both those before him whose which foundations he built, those who worked with him in developing and applying plasma codes in supercomputers, and to more advanced code developments, also by others, as well. As interesting as his experiments and conclusions are, he hasn't really published much on plasma physics since the mid-1990's or so. I don't have a good explanation for that.

In terms of perspectives, and there are nearly as many as there are people, or people interested in pursuit of a particular area of knowledge, one distinction always fascinates me. That is the relationships among theoretical astro-physics (using your terminology as a convenient combination), applied astrophysics, and engineering. Theory might explain that stars emit EM radiation through this mechanism or that. Applied might say, that yields a continuous spectrum which is found to be proportional to the 4th power of thermal temperature (approximately a blockbody radiator, with approximately writ a little larger, cluttered with absorption lines and prominent emission lines, as well as observations of magnetic fields and radial particle accelerations due to electric fields etc.. Engineering might tend to say that this works like this or that well-known physical or gravitational or electromagnetic phenomenon and how can we use it to get a better picture of what is going on, or to get the best data for the applied astrophysicists in their various specialized pursuits?

It's like everybody is partially sighted, trying to make out the details of a herd of elephants... I look forward to the benefit of your overview of other attempts to model and interpret what goes on in cosmic plasma.

Feliz año nuevo!

Jim

[Goldminer]

Quote from MrAmsterdam's posting at wikipedia:

To this principle it adds a materialist connection: All the processes of logic which interpret, organize and abstract observations, are physical phenomena which take place in real time and physical space: namely, in the brains of human beings.

New insights may come from simple reanalysis of terms, definitions, and objectives concerning previously obliquely and overcomplicated expositions of imagined relationships between, for example: time and space, or whether the Sun is primarily powered internally or externally. A simple explanation may be shunned in favor of a more complicated but widely accepted one for various reasons discussed in this thread. Cognitive dissonance can prevent the very thought from entering consideration. For example; It can't be that simple, somebody would have already thought of it, or "I" would have thought of it, or "you" can't do it that way, or that's impossible. Hide and watch.

[JaJa]

A simple explanation may be shunned in favor of a more complicated but widely accepted one for various reasons discussed in this thread. Cognitive dissonance can prevent the very thought from entering consideration. For example; It can't be that simple, somebody would have already thought of it, or "I" would have thought of it, or "you" can't do it that way, or that's impossible. Hide and watch.

This is a curious part of human psychology Goldminer - I see it around me all the time, we are given a project to write, and unless the lecturer specifies a set number of words, fellow students have come back with their own version of war and peace. I find it bizarre, especially when a student picks up a poor grade and says "but I wrote 50 pages of information..." in protest - they can't understand how someone who wrote 3 pages picked up a better grade and then they cry about being victimized.

What do you think is the root cause of that?

JJ

[Goldminer]

Its the cube root Hyperbolic absolute derivative integrated tensor, or it could be just c+v. I guess some teachers can distill understanding from Oops! That would be the professor I would study under.

[Nereid]

jjohnson, JaJa, Goldminer,

The quantum story, if one may call it that, may explain - to a large extent - why physics is held in such high regard.

It is certainly possible to design and build power stations - whether gas-fired, hydro, nuclear, wind-powered, or solar powered (or anything else) - GPS systems, medical MRI machines, PCs and smartphones, etc, etc, etc without a deep knowledge and understanding of quantum physics/classical physics/relativity, and I imagine it may well be possible to come up with explanations of how all these goodies work the way they do, without reference to quantum physics/classical physics/relativity.

However, I don't think anyone has found an effective and efficient means of at least designing such things without at least a working knowledge and understanding of those parts of physics, so as long as efficiency and effectiveness have some value, the role of physics education isn't going to go away.

When it comes to explanations, well, what's the alternative? As far as I know there is none.

And may I close with zhu nimen xinnian kuaile!

[Goldminer]

Well, Nereid,
Blwyddyn newydd dda! to you.

One opens a "modern" physics "text" book, and before them is a bunch of meaningless symbols and complicated diagrams. Unless one has become an "adept," they might as well stare at a railroad boxcar full of graffiti! Once the symbolism is mastered, logic is still at risk, since the goal of the explanation may have been improperly posed. "Mastering" physics is more a process of rote memory exercise, than an analysis and critical examination of the subject. Students should be encouraged to come up with alternate ideas, and be given the opportunity to argue as to why their "answer" is wrong. Both the "lecturer" and the students may prosper from the interchange, don't you think?

[Nereid]

Well, Nereid,
Blwyddyn newydd dda! to you.

One opens a "modern" physics "text" book, and before them is a bunch of meaningless symbols and complicated diagrams.

Perhaps "meaningless" and "complicated" are, like beauty, in the eye of the beholder?

If you meet someone who says that, to her, a modern physics textbook is pure joy to read - the best of which are sheer brilliance in terms of their simplicity, clarity, and profundity - what would you say? Would you, perhaps, deny this person her honestly reported personal experiences?

Students should be encouraged to come up with alternate ideas, and be given the opportunity to argue as to why their "answer" is wrong. Both the "lecturer" and the students may prosper from the interchange, don't you think?

I, myself, have had a teacher (of physics) who did pretty much what you suggest; he was one of my most memorable teachers (though he seemed to take delight in crushing the egos of those who presented their alternatives with more than humility and extreme tentativeness). Most - perhaps all - students very quickly learned that what's standard in the physics textbook is a distillation of an enormous amount of work, often by exceedingly bright people, stretching back centuries. What do you think a corollary to that discovery might be?

[Nereid]

(continued and concluded)

It's like everybody is partially sighted, trying to make out the details of a herd of elephants... I look forward to the benefit of your overview of other attempts to model and interpret what goes on in cosmic plasma.

I think carving up our - humans, collectively, or in general - understanding of the universe into chunks (theoretical, observational, applied, etc) is, dare I say it, universal. And in some fields it's far more complicated than in astronomy/physics; biology for example ... I read an engaging account of how many different kinds of (biological) answer there are to the simple question 'why did the frog jump when it saw the snake?'

Perhaps the easiest way to grasp this is to simply say that each approach has its own, at least somewhat different, purpose, and so the nature of the understanding/explanation/etc they arrive at is that which best suits their purpose.

[Goldminer]

Most - perhaps all - students very quickly learned that what's standard in the physics textbook is a distillation of an enormous amount of work, often by exceedingly bright people, stretching back centuries. What do you think a corollary to that discovery might be?

I dunno . . . Maybe: Giants stood on my shoulders?

But I got away!