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The undergraduate effect and the gravity wells of knowledge

Last updated on 22 Jun 2018

As usual, Randall Munroe nails it (although if I were playing with that metaphor, I’d say that density distorts the sheet). But I like metaphors, because unfortunately I have the mathematical ability and skills of a drunken frog. So I am going to use a metaphor as a metaphor, if you can follow me.

It is about specialisation in science. Scientists know various information to different degrees of sophistication and exactness. Often you will find scientists defending definitions like what a species is, when they have not done any work on species themselves, simply because they learned a particular definition as undergraduates, or because their advisor had and passed it onto them. The real knowledge about which they are competent to speak are the matters they do their research on, and which they have read, absorbed and critically thought about the literature of others in the subsubfield in which their doctorate or research grants are pursued.

However, there is a tradeoff between depth of knowledge and breadth of knowledge, in part because we all have limited time and mental resources. The deeper one knows a field the less generally one knows the wider context in which that field is situated. Somebody who did their work on a particular signal transduction pathway in murine cells as they develop cancer is not going to have a broad knowledge of, say, climate science. They are no better than any randomly chosen science undergraduate unless they have since specialised on climatology or a closely related field.

The defensiveness of scientists about undergraduate knowledge I call the “undergraduate effect”. It is, if you like, an economic decision: do I spend time reading and thinking about these basic concepts, and take time away from my real work, or will I just state as fact what Professor Authority-figure told me in Specialisation 101? The answer is pretty obvious. Unfortunately some therefore think that their Pareto optimal is a universal truth. A few think that having done Specialisation 101 means they can criticise those specialists who have done real research on the field, as we are seeing with those who claim that climatology is wrong in its consensus that human industry is causing global warming.

Knowledge is a kind of conceptual density that distorts the conceptual continuum. We can think of the depth of one’s knowledge as a literal depth if we think of knowledge as a gravity well (hence, the metaphor using a metaphor). Here is how I conceive it in my drunken frog manner:

Undergraduate effect.png

The red curve represents the gravity well of a real expert, whose work at the bottom of that well is cutting edge research. [Actually, if we take the metaphor literally, the cutting edge is beneath that curve, but in terms of knowledge rather than current conjecture or active experimentation, etc., the curve represents the depth of what that person knows.] The blue curve represents somebody who learned a lot but did not go on to do research of a fundamental kind in that field. It is fairly obvious that a science, indeed all science, will have many such overlapping gravity wells, and that any single researcher, no matter how broad their knowledge, will not know much about a lot of science past undergraduate level. It is also obvious that someone who has not studied science past high school is not in general going to be competent to criticise those who do the research, even if they did a politics or economics degree.

The gravity well explains why many sensible and otherwise brilliant scientists tend to go off the rails. The number of Nobel laureates who write politically naive or simply objectionable things (for example, about eugenics, which is a repeated pattern) once they are recognised is too many to easily count. Once they move out of the field in which they did their work, they are no better off than any undergraduate at the end of an all-night bull session. This also indicates why consensus is needed in a scientific field. While Researcher A may know as much as is known about the signal transduction pathway, the state of the knowledge of the science is not the property of any single person or source. It is the property of a parliament of experts. And it becomes clear that there are levels of expertise.

This metaphor may help you, or it may not. What do I know? I’m no expert on these things…


  1. Neetronic Neetronic

    Nice one.

  2. There is a memorable illustration of what you call the “undergraduate effect” in the movie A Serious Man.

    Clive Park: I received an unsatisfactory grade. In fact: F, the failing grade.

    Larry Gopnik: Uh, yes. You failed the mid-term. That’s accurate.

    Clive Park: Yes, but this is not just. I was unaware to be examined on the mathematics.

    Larry Gopnik: Well, you can’t do physics without mathematics, really, can you?

    Clive Park: If I receive failing grade I lose my scholarship, and feel shame. I understand the physics. I understand the dead cat.

    Larry Gopnik: You understand the dead cat? But… you… you can’t really understand the physics without understanding the math. The math tells how it really works. That’s the real thing; the stories I give you in class are just illustrative; they’re like, fables, say, to help give you a picture. An imperfect model. I mean – even I don’t understand the dead cat. The math is how it really works.

    Clive Park: Very difficult… very difficult…

    • That is a great film, and that sequence had me squirming. [In fact the entire film had me squirming.]

  3. Correction: My example does not illustrate the undergraduate effect exactly, but it does illustrate one part of the phenomenon.

  4. Jim Thomerson Jim Thomerson

    Because of BS and MS in geology, and PhD in zoology, I had a different background than many biology professors. I taught introductory major and general education biology courses and learned a lot in the process. I also taught an introductory animal survey course, and specialized courses in evolution, ecology, limnology, ichthyology, natural resources and environmental assessment. I thought my background deficient in microbiology, cell biology, and biochemistry. At one time I was a member of eleven societies and received 23 different science related publications. My interests were fairly broad, compared to many of my colleagues, I think. Most of my research had something to do with fish.

    • Nevertheless, you have a lot of broad and shallow knowledge, about chemistry, computers and cooking, right?

  5. Jim Thomerson Jim Thomerson

    Actually I am an expert cook. Never mind that my children, now in their 40’s, still complain about the time I put crumbled up cornbread and pinto beans in the meatloaf. Even so, I am still convinced it was forward thinking and innovative cooking.

