In praise of coursebooks

Writing a coursebook is both a lot harder and a lot more rewarding than one might imagine.

Two months ago (or so) I was contacted by the physics department of the Regional Institute of Education, India, who asked me if I would be interested in writing a coursebook for secondary schools. It seemed like an exciting thing to do so, after going over the specifics and discussing the entire project, I accepted.

How it all started

The Institute had the purpose of the book set up right from the start (it was supposed to be a teacher’s resource) but, as I began to plan the contents of the book and draw up an outline, I felt myself gravitating towards making it slightly different from a regular teacher’s resource.

Part of the project involved updating existing resources that had been published in-house exclusively for the Institute but we quickly moved past that and expanded the scope of the project: rather than simply updating material (some of which I was not comfortable with anyway), it was finally decided that I would start from scratch, define my own scope, and get a completely free rein. I only had to ensure that I covered as much physics as (and, perhaps a little more than) we expect students to be familiar by the time they apply to undergraduate colleges.

Of course there is a committee of physicists going over every word I write, as there should be. Part of academia, for better or worse, is peer review and it helps keep things grounded, promotes arguments, prevents errors (at least better than what one man alone can do) and, as a whole, is expected to improve the quality of such works.

I also decided, at this point, that I would not write a teacher’s resource to accompany existing texts alone but, rather, re-write the coursebook itself, producing a single, combined text that would serve as both the coursebook for sixth form students and a teacher’s resource. I wanted it to be something both students and teachers could use in a classroom as well as something that was designed to enable self-teaching.

Bringing in a new perspective

Among the many things I was hoping to do, perhaps the most difficult was to think like potential student or teacher readers might. Standing about halfway through the first of two volumes now, it has been difficult to think about what questions they might have and what they might not think about that they should. I think it helps that I am young enough to still remember modern, early education compared to a fifty-year-old professor who has, in all likelihood, lost touch with being a student1 in the traditional sense of the word.

Writing a coursebook is ‘infinitely more work than you think, and it’s also much more satisfying’, says Anne Houtman of the Rochester Institute of Technology; this is a thought I am more than inclined to agree with.

I do have readers (who will go unnamed) who are helping out by reading the book as it is being written and questioning sections of the content, offering advice, pointing out errors et cetera, all of which have been incredibly helpful for me so far. I think it has bettered the textbook in a way I could hardly have done by myself.

The layout and approach is also something I have given considerable thought to. I finally decided on arranging the book as a main text and several side notes, the former being exclusively for students and the latter for teachers and readers teaching themselves. Keeping in tone with the older volumes (which my new volumes are intended to succeed) I have included several classroom activities that, besides regular laboratory sessions, will make physics more ‘hands-on’.

The philosophy behind the book

Although I would prefer to steer clear of big words like defining a ‘philosophy’ behind my book I do think it is important to be clear on the whys and on what problems I hope my book addresses.

Right from the start my biggest question was how I would handle mathematics in the book. Introducing mathematics as a standalone chapter and then moving onto physics, while appealing, is hardly the most effective method of learning in my opinion. Mathematics has to be taught in context to physicists rather than in the gloriously abstract regime so many mathematicians seem to prefer.

My solution was to have a sort of referential chapter at the start of the book that would outline all the mathematical tools a reader of the book would need. The introductions were all done in the context of physics, with examples they would have come across by then or would come across soon. More importantly, though, rather than being a dictionary of mathematics for physicists (which was what I was against) the chapter is intended to be something readers would turn back to constantly throughout their reading of the rest of the text.

This means most of the chapter invokes physical ideas from elsewhere in the book and, mutually, the two chapters would strengthen the notions introduced by each other. This has called for a constant revision of that particular chapter as the rest of the book is written, which is something I am fine with.

Also, on a deeper level, I want the book to address some problems I have, myself, seen many students experience. It could be something as specific as a calculus shock, where students are shoved into the manner of thinking and the ideas of calculus rather than eased into it2, or a complete lack of grip on the structure of a physics course, or worst of all, an examination-focussed, type-of-problem based learning rather than learning directed towards appreciating the ideas and thinking that underlies most of physics3 I will not bore you with the details of how I am addressing these, but if there is anything I have left out, I always appreciate ( text:a helpful e-mail).

