Sunday, December 15, 2013

Mathematics, the language of nature. What are you sinking about?

Swedish alphabet. Note lack of W. [Source]

“I was always bad at math” is an excuse I have heard many of my colleagues complain about. I’m reluctant to join their complaints. I’ve been living in Sweden for four years now and still don’t speak Swedish. If somebody asks me, I’ll say I was always bad with languages. So who am I to judge people for not wanting to make an effort with math?

People don’t learn math for the same reason I haven’t learned Swedish: They don’t need it. It’s a fact that my complaining colleagues are tiptoeing around but I think we’d better acknowledge it if we ever want to raise mathematic literacy.

Sweden is very welcoming to immigrants and almost everybody happily speaks English with me, often so well that I can’t tell if they’re native Swedes or Brits. At my workplace, the default language is English, both written and spoken. I have neither the exposure, nor the need, nor the use for Swedish. As a theoretical physicist, I have plenty of need for and exposure to math. But most people don’t.

The NYT recently collected opinions on how to make math and science relevant to “more than just geeks,” and Kimberly Brenneman, Director of the Early Childhood STEM Lab at Rutgers, informs us that
“My STEM education colleagues like to point out that few adults would happily admit to not being able to read, but these same people have no trouble saying they’re bad at math.”
I like to point out it’s more surprising they like to point this out than this being the case. Life is extremely difficult when one can’t read neither manuals, nor bills, nor all the forms and documents that are sometimes mistaken for hallmarks of civilization. Not being able to read is such a disadvantage that it makes people wonder what’s wrong with you. But besides the basics that come in handy to decipher the fine print on your contracts, math is relevant only to specific professions.

I am lying of course when I say I was always bad with languages. I was bad with French and Latin and as my teachers told me often enough, that was sheer laziness. Je sais, tu sais, nous savons - Why make the effort? I never wanted to move to France. I learned English just fine: it was useful and I heard it frequently. And while my active Swedish vocabulary never proceeded beyond the very basics, I quickly learned Swedish to the extent that I need it. For all these insurance forms and other hallmarks of civilization, to read product labels, street signs and parking tickets (working on it).

I think that most people are also lying when they say they were always bad at math. They most likely weren’t bad, they were just lazy, never made an effort and got away with it, just as I did with my spotty Latin. The human brain is energetically highly efficient, but the downside is the inertia we feel when having to learn something new, the inertia that’s asking “Is it worth it? Wouldn’t I be better off hitting on that guy because he looks like he’ll be able to bring home food for a family?”

But mathematics isn’t the language of a Northern European country with a population less than that of other countries’ cities. Mathematics is the language of nature. You can move out of Sweden, but you can’t move out of the universe. And much like one can’t truly understand the culture of a nation without knowing the words at the basis of their literature and lyrics, one can’t truly understand the world without knowing mathematics.

Almost everybody uses some math intuitively. Elementary logic, statistics, and extrapolations are to some extent hardwired in our brains. Beyond that it takes some effort, yes. The reward for this effort is the ability to see the manifold ways in which natural phenomena are related, how complexity arises from simplicity, and the tempting beauty of unifying frameworks. It’s more than worth the effort.

One should make a distinction here between reading and speaking mathematics.

If you work in a profession that uses math productively or creatively, you need to speak math. But for the sake of understanding, being able to read math is sufficient. It’s the difference between knowing the meaning of a differential equation, and being able to derive and solve it. It’s the difference between understanding the relevance of a theorem, and leading the proof. I believe that the ability to ‘read’ math alone would enrich almost everybody’s life and it would also benefit scientific literacy generally.

So needless to say, I am supportive of attempts to raise interest in math. I am just reluctant to join complaints about the bad-at-math excuse because this discussion more often than not leaves aside that people aren’t interested because it’s not relevant to them. And that what is relevant to them most mathematicians wouldn’t even call math. Without addressing this point, we’ll never convince anybody to make the effort to decipher a differential equation.

