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Academia (vs. Industry)

The Bones of the World

These two posts (here and here) over at Uncertain Principles are well worth reading if you like discussions of the divide between people who understand science and people who don’t. Chad Orzel, being a physicist, instantly translates “doesn’t understand science” to “doesn’t understand math”, which is fair enough, especially for physics. His analogy to the language of critical theory, as found in English literature classes and the like, has threatened to turn the comments threads for both posts into debates about that instead, but Chad’s doing a good job of trying to keep things on topic.
What he’s wondering about, from his academic perspective, is how to teach people about science if they’re not scientists. Can it be really done without math? He’s right that a fear of mathematics isn’t seen as nearly as much of a handicap as it really is, and he’s also right that physics (especially) can’t truly be taught without it. But I have to say that I think that a lot of biology (and a good swath of chemistry) can.
Or can they? Perhaps I’m not thinking this through. It’s true that subjects like organic chemistry and molecular biology are notably non-mathematical. You can go through entire advanced courses in either field without seeing a single equation on a blackboard. But note that I said “advanced”. I can go for months in my work without overtly using mathematics, but my understanding of what I’m doing is built on an understanding of math and its uses. It’s just become such a part of my thinking that I don’t notice it any more.
Here are some examples from the past couple of weeks: a colleague of mine spoke about a reaction that goes through a reactive intermediate, an electrically charged species which is in equilibrium with a far less reactive one (which doesn’t do much at all.) That equilibrium is hugely shifted toward the inert one, but pretty much all the product is found to have gone through the path that involves the minor species. That might seem odd, but it’s not surprising at all to someone who knows organic chemistry well. A less reactive species is, other things being equal, usually more energetically stable than a more reactive one, and the more stable one is (fittingly) present in greater amount. But since the two can interconvert, when the more reactive one goes on to the product, it drains off the less reactive one like opening a tap. There’s a good way to sketch this out on a napkin, where the energy of the system is the Y coordinate of a graph – anyone who’s taken physical chemistry will have done just that, and plenty of times.
Here’s another: a fellow down the hall was telling us about a reaction that gave a wide range of products. Every time he ran one of these, he’d get a mix, and bery minor changes in the structure of the starting material would give you very different ratios of the final compounds. That’s not too uncommon, but it only happens in a particular situation, when the energetic pathways a reaction can take are all pretty close to each other. The picture that came to my mind instantly was of the energy surface of the reaction system. Now, that’s not a real object, but in my mental picture it was a kind of lumpy, rubbery sheet with gentle hills and curving valleys running between them. Rolling a ball across this landscape could send it down any of several paths, many of them taking it to a completely different resting place. Small adjustments from underneath the sheet (changing the height and position of the starting point, or the curvature of the hills) would alter the landscape completely. Those are your changes in the starting material structure, altering the energy profile of all the chemical species. A handful of balls, dropped one after the other, would pile up in completely different patterns at the end after such changes – and there are your product ratios.
Well, as you can see, I can explain these things in words, but it takes a few paragraphs. But there’s a level of mathematical facility that makes it much easier to work with. For example, without a grounding in basic mathematics, I don’t think that that picture of an energy surface would even occur to a person. I believe that a good grasp of the graphical representation of data is essential even for seemingly nonmathematical sciences like mine. If you have that, you’ve also earned a familiarity with things like exponential growth and decay, asymptotes, superposition of curves, comparison of the areas under curves and other foundations of basic mathematical understanding. These are constant themes in the natural world, and unless they’re your old friends, you’re going to have a hard time doing science.
That said, I can also see the point of one of his commentators that for many people, it would be a step up to be told that mathematics really is the underpinning of the natural world, even if some of the details have to be glossed over. Even if some of them don’t hit you completely without the math, a quick exposure to, say, atomic theory, Newtonian mechanics, the laws of thermodynamics, simple molecular biology and the evidence for evolution would do a lot of folks good, particularly those who would style themselves well-educated.

