Thursday, November 03, 2016

Do We Still Need Great Minds?

An anonymous comment on a recent post on alternate histories.
As far as science is concerned I don't believe that the great minds are needed anymore. They only speed things up that would later have been developed by an industry of a great mass of brilliant but more mediocre researchers. The best examples are Godel's and Turing's work which would have been done necessarily by the next generation of logicians or theoretical computer scientists. Regarding your own contributions it is fair to say that "the future doesn't need you." Anything important would also be created sooner or later by others, only some idiosyncratic work of minor importance could be left undone forever.
Depressing. So we do either mediocre work or work that others would later do anyway.

Of course we can never know. We can't tell if some great idea today may not have existed if a single genius didn't create it. We also don't know what technology we don't have because of someone who became a playwright instead of a scientist.

I don't doubt we'd have the P v NP question without Cook, Karp and Levin, though our understanding of the problem would have a very different flavor.

Take someone like Manuel Blum. Through him and his students we got formal models of cryptography that led to zero-knowledge proofs, interactive proofs, probabilistically checkable proofs, lower bounds on approximation and major advances in coding theory, among so much more. Would we have all this work if Manuel never existed? Maybe, eventually, but we'd live in a whole different theory world without him. And that world would always look different until we find a new Manuel to unify it.


  1. Yes if X never existed someone else would have discovered Y within time n, but n matters!

    For calculus we had Newton and Leibnitz- but if neither existed then calculus may have been a long time in coming.

    The invention of paper was somewhat unique- if Cai Lun had not lived we paper may not have been discoveed for a long time. And this matters.

    But I grant most things, especially now with so many more people around and able to contribute, most things would have been discovered later and not too much later.

    But I reiterate- n matters!

  2. The premise of the quoted comment is a kind of ad hominem fallacy: that there are sharply defined Great Minds and mediocre minds, the former of whom will in a brilliant and timely way deliver pearls of wisdom, and the latter, like a million monkeys with a million typewriters, who will accidentally produce those pearls anyway given a little more time.

    Obvious nonsense: minds can be prepared and persevering, but if and when they produce Great Ideas and Great Thinking, now or later, that is how intellectual progress is made, regardless of how we judge the "greatness" of the thinker.

    Indoor plumbing is a boon and a miracle whether a "Genius" or a "plodder" devised it.

  3. This really just asks if we're OK with slower growth. The answer for almost everyone, very likely including the commenter (whether they know it or not), is "no".

    1. I think the point is different - the paradigm-shifting thinkers like Newton or Einstein are not going to happen anymore, and today being brilliant just means speeding up research along the path it has been going anyway.

  4. It may be interesting to describe the current state of science especially TCS in terms of Thomas Kuhn’s “The Structure of Scientific Revolutions”. Did we experience paradigm shifts or are we in a state of “normal science” where we attempt to enlarge the central paradigm by piecemeal work of “puzzle solving?” Regarding TCS, the central paradigm of computing was created by Turing and Post. From a sufficiently abstract view there was no shift of paradigms ever since but much work to enlarge it in all directions (including for instance probabilistic computation), all still within normal science which has become an industry by now. In this situation it is very hard to believe in the unique importance of individual contributions.
    Regarding your own work, just think about your brilliant co-authors and colleagues and do the experiment of shifting your interest to a new field. Then look again at your old field 10-20 years later and you will see that it has developed properly without you and many of your open problems have been solved (even if you kept them secret; if important they were rediscovered quickly).

  5. They may be fewer-and-farther-between, but I suspect there will still be monumental advances (even paradigm shifts) brought on by individual great minds and groups going into the future, and their timing (earlier rather than later) can be important. Every generation seems to think there's not a lot of major/unknown science left to discover... almost certainly wrong; better to assume our state of knowledge is still primitive.

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