Monday, January 17, 2011

Can the laymen learn advanced physics?

I have actually downloaded 10 and watched 6 iTunes Stanford lectures by
Lenny Susskind on supersymmetry, grand unification, and string theory
After having listened to a big part of the first six lectures - which have been about supersymmetry so far - I can wholeheartedly recommend you to download them if you have an iPhone or iPad or iPod Touch. They seem excellent and relaxed at the same moment.

It's my understanding that Lenny's explanations were addressed to the Stanford Continuing Studies Program which is probably organized for older and retired folks who decided to become students - somewhat older students than the typical students you usually think of. Also, I think that none of them has been trained as a high-energy or theoretical physicist.

The lectures are fresh and interactive. You can hear lots of questions from the audience and I would say that a large majority of them shows that the students didn't have much chance to understand Susskind's explanation which were accessible but still kind of advanced.

Don't get me wrong. There exist situations in which the students actually manage to catch a mistake that Lenny has made. For example, he says that a double Grassmannian integral vanishes because of one factor but it vanishes because of the other; or when Lenny expands exp(iX)exp(iY)exp(-iX)exp(-iY) to show the relationship between commutators at the Lie group and Lie algebra levels, some people in the audience are actually more capable to apply the distributive law than he is, in order to isolate the right coefficient in front of the [X,Y] term which is -1 (arising as -2+1 for the XY terms and -1 for the -YX term) in my normalizations.

But in all these cases, they're either about insights that the math-oriented people have known since their childhood - like the distributive law - or rules that Susskind would have explained just a few minutes earlier.

Otherwise, the bulk of the questions could be classified as evidence that the explanations were pretty much hopeless. There have been many patterns of flawed thinking that I wanted to remember - except that I have forgotten many of them. Some of them mix the particular concepts with totally different - or very remotely related concepts. They can't distinguish the Higgs boson from the vacuum - and many other confusions that may look incredible to a physicist.

There is one extra laymen's pattern of a "fake superior understanding". For example, Lenny has been told by his student that in equations similar to
L|psi> = 0,
he should have written
L|psi> = |0>
instead. Obviously, the correction was completely wrong and showed that the student couldn't have possibly understood the complicated explanations about the supersymmetry because he couldn't have distinguished the vanishing vector on the Hilbert space from the vacuum.

Now, I hope that I don't have to explain you the difference. The zero vector has length equal to zero and if you add it to anything, you get the same anything back. The vector "vacuum" has length equal to one and if you add it to something else, you get a different vector. This text is not supposed to be a catalog correcting all frequent technical mistakes of this kind.

Instead, I want to say something more general. Why would you try to argue that the vector zero should be replaced by the vacuum? Well, my hypothesis is that it's because you have seen the symbol |0> somewhere and you didn't know what it actually meant - at least not at any reliable level. And you have never managed to find it out. So you decided it had to be just a fancy way of writing zero that is appropriate for the vectors in Hilbert spaces.

So you could have thought: the physicists want to look fancy so instead of zero, they write this funny zero in the Dirac bracket. For me to look smarter, I have to write |0> instead 0, too. It is not surprising that such a person will correct Leonard Susskind when he writes just 0: if you want to be our peer, Susskind, you have to learn how to write the fancy |0> as well.

Except that this is not how these vectors work. And much more generally, it is not true that physicists like to write complicated symbols and use convoluted notation just for fun, in order to look smarter. In fact, physicists don't think that other people are smart just because they use an unnecessarily complicated notation or terminology. They try to use as simple notation and terminology as possible so that they can effectively exchange ideas, without a risk of errors, and without the need to rewrite lots of older literature. Physics tries to describe complex and confusing phenomena in a crisp, comprehensible, and unambiguous language.

Many people haven't yet noticed that this is how physicists are thinking. Physicists - at least the good and/or intuitively powerful ones such as Leonard Susskind - are no-nonsense people.

There have been many other questions that were bizarre - well, the same kind of questions you often see on the Internet except that those were simply asked by "Stanford students" of some unusual kind. But otherwise there was no difference. A much broader class of these questions could be described by saying that the students wanted to convince themselves that they understood something except that they had to know very well that they didn't.

Quite generally, to understand what various concepts - such as the Hilbert space and operators acting on it or virtual particles or anything else - mean, you have to play with these tools yourself, ideally in the silence of your home, uninterrupted by others. One can't understand too many things just by hearing them from others. Well, one can parrot others - but parroting others is something very different from the understanding.

