Sunday, February 08, 2015

Pros and Cons of students being wikiheads

A wikihead   is someone who learns things from the web (not necc. Wikipedia) but either learns things that are not correct or misinterprets them. I've also heard the term webhead but thats ambigous since it  also refers to fans of Spiderman.

I like to end the first lecture of Discrete Math by talking about SAT and asking the students if they think it can be solved much faster than the obvious 2^n algorithm. This  semester in  honors DM I got the usual heuristics (look for a contradiction!) that may well help but certainly won't get down to much better than 2^n in all cases. This leads to nice discussions of worst-case vs avg-case and formal vs what-works-in-practice.

I also got the following answers:

SAT cannot be done better than 2^n since P  ≠ NP.


SAT can be done in O(n) time with a Quantum Computer.

They both made there assertions boldly! I gently corrected them. They had both read it on the web.

I suspect that the P ≠ NP person read something that was correct (perhaps a survey that said 80% of all theorists THINK P ≠ NP)  and misconstrued it, while the second person read something that was just wrong (perhaps one of those by the many worlds quantum theory a quantum computer can look at all possibilities at the same time people).

 SO- they went and looked up stuff on their own (YEAH) but didn't quite understand it (BOO)
or read incorrect things (BOO). But I will correct them (YEAH). But there are other people who will never get corrected (BOO). But there are others who will get interested in these things because of the false things they read (YEAH?) The quantum person might either NOT go into quantum computing since he thinks its all bogus now, or GO INTO it since he is now curious about what is really going on.

SO the real question is: if people get excited about math or science for the wrong reasons, is that good?bad? Do you know of examples where incorrect but exciting science writing lead to someone doing real science?


  1. You can also get stuff wrong from books. I don't see anything new / special here.

    > if people get excited about math or science for the wrong reasons

    I don't really understand what you mean by "wrong reasons". I don't think people get excited about math / science by simple statements, but rather by things which can be stated / applications. Even if they get the facts wrong, being interested in the topic will (hopefully) lead them to a point when they realize it.

    > Do you know of examples where incorrect but exciting science writing lead to someone doing real science?

    I'm not sure if it counts, but I've heard of some people who were excited by sci-fi (e.g. Star Trek) and studied physics / engineering.

  2. I think this is less about the "wrong reasons" and more about the lack of curiosity. One of the problems with many people who take Set Theory or Discrete Math for the first time after for so long being in a world where the end-all-be-all of math was based on ability to do arithmetic. When they're hit with the theoretical side of math, sometimes that lack of curiosity kicks in and I see them drop very quickly. Same goes with the transition from undergrad to grad

  3. -----
    GASARCH asks for examples of "incorrect but exciting science writing [that] leads to someone doing real science?"

    The first-rank physicist Steven Weinberg wrote an essay of advice to students ("Four golden lessons", Nature, 2003) which advised them to steer toward the "rough waters" of "messy problems" because "that's where the action is".

    Needless to say, these "messy rough-water problems" are precisely the problems for which the entire scientific literature is (in GASARCH's phrase) "incorrect but exciting."

    This combined GASARCH/Weinberg guidance — "students are well-advised to steer toward messy-but-exciting problems" — delightfully illuminates (as it seems to me anyway) the entire literature of complexity theory and quantum information theory (CT/QIP).

    Particularly recommended to younger CT/QIP students (by me anyway) is skateboarder Rodney Mullen's on-line video essay "A Beautiful Mind" Be aware that Rodney's appreciation of "Cedric" refers to Fields Medalist Cédric Villani in classical and quantum statistical mechanics.

    Not for nothing is Rodney Mullen universally appreciated as the Alexander Grothendieck of creative skateboarding-science!

    Conclusion The meditations by GASARCH, Weinberg and Mullen motivate students to read, with building excitement, synoptic-but-dry reviews like this week's "Quantum many-body systems out of equilibrium" (Eisert, Friesdorf and Gogolin, Nature Physics, 2015) and to watch, with undaunted courage, four synoptic-but-scary lectures like Gromov's "Mathematical Structures arising from Genetics and Molecular Biology" (2013,

    Caveat  As Scott Aaronson has been sagely reminding his readers, it is well to "read the fine print" of the above-referenced GASARCH/Weinberg/Mullen/Gromov meditations carefully, as they lead us to appreciate, and grapple with, the "messy rough-water notion" that we are all of us ourselves "quantum many-body systems out of equilibrium."

  4. Hi Professor GASARCH!!!

    I have first discovered the P versus NP Problem on internet and later in classses. I have become in a deep fan of this problem since then, even though I'm not an expert. However, the lack of literature when I was in college, force me to find the basic information on internet. Then, I begin to know bit to bit this problem and when I start to work I decided to send a preprint in the web. Now, I look this first intent and I see it very superficial and a trivial flaw. However, the improvement of this paper and the rewriting of others (which may be lees flawly) changes me in a better person, because I improved my skills in English (that is not my mother tongue), understood more the complexity theory and found some friends by email.

    Let's me give a simple example. Today, I submitted a preprint paper on internet for the purpose of sharing with my cuban friends that are studying the doctorate in Germany. Perphaps, this is another flaw intent, but I really love to share my ideas on the web. Those ideas that I start to learn from internet.

    I would also wish to share the link of the preprint for you,

    and the pdf file in

    because this is what wikiheads do :).