Saturday, February 25, 2017

Should physics teaching respect the historical chronology?

At his Forbes blog, Chad Orzel wrote the essay
Why Do We Spend So Much Time Teaching Historical Physics?
which, in my opinion, sensibly describes the advantages and disadvantages of "following the sequence of events in the history" while teaching physics. Maybe I could say that I agree both with his points and their balance.

Orzel starts by saying that there are people who find it natural to bring the undergraduate freshmen as quickly as they can near the cutting edge of physics – to modern physics that includes relativity and quantum mechanics – once they get into the college. People don't want the well-known 19th century stuff and the nontrivial new things that the laymen usually don't know make the university a cooler place.

In the past, some of us were defending some exposure of students of high schools if not basic schools to quantum mechanics, too.

However, when this strategy is applied, he argues, one usually ends up with lots of students who just don't understand why some idea – like the wave-particle duality – was introduced at all. Like other instructors, Orzel often answers "Because I say so" when he is asked some "Why" questions. The pedagogic procedures often rely on references to the authorities which is counterproductive and unscientific in spirit.

Let me say that my undergraduate courses in Prague took a mixed attitude. The "standardized" physics courses for the freshmen did cover mainly classical physics – from mechanics to electromagnetism, statistical physics and thermodynamics, relativity, etc. – but as the freshmen, we also had a seminar that was trying to introduce us to some modern physics and its mathematical methods early on. I was studying many things on my own so the organization of the courses didn't matter much to me but it is relevant for many others who first hear at school about most of the school-like things.

Before I discuss the paradoxical consequences of both types of teaching, I must mention a weird thing. In the first sentence of his text, Orzel talks about "modern physics". So the phrase "historical physics" in his title is clearly meant to be the "opposite" of modern physics. When physics isn't modern, it is, well... historical.

Except that he must know that this is not the standard way of "negating" the adjective. When "modern physics" appears as a title of some "part of the learning process" in the universities, it's often a chunk of exams. We had a "modern physics" PhD qualifying exam at Rutgers. What was the other part? Well, yes, it was "classical physics" rather than "historical physics". Here is a Columbia page that divides the qualifiers in a similar way – but they also have a "general physics" part. I believe that the oral exams at Rutgers had two parts while the written ones had three parts, possibly just like the parts at Columbia.

Fine. Orzel reasonably defines classical physics as anything found up to 1899. In 1900, modern physics (as understood by the exams) began – that already included Planck's modern derivation of the black body curve. Orzel also says that "modern physics" has ended in 1950 – we've probably lived in postmodern physics for some 67 years. ;-) But what he really discusses isn't so much about the "new vs old" physics but rather about the "chronological vs achronological" education. It's time to reiterate the advantages and disadvantages.

When I was a curious kid, I really didn't give a damn about the history and similar humanities things. One may say that I am "much more" into all this kind of stuff than when I was a kid. In particular, I would always resolutely insist that it just doesn't matter who exactly discovered something, when, how many siblings she or more likely he had, and so on. So why can't the students be told the pure truth about the laws of Nature, without all the random historical and sociological decorations?

And yes, that's how the studies often proceed: one just lists the axioms, the evidence, and derivations of additional truths from them. But as Orzel correctly says, this approach is usually successful only in the advanced courses – which are basically addressed to someone (e.g. graduate students) who have already mastered much of the physics at a "simpler or less rigorous level".

When the "most up-to-date insights" approach is used for younger students such as undergraduate freshmen, it usually ends up with very serious problems. Note that I motivated this approach that is "free of history and sociology" as a way to increase the percentage of the "pure physics" and decrease the percentage of the historical and sociological junk in it. However, ironically, the effect of this effort is often opposite because the motivation for many claims, moves, and definitions tends to be so incomprehensible to the students that they view the whole teaching process as a manifestation of the absolute dictatorial authority of their instructor who is pumping some weird stuff to their skulls.

So psychologically, it has some advantage to follow the history chronologically. After all, some things are "easier" to be learned and understood than others and when an individual kid or person is learning about the world around him, the process is rather similar to the historical collective efforts of the mankind that was learning some things in the past. It makes some sense for a 10-year-old kid to know "basically everything" that reasonably educated people knew about physics in the ancient Rome. By the age of 12, the kid should surely know lots of things known to Galileo or Newton or their contemporaries. Around the age of 19, a physics student should unquestionably be familiar with many physics insights from the early 20th century, and so on. If you know nothing about string dualities of the 1990s before your 50th birthday, you are a retarded kid who was left behind but it may already be too late. ;-)

A problem of this strategy to follow the history is that historically, people also used to believe lots of things that we consider incorrect or misleading or otherwise unworthy. We naturally want to suppress all of these dead ends because it's a waste of time – or something worse – when students are learning outdated ideas.

