The Unexamined Scientific Life


Busy day at, so only a slight puzzle.

If you want to be a scientist, it is essential—I speak in earnest—to learn the calculus. Indeed, the importance of this branch of mathematics is impossible to overstate. Without it, you will never have more than an imperfect sketchy fractional crude view of any modern scientific field.

But since calculus takes time to master—it is difficult, vast, and subtle—the years spent learning it can be put to better use doing actual science. Anyway, calculus permeates university and even ordinary life. We’ve all seen calculus equations in newspapers, on Facebook, Twitter, everywhere. You can surely absorb what you need as you go along, just by being part of our modern scientific culture

Consider that the subject is on everbody’s mind, it’s part of the daily discourse, it is “built in”, so to speak, to everything. Why, after five or ten years, by sheer osmosis you’ll have had enough of it knocked into your head that you could write books on the subject. Or, if you were feeling especially ambitious and had a free afternoon, you could always read a popular account penned by some science writer—a book or Wikipedia article which hits the highlights.

Could be a waste of time with Wikipedia, though. You could be out doing science instead. Just get on with it!


  1. Ray

    In engineering school you take calculus as a freshman. If you can’t do calculus you don’t become an engineer. If you pass then you go on to differential equations, vector analysis, complex variables, etc. At least that was the way it used to be. Today I’m not sure.

  2. Duplicating what I wrote on Farcebook:

    It’s over-rated.

    Calculus is at least partially derivative. As an under-grad, it made my toes curl failing to integrate. I prayed for div-ine identities while scanning the Green lines. I procrastinated in LaPlace admiring the smooth and piece-wise smooth curves as they passed diminishingly before my eyes. On the surface, they did not appear normal.

    Whatever Stokes the imagination, we may Navier know. In the flow of the continuous, it’s not always hard to be discrete and finite. We have our limits. Even if it is our field.

  3. Hey, who has been eating which kind of mushrooms? Well, in the spirit of the enterprise, here are three quotes:
    “I was more interested in skating and the girls and traveling than I was in calculus.”
    Scott Hamilton, Olympic Figure Skating Champion.
    “Gout produces calculus in the kidney… the patient has frequently to entertain the painful speculation as to whether gout or stone be the worst disease.”
    Thomas Sydenham
    “God does not care about our mathematical difficulties – he integrates empirically” — Albert Einstein

  4. Mike B.

    My guess at the puzzle is that this is a paraphrased actual quote, where Briggs has substituted “calculus” for something else. Perhaps philosophy?

  5. Mike, you have it! And the substitution is for “statistics”.

  6. Scotian

    Mike B., I would say statistics.

  7. max

    Stats is what calculus replaces, no one realistically expects scientists to pick up calculus by osmosis, the same apparently can not be said for statistics. I use “apparently” because I don’t spend much time in higher education environments and in my admittedly limited experience scientists are required to at least take statistics course. For example, as an undergrad many moons ago I had to beg for an exception to take regression analysis concurrently with a genetics course instead of as a prerequisite. Seeing how statistics are misused by many so called scientists leads me to suspect that my experiences are atypical and I wonder if I have forgotten more about stats than many scientists have ever learned.

  8. Sheri

    Johan: I am having visions of “Common Core” now! (Maybe this was the inspiration?)
    Max: I took statistics for psych majors and then to get some real math, I took statistics for math/science majors. The two were very, very different in approaches.

  9. Briggs

    Mike B is right.

    As the fellow said, “The unexamined life is not worth living for man.”

  10. Brandon Gates

    “Shut up and calculate!” ~David Mermin

  11. Briggs, do you mean “philosophy”—> “the calculus”? Hard to fathom in the context of the post. “statistics” —> “the calculus” seems better.

  12. James Gibbons

    In physics class they teach calculus a little different than they do in math class. You actually learn what the d in dx/dt=v means. Actually solving dynamics equations can be fun. They form the basis for almost all computer games when things crash and explode:

    There are much better methods than the simple Euler’s method I used, but you need some classes in numerical analysis for that and they run quite a bit slower. The simple methods are fine for games where a few pixels of inaccuracy don’t matter.

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