12 comments on “The Bones of the World”

  1. solyom says:

    Two things that are important to note:
    1) Too much gratuitous math is also undesirable. For a lucid example, take a look at almost any econometrics paper published today. You will encounter a fury of tangled math —- amounting to nothing more than largely meaningless mathematical onanism. I think Dierdre McCloskey as well as Arnold King have written about this too.
    2) My guess is that a large part of this fear of mathematics during college that drives the demand for “Physics for Poets”-type classes — is due to the iron grip that the the teacher’s unions have on the primary and secondary education. Essentially, math is poorly taught at these levels, and many students come away with a bad taste in their mouth, shying away from math thereafter.

  2. Charlie Hendrix says:

    I retired from a major corporation (organic chemicals & plastics) after 40 years in R/D I’m a chemical engineer and a statistician. Most of my work (about 37 years) was in applied statistical methods. I was also heavily involved in building kinetic models from first order differential equations. As you might suspect, I’m from the dark side of this discussion.
    A lot of my work involved teaching applied statistics (which I still do as a consultant) and a lot of that teaching was concerned with “designed experiments”. In this context designed experiments are concerning with studying all of the variables (Rx temperature, concentrations, catalyst variables, etc.) simultaneously. Done well, the product of this is models (equations) capable of predicting outcomes and possibly kinetic models and ultimately “optimization of the process”. As you can imagine, convincing organic chemists (and some engineers as well) to use designed experiments to advantage was not easy. Most of my career was about convincing, jawboning, teaching, demonstrating, etc. Sadly, most scientists are taught (overtly or covertly) to “hold everything constant and change one thing at a time”. In a multivariable world, that is usually the worst possible strategy. There are exceptions.
    Your description of the surface with hills and valleys is apt. My position was usually “let’s learn about that surface… its shape and structure… by building models and creating ‘maps’ from those models.” There is a lot of resistance to doing that. Some who came along with me were very successful. Others paid lip service to these concepts to the detriment of their careers. We had some people who resisted to the extent that it was amusing. Some left the company for various reasons, and *then* called me for help in their jobs in their new company. My practice was to always offer help unless there was an obvious conflict of interest.
    Is this strategy always infallable? Hardly. I made some real boo-boos along the way. But I can honestly say that those who bought into this and who stuck with it were well rewarded for their efforts.
    Statisticians working in industry can be very difficult people. Over 40 years I had about 12 of them working for me at one time or another. They can be dogmatic, unrealistic, downright testy, and they give these concepts a bad name. Trust me when I say there are some clever methods for studying multivariable systems (typical of organic reactions) that are not discussed in textbooks or in the usual “canned courses”. We can do a lot better than the conventional academic courses. Therein is one of the problems… statisticians (especially in academia) are stuck with concepts from the 1950s.
    Most are strongly titled toward “software”, thereby missing the point completely.
    But the funny thing is that when I offer to bring these notions… packaged as “experimental strategy”… to academia (including chemistry depts. and chemical engineering depts.) I get a cold shoulder. The problem lies in academia. As a consequence, the first thing we did with new employees in R/D was to enroll them in a course in designed experiments… and many of them liked it, saw the light, and came along with us for a successful career.
    This is not intended as a criticism, just an observation. Shoot the messenger if you wish!!
    I answer e-mails
    Derek… I really enjoy your blogs.
    Be of good cheer…
    Charlie H. Feb. 11 10:24 a. EST
    “Statistics is about communicating information from one person to another.”
    “A poorly designed experiment cannot be rescued by a more sophisticated analysis of the data.”

  3. Derek Lowe says:

    Design of Experiments baffled me when I first heard about it in graduate school. But it’s valuable stuff, especially in the process and optimization side of the business. Doing drug discovery, we usually don’t care at first what the yield of a reaction is, or whether we’ve optimized the synthesis in any way. As long as we get enough to test, we’re happy. But any interesting compound gets past that stage pretty quickly – and you’re right, we have so many variables that trying to change one of them at a time is always time-consuming and often misleading.

