[math-fun] Explaining math to non-math people
I've seen a lot of videos of people trying to teach math ideas to non-math people, and many of these presentations fall completely flat for the non-mathematicians. For example, at some point, I'd like to be able to explain "fat-tailed" v. "thin-tailed" distributions to non-mathematicians, and this is not going to be easy. In particular, I'd like to show how the tail of exp(-x^2) is a lot thinner than exp(-x), which is a lot thinner than 1/x. Nassim Taleb ("The Black Swan") has probably tried the hardest to explain these ideas, coming up with the idealized countries of "Mediocristan" and "Extremistan" where thin-tailed and fat-tailed distributions (respectively) reign. But I still think that many (most?) non-mathematicians still get lost after hearing Taleb. http://en.wikipedia.org/wiki/The_Black_Swan_%28Taleb_book%29 http://www.fooledbyrandomness.com/ http://www.econtalk.org/archives/2009/03/taleb_on_the_fi.html --- Someone who used to work at NSF once told me a (probably apocryphal) story about testifying to Congress, where he said that some indicator number had to reach 10^20 for a project to be successful, but that the current best indicator that the project had demonstrated to date was 10^10. One of the Congressmen then said -- without a trace of irony -- "then we're halfway there". --- Has anyone here had any (successful) experience in explaining sophisticated mathematical concepts of this nature to non-mathematicians?
Without further context, the Congresspersons comment could be perfectly reasonable. For example, if the indicator number was the ordinate of an exponential curve. On 12/30/2011 8:12 AM, Henry Baker wrote:
Someone who used to work at NSF once told me a (probably apocryphal) story about testifying to Congress, where he said that some indicator number had to reach 10^20 for a project to be successful, but that the current best indicator that the project had demonstrated to date was 10^10. One of the Congressmen then said -- without a trace of irony -- "then we're halfway there".
Yes, I suppose that the person testifying might have screwed up by showing some sort of log plot. But if that is the explanation, then it just goes to show you how using a log plot -- which might _simplify_ things for a mathematician/engineer -- only further confuses things for the non-mathematician/non-engineer. At 05:31 AM 12/30/2011, you wrote:
Without further context, the Congresspersons comment could be perfectly reasonable. For example, if the indicator number was the ordinate of an exponential curve.
On 12/30/2011 8:12 AM, Henry Baker wrote:
Someone who used to work at NSF once told me a (probably apocryphal) story about testifying to Congress, where he said that some indicator number had to reach 10^20 for a project to be successful, but that the current best indicator that the project had demonstrated to date was 10^10. One of the Congressmen then said -- without a trace of irony -- "then we're halfway there".
allow me to represent 'non-math' people in some way, and argue that the communication gap is caused by the inadequacy of everyday language and its underlying concepts. Take "orderless" for example: if a collection is in itself orderless, then it is best represented after nicely sorting it. So, when its ordering contains no info, you can freely sort it (if you can). And that's different from 'has no property by which it can be ordered'. More such underlying concepts (in any language) make for troubled communication. Try ro read any publication, and you're swamped by nouns with a particular meaning, known to all who know about such things, but pointing (but often not) the uninitiated to other places where they are 'explained'. Ha! In concreto, I've tried to reconstruct http://www.math.umn.edu/~tlawson/old/18.704/symmetric1.pdf pg. 2, where the author tries to explain how to gently generate the character table of group S4 : "Let’s write the characters of these permutation representations in a table for S4. To do this, we have to do some work and figure out how many tabloids are fixed by each cycle type; " I've not succeeded. Been trying for days. The concepts are not clear enough to me. I follow C. E. Shannon in this: you need a common reference basis to exchange info. And such 'common concepts' are best acquired young, and by face-to-face interaction. It takes a darn good Knuthly writer to achieve this by text only. no? Wouter.
="Wouter Meeussen" <wouter.meeussen@telenet.be>
More such underlying concepts (in any language) make for troubled
communication. Try ro read any publication, and you're swamped by nouns with
a particular meaning, known to all who know about such things, but pointing (but often not) the uninitiated to other places where they are 'explained'. Ha!
I agree, but moreover think this is an intrinsic difficulty that can only be surmounted by investing appropriate effort in each case. Technical terms by definition(!) rest atop a foundation of other such terms and their restricted interpretations. The amount of effort required to reach a common understanding depends on how much common vocabulary is shared to start with. There are no shortcuts. But the same applies to formal systems. Proofs starting from only axioms are more labor-intensive than those that proceed from derived results. Further, even the simplest words may carry wildly divergent connotations for different listeners that require effort to be brought into alignment. For example few years back my non-mathy wife and I realized that we react very differently to the word "problem". For her a problem is always a bad thing, a difficulty that must be overcome. Thus my unthinking mathy use of the phrase "interesting problem" in everyday contexts was to her an unsettling oxymoron. A friend still chuckles about inadvertently miscuing Bill Gosper to vastly overestimate his own level of understanding of some hypergeometric arcana, and the mutually unintelligible merriment that ensued. Another friend, reviewing a draft with me, noted that my inept phrase seemed to imply we were standing on our own shoulders. "I'd pay to see that!" So on top of the challenge of conveying the material itself, it can take considerable effort and empathic talent to monitor what you are saying, listening from the other guys shoes (so to speak).
participants (4)
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Henry Baker -
Marc LeBrun -
Mike Speciner -
Wouter Meeussen