But of course people learn all the time things they don’t need! They learn to dance Gangnam style, speak Sindarin, or memorize the cast of Harry Potter. They do this because the cultural context is present. Their knowledge is useful for social reasons. And that is why I think to raise mathematic literacy the most important points are:


Popular science writing rarely if ever uses any math. I want to see the central equations and variables. It’s not only that metaphors and analogies inevitably have shortcomings, but more importantly it’s that the reader gets away with the idea that one doesn’t actually need all these complicated equations. It’s a slippery slope that leads to the question what we need all these physicists for anyway. The more often you see something, the more likely you are to think and talk about it. That’s why we’re flooded with frequently nonsensical adverts that communicate little more than a brand name, and that’s why just showing people the math would work towards mathematic literacy.

I would also really like to see more math in news items generally. If experts are discussing what they learned from the debris of a plane crash, I would be curious to hear what they did. Not in great detail, but just to get a general idea. I want to know how the number quoted for energy return on investment was calculated, and I want to know how they arrived at the projected carbon capture rate. I want to see a public discussion of the Stiglitz theorem. I want people to know just how often math plays a role for what shapes their life and the lives of those who will come after us.

Don’t tell me it’s too complicated and people won’t understand it and it’s too many technical terms and, yikes, it won’t sell. Look at the financial part of a newspaper. How many people really understand all the terms and details, all the graphs and stats? And does that prevent them from having passionate discussions about the stock market? No, it doesn’t. Because if you’ve seen and heard it sufficiently often, the new becomes familiar, and people talk about what they see.


We don’t talk about math enough. The residue theorem in complex analysis is one of my favorite theorems. But I’m far more likely to have a discussion about the greatest songs of the 60s than about the greatest theorems of the 19th century. (Sympathy for the devil.) The origin of this problem is lack of exposure, but even with the exposure people still need the social context to put their knowledge to use. So by all means, talk about math if you can and tell us what you’re sinking about!


  1. Very nice piece Sabine. I've always thought for people to be interested in math they need to feel the passion expressed for it from someone who not only understands it, but also one who can get across to people why they love it so. Believing that I've long been convinced that if all the math phobes/deniers would only promise themselves to read this book in it's entirety I'm certain most would not simply come away being enriched by the experience, but also the world many of us would like come to be would be a little closer to becoming a reality.

    "If we could discover the little backstairs door that for any age serves as the secret entrance way to knowledge we will do well to look for certain unobtrusive words with uncertain meanings that are permitted to slip off the tongue or the pen without fear and without research; words which having from constant repetition lost their metaphorical significance, are unconsciously mistaken for objective realities. "

    -Carl Becker as quoted by John D. Barrow, Pi in The Sky; Counting,Thinking, and Being (page 1)

  2. STEM is a bad joke. It creates an overflowing pool of overskilled underpaid menial laborers who must go "back to school" to improve their meniality.

    Stiglitz is an economist. "government could potentially almost always improve upon the market's resource allocation." USSR, Pol Pot, North Korea, OPEC, Obamunism. "Potentially."

    US fast food cash registers have pictures on their touch pads, not numbers. The best first step in slavery is rendering people unable to conceive of freedom by denying them language containing the concept. We may see the end of science in our time. "to be performed only in the national interest" Yay Stiglitz.

  3. I doubt that you are right about the math phobic. Many people do seem to have trouble with math starting very early.

  4. I think that one of the main problems of math illiteracy is bad education in primary schools and high schools. Math, physics and sciences are being taught by people who are sometimes very ill-prepared (if not incompetent) to teach those subjects properly.

    And teaching math to children is a very delicate job --- if not done properly, math becomes "hard", "geeky", "nerdy", children tend to be afraid of math exams, etc.

    I'd dare to say that people who are math&science teachers in primary and high schools are typically academic washouts --- those who have tried and failed to become professional scientists, and then found a "lesser" job for their skillset. And they are washouts because they tend to not understand the basic concepts themselves, let alone teach young children those concepts. It is like learning literature from a person who is a failed writer, or music from someone who failed at the audition for the symphonic orchestra and then found a job at a local school.