Each person's mind is innately designed - and has been shaped by the experience - somewhat differently. So each person also has somewhat different obstacles as well as flawed and inappropriately overgeneralized assumptions that he or she has to overcome in order to understand something. That's why an individual learning or research is almost always necessary for someone to understand some advanced physics.

For some insights, you may want to spend much more time than others in order to understand the thing - or, literally, in order to believe it. But in the case of other insights, you may simply be bored by other people's words because the thing looks obvious to you or you have at least no serious reason to doubt it even if you can't fully prove it. And sometimes you really know what the proof is and you think it doesn't deserve an extra minute of your time. Excessively slow comments about this topic that you hear from others will turn you off.

Topics such as supersymmetry depend on many layers of physics knowledge and there is almost certainly no shortcut that would allow one to understand supersymmetry without understanding the whole relevant subpyramid of knowledge - mechanics, abstract mechanics, quantum mechanics, classical field theory, quantum field theory, Feynman diagrams, group in physics, and other things. And I am talking not only about the full understanding that you need to acquire in order to do serious research.

I am even talking about the level of understanding that is needed for you to appreciate that a whole discipline of science isn't just meaningless hocus pocus (assuming that it's not) - i.e. to believe that the professional physicists that study a certain subdiscipline aren't completely deluded (assuming that they aren't). Even this more modest level of understanding if impossible without having mastered much of the pyramid of knowledge that underlies the particular topic.

To summarize, there probably exist no magic pedagogical methods that would allow one to master a portion of physics up to a certain point much more effectively than others with the same innate aptitude have managed to do. If you decide to speed up a portion of the education, you may pay a big price in the future. Without a sufficient experience and feeling for some questions, you will be permanently confused in the future which will probably slow you down much more brutally than if you learned the simpler material in much more detail. Certain insights and skills get recycles and reused very many times so it's a good idea to be damn sure about them.

All these things are difficult and almost tautologically, most people will always be ignorant about sufficiently advanced portions of science. At the same moment, it is critically important for the health of the society that for every level of science, there exists a certain sufficient number of people who have a clue what is going on. The profile - the dependence of the number of people on the degree of complexity of a scientific issue - is primarily dictated by the distribution of the human IQ and the people's will to dedicate a certain amount of time to certain abstract questions.

However, it's conceivable that the profile could be improved. In other words, people who are responsible for the education may want to think more carefully about the difficulty of the stuff that is being taught to various students - and about the number of students who will be showed the material at a certain degree of complexity - to achieve optimal results.

In particular, I think that general insights that are likely to be reused many times - and those that are likely to play an important role in future neverending polemics - should be given much more exposure at schools. On the other hand, insights that are only used "once" and that you may immediately forget - and that you may quickly re-learn when you need them again - should be suppressed.


  1. This is a very insightful article.
    The comment that
    "If you decide to speed up a portion of the education, you may pay a big price in the future. Without a sufficient experience and feeling for some questions, you will be permanently confused in the future which will probably slow you down much more brutally than if you learned the simpler material in much more detail."
    should be highlighted to every aspiring hotshot scientist or researcher. A fuzzy grasp of core ideas is a permanent handicap to understanding.

  2. Just a datapoint. I'm a 30-something professional who never went past pre-calculus in college, and I've been trying to learn more about advanced math and physics for the past couple of years. I've found both the Khan Academy videos on math and the Susskind videos on physics to be tremendously useful.

    I'm not trying to be a physicist, and I'm not really trying to understand the topic on a deep level. For me, so far, it's really just about getting a rough idea of the territory. I've also been frustrated watching the Susskind videos by what I've thought of as kind of 'dumb questions', but it's also been kind of edifying to see Susskind himself get lost in the math from time to time. This is complicated, difficult to understand stuff, and the experts can get tripped up on even the 'basics', if they aren't careful, which is important to understand I think. It kind of demonstrates the importance of being methodical and careful.

    I can't say that I remotely understand how to 'do' the math, but I do now have a rough idea of how the pieces fit together in a lot of cases, and I can now 'follow along' with physics papers and don't feel like I really need a pop-science explanation from a science journalist to understand them -- or at least a science journalist wouldn't do much to improve my understanding.