In Praise of Textbooks with Tons of Formulas (or: The Joy of Firefighting)

I know. I am repeating myself.

Maurice Barry has not only recommended Kahneman’s Thinking, Fast and Slow to me, but he also runs an interesting series of posts on his eLearning blog.

These got mixed and entangled in my mind, and I cannot help but returning to that pet topic of mine. First, some statistically irrelevant facts of my personal observations – probably an example of narrative fallacy or mistaking correlation for causation:

As you know I had planned to reconnect to my roots as a physicist for a long time despite working crazy schedules as a so-called corporate knowledge worker. Besides making the domain subversiv.at mine and populating it with content similar to the weirdest in this blog I invented my personal therapy to deflect menacing burn-out: I started reading or better working with my old physics textbooks. Due to time constraints I sometimes had to do this very early in the morning – and I am not a lark. I have read three books on sleep research recently – I know that both my sleep duration as well as my midsleep are above average and I lived in a severely sleep-deprived state most of my adult life.

Anyway, the point was: Physics textbooks gave me some rehash of things I had forgotten and prepared me to e.g. work with the heat transfer equation again. But what was more important was: These books transformed my mind in unexpected ways. Neither entertaining science-is-cool pop-sci books nor philosophical / psychological books about life, the universe and everything could do this for me at that level. (For the records: I tried these to, and I am not shy to admit I picked some self-help books also. Dale Carnegie, no less.)

There were at least two positive effects – I try to describe them in my armchair psychologist’s language. Better interpretations welcome!

Concentrating and abstract reasoning seems to be effective in stopping or overruling the internal over-thinking machine that runs in circles if you feel trapped in your life or career. Probably people like me try to over-analyze what has to be decided intuitively anyway. Keeping the thinking engine busy lets the intuitive part do its work. Whatever it was – it was pleasant, and despite the additional strain on sleep and schedule it left me more energetic, more optimistic, and above all more motivated and passionate about that non-physics work.

I also found that my work related results – the deliverables as we say – improved. I have been the utmost perfectionist ever since and my ability to create extensive documentation in parallel to doing the equivalent of cardiac surgery to IT systems is legendary (so she says in her modest manner). Nevertheless, plowing through tensor calculus and field equations helps to hone these skills even more. For those who aren’t familiar with that biotope: The mantra of other Clint-Eastwood-like firefighters is rather: Real experts don’t provide documentation!

I would lie if I would describe troubleshooting issues with digital certificates as closely related to theoretical physics. You can make some remote connections between skills that sort of related such as cryptography is math after all, but I am not operating at that deep mathematical level most of the time. I rather believe that anything rigorous and mathy puts your mind – or better its analytical subsystem – in a advanced state. Advanced refers to the better prepration to tackle a specific class of problems. The caveat is that you lose this ability if you stop reading textbooks at 4:00 AM.

Using Kahneman’s terminology (mentioned briefly in my previous post) I consider mathy science the ultimate training for system 2 – your typically slow rational decision making engine. It takes hard work and dedication at the beginning to make system 2 work effortless in some domains. In my very first lecture at the university ever the math professor stated that mathematics will purge and accelerate your brain – and right he was.

Hence I am so skeptical about joyful learning and using that science-is-cool-look-at-that-great-geeky-video-of-blackholes-and-curved-space approach. There is no simple and easy shortcut and you absolutely, positively have to love the so-called tedious work you need to put in. You are rewarded later with that grand view from the top of the mountain. The ‘trick’ is that you don’t consider it tedious work.

Kahneman is critical of so-called intuition – effortless intuitive system 1 at work – and he gives convincing accounts of cold-hearted algorithms beating humans, e.g. in picking the best candidate for a job. However, he describes his struggles with another school of thought of psychologists who are wary of algorithms. I have scathed dumb HR-acronym-checking-bots at this blog, too. But Kahneman finally reached an agreement with algorithm haters as he acknowledged that there is a specific type of expert intuition that appears like magic to outsiders. His examples: Firefighters and nurses who feel what is wrong – and act accordingly – before they can articulate it. He still believes that picking stocks or picking job applicants is not a skill and positive results don’t correlate at with skill but are completely random.