  4. qetzal says:

    IMO, the key distinction is whether you want to teach non-scientists about science, or actually teach them basic science.

    I think there’s quite a lot you can teach about science, with little or no math. The non-scientific, non-engineering public generally seems to have a pretty poor understanding of what science is about, how it’s pursued, refined and applied, etc.

    One example is the creationist argument that evolution is “just” a theory. Another is the public’s (or at least the media’s) frequent over-reaction to “new” health-related “findings.” Of course, some people intentionally distort or misrepresent such things for their own ulterior motives. But many people simply lack a sufficient understanding about science.

    I think there is great value in better educating people about science, even if they learn relatively little about any specific branch or field. And I think that could often be done quite effectively with little or no math.

    The down side is that you can only teach them about science, and hope they accept what you say as true. If you want people to see some scientific point for themselves, then I agree that you have to teach them the actual science, and that will usually involve math.

  5. Doug Sundseth says:

    I find that I need to internalize the concept at issue before the math means much to me. (Perhaps I should note that my university training was in physics and astrophysics.) E.g., until I built an internal model of how (and why) complex three-dimensional objects rotate the way that they do, the tensors didn’t make any sense at all.
    So, is this true for others? (Derek’s description of how he conceptualizes energy fields sounds (to me) similar to the way that I relate to complex and fundamentally mathematical concepts.)
    If it is true, can this intuitive understanding be built even without an understanding of the actual math? (I suspect it can, but only by a teacher that has such a model himself. Understanding the concepts is more important than understanding the actual curve equations.)

  6. Harry says:

    In general, I agree with most of the points you made, with one notable exception. You state;”That said, I can also see the point of one of his commentators that for many people, it would be a step up to be told that mathematics really is the underpinning of the natural world, even if some of the details have to be glossed over.” This is exactly backwards. The math is our (simplified) way of modeling the natural world. For too many people , the math becomes all important at the expense of the insight into natural processes, which is the real utility of math,(at least in the areas we’re discussing). It is wayyy too easy to believe in the model at the expense of the real world (one example is the use of epicycles to shoehorn the plantetary motions into the geocentric model, another is the insistence of some climatologists on the usefulness of predictive models that cannot reproduce climatological conditions known to have occured in the past). I think that the disconnect between math as taught in pre-collegiate (and even some collegiate)programs and the “real” world accounts for at least some of the “Math Fear” we see today.

  7. John Johnson says:

    In a response to point made by Charlie Hendrix:

    My favorite story illustrating the fallacy of one-factor-at-a-time analysis comes from George Box. Imagine an experiment examining the number of offspring of deer. One run has no deer, and, of course, no offspring are produced. One run has a doe only, and you can guess the outcome. A third run has only the male, and, well, you get the picture. The fourth run has both deer, and several offspring are produced.

    This “interaction” cannot be discovered through one-factor at a time, nor can it be transformed into “principal components” or any of the other statistical tricks we often employ.

    I have to say, having taught math at middle school, high school, and college (really statistics in college), we do a pretty poor job fostering even an appreciation for math. We teach concepts divorced from real application, and the “word problems” are typically contrived problems that at least I have never encountered in a natural setting.

    Since Newton developed his version of the calculus to handle his laws of mechanics, I think it’s going to be hard to divorce physics from mathematics. And, somewhere down the line, chemical and biological systems have to follow the laws of physics, so mathematical logic will be nearby, if in disguised form.

  8. SRC says:

    I think that this discussion confuses science with technical knowledge – an ubiquitous problem.

    Science is not defined by use of differential equations, energy surfaces, reaction mechanisms or the like, but rather by use of scientific method – working from observations to generate and test falsifiable hypotheses, and modify those hypotheses in light of experimental results – a process of ratiocination that can certainly be taught without use of mathematics (which are basically a detail).