    If we want more math literacy in general population, we need to organize better math education at the source level --- in primary schools. This will not happen on its own, it needs to be organized and "pushed" institutionally.

    Best, :-)

  5. Marko,

    I agree with that, but this will take generations. I'm more concerned about all the people who we can't reach this way anymore. Best,


  6. CIP: Whole nations have proven you wrong.

  7. Mathematics is the lingua franca of contemporary science, theoretical physics the more and it has no meaning to think about alternatives, simply because there still don't exist any.

    But in emergent dense aether model the formal math has its apparent limits. We even cannot solve the N-body system or Kepler conjecture for three and more particles.. I'm sure, these old era physicists will still struggle to expand their mathematical descriptions, but with respect to their practical results (100E+500 landscapes of string theory solutions) such an effort will be increasingly pointless and ineffective.

    I'm usually explaining this evolution with geometry of water surface scattering during splash. At the proximity these ripples are chaotic and turbulent and as such impossible to describe in deterministic way. With increasing distance these turbulences compensate mutually and the ripples are spreading in background independent way in regular circles. This corresponds the golden era of formal physics, during which the quantum mechanics and general relativity theories were developed. Please note, that this advanced physics doesn't bother about phenomena at the human distance scale anyway - they're simply too much complex for it.

    Unfortunately, when the surface waves expand even more, they're getting scattered in additional dimensions of underwater again. And the seemingly deterministic world becomes as chaotic and complex, as the world at the human observer scale. Thanks to expanding perspective of human observation this is just the situation, which the mainstream physics faces by now.

  8. The evolution of complexity in computer programming gives us a good clue, what will happen next. At the very beginning, I mean in old golden times of computer programming the experts learned to use to program computers in solely deterministic way via machine code or assembly language. But such an approach soon did become too tedious, intellectually rewarding and plainly ineffective - so that the programming languages of higher and higher level were developed. The dense aether model is the first attempt in this direction in physics.

    Of course, the old golden era programmers called these ones using Pascal and Cobol the "cake eaters" and didn't consider them seriously - but it cannot help them in increasing competition at the market. The idea of deterministic programming or rigorous approach to hyperdimensional physics may appear elegant and beautiful for someone - but it's just terribly ineffective. It can find its justification only at the rather special cases.

  9. Dear Bee,

    Blogs can make a start in talking about mathematics more than the usual suspects.

    Best wishes,

  10. BTW In this study the (Schrodinger equation of) quantum mechanics is derived from Brownian motion geometry (and applied to chaotic financial markets). We even have experimentally confirmed examples of quantum mechanic behavior of large ensemble of material particles.

    So we can derive the quantum mechanics just with simulation of collisions of sufficiently large system of particles and we needn't to bother about any math during this in the same way, like we aren't bothering about actual solution of Navier-Stokes equations during particle simulations. The computers will do most of the hard intellectual work for us.

    For example, I do believe, that the atom nuclei could be modeled in their entirety like the density fluctuations of extremely dense particle fluid just with the above naive approach.

  11. I think part of the problem is that just about everyone can truthfully say 'I'm not very good at maths' even highly skilled people although maybe not theoretical physicists.The reason being that there is so much maths to master that sooner or later almost everybody finds an area they don't 'get' and can say it.I strongly believe (with no evidence) that it would be useful to separate mathematics from arithmetic, almost no one should be allowed to say 'I'm no good at arithmetic'. Once competence in arithmetic is achieved beginning maths should be easy.

  12. A very good post about an observation and inference that is quite consistent with many other observations, which does not have the inconsistencies of the ole talk models that get the attention.

  13. I agree with you, Sabine. Moreover, recent research supports you.
    In my youth, I found learning to be hard but rewarding work. Math was the hardest work of all. Now and for the 50 years subsequent to elementary school, I am considered by those around me to be somewhat of a math whiz. Nope. It's just hard work, every day, and still rewarding.

  14. If you want to enjoy math, subscribe to Vihart on youtube. What she does there will make math interesting and fun for almost any age or passing interest...

