> > The chapter on interest calculations in Liber Abaci was particularly > important. >
I'm sure you're right. Euler added to the interest calculations literature as well. Nasty stuff, interest, really gets out of hand. But then nature is full of exponentially curved responses. I don't wonder that humans have a heckuva time figuring any of it out. Simulations have been helpful. Lets do more of those. Threading on math-teach about that (instead of "programming games" we're "programming simulations" -- then it's less trivial all of a sudden). > No, in spite of the title, not based on the abacus, any more than > calculus is based on pebbles. > Understood: Fibonacci was showing algorithms that'd obviate the need for a contraption (device). I was simply pointing out that the Indian-Arabic numbers map to the abacus, with 0 holding a "no beads" position i.e. the symbolic sand-scribbles make up for not having a real device handy. You're saying Roman numerals mapped to the abacus too, which somewhat surprises me, as I don't see what they're using for a zero (no beads). It all seems really cumber- some, but I guess that's because I'm not Roman (I only lived in Rome for six years and by then most had converted to the new system -- I spent my first year learning about non-decimal money but that's cuz this was Junior English and I had to wear a tie). > In the mathematical theory of languages, we can regard any > Turing-complete symbol-and-rule set as a way to express all of > mathematics, but that is outside the question of what language to > teach or publish in, when the aim is communication with humans. > One could argue that I suppose. I hail from the Wittgenstein camp. We don't necessarily boast of any "mathematical theory of languages". I consider the basis of mathematics more anthropological than logical, if ya know what I mean. When I teach Martian Math, it's all about Axiom Castles along the beach, picturing Oregon Coast. These sandcastles build on axiomatic foundations, but what underpins them all (sand) is not axiomatic and does not forbid multiple sandcastles. Is chess a mathematical language game? Must there be a 'right answer'? Must all mathematical structures be Axiom Castles? Good questions. Martian Math dispenses with a lot of 20th century "dimension talk" i.e. it uses the "dimension" concept differently. So what though? There are already multiple meanings after the shake-out, with Coxeter's not the same as Einstein's, per page 119 of 'Regular Polytopes' ( "tesseract not equal time machine" might be a fun way to memorize this fact). I bring in Karl Menger's "geometry of lumps" and link it to a minimum topology (the simplex) of unit volume, thereby getting a rationalized volumes table for the Platonics and their dual-combos. Fun game, works in Chinese as well, other languages. Lots of published literature, including in illuminated text. http://coffeeshopsnet.blogspot.com/2009/03/res-extensa.html Does this Martian Math threaten the other sandcastles? Not in Oregon it doesn't. We have that live and let live attitude. Euclideans go in peace among us, often unaware of our presence. >> Also, one could argue that all creatures are mathematicians in some >> innate way (Keith Devlin's point). > > So they are, beyond argument. So why are we telling them how they want > to do math and computing? The mindset of "When I want to hear your > opinion, I'll tell it to you" is what I hate most about education > systems of the past and present. > Who is "we" here? Are you included? >> Carving out a special caste of humans and calling them "mathematicians" >> is a practice within various institutions. > > Mathematicians are not a caste, but a guild with stiff entry > requirements. I am not a full member, since I quit after my BA and > went to teach in the Peace Corps. > You might see it that way. Or maybe you found in the Peace Corps that all kinds of brilliant people never have the privilege to participate in any university system, given how the curriculum sucks so bad and everyone is way too over-specialized. If our curriculum were any good at all, the Global University would be far less FUBAR. Let's keep reminding ourselves and our teachers that we're not OK with this status quo. The mathematics must be seriously flawed, given how we're so messed up (is, I think, a responsible attitude, vs. trying to always render all practicing professionals above reproach, off the hook -- we have serious reforms to implement). One of the coolest mathematicians I work with is an HVAC engineer. >> I've noticed many of these institutions promote a kind of snobbery, >> but then such is the human ego. > > See The Theory of the Leisure Class, by Thorstein Veblen, and Buddhist > teachings on no-self. Reverse snobbery is also a feature of human ego. > I miss Bhutan. Really cool people, great scenery (scary-big mountains). >> Note that numpy shares some of APL's and J's ability to shape data >> into multi-dimensional objects with rank. > > Yes. It would be more productive to discuss numpy here rather than > fight a meaningless rwar. > I tend to agree with Wolfram that "intelligence", whatever it may be, should probably not be mapped to the human animal in any way exclusive to such. I call myself a Quaker animist and am a member of a science club that admits non-humans as honored members (some non-humans have military rank too I've noticed -- recalling a CBS News story). I agree with Wittgenstein when he says thinking "language" is distinct from the rest of what goes on is more superstition than a basis for logical thought. >> Thanks for your remarks Christian. Don't let this Ed character bully >> or intimidate you. He likes to show off, which is fine, but he lacks >> diplomatic skills IMO. But then some say the same about me. > > I don't like to show off. I like to get facts straight. The lack of > diplomatic skills is a symptom of my strong ADHD. > Thanks for restoring some of my faith in Roman civilization, maybe there's hope for "us" yet. Lots of these queries, e.g. "what is mathematics?" or "is chess a mathematics?" are queries in the Quakerly sense: one speaks to them perennially but one does not answer them with certainty in some misguided attempt to make the questioning stop. The "having the right answer syndrome" is psychologically slowing so we don't want too much of that around impressionable young children do we? That being said, it's fun to have these strict interpreters, like J's, Logo's, Scheme's, APL's and yes, Python's. "Playing by the rules" is a mathematical exercise -- like being a guest in some Axiom Castle, learning how to think like a Roman when in Rome. "Keep the 'big questions' more open-ended and you'll be better off" is consistent with Constructivist philosophy don't ya think? I'm thinking Karplus was more successful with science education reforms than any counterpart in math education. I wrote a short essay about that. I learned about Karplus from his student and collaborator Dr. Bob Fuller, University of Nebraska at Lincoln. But then the sciences have been seen as experimental / empirical, whereas maths seem to hold out the possibility of synthetic judgments a priori. Authoritarians, in need of certainty, tend to gravitate to so-called "unquestionable" subjects (an occupational hazard). The drive to be super-specialized is somewhat similar (as in "no one will question me once my language is purely private"). I use "maths" in the plural advisedly. Congratulations on your many strong contributions here by the way, and on other lists we frequent. I liked that you expressed admiration for Parrot on math-thinking-l, even though many of these functional programmers dislike the very sound of OO birds chirping. You seem to transcend these divisions in your own approach, understand it's more about both/and, less about either/or. Kirby > -- > Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin > Silent Thunder is my name, and Children are my nation. > The Cosmos is my dwelling place, the Truth my destination. > http://www.earthtreasury.org/ > _______________________________________________ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