    In this connection, most Ph.D.’s are not really scientists (most merely being technically trained in what to mix with what, and what knobs to turn on instruments). The notion of generating falsifiable hypotheses, constructing a decision tree based upon them (preferably with binary branching) and systematically approaching problems is lost on all too many).

    Think about it: How often does one see Ph.D.’s flailing wildly trying to solve a problem (e.g., repeating precisely the same experiment over and over, hoping against hope that cruel Fate will relent, with no hypothesis as to why the experiment failed previously)? Biologists in particular are prone to an almost animist mindset (happily advancing contrathermodynamic arguments based upon, e.g., proteins folding and unfolding at opportune times, a la Maxwell’s Demon, with no energetic consequences). (This accounts, by the way, for the parlous state of the biological literature, too much of which is rubbish.) Paradoxically, while not doing science, obviously, auto mechanics have a much better grasp of the intellectual process of science than most Ph.D.’s.

    So science has nothing labcoats, and everything to do with epistemology, and that can be taught without use of mathematics. If “civilians” understood the thought process of science (observation, conjecture, hypothesis, experiment, modification of hypothesis), even in a prosaic, easily grasped context (troubleshooting software or electrical equipment), they’d be more sceptical of what scientists say and ask themselves the critical question: “How do they know?”

  9. Charlie Hendrix says:

    You’ve touched on one of the things that caused me a lot of problems over the years. That is, accelerating the rate of discovery as opposed to “optimizing” a process. Much of my work was with catalysts. We were pretty good at “optimizing” catalyst systems, but “discovering” new ones was another matter.
    Working with bold chemists we evolved to using some exceedingly thin screening designs (hyper-greco-latin squares, supersaturated designs, and variations on these) and learned to incorporate many variables at the earliest stages of catalyst research projects. Until that point in time I got a lot of thumps from scientists in the discovery business. All it took to change some thinking was a major discovery (remarkable new catalyst) found by a new employee who had only a masters in chemistry… and done six weeks on the job.
    From this we evolved to even thinner designs, including (hold your breath) “random experiments” which produced several more patentable and commercial useful discoveries. This was in the late 1960s. The concept of “running experiments at random” somewhat like a monkey pecking on a typewriter has some mathematical basis. It works nicely in some well-defined circumstances. It’s not for every situation. Armed with exceedingly thin screening designs and random experiments and concepts “in between those” we significantly reduced the time to “discovery” and (this is important) learned when to stop unfruitful projects. That may have been the best of all. Until that time we have no solid basis for declaring “the odds are against us… stop this and go do something else.” It’s relatively easy to start a project… it’s very difficult to find hard evidence to say “it’s not working… stop it.”

  10. Biophysical Chemist says:

    You linked to this ages ago and it seems apropos.

  11. Rob Sperry says:

    I think the life and work of Faraday should be a refutation that you need math to do physics. Granted Maxwell was able to go much further by adding math to Faraday’s insights, but he was just building on those insights. Doing academical physics requires math because they only teach you to figure out already known problems in a way thats easy to check the answer. However discovering and thinking about physics is often done in a totally visual and kinesthetic mode where math is only added at the end.

    As for the designed experiments sub-thread…

    I worked at a company (HP) that sent everyone that was just out of school to a designed experiments class. It was fantastic! I was amazed to learn that I went through a full undergraduate program in physics without ever having done a real experiment! Its almost as if undergraduate educators expect people to go into the world and find problems that come with a pre-made lab book, the methodology worked out and a series of questions to answer. Where as my boss had the idea that he would give me a vague description of a problem and that I should go figure out the rest.

  12. jihn says:

    Math is tautologies. To say that the world obeys mathematics, is to say that it doesn’t contradict itself. But we already knew that. Non-contradiction is what needs to be understood.
    Maths aren’t the Platonic forms. And maths are not as philosophically significant as mathematicians make out.

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