I absolutely love the example of firefighters as I can literally relate to it. Kahneman demystifies their magic abilities though as he states that this is basically pattern recognition – you have gathered similar experience, and after many years of exposure system 1 can draw from that wealth of patterns unconsciously.

Returning to my statistically irrelevant narrative this does still not explain completely why exposure to theoretical physics should make me better at analyzing faulty security protocols. Physics textbooks make you an expert in solving physics textbook problems, this is: in recognizing patterns and provide you with ideas of that type of out-of-the-box idea you sometimes need to find a clever mathematical proof. You might get better in solving that physics puzzles people enjoy sharing on social media.

But probably the relation to troubleshooting tech problems is very simple and boils down to the fact that you love to tackle formal, technical problems again and again even if many attempts are in vain. The motivation and the challenge is in looking at the problem as a black box and trying to find a clever way to get in. Every time you fail you learn something nonetheless, and that learning is a pleasure in its own right.

DOD mobile aircraft firefighting training device

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38 thoughts on “In Praise of Textbooks with Tons of Formulas (or: The Joy of Firefighting)

  1. Pingback: Learning General Relativity | elkemental Force

  2. Pingback: On Learning | Theory and Practice of Trying to Combine Just Anything

  3. Yes, 7 is too many so lets start at the top again. Each time PISA or TIMS results get published there’s a flurry of activity between governments and the press with the focus usually on how “our” country ranked next to “others” with the implication that we’re either really really superior and wonderful or in terrible shape. It seems to me though that two things go badly wrong:
    1–we forget to compare ourselves now to how we have been previously, in other words compare apples to apples
    or
    2–really distort the whole thing and start focusing our entire energies to teaching toward this test; something that we know is distorted as tests are only one among several indicators that need to be used together.
    On balance I would say a resounding yes to international testing but in the same breath I would also say “Please muzzle the politicians and instead read the discussion that is also published as well as the reaction from the educational (as opposed to political) community.” The truth and usefulness of these instruments is something that cannot be transmitted, understood or used easily.

    • In Austria standardized, centralized tests for the final exams at high schools are just being rolled out – and critical experts also fear that this will foster “teach to the test” mentality.

      • They’ve always been around on Newfoundland. In fact, I led that process, on a provincial level, for physics and earth science for two years. To some extent it does change things for the worse and I I said that it does not happen here that would be untrue.
        We get around it in several ways though.
        1. Teams of teachers construct the test items.
        2. A separate team of teachers validates the test, that is, ensures that it matches the table of specifications for the test.
        3. The final grade is a shared evaluation, ideally a 50:50 split between a mark the school sends in and the raw score from the test.
        4. A statistical analysis is done, class by class to ensure that school-submitted marks are not inflated or deflated. When this is detected–and it happens–then the school marks are adjusted.
        It’s sort-of okay. Most of us see this as a necessary evil; a means to ensure that grades mean something. I would like changes though. Two come to mind: 1–I would rather that the provincial exam counted for 30%, not 50% and 2–I would like to see us develop game-based simulations that would be substituted for many test items; put students in a more or less real situation and let them apply physics to sort it out.

        • I understand the idea of standarization – at a global level – and mitigating the actions of unjust teachers. In Austria we use to quote a famous novel, about a student who killed himself because he believes he failed the math exam. Probably we have a tradition of sadistic teachers, I don’t now.

          It might be odd but I wished final exams were more “socratic dialogues” about concepts and having a student developing ideas (incl mathy derivations in front of you e.g.) rather than anything that lends itself to standardization. But a confession: As a teacher or trainer I really, really loathed designing tests and grading unless it was an oral exam.

