While much of the conversation below is steeped in issues I only peripherally understand, from a pedagogical perspective I am in complete agreement with Benjamin. A basic understanding of probability and statistics is more likely to be achieved by students, and would be more useful in most of their lives than a basic understanding of calculus. Calculus is a big stumbling block even for many students who enjoyed the math before that. I'm not sure how the high school curriculum would change to accommodate the new agenda, but I'd be really interested in finding out.
Eric On Mon, Jun 29, 2009 11:19 PM, Owen Densmore <o...@backspaces.net> wrote: > Hi joe. > >> However, I don't understand your comment that math notation is the >> roman >> numerals of our times. Which branch of math do you have in mind? >> Certainly >> not calculus, where, as you know, we use Leibniz's elegant notation. > >The core problem is the clash between two cultures: not the humanities >vs the sciences, but that between mathematics and computing. Or more >precisely, between mathematics and algorithms. > >This is a large topic: it includes the lack of good mathematical >languages (like APL of old, and J today) > http://www.jsoftware.com/ > http://www.jsoftware.com/jwiki/Guides/Getting%20Started >..which bridge the gap between symbolic computing and MN. It also >refers to the impossibility of parsing mathematics .. it is ill- >defined as a language. I.e. AB may mean A * B or the single variable >named AB. > >It extends to the "Asymptotic Assumption" made by many mathematicians > >when a discrete problem is more easily solved by converting to >continuous. (Reminds one of ABM vs Math modeling) Knuth has a good >discussion on this in his book Concrete Mathematics (CON=Continuous, >Crete=Discrete). Basically he makes the case that, although the leap >is reasonable at some point, it generally is taken too quickly. > >So Roman Numerals == notational roadblock. MN is not only is >impossible to parse (and apply semantics to), it does not include any > >notion of "scripting" .. i.e. pseudo-code. > >> I also don't follow your comment about discrete versus continuous. >> Among theoretical computer scientists, people who want to understand >> the power of the computer and questions such as P vs NP study discrete >> problems whereas people like me who want to solve problems >> coming from, say, physics or computational finance think about >> solving continuous problems such as path integration. > >See above on Asymptotic Assumption and MN vs scripting. Certainly >computing, intrinsically discrete, provides wonderful approximations >to continuous problems. > >Interestingly enough, the Sage system: > http://www.sagemath.org/ >.. was originated by mathematicians who *required* open source so that >their theorems could be solved knowing the system on which they were >built. Sage is the first system I know of that has variable >declarations of Ring, Field, and so on. What would happen if Euclid >were propriatorey and only the results, not proofs were public >knowledge? > >Computer use by mathematicians remind me of Statistics use by social >scientists. Often the techniques are used without understanding the >domain within which they are valid. If nothing else, the power law >distribution made many of us run back to see if our assumptions were >reasonable. Economics has fallen prey to this, the Black–Scholes >model apparently assumed a Gaussian where a fatter tail was needed. > >This rant is a long one, but the summary is simple enough: Mathematics >and Computing/Algorithms need to be reconciled. Modern MN needs >(minor) changes to be at least machine readable. Computing languages > >for mathematics need to bridge the gap between pseudo-code and >symbolics. APL/J are close. > >How about a beer or glass of wine over this fascinating topic! > > -- Owen > > >On Jun 29, 2009, at 8:19 PM, Joseph Traub wrote: > >> Owen, >> >> I find nothing to argue with in Benjamin's talk. He says that students >> studying economics, science, engineering, or math should learn >> calculus >> but that it may not be needed by other students who should study >> probability and statistics. >> >> However, I don't understand your comment that math notation is the >> roman >> numerals of our times. Which branch of math do you have in mind? >> Certainly >> not calculus, where, as you know, we use Leibniz's elegant notation. >> >> I also don't follow your comment about discrete versus continuous. >> Among theoretical computer scientists, people who want to understand >> the power of the computer and questions such as P vs NP study discrete >> problems whereas people like me who want to solve problems >> coming from, say, physics or computational finance think about >> solving continuous problems such as path integration. >> >> Best, Joe >> <> >> >> Joseph F. Traub, Edwin Howard Armstrong Professor of Computer >> Science >> and External Professor, Santa Fe Institute >> >> tr...@cs.columbia.edu http://www.cs.columbia.edu/~traub >> >> Phone: (212) 939-7013 Messages: (212) 939-7000 >Fax: (212) >> 666-0140 >> >> Columbia University >> Computer Science Department >> 1214 Amsterdam Avenue, MC0401 >> New York, NY 10027 >> USA >> >> Administrative Assistant: Sophie Majewski >> sop...@cs.columbia.edu (212)939-7023 >> >> >> ************************************************************** >> >> From: Owen Densmore <o...@backspaces.net> >> Date: June 29, 2009 12:07:14 PM MDT >> To: The Friday Morning Applied Complexity Coffee Group ><friam@redfish.com >> >, >> General topics & issues <disc...@lists.sfcomplex.org> >> Subject: [FRIAM] Arthur Benjamin's formula for changing math >> education | >> Video on TED.com >> Reply-To: The Friday Morning Applied Complexity Coffee Group >> <friam@redfish.com> >> >> This is kinda cool and less than 3 minutes long! >> >http://www.ted.com/talks/arthur_benjamin_s_formula_for_changing_math_education.h >> tml >> >> The thesis is a different spin on my claim that modern Math Notation >> (MN) is >> the roman numerals of our times. Arthur Benjamin clearly explains >> that statistics and probability should be the "pinnacle" of our >> basic math >> education, not calculus. His reasoning includes the discrete vs >> continuous >> argument that resonates with my MN vs Algorithm (or MN vs script) >> concern, >> which I'd love to see resolved in a parsable reworking of MN. >> >> -- Owen >> >> >> ============================================================ >> FRIAM Applied Complexity Group listserv >> Meets Fridays 9a-11:30 at cafe at St. John's College >> lectures, archives, unsubscribe, maps at http://www.friam.org > > >============================================================ >FRIAM Applied Complexity Group listserv >Meets Fridays 9a-11:30 at cafe at St. John's College >lectures, archives, unsubscribe, maps at http://www.friam.org > > > Eric Charles Professional Student and Assistant Professor of Psychology Penn State University Altoona, PA 16601
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