The other major challenge has been problems. Problem solving is at the heart of physics and thinking up new problems creatively is notoriously difficult. In fact, all of this has given me a newfound respect for all the coursebooks we read and tossed aside during our formal education. Criticise a book all you want, but you cannot deny the effort that went into writing one4.

In praise of coursebooks

Says Anne Houtman, a behavioral ecologist and head of the School of Life Sciences at the Rochester Institute of Technology, that writing a coursebook is ‘infinitely more work than you think, and it’s also much more satisfying’. This is a thought I am more than inclined to agree with.

The manner in which an idea is introduced, the harmony between ideas across pages and chapters and volumes, and the thought that the words you put to paper will define how someone views the field for a long time are not so much daunting as constant reminders of the huge responsibility that comes with writing a good quality book. More localised concerns include ensuring the same notation across chapters and the same approach to making statements, offering proof and putting the mathematics in a physical perspective.

As Dr Houtman points out, coursebooks will effectively be reviewed by more peers and for longer in its lifetime than more than most research papers. Also, unlike papers again, coursebooks will likely be critiqued and reviewed by students and the public too (but in a manner different from most scientists’ reviews).

Although my intended audience are sixth form students, I have ensured that they are introduced to ideas they will encounter in higher studies too, and not merely verbally. This means, unlike older volumes of books from the Institute targeting students, my two volumes do not treat calculus as optional. There is some hand-holding but no spoon-feeding, although, by the end of every chapter the learning becomes more independent. I also managed to add in some external references for students and teachers interested in further reading because, just as there will be students who find the book hard to cover, there will be those who cover it with ease and may look for more reading materials.

All-in-all, perhaps this has been the only thing I have constantly looked forward to working on everyday besides my research; and I was right in my thinking the day I was first contacted by the Institute: this is exciting work. But it calls for more thought than I had ever expected and I like that too because it makes my work that much more meaningful for me and that is something I value greatly. Also, taking a moment like this to put my thoughts into words has been somewhat encouraging (not that I have ever had any shortage of that). And if you will excuse me now, I have a coursebook to write.

  1. All scientists are students, but not in the classroom sense, which is an entirely different thing from the constant self-teaching that most of us in academia are wont to do. ↩︎

  2. This is funny to some extent: schools rarely introduce arithmetic to young kids by calling it arithmetic, likewise with algebra. They are both is introduced as part of mathematics rather than as some complex technique supposedly important in the grand scheme of things. Calculus, on the other hand, walks onto the stage with an aura of toughness and complexity most people cannot understand. This is silly. It has, all through history, worked against calculus and left us with students who never could wrap their head around it because they were told it was difficult. And this is also why most non-scientists end up criticising higher level maths and physics as something they do not need in their daily lives: when one never learns to appreciate the nuances of calculus or trigonometry, they will never realise how often they can potentially make use of it to gain a different perspective on situations. ↩︎

  3. That last point felt nonsensical even to describe. ↩︎

  4. There are exceptions to this: some books are clearly devoid of effort and originality while others were written by ghost writers. These are both little more than disgraces and we should all probably agree to never speak of them again. ↩︎

Our universe: marble or wood?

The idea of a probabilistic universe did not appeal to Einstein.

If there is any fundamental quality of nature that has eluded physicists and sparked debates of a fearful scale, it is the question as to whether the universe has a simple (beautiful) underlying principle that runs quite everything in existence.

Undoubtedly, the dream of every physicist is, as Leonard Lederman creatively summed it up, ‘…to live to see all of physics reduced to a formula so elegant and simple that it will fit easily on the front of a T-shirt.’ On a serious note, this highlights the strong belief in most physicists that nature is elegance and simplicity bundled into one.

Physicist Albert Einstein likened this world to marble. In the pith his idea was that the world as we first see it would appear to the observer like wood. Various observations would seem vastly different, unpredictable and complicated. It was his strong belief that we could, on further investigation, chop off these wooden structures to reveal an inside made of marble. Marble he likened to an elegant and simple universe with predictability. Apart from the fact that wood and marble seemed, for some reason, to represent chaos and cosmos to Einstein, it was also an idea that would hold true for almost all discoveries in physics preceding, and including, relativity.