          You might argue this is the most subjective of all but I feel it is what is closest to the “exams” you will face later in life. I am wary of “standardization” and “quality management” re any aspect of life or work so I only worry about teachers that will either inflate grades or tortue students:
          Wouldn’t it help the basic idea more if teachers are better trained to cope with the difficult task of judgment and/or if students who want to become teachers are carefully picked in order to meet that requirement? I mean if the money thrown at standardization would go into “psychological” education or support of teachers? I know from teachers that today parents nearly sue you if their kids don’t get an A – for sure not an easy thing to deal with. Standardization moves the accountability away from teachers to some anonymous, unassailable bureaucracy in a sense (from the perspective of parents)… It sounds kind of right – but I feel it is as weird as “objective” and “neutral” algorithms picking job candidates. Our society doesn’t reward or encourage personal accountability for difficult decisions – and I don’t like this.

    • In defense of PISA, if you look at the math sections they look perfectly reasonable. And you don’t learn math by rote.

      When Germany did terribly in the first PISA results it helped to quickly identify one of the main shortcomings: Germany failed its immigrants (partly by pretending they weren’t immigrants but only temporary residents).

      There is no program to teach kids German if that’s not their first language. This way generations were lost by condemning them to failure. Compare and contrast to Canada, were it is perfectly normal for immigrants to rely on pre-school and kindergarten to teach their kids English. And the teachers are well qualified and capable at doing so.

      The fact that the US is doing so dismal is really not surprising either. After all the same disparity shows up in other quality of life measures as well e.g. infant mortalitywhere even Cuba has consistently out-performed the US. The country has inner city poverty levels and a wealth disparity on par with many 3rd world countries. And it is this (growing) undeserved sector of the population that puts a massive drag on these metrics.

  4. There’s a lot in this post–as is often the case–but by far my favourite bit is the assertion that we do no good when we pretend to make things easy by either dumbing it down or by resorting to system 1 when we really need system 2. This cannot be understated and is something that bears repeating!

    • Thanks, Maurice! I forgot to reply to this one in this fractal structure of comments 🙂 I believe this is related to instant versus delayed gratifications as the psychologists say. Using system 2 (forcing yourself to use it) rewards you later with that expert’s magic Kahneman mentions. However, this will not happen if your attention span just covers skimming “science memes”.

  5. I’ll be honest Elke in reporting that after reading this post I found myself thinking quite hard about what it was your were trying to get across. Perhaps it is something in the last couple of paragraphs. You’re asking what makes for a good problem solver. And I believe you’ve provided an answer which is applicable to all fields of inquiry … not simply IT or theoretical physics. The reading you describe is simply predisposing you to a condition of mental flexibility … that is all. If you happen to learn something during your early morning sessions that is simply a dividend of pushing your mind into a state of relaxed preparedness (what a weird way of thinking about it). Although I hate the phrase, it is important that you think outside the box when problem solving. One needs to stand away from the problem and look at it from the outside. Being on the inside has too many distractions and also there’s too much of a feel that one should solve the problem using tools and solutions that others have already used. Sometimes we had to come up with unique solutions … and this only happens from the outside. To be able to think on the outside you have to be flexible and willing to fail. Your early morning reads are giving you the mental flexibility needed to solve complex problems. You aren’t finding solutions in the equations … you’re making your mind work through avenues that might be useful later. Once a mental avenue has been experienced … whether to solve a real-world problem or not … it is easier to travel that avenue once again. The work you are doing is preparing you to think broadly and unfettered. There … have I gotten it? D

    • Thanks for the great analysis, Dave! It was more a stream-of-consciousness post – I am not sure if I wanted to get a message across. And I was really interested in interpretations – I knew clever commenters would come up with insights! 😉
      “Relaxed preparedness” is a great term – I can relate to that, and also to “thinking outside the box”. But I guess we feel the same way when using that phrase: It has been beaten to death by management consultants and self-help gurus … and these do often not justice to focused real-world problem solving. “Out-of-the box” sounds so grand and so fluffy – and if somebody without subject matter expertise would be able to make a substantial contribution to problem solving by throwing in some “creative” remark. (Problem there is a hidden message / rant in this post I need to uncover ;-)).
      But you described it very well: Flexibility, willingness to fail, and “making your mind work through avenues that might be useful later”. You also said “You aren’t finding solutions in the equations” which is similar to NicoLite’s comment about the benefits of solving physics puzzles when you actually do not need to “perform” and succeed. Yes – the paradoxical effect of succeeding effortless if you don’t have to.