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  16. Arun,

    Yes, I agree. Except that embedding equations is still cumbersome. Alas, the issue with blogs is that the audience is strongly self-selecting. If you write about math, you're most likely to attract people who are already fond of math anyway. That's why I think it would make much more of a difference if 'normal' news that most people get to see every know and then would sneak in some math speak every now and then. Best,


  17. Rab,

    Thanks for the reference which I had missed. This is interesting. Best,


  18. /* It's just hard work, every day, and still rewarding */

    IMO for ability for math learning exist the same difference as for whatever else ability (like the music). While the hard training can wipe out much of differences, the difference in learning abilities still persist.

    BTW The math is not the language of nature - this is just an ideology of people, who are payed for teaching/learning of math in the same way like the theologists of recent era were payed for their theology. In real life the math can be applied to only very few schematic cases.

  19. "Swedish alphabet. Note lack of W"

    While rare, W has been in the Swedish alphabet for a while, though until recently alphabetized along with V (the way that, for example, ä is sometimes alphabetized with a (though never in Swedish)). Recently, however, W was promoted to an actual Swedish letter.

    As someone who has learned Swedish without ever having lived there (though I have spent almost a year there over the last 30 years), please take the opportunity. For someone who speaks both German and English, it is probably the easiest language to learn, even easier than Dutch. You don't know what you're missing! :-) The fact that most Swedes speak English (and many speak German) well is beside the point.

  20. Really? Tell me a Swedish word with W then! Yes, well, as I said I did learn the basics and if I find the time, I'll also read the rest of the book. Maybe. After I've written this referee report and that grant proposal and submitted these proceedings... Best,


  21. "Tell me a Swedish word with W then!"

    Almost all are proper names and/or foreign words, but there are many names with W (usually as the initial letter).

    By the way, here's announcement of the official promotion of W to a fully fledged letter: W.

  22. In school I learned that "the alphabeth has 28 letters, or 29 if you count W". Will check with my children if that is still what is taught.

    In Swedish Q is probably even more scarce than W. But obsolete characters are not uncommon in other languages. How often does a German use Y (not Ü), or an Italian use K (except in sms:ese).

  23. According to my youngest daughter, the status of W as an independent letter is still unclear, at least from what they learn in school.

    How much Swedish people learn is probably a matter of personaliby. My oldest daughter's fiancee, who is English, has been staying with us for eight months and now speaks decent Swedish.

  24. As a formal footnote after reading the posts so far here including a useful doubling of alphabet symbols as mirroring or for individual letters such as "V", consider these questions as to how well our language as math depicts Nature:
    *1. Given a sequence of integers K, how many numbers or pictures must a student memorize before they can add easily and without gaps in the results?

    *2 If to this sequence we add zero does it have to have a place at the beginning, somewhere between, or the end?

    *3 What miminum integer K describes the microwave vibrations of methane?

  25. "My oldest daughter's fiancee"

    That should be fiancé, or course. My Swedish is better than my French.

  26. I enjoyed the post as usual and I also wish popular science books (e.g., "Chaos" by James Glick) had more math in them. I vaguely recall that books I read by George Gamov in my youth had a bit of math in them, which made them more interesting.

    What I like to argue (perhaps simplistically) that math is just thinking, thinking math. That is when you have three errands to do in a certain amount of time and decide what order to do them in, you are doing math. You probably are not doing it as well as if you had studied math, learned some techniques, and done a lot of practice (assuming you haven't), but you are doing math, or trying to. Only people who never think before making decisions don't do math. (Or that's what I calculate.)

  27. Zephir, have you heard that from the expanding wave fronts of ever more complex reflections of sonar we CAN trace things backward to pinpoint the location of a submarine?

  28. /* from the expanding wave fronts of ever more complex reflections of sonar we CAN trace things backward to pinpoint the location of a submarine */

    Of course, I'm aware of it, as this is a typical emergent approach, which is using longitudinal waves. But the mainstream physicists don't use it, as they're focused to Lorentz symmetry of transverse wave spreading. They're seeking for deterministic connections and clues, which are enabled to formal deterministic description.