  6. Adam Adam

    I’ll offer a slight objection to the following:

    “They are no better than any randomly chosen science undergraduate unless they have since specialised on climatology or a closely related field.”

    Given a week to study a new science topic, most practicing scientists will develop expertise more quickly than some randomly chosen science undergrad.

    There are a few reasons for this. The most interesting ones relate to the experience of doing research:
    1) Some techniques are applicable across diverse fields (e.g. statistics and computer modeling), so the experience scientist will typically be better able to interpret data from a new field more quickly than someone who has not conducted serious research.
    2) There are commonalities in the structures of hypotheses across fields. An experienced scientist will be able to devise alternative hypotheses more quickly than a novice regardless of the scientist’s field expertise. The experienced scientist will also have a better sense of how much evidence is sufficient to demonstrate the validity of a theory.
    3) The experienced scientist will be a better judge of expertise. He will find high-quality literature more quickly, and will be better at interpreting the status of ongoing debates.

    More generically:
    4) Professional scientists were selected for being effective scientists. Therefore, their scientific reasoning skill should be compared to that of the BEST science undergrads, not the entire population of science undergrads.
    5) The experienced scientist is probably older than the randomly chosen undergrad, and therefore has read more general science articles. Even if we control for age, full-time researchers have typically been exposed to more general science than those who studied science in school but then left the academic/research community.

    • The generality of technique is a good point to raise. A couple of observations:

      1. Scientists tend to follow fashions with techniques, not because they are good, but because they might be, and all the cool kids are using [technique: it might be microarrays, Bayesian analysis, or some computational method of data mining]. It is rarely the case, however, that a technique can generalise without local variations on interpretation and implementation. The mere fact that Bayes is universal (if it is) doesn’t mean that a physicist who uses it in one domain can say much sensible about another domain (say, cancer research) in which it is also used.

      2. Scientists often over-emphasise the generality of knowledge, and in my observation it turns out they are projecting their discipline to another more often than not. In trying to comment about biology, for example, physicists try to make it a kind of physics. This has hilarious and often tragic results. For every Schrödinger, there’s a dozen Paul Davies.

      3. It is unclear to me there are general modes of inference, whether under the rubric of “scientific method” or not, across all disciplines. As my academic grandpére, Paul Feyerabend once said, if you need to find a single universal scientific method it can only be “anything goes”, because there are no universal aspects of science. I don’t want to overplay this point either, as there is a “family resemblance” of methods (his point too).

      But that all said, I take your point. A scientist can be quicker to get into a field than a non-scientist. This may be because the undergraduate level of knowledge is shared (most disciplines use differential calculus, for example), however. But by the same token a scientist can make serious mistakes in a foreign discipline for the reason that those trained in them do not: they have nobody to correct their errors before they get too serious. Science is an apprenticeship – like most disciplines you need to learn by doing and imitation as well as book-larnin.

  7. In his book Homo Academicus, the sociologist Pierre Bourdieu analyzed the circumstances under which various intellectual figures in France get the right to sound off on subjects outside of their official areas of expertise. He wasn’t writing about scientists specifically and the French do things differently than the Americans, Brits, or Germans; but some of his account of how a select group of “consecrated heretics” acquire their orbita dictum licenses sounds familiar. I do think that any account of “why many sensible and otherwise brilliant scientists tend to go off the rails” should consider the cases where going off the rails has a good outcome.

    Science works by imposing powerful constraints on discourse, but the same restrictions that make it possible at all create a high entry price for new ideas. Of course most of the complaints about the iron grip of orthodoxy are made on the behalf of alternatives that are even more narrow and stereotyped (creationism, astrology, romantic biology, etc.), but it does seem that coloring outside of the lines plays a critical role. In particular, I’m thinking of the tendency of certain important scientific figures to work outside of their original fields–the type specimen being the chemist Pasteur, but one can also point to somebody like Jim Watson who played at biochemistry even though, to believe his own biography, he knew amazingly little about it. Mostly this sort of poaching doesn’t work, but it seems to me that the situation is rather like what obtains in sex: the only appropriate pass is the one that succeeds.

  8. Adam Adam

    “Once they move out of the field in which they did their work, they are no better off than any undergraduate at the end of an all-night bull session.”

    This line of thought needs to be put in the the proper context. The reality is that very few of the people who dominate public debates are any better off than any random person. This includes the politicians, businessmen, journalists, and actors who get so much attention in America. Perhaps a political scientist could have some more information on this, but as an attentive layman, it seems to me that the only requirement getting for media attention (in America) is being articulate, with bonus points for having accomplished something of note in your life.

    If a successful scientist wants to throw out some ideas for consideration — even those that have been dismissed by philosophers (typically for reasons that are opaque to non-philosophers) — then I see no harm in that.

    I only emphasize this point because many people assert that scientists should be excluded from public debate on the basis that such debates are outside of their field of expertise.

    • I am not assessing harm here, merely noting what I take to be the cognitive structure of science. If I held that speculation was harmful, I’d rapidly cease being a philosopher.

      Speculation, informed or otherwise, is a necessary part of an ampliative research program. If all we were doing was deduction from certain axioms, then it would be a bad thing, but science is not an axiomatic system of theorems (not much, anyway).

  9. Gosh. I think you’ve just uncovered the general theory underpinning the entire Group Selection/Kin Selection debate.

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