    • That’s an interesting point–and one I find myself in total agreement with. So then I have to contrast what we need to be doing with our young people in school with what we relay are doing. Despite all of the talk about 21st century skills it seems to me that schools in all of our places (USA, EU and CA) are still devoting an inordinate time to one type of learning–that which comes from books and such. I was horrified over the fall when I learned how few physics labs are actually being done any more. When I taught we did between 10 and 12–and we did that in distance ed too. Now, it seems that the expectation is that students only need to around 6 per year and, get this, most don’t even do that. Many do none at all. How in the world can problem solving ever be encouraged if students don’t get to face the real world, whether it be through motion apparatus, laboratory chemicals and glassware or living (or once living) material!

      • And that doesn’t even open the can-o-worms that we’ve got here in the States which requires that schools perform to certain standards to assure the flow of federal funds. No longer are teachers teaching in ways that encourage students to think creatively … even though there’s much lip service given to learning by inquiry, I’m not sure that really happens. Am I sounding old or perhaps disillusioned? D

        • It’s not Cynical at all. I have heard whiny, one sided litanies of complaint about the new standards. Complaints that book down to this: I don’t want to change. That’s not what you are saying at all though. Dave, we are now two for two on one thread line 🙂 we get some of that here but to a lesser extent as provincial departments of Education tend to be more sensible than are federal ones (in Canada education is NOT federal) so the testing tends to be used to evaluate programs not schools. Yes there’s some of that but it’s a bit tempered. That said we are not devoid of wing nuts 🙂

          • I know that good schools exit. I know that good programs exist. I know that good teachers exist. I know that there are students out there who are genuinely learning how to think and how to learn … and they’ll be the ones who go on to do good things upon graduation. I worry however about that least-common-denominator … what can we say about that pool? Will it fall prey to the flavor-of-the-day sort of programs that we tend to have today? Please say something positive Maurice! D PS: I think we’ve departed, somewhat, from what Elke was trying to say to us!

            • Let’s start with politics and let’s not talk about normal people but, rather, the dyed-in-the-wool extremists who often dictate policy. So in general…
              A democrat (or in CA, New Democrat ) believes in the goodness inherent in everyone. There are no bad people, only bad choices. Schools should capitalize on this and focus on developing the individual, not the herd.Personal best is what counts. Democrats think republicans are mean because they don’t feel this way. They certainly should not be left in charge else we shall all be enslaved to the system.
              A Republican (or in CA, a Conservative) believes that we are all fundamentally flawed and that there is a clear difference between good and evil. We need to be kept within our limits or else. Schools need to deal with the realities of life: the need for a strong economy buoyed by people who are at some level lazy and therefore need to be …errrr…watched. Schools need to be kept in-line and need to focus on practical stuff. Republicans, by the way, think that democrats are naive and a bit stupid; they certainly should not be left in charge or the country will go bankrupt.
              So that means for the US, which has an education system governed federally that there will always be bitter acrimony. Each side thinks the other a bunch of incompetent nincompoops and that the ed system they create is asinine.
              Funny–what with Apple, IBM, GM, Ford, Intel, NASA, Google, Microsoft, Boeing (I’ll stop here) coming from its kids the US system seems to be working reasonably well to me 🙂
              Here’s something nobody in the US is talking about: It tries to educate EVERYONE and a significant proportion of US kids (a) come from socially disadvantaged homes and (b) do not speak English well (the language in which they are evaluated). The US plays nice and gets all of its kids to write the tests. The results are therefore reasonably representative. Other countries do not play so nice, instead of finding all sorts of reasons to omit the results of weaker students. When you see a country ranking high ask these questions: (1) is the subject in question the only thing the kids focus on (2) is it a totalitarian country (3) does everyone in that country speak a common language and finally (4) was everyone used as a sample or were the students cherry-picked.
              There is one thing, though, about US education that I do not like and it is the APPARENT (as portrayed in movies and TV) low status that teachers have. I have heard this far too often on TV, “Oh, I’m only a 3rd grade teacher.” or whatever. With an apparently low status, it’s hard for kids and parents to respect teachers and, by extension schools and the system at large. Teachers, after all, are well trained, hardworking and, let’s face it, have an extremely difficult yet crucial job to do. Why not give them respect?
              Oh, and regarding Republicans and Democrats, fortunately most of them are not that extreme and see at least some weakness in their own position and some merit in that of the others. At least I hope so.