    Typical example is the (ignorance of) research of cold fusion - which doesn't exist despite many indicia, until someone will not propose deterministic theory for it. Another example is the geothermal origin of global warming, which can be deduced from many indicia.

    Maybe in future we will learn, how to handle the various infinitesimal indeterministic clues of many seemingly unrelated experiments and observations and connect them into most probable optimal solution. But currently for physicists the delayed strictly deterministic approach is more advantageous from occupational reasons.

  29. If you're believing, that the formal math is the only reliable way for description of reality, I can have nothing against it - but such a philosophy will introduce a gnoseologic bias under situation, when the observable reality becomes fragmented into multiple deterministic solutions. I already explained it with water surface analogy.

    Recently Lee Smolin proposed a concept of relative locality, which is exactly what the surface wave analogies of dense aether model are about. At the water surface you can have a situation, when one observer can see the expanding space-time for another distant observer, which does observe any expanding space-time locally, but he observers it for first observer instead.

    While the multiversality of observational reference frames appears perfectly natural for water surface, from perspective of deterministic formal math rigor such a situation is a pure disaster. You cannot be sure with any global deterministic law after then.

    1. Zephir, I see. In Dirac's he said as much and in a sort of multiplicity of functions generated by bfa ket notation. Why can we not accept more relaxed methods in view of probing experiments and issues of obserstion. So we for the standard research as physics can only imagine visible light and that broken into a corpuscular spectrum to view it
      like we do holograms. The totality which would be issues if contained by a vague quasi-local region. Then gives us a totality as a cloak of invisibility. In view of no or unobservable axions is this not suggestive of something like dark matter or superdeterminism for time phase and flux as dark energy?
      So proper science continues with Feynman as strict upon rotation particle and wave. Yet from a global view a totality can be dynamically as physical where perhaps Nature can see a little wider than she does as we do with dimensions.
      A global "quason " can exsist beneath the razzle dazzdazle
      and camoflague of appearences into coherent essences.
      This is at least four fold logic or as 3+1, I see as umber, ochre, amber, and initiator analog to DNA.
      But sure we need to build for solid effort and work. Then we can reach for even higher theory than the drama we have today that needs better logic and mathematical physics.

  30. Bee - my belief is that schools, in particular here in the USA, are hell bent on "fixing" and refuse to stop and assess whether anything they have attempted in the past 40 to 50 years has had a measurable benefit on studetns understanding in any of of the "3 R's". The average high school student back in days of yore had a pretty good grounding in the basics. And there was still room for more advanced material for those showing an inclination or talent. Now we spread things so thin that nothing much is really learned least of all well.

    In regards science writing - I too would like to see more equations and the like though I do understand the need to keep audience attention and capture as wide an audience as possible. The easy answer is to use footnotes for the equations. If a reader is interested, they can look. If not, no harm no foul.

  31. Bee is moving on up and congratulations! Today a D (Physical Review D), not the best grade, but tomorrow an A (Physical Review A)!

  32. Interesting post.

    I have the Feynman lectures on Physics. A most intersting observation about these is that there is very little maths involved - mostly it is presented as a logical argument. (If we know A is true, and we observe B then C most therefore be true, and so on.)

    There is merit in this approach, as well as maths. I've seen in many scientific and engineering papers a tendency to rush to maths with insufficient words to explain what's going on.

    A balance is needed where each support the other. This then might make the math less intimidating, as well as easier to understand. This could be applied from very basic concepts (compound interest, perhaps) through to the deepest corners of physics.

  33. I loved the article! Especially because I understand what is like being "bad at math". In school it was an excruciating exercise mostly because I didn't understand it properly not to mention it had stressful consequences, like bad grades. Later on I started reading the science popularization books you talk about and wanted to see the equations because I felt I didn't exactly understand the subject at hand without them. So I looked for the math and understood what it meant but not exactly how it worked. It was like a half forgotten language, one that you never learned. So I started learning to speak math as a hobby. Since this time it was all good and easy, I infer it must have been my teacher and not me who was bad at math.


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