Grounded versus Pure Theory

My previous blog post generated quite a number of comments and much criticism. Let me summarize the main objections:

  • What I describe is not pure theory but bad research.
  • Pure theory is useful: consider the n log n lower bound on sorting.

My replies:

  • Our brains are bandwidth-driven machines, not standalone computers. You will only thrive given sufficient feedback. And peer review is a low-bandwidth high-latency feedback system.
  • Pure theory is low-bandwidth Science: few results depend on it, whether it is useful or powerful is entirely a matter of opinion. It is pure because it is not tainted by external feedback.
  • Theoretical results are the reason why we do Science.
  • Pure theorists are likely to describe themselves as engineers.
  • I have done and will do pure theory work. It is a very tempting trap.
  • If a new Engineering concept seems like a good idea, wait before you make a book out of it. Try it out in practice first.
  • If a theorem seems useful to you, wait before you make a career out of it. Can you relate it to anything in the world out there?

8 thoughts on “Grounded versus Pure Theory”

  1. In this post, you do not answer your critics, you try to confuse them.

    Instead of owning up and saying that you didn’t really think your last post through and that you don’t agree with it anymore, you give a fragmentary reply which gives no information at all, but is almost impossible to reply to. This practice, to the best of my judgment, is aimed to avoid having to admit that you were wrong.

    Here are a few specific points and replies to some of the items in your post. I cannot directly reply to your general argument, because you did not make any concrete argument, nor does your bulleted list imply any argument.

    1. You state that the list is “your reply”. What claim does each item reply to?

    2. You don’t state whether you still support your previous post, but the sentence “I have done and will do pure theory work. It is a very tempting trap” seems like a half-hearted retraction.

    2A. However, that sentence is only a veiled attack against your critics: it implies that “pure” theorists cannot possibly be relied upon to defend their field, because they themselves are sitting blindfolded in a cave, and can never be made aware of the deficiencies of their field, unless some kind soul unshackles them and makes them see the light. This argument is of anti-intellectual nature. It implies that only a person “from outside” can see the deficiencies of the field. That’s the same argument that Intelligent Design proponents are making against scientists.

    3. Some of your points are unclear to the point of obscurity. For example, your claim that “Theoretical results are the reason why we do Science” or that “few results depend on [pure theory], whether it is useful or powerful is entirely a matter of opinion”. As in these examples, many of your claims are empty or use terms which are not defined to the precision in which you use them. Thus, your post can be characterized as frenchspeak of the bad kind. You apply the following recipe: First, use in a very precise manner a bunch of terms that you have not defined or have loosely defined; Furthermore, use them in unconventional ways; Finally, wait for your readers to scratch their head and lose the ability to argue with your point.

    3A. So, to be specific: Are theoretical results really the reason that we do science? Don’t we do science in order to understand things? Can things be understood in ways other than theoretical results? (Say, by asking clever questions, or defining things in a “correct” way?) What do you call “theoretical results” in this context? Do you distinguish between “pure theoretical results” and other “theoretical results”? What is the distinction?

    3B. What’s going to happen in the discussion from now on, is that you’ll keep pointing out that theoretical results are good, pure theory is bad, and keep juggling with this undefined distinction around until the people you’re talking with get confused and tire of the discussion.

    3C. When you say that “few results depend on [pure theory]”, are you by any chance defining pure theory to be whatever few results depend on? Is this really the right definition for pure theory? For example, consider that Number theory could have been viewed as pure theory 50 years ago. Likewise for the study of cardinality of sets. Likewise complexity theory. Etcetera.

    3D. The same comment applies to your sentence “Pure theorists are likely to describe themselves as engineers”. What are “engineers” in this context? What are pure theorists? I have never defined myself as an engineer, and neither has any pure theorist that I know; so who are you talking about?

    4. I have other problems with your post, but I think I have said enough. The readers can judge for themselves, and pick their favorite claim to criticize.

    5. Finally, regarding your previous post: I, and many others I believe, fully understand that you didn’t mean the things you said to the full extend in which you said them. You were voicing reasonable, although high exaggerated, criticism that applies to some theoretical research.

    However, you fell into the trap of over-generalization and overstatement, and said something which is obviously false, inflammatory, and flat out ridiculous (“Why pure theory is wasteful”?! Jeez, come on). As one of the commenter wrote, you sounded a bit like a troll. Were you trying to draw more commenters?

    In any case, I think the final conclusion is: We understand what statement you were trying to make in your previous post. We understand what you meant by it. Even when your opinions are toned-down to the amount in which you meant them, they are still exaggerated. Read some top papers from theory conferences, understand them, then tell us what you found out.

  2. I do not know enough Google engineers to be able to classify their work, in general. Maybe they are not doing good Science, however. Maybe they are just making things work.

    I doubt however that we can put them all in a single bag.

  3. I have a question about this statement, too:

    Pure theorists are likely to describe themselves as engineers.

    This is very confusing to me. I thought engineers are the polar opposite of pure theorists. What I thought is that pure theorists only draw symbolic / logical conclusions. Engineers demonstrate via implementations.

    I am just not understanding something correctly? This is not a criticism. This is me pleading woeful ignorance.

  4. What is your opinion of, say, Google engineers? Are they also often pure theorists? Because my impression is that they emphasize empirical results, and don’t really care how those results were arrived at (i.e. results trumps theory). See for example Greg Linden’s recent “machines vs. humans” post.

  5. Ok, let me try again. I do not literally mean the Google Engineers, as people. I mean the Google publicly-announced notion of what Engineering is… i.e. experimental, user-driven, data-driven, rapid iteration development of ideas. Google Engineering as a concept, not as a person.

    What is your opinion of that concept, and how it relates to pure theory vs. engineering. Is that Google approach what you mean by Engineering, rather than Pure Theory?

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