However, the complete elimination of this wrong historical stuff is bound to be counterproductive primarily because
[t]hose who cannot learn from history are doomed to repeat it [or its mistakes].
as George Santayana said. This quote was probably meant to be mostly about wars and similar stuff. But I think that it largely holds for the history of science and physics, too. If you don't know anything about the luminiferous aether and you spend lots of time by inventing ideas at a certain level, you are very likely to rediscover it. In the same way, you will probably rediscover phlogiston, creationism, Planet X, loop quantum gravity, and many other straightforward enough ideas that the current science considers incorrect.

So does it really make sense to avoid those in the education process? They will steal some of the students' time, anyway. I think that a part of the education process should be dedicated to many of these wrong ideas – and explanations why science doesn't consider them correct today. Obviously, many wrong scientists and crackpots have spent an incredible amount of time with the work on details of their flawed theories and you don't want the students to waste this huge time again – they would need many lives of time to do that, anyway. But it doesn't make sense to promote the wrong theories to a taboo.

These wrong ideas are natural "local minima" of the energy in the space of possible ideas which is why it's largely unavoidable that some students will be stuck in these minima and believe creationism, loop quantum gravity, or any other wrong theory from the dumping ground of science. It makes no sense to deny this fact – or pretend that everyone will avoid the trap just because the trap isn't ever mentioned. Even if the kids don't hear a single letter about wrong theories in the university, they will hear lots of wrong and outdated sciencey things from their relatives, friends, in their church, mosque, Greenpeace convention at the treetops, or at the Perimeter Institute. And some of them will truly rediscover these flawed ideas on their own.

The chronological teaching is particularly well-motivated in the case of quantum mechanics because, as I have argued many times, the founding fathers of quantum mechanics really understood the new logic of quantum mechanics – why it was new, what the novelty was really all about, and why this novelty was unavoidable or experimentally proven – much more than the average physicists who are living today. Lots of folks who are alive today are still dreaming about some kind of restoration of classical physics – in one way or another. But folks like Heisenberg, Bohr, Pauli, Dirac, Jordan, von Neumann, and others really understood why it was impossible. They could tell you lots of arguments and thought experiments that led to the correct conclusions – and they could always find mistakes in the reasoning by others, e.g. Albert Einstein, who were trying to find a problem with quantum mechanics or a theoretical explanation of the quantum phenomena that remains spiritually rooted in classical physics.

Yesterday I was planning to write another blog post about the quantum foundations – a clarified blog post explaining why any realist theory of matter etc. unavoidably leads to unacceptably huge heat capacity of gases etc. If your atoms have a nonzero spins and if you assume that the maximum projection of the spin with respect to the axis \(n\), i.e. \(j_n = j\), defines a state that is in principle distinguishable from all others corresponding to other axes \(n\), then you will simply have at least a two-sphere-worth of distinct, mutually exclusive states. Each atom will contain at least the latitude and longitude to parameterize this point on the \(S^2\). And this degeneracy of states will equip the gas with a high entropy.

The entropy is really infinite because the number of points on an \(S^2\) is infinite – and even the logarithm of this number is infinite. This is actually true not only for an \(S^2\) but for any "continuum". Whenever classical physics contained continuous degrees of freedom, and it basically always did, the entropy was naturally infinite and the only way how you could get a finite result was to impose a "cutoff on the precision" with which the points on the phase space could have been distinguished from each other. The undetermined choice of the cutoff was also responsible for the "unknown additive term in the entropy" that was always making the classical statistical physics (and especially the third law of thermodynamics) "ugly and incomplete". Quantum mechanics does these things naturally – \((2\pi \hbar)^N\) is the natural "minimum cell in the phase space" and the volume of a region in the phase space basically becomes an integer within quantum mechanics – this integer is identified with the dimension of the relevant Hilbert space. Quantum mechanics also fixes the additive constant and it allows you to say that materials frozen to \(T=0\,{\rm K}\) have \(S=0\) instead of some undetermined \(S_0\).

The founders of quantum mechanics understood these things because they had actually spend some time – before the victorious advances around 1925 that actually worked – with the unsuccessful efforts to explain away the ultraviolet catastrophe, low heat capacity of materials, and many other things that apparently (and, yes, really) violated the predictions of classical physics. Much of their wisdom was accumulated during their serious but failed efforts to make the classical theories work. What doesn't kill you makes you stronger.

Contemporary physicists – and physics students – are never going through this exercise of "guaranteed to be doomed" attempts to explain all these basic features of Nature using a basically classical theory. Or at least, they don't have the same standards and don't demand themselves to actually calculate the numbers and other details – "philosophically pleasing" vague garbage is often sufficient to satisfy many people today. So lots of them end up completely misunderstanding why e.g. Bohmian mechanics is a pile of junk that suffers from almost all the lethal problems as the failed classical theories in the pre-1925 but modern era.

So even though I didn't like excessive "history and sociology", especially not in physics classes, I would actually include a significant amount of it. After all, it's impossible – and probably undesirable – to shield physics students from all sociology, history, and other inferior social sciences and other pseudosciences. And by learning some history, they may understand why some attempts that are repeated all the time (with refreshed names) are indeed failing.