Maybe nature is fundamentally ugly, chaotic and complicated. But if it’s like that, then I want out. Steven Weinberg

From Newton’s laws to Maxwell’s equations to Einstein’s relativity, with every passing discovery we seemed to have united another chunk of our universe to form a whole; and it was as if we either found new explanations for phenomena or found that new, unexplained phenomena happened to be in coherence with previously explained processes/laws. It was like a work of fiction where everything, right up to the climax, would remain perfectly alright, going without a hitch and then, out of the blue, the whole idea of a world of marble collapses.

Einstein was one of the founders of Quantum theory through his explanation of the photoelectric effect wherein he said that light—much like was predicted for other forms of energy, by Max Planck—was really made up of discrete packets of energy he dubbed photons.

At first the idea appeared perfectly alright (and Einstein went on to win the Nobel prize for this many years later). To physicists, by and large, the idea seemed to boil down to one phrase: waves could, at times, act as particles.

The problem arose when Erwin Schrödinger took it upon himself—under the belief that the vice versa could also be true—to theorise how particles could convert into waves. After a year-long vacation, he returned to the physics society with his magnum opus, what is called the Schrödinger equation. Einstein and Schrödinger both believed then that this would describe the wave equation of a solid particle; but the reality was—as other quantum physicists like Max Planck, Wolfgang Pauli and Werner Heisenberg were quick to point out—this did not completely make sense.

At first both Einstein and Schrödinger were pleased with the resulting equation, but they had made a fatal flaw: they had failed to fully analyse the implications of the equation as soon as they realised it satisfied all properties they originally expected of it. And when the others studied it completely, they realised that it allowed for almost fantastic occurrences. Quantum physics was predicting that we needed to crack the marble to reveal a world of wood—and nothing could prove it wrong.

Einstein rejected the theory almost in its entirety simply because it went head-on against his personal belief of a world made of marble. When chance was introduced to the very core of physics; when we realised that these new developments allowed for the mathematical possibility of the unthinkable and the presence of a chance, however small, of contradictory occurrences, Einstein and Schrödinger shared the idea that this was outrageous. This even prompted Einstein to write memorable words about it:

Quantum mechanics calls for a great deal of respect. But some inner voice tells me that this is not the true Jacob. The theory offers a lot, but it hardly brings us any closer to the Old Man’s secret. For my part, at least, I am convinced that He doesn’t throw dice.

The Old Man was how Einstein referred to God in most of his writings. This debate rages to this day, even if subtly. While quantum theory, siding with wood, has not found a phenomenon that can prove it wrong, neither has relativity, which sides with marble.

Perhaps the most powerful analogy we have to date is that of Schrödinger’s Cat. Quantum theory tells us that an observation depends entirely on the observer—literally. Let us have Schrödinger’s Cat clarify this: imagine you had a box with a cat in it. It was alive when you put it.

You keep it closed for a while (that is to say, you are not making any observation of it as yet). Then you open the box and find the cat happily playing, or sleeping sound. But what quantum theory suggests is that the only reason the cat is doing any of that is because you are observing it.

To go a step further, when you are not observing it, the cat may be doing something else. While this may seem all too commonplace, what is startling is that quantum theory defines the clause something else very differently: the theory, in fact, allows for the possibility that the cat may be dead when you are not making an observation of it!

A further complication is that neither of these two major theories, Quantum or Relativity, come in the other’s way. While quantum physics laws rule the smallest of particles, atoms, electrons and the like, relativity seems to apply to the largest of them, like our Earth or even our whole massive galaxy. To clarify this further, quantum theory actually breaks down at relativistic dimensions and relativistic laws break down at atomic levels.

It therefore seems to me at times that there is a possibility of these two theories themselves being manifestations of the same fundamental principle; that our race to uncover the basic law that runs the universe really lies in our ability to see through these theories at the point where they appear to contradict. Perhaps, like atoms making up galaxies, the quantum theory is really a microscopic view of relativity.

Perhaps the reason why quantum theory backs wood and relativity backs marble is because quantum theory really makes up relativity so long as we are able to take ten steps aside and view it from a different angle. Perhaps, in the end, wood is what observation suggests to us and marble is what investigation does. Perhaps the world is really made of marble. We are just not seeing it with a perspective that is broad enough.

You may not have anything to do with physics, or you may be a physicist yourself, but do share your views below. What do you think our universe is made of? Does it have an underlying principle? Is it predictable, or does chance really rule it? Or will we just have to excuse ourselves, ultimately, like Schrödinger who said, ‘I don’t like it. I’m sorry I ever had anything to do with it.’?