Tuesday, June 05, 2007

Math Terms used in real life-good or bad?

Paul Beame's comment on my last blog ASK THE ALGORITHM, and one email comment that I got from someone who was hesitant to post since she thought people would ask if she was on crack, made the point that even if the ad campaign is misleading about what an algorithm is, it gets the word and concept out there, and this is all to the good. I tend to agree.

This raises the question: if a math or CS term is getting out there, even incorrectly, does it help the field? How incorrect? How much does it help? Examples:
  1. On 24, season two, there was a line `we can't break in, its been Huffman coded!' This makes no sense mathematically but it raises awareness of security issues.
  2. On NUMB3RS there are too many examples to count, but I'll pick my favorite: In Season one there was an episode where they claimed that once you solved the Riemann Hypothesis you could factor numbers and break various security systems EASILY. That is, the time from the proof being completed to the code cracking the systems would be less than an hour. While this is absurd, it does let people know that computer security can use some high powered math.
  3. On a radio station I heard the DJ say
    Here at WCOZ we have an axiom, thats like a saying man, that weekends should be seven days long!
    I don't think this helps people understand what an axiom is.
  4. A commercial once said
    And to prove we have the lowest prices in town we will give you a free camera for just visiting our store!
    Not the sense of rigor I want to instill in my students


  1. As a junkie, I wonfer if a drug culture term is getting out there, even incorrectly, does it help? For example, you talk about people thinking that someone "was on crack". True crack addicts tend to shuffle about aimlessly looking for the next hit, but maybe it is useful to raise awareness of addiction issues.

  2. Professors should make a list of "fancy words that you should think carefully before using it" in the undergraduate classes. One such example is "paradox"---mostly it only means something weird but not paradox. I call this "the paradox paradox".

  3. Here at WCOZ we have an axiom, thats like a saying man, that weekends should be seven days long!

    DJ probably meant to say "maxim"...?

    And to prove we have the lowest prices in town we will give you a free camera for just visiting our store!

    Sounds like a good proof that their camera prices are the lowest in town...

  4. "This raises the question: if a math or CS term is getting out there, even incorrectly, does it help the field? How incorrect? How much does it help?"

    It might help in the sense that mathematicians and computer scientists would be so irritated by incorrect usage in a TV show that they would be willing to check future shows for correctness for free.

  5. I find Numb3rs almost unwatchable for this reason.

    On the other hand, look what CSI has done for interest in forensic pathology on college campuses.

  6. It really depends on what your intent is; you mention that a plus of your first two examples is that "it raises awareness of security issues." But I think that the general public already has such an awareness and also has the intuition that a lot of smart people and complicated math is behind such things. In fact, your own examples demonstrate it; the writers slapped some math-sounding terms together and rightfully realized that the audience would get the point.

    The second two examples are not really relevant: axiom (maxim) and "prove", like many mathematical terms, are used in everyday English. They don't carry the same meaning in a mathematical context, and I think a lot of people would understand that as well. If a bunch of mathematicians were talking about the properties of an abelian group, I doubt many people would misinterpret it as the real estate holdings of some investment firm.

    To throw in my two cents; I don't think it helps or hurts if math terms get some exposure, used correctly or incorrectly.

  7. No. People use jargon to suspend the disbelief of the viewer. Think Star Trek technobabble, only misusing real phrases and words. To this effect they attribute all sorts of crazy things to quantum mechanics or relativity. This naturally leads to more people using the same jargon in their scripts, until it becomes a fictional cliche.

    It doesn't do a lot to advance knowledge of the subject the jargon is taken from. Except perhaps to encourage people to lookup the word at Wikipedia, realize that they don't have the knowledge to understand what it means, and go back to their lives.

    It probably doesn't do a lot of harm, since the viewers at best are left with some vague notion of magical possibilities of science. If anyone you know of tried to gain super powers in the '70s from gamma radiation then my apologies.

    In any event I wish they wouldn't do it. I would rather be ignored than mischaracterized, even it is to make me seem more dramatic and powerful through association.

  8. First poster, you are so right. The term "on crack" is so thrown around by people who have no clue whatsoever. Whereas some people use math terms to attempt sounding more intelligent, others use drug terms to attempt sounding more cool. Personally, I've become quite tired of people using weak or baseless comparisons - after all, that's the point of using "jargon" where it doesn't belong. Just give it up.

  9. Give it up for poster #8! Hear, hear! or is it Here, here!---? The exception "proves" the rule...because we have forgotten that PROVE and PROBE were originally the same word! Even if it's not an axiom, the self-evidence of this kind of meaning drift makes it axiomatic (yea-though one can study formal systems whose axioms are false in "the" standard model). I guess I'm not making my point about the canuteness. of trying to contain language drift with minimum redundancy (and I could have spared the prefix on "give it up" now meaning "applaud"), so it's not Huffman coded.

    Nassim Taleb on pp71-72 of Fooled By Randomness (2nd ed., Random House paperback) rails against the literary misuse of "scientific buzzwords, like 'uncertainty principle', 'Go"del's theorem', 'parallel universe', or 'relativity',"---and he goes on to the Alan Sokal affaire. Should he cast the first stone? Nawp. He mis-defines ergodicity on pp57-58 as "roughly, that (under certain conditions) very long sample paths would end up resembling each other." On p96 it means "rare events that can blow you up eventually happen", another consequence-not-definition which is carried into a section titled "Ergodicity" on pp156-157. Finally on p254 it means "the detection of long-term properties, particularly when these exist." My random sampling of Taleb's book (I haven't finished reading it yet) turns up no trace of: walks that fill up all measurable sub-volumes of the sample space proportionately, per the first sentence here. That's the sense we need in order to assess how the methods in the Green-Tao paper on arithmetical progressions of primes may impact P vs. NP, not to mention the Riemann Hypothesis.

    To hit Bill's NUMB3RS example in a technical way, the main theorem of the Razborov-Rudich "Natural Proofs" paper does say that a certain kind of proof of SAT \notin P/poly would allow you to factor numbers in subexponential (expected) time. And of course proving 2^{\Omega(n)} circuit lower bounds for problems in E de-randomizes a lot of stuff. Does anyone know of extensions showing that this or certain other kinds of circuit-separation proofs would impact stuff like "Minicrypt vs. Cryptomania", or help create collision-resistant hash functions, etc.?