Q: How many mathematicians/physicists does it take to screw in a light bulb?

Mathematician:

Theorem (Bulb Screwing)

It only takes one mathematician to screw in a light bulb.

Proof:
Let the “bulb screwing number” N_{p} of a profession p, be the minimum number of people of profession p that must be assembled to screw in a light bulb. For any pair of professions p_{a} and p_{b} with p_{a} \ne p_{b} and N_{p_{b}} finite, there exists a “hiring” operation such that any one person of profession p_{a} can hire a collection of size N_{p_{b}} of appropriate people of profession p_{b} such that the collection of such people can screw in a light bulb. By the transitive property of light bulb screwing with respect to hiring, a single member of profession p_{a} can screw in a light bulb by hiring N_{p_{b}} people of profession p_{b} and therefore, so long as there exists a profession p_{b} \ne p_{a} with finite bulb screwing number, the existence of this hiring operation implies that the bulb screwing number N_{p_{a}} of p_{a} is at most 1. But, since we know there exists at least one light bulb that has been screwed in by at least one person of some non-mathematician profession, and there has only ever been a finite number of people, there must exist some other profession with finite bulb screwing number, so the bulb screwing number for mathematicians is 1. QED


Physicist: The computers capable of accurately doing this simulation haven’t been invented (yet).  So we’ve fallen back on some reasonable approximations, like massless light bulbs and spherical physicists.

So far, it looks like physicists can’t pick up light bulbs, but two physicists can break a bulb between them.

This is probably an NP problem or something, which means that the only remaining option is empirical research.  So, once the NSF frees up the funding for us to hire a team of experimental physicists (to experiment on), build a lab, and buy a light bulb, we’ll have something to publish in a year or two.

This entry was posted in -- By the Mathematician, -- By the Physicist, Brain Teaser, Philosophical. Bookmark the permalink.

20 Responses to Q: How many mathematicians/physicists does it take to screw in a light bulb?

  1. Delta Law says:

    That’s really great. I wonder how many engineers will be needed?

  2. The Physicist The Physicist says:

    it takes two engineers to screw in a light bulb. So let’s say four, just to be safe.

  3. me says:

    how many light bulbs does it take to screw in a mathematician/physicist?

  4. Richie says:

    Q : How many mathematicians does it take to screw a light bulb?
    A : It is left for you as homework! ;)

    Btw, this is a great blog! I recently stumbled upon this website and I am loving every article.. I am a Physics and Math buff and reading your Q&A will make me cherish it even more…

    Richie, (from India) :)

  5. Cheyenne says:

    it take Zero engineers to screw in a light bulb because the engineer just Thinks IT.
    and it gets done ;)
    by a mathematician and a physicists of course :)

  6. Eric says:

    It only takes one engineer, but he’ll have to get a permit first.

  7. Andrea says:

    Q: How many statisticians does it take to screw in a light bulb?
    A: 1.37286, but we’ll just estimate 1.

  8. Engineer says:

    There is a typo in your proof. At line 6, pb should be pa, that is, it should read “a single member of profession *pa* can screw in a light bulb by hiring Npb people of profession *pb*”.
    It gave me a good laughter anyhow. Nicely done :)

  9. The Mathematician The Mathematician says:

    You’re absolutely right! Thanks for the correction. It’s now fixed.

  10. Bill LaChenal says:

    My understanding is that it takes two, but how you get them into the light-bulb is a problem for the engineers.

  11. Ken Taylor says:

    Are all functions derivatives and anti-derivatives of other functions? Or at least partly so within a certain set of conditions (continuity, etc…)

  12. Ken Taylor says:

    Is energy required to exert a force?

  13. The Physicist The Physicist says:

    Yes. If something is moved by a force it gains energy, and ultimately that energy has to come from somewhere.

  14. The Physicist The Physicist says:

    It depends on how much you’re willing to twist up the idea of a function. For example, restricting your attention only to functions that are defined at every point: A function is the anti-derivative of another function if and only if it is absolutely continuous.
    Most people aren’t tremendously bothered by the idea that the Dirac delta function is the derivative of the Heaviside function. Mathematicians like to call foul, because the Delta function isn’t a real function (technically, it’s a “distribution“).
    Luckily, physicists are made of sterner stuff.

  15. Toeclippers says:

    Q: How many engineers does it take to screw in a light bulb?
    A: 20, one to screw it in and the other 19 to engineer it in such a way that it never has to be changed again.

  16. john says:

    The assumption behind your calculation is that within the population of physicists/mathemeticians there is at least one who is able bodied in this context. Although this is probable it is by no means certain. Therefore the proof is invalid.

  17. Anthony Rose says:

    Love this site!!

  18. Kay Gee says:

    It takes Ten, one to screw in the light bulb and nine others to explain it.

  19. Gemhunter says:

    It takes a minimum of two, however, the light bulb has to be big enough for them to fit in…

  20. Flavian Popa says:

    This blog is great! I simply love each and everyday I read several entries from it.
    May you keep up this good work!
    Best regards from Bucharest, Eastern Europe

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