            • Maurice, your neighbor to the North is pretty similar to the US overall. And we have much higher percentage of students that don’t learn English at home. Canada after all still has a very active immigration policy. Yet, the school system up here is overall doing much better when measured against the same scale (and no, we don’t cheat that’ll be very un-Canadian).

              Having lived in the US I am not surprised about the difference. Down there the neighborhood you live in is the key factor for how well your school is funded. Up here teachers overall are much better paid, and you get what you pay for.

            • This is very interesting (and I really should not allow for 7 nested levels). I have come across that article that seems to imply that education based on rote yields better PISA results: http://www.zorbitsmath.com/north-america-pull-plug-discovery-based-math-education/
              I have asked myself – in case this is true – if then the test probably focuses on “knowledge” acquired by rote, too?
              Our politians belabor PISA results, too – but does the test as such make any sense?

  6. Another inspiring post Elke! Really enjoy your blog.

    I can glance across the room and spot all my old math texts…. I wonder what would happen to my life if I started the day reviewing some real analysis, abstract algebra or topology! I fear something would snap… 😉

    • Probably you would found a new school of thought in your discipline such as “Topological marketing” or “Abstract Social Media Marketing” 😉 … or the fabric of spacetime would collapse…
      Thanks, Gary, for all your support, retweets, mentions etc. – I do really appreciate it!!

  7. to my mind, it boils down to your flexing your brain as a warm-up practice early in the morning. Athletes subject their bodies to a light strain before training or competition to increase performance and avoid injury, and since you are very much familiar with mathy physics from years of studying, and there is no pressure to perform in a sense that you do not have to determine a degree of success from reading a physics textbook, your mind becomes keener in general and you are more focused, and you might avoid stress-related mental health issues as well

    • Thanks – that’s really a plausible explanation. You are right – it is great to tackle something “difficult” without the pressure to perform though. Probably it’s also about “succeeding” in something you don’t have to and thus lowering expectations about having to “succeed” in troubleshooting … which in a paradoxical way actually contributes to the very success of firefighting either because I have lowered my expectations or because I am really more successful as more relaxed and “creative”.

  8. Feynman enjoyed picking locks, inquisitive minds seems to strive on these kind of puzzles 🙂

    But there’s own reason why these days I don’t tend to go back to my old textbooks, ever since I learned about Hestenes geometric algebra – a Clifford algebra much more better suited for vector calculus. Now I always want my physics using this mathematical framework that so beautifully combines complex, quaterion, tensor and linear algebra.

    • Ups … that’s meant to be “there’s one reason” …

      Actually, when looking at the history of Clifford algebra its quite upsetting that our old textbooks aren’t already using this framework, and rather got stuck on Gibbs vector calculus.

      • Thanks a lot, Henning, for the great link! This article is a treasure trove!!
        However, I believe the old textbooks I have picked are not that bad given this author’s arguments. I really liked the section about “vector avoidance” in the article because my favorite ancient textbook author had quite the same approach here. He used vectors and tensors basically only as entities in their own rights and hardly ever fell back on coordinates.
        My professor in theoretical physics was Wilhelm Macke, Heisenberg’s last graduate student (http://de.wikipedia.org/wiki/Wilhelm_Macke) and I am using his 6 volumes on theoretical physics written in the 1960s. His special condensed – and elegant – way of using abstract objects was called ‘Mackemathics’ among students tongue-in-cheek.
        I have not read studied other theoretical physics textbooks in their entireties but from my comparison with publicly available lecture notes his concise use of these objects always stood out. So I am even more compelled to compare the full series of old textbooks to alternative approach described in this article.