Finally, let me comment on related topics that transgress the university education. As a kid, I had various books that affected me and one of them was
Joe Kaufman's "What Makes It Go? What Makes It Work? What Makes It Fly? What Makes It Float?" (1971)
The title seems rather long so you will surely be pleased to learn that the 1981 Czech translation was titled "Why And How" ("Proč a jak"). The compactification of the title is simply clever, isn't it? Maybe I could still find the book somewhere but I don't see it right now. The book explained how many things – especially engines and other man-made and engineering products and/or parts of the economy – worked. I don't remember almost any details – except that I know that two pages contained two mothers with their kids, a brunette and a blonde. One of them was using a gas oven and the other one had an electric oven. The pages said something about how the two ovens work which I found at least somewhat insightful when I was 7. ;-)

Can you remember that you didn't really know most of these things?

There are all the questions about "why the humans are around" and "how they reproduce". At some moment, you learned that there are no birds who are bringing the children. But the more correct answer opens many other questions. How the organs, cells, evolution work etc.? A typical natural scientist focuses on the question "how things in Nature that would exist even without humans work?" But this Kaufman book was more engineering-oriented.

It was answering all the questions about "how this device or another that men invented and produce work?" How is it possible that those things work? That they were invented? Why do they have the pieces they have? And so on.

At the end, there are lots of questions like that – and one may understand "how the world works" at many levels of detail. Once the dust settles, I do believe that the chronological attitude is basically a very sensible way to learn about all these things. Many complicated things have evolved from the simpler ones – it's the spirit of evolution that works in biology but it also works elsewhere. As the matter in the Universe, life on Earth, and the human civilizations evolved, new useful structure and improvements were being added (and sometimes subtracted). In particular, I think that the people who completely fail to understand economics and politics and "what is needed for the human society to work well and to advance" – for example, the leftists – may blame their misunderstanding of the "contemporary politics and economics" on their ignorance of the history, too.

In effect, lots of kids and teenagers were already brainwashed by some similarly "ahistorical" lessons about the human society. They are made to think about some "progressive utopia" in the asymptotic future as their zeroth approximation of the human society. In Europe, their understanding of the history starts after 1945 when something like (the United Nations and) the European Union was created and established a paradise on Earth – which was previously Hell, one that doesn't deserve to be studied – and the remaining task was to make the society perfectly egalitarian and PC. And they're trained to react anxiously to anything that deviates from such a "progressive utopia". But for some reasons, these kids are never taught why the progressive utopia is a pile of šit, why it can never work well, and – which is relevant in this discussion – why it has never worked like that.

They're not taught that many things that they are trained to hate – e.g. many sorts of asymmetric relationships between the people – have been absolutely vital (and still are vital) for the humans to get where we are and to enable further progress (or at least reproduction). They don't even learn that the national interests, wars, and similar things have been inseparable parts of the human societies throughout the human history. They don't understand that people must divide their duties and specialize for things to work well – and they have always done it. They don't understand how the concentration of capital was essential for the transformation of the human society from a bunch of poor monkeys with bare buttocks to an actual civilization. They don't understand that almost any change or regulation in the society costs something and one simply can't neglect the costs in most cases. They don't understand that people who aren't accountable will start to abuse their position, that in most of the contemporary dilemmas, the government isn't the solution of the problem but the problem itself. They don't understand that it's been often normal or desirable to defeat, enslave, or reeducate another tribe or nation.

In the Western schools, kids are often trained as overly sensitive politically correct slaves disconnected from the historical truth, from their national or religious heritage, from their families, sometimes even from their sexual identity, and lots of other things – kids are reduced to jihad-like building blocks of a global, non-national, perfectly egalitarian, significantly and uniformly colored, half-lesbian, half-gay, half-transsexual pseudohuman society who don't have any balls (and breasts). The communist regime that I was exposed to as the kid did deform various things at school but it's a sad fact that the deformation at today's PC schools is worse than what we knew in the Soviet bloc of the 1980s and many teachers and administrators who are responsible for these deformations are far more enthusiastic about their delusions than most Czechoslovak teachers were in the lukewarm "advanced socialist society" of the 1980s.

This is a more political discussion than the discussion about the "historical teaching of physics" but some similarities between the two topics are obvious. The message of this essay in both situations is:
The world was imperfect, cruel, inhuman, animalistic, violent, ignorant, brainwashed, confused etc. in the past but if you're educated to be completely ignorant about the past – or if you even treat the past as a dirty taboo that you don't want to hear about – you are or the whole human society is basically guaranteed to be even more clueless, unusable, not very viable, easy to be brainwashed and ready to become an accomplice in even worse cases of mass manipulation, wars, and suppression than your nation's history has ever known. Without knowing their roots, people are guaranteed to repeat the history's mistakes and put some of them on steroids.
And that's the memo.

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