        Probably I also use these books to revive the memories of Macke’s lectures I had attended – it felt a bit like Heisenberg, Dirac, Bohr et al. time-traveling to our times.

        • My dissing of old textbooks was a bit tongue in cheek, won’t ditch my old ones either 🙂

          There is for instance a pretty straightforward connection between geometric algebra and differential forms in GR. Then the most prominent example in QM is the Pauli matrices that form a Clifford Algebra isomorphic to GA. Hestenes used this to tackle the Dirac equation.

          The beauty of GA is that it allows to maintain and stress the geometric aspects from the get go and I am still marveling at how illuminating this is. It just brings so many disparate aspects together. The only thing I can compare it to, is when I first learned about Euler’s identity, and marveled at the unifying power of complex numbers. This is no coincidence, as complex numbers are isomorphic to grade 2 GA, and the latter is essentially just bring the same power of geometry to bear in higher dimensions. And I am still at the very beginning to take stock. I’ve just been introduced to GA last year when emailing with another physicist down under (a guy who probably forgot more physics than I ever knew),

          For instance with respect to QM it becomes clear that spin is not some intrinsic aspect of the quantum domain, on the other hand when GA is applied to EM, the magnetic field is most naturally expressed as a bivector. Hence the symmetric appearance in the tradition vector calculus, that so strongly suggested a magnetic monopole, may very well be an aberration that sent score of physicists on a wild goose chase.

          So my two most read textbooks right now are Geometric Algebra for Physicists and
          Understanding Geometric Algebra for Electromagnetic Theory but there are also many free resources online (e.g. this one) and then all of the GA papers in arxiv (like this one).

          • Great resources, thanks! Yes – I have read part of Sean Carroll’s notes on GR, and noticed the similarities. Finally you realize that Gauss and Stokes law are “all the same”. So GR might be much easier to understand if you start from Geometric Algebra.
            I also do remember the grand discoveries of learning about the EM field tensor for the first time. It’s true – why are these insights about unification and isomorphies presented rather late in traditional courses… You could save time (and use it to present contempoary physics, explain the Higgs boson etc.) instead of presenting the same material in different ways.
            Should we then probably ditch the traditional start-from-F=ma-approach and use 4-vectors in the very first class in classical mechanics?

  9. I’m not sure I completely understand your thought process that you describe here Elke, in fact I know I don’t, but it seems to me that the way your mind works is a gift and the fact that you enthusiastically use it to try to understand how things work and to fix them or make them work better is a wonderful thing. I would say my mind works partially like that, but it’s not the dominating force. I’m kind of interested in how things work, and I get a kick out of fixing them, but I am actually very intimidated by puzzles. You on the other hand deal with these things even in your sleep! And I’ve always admired that quality in people. To actually enjoy “failing to get into the black box” is quite a rare quality that most people do not possess, so be happy and get some more sleep 😉

    • Thanks, Mike, I am more than happy if a small number of readers could relate in part of what I stated here 🙂 It took me a long time to figure out those connections myself. I am also not sure if this is the “dominating force” in my mind. But it is important for me as it helped to finally “find my passion” and “combine anything” in relation to my professional work. After all, it has some advantages if you (as a consultant) really like doing something that most other people don’t.
      I still have a more intuitive side, too Check the search term poems 😉 And yes, I try to get more sleep now – I still read textbooks in the morning, but not at 4:00 AM.

  10. The firefighter metaphor is really cool. I sometimes think of corporate troubleshooting as a computer game… it is very relieving to tell yourself “ah, so I have now mastered this level and got to the next level” when things are turning our really tough.

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