[Fis] Tough question: Decolonizing mathematics?

[Roy Morrison]

My neighbor the late Doug Newton was a logger by trade with a background studying Quantum Electro Dynamics. Doug found he could teach his first grade son Ben algebra when he presented solving equations as a puzzle. Beyond an N of one, my son could do the same.This required no axioms or formalism but an expression of inherent ability that is coevolutionarily expressed and refined as one of life attributes.
Roy

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  On Wed, Feb 8, 2023 at 10:11 AM, Pedro C. Marijuán<pedroc.marijuan at gmail.com> wrote:     Dear FISers, 
  Some days ago Plamen sent this link and some criticisms to a discussion group about a strange article in Nature on how to make Maths "truly Universal" --say, "decolonizing" them: https://urldefense.com/v3/__https://www.nature.com/articles/d41586-023-00223-w?utm_campaign=nature-careers-newsletter&utm_medium=email&utm_edition=202302030500&utm_source=newsletter__;!!D9dNQwwGXtA!UIgba6qM42YdBcvs6VbJT0DCttuOWvJqWNCV7sBwteIqFmF6vefQjTTNpvJ11u8HS4NaoEmBFTqLL65n8GiNEbaCBAU-$  
  I copy below interesting responses from Lou Kauffman and Bernard Baars. 
  They make an interesting read. Best--Pedro
   ---------------------------- Dear Plamen, On the one hand I agree completely with you. On the other, I feel that this idea of looking at cultural background in relation to mathematics is crucially important. All mathematics, developed in cultures the world over, depends on fundamental distinctions made in those cultures. These distinctions that become the wide ranging abstractions on which the mathematics is based. All mathematics comes from creating/imagining such distinctions and finding ways to indicate them and combine them. Even in the case of our familiar mathematics, we treat it differently depending on time and culture. The geometry of the Greeks in 500BC was codified in Euclid and it is in the unwritten background about concepts of space and time for the Greeks that this geometry differs so much from our modern conceptions. Two points determine a line in Euclid, but the line is not regarded as an infinite collection of points held together by a metric topology — that is our inheritance from 19th century mathematics. And so it goes. We are skeptical of the real line and of the cartesian space as an articulation of a background for physics and rightly so. Other cultural experience may make a difference in the pattern of distinctions. We like to frame our main line of mathematics in boolean terms but even within our own culture there are those who would think differently and keep track of in-between states of logical value.  
  In teaching mathematics it is important to bring examples that students can understand. Backgrounds vary.  
  I feel strongly that one should, before engaging in cultural/mathematical projects, understand that mathematics is not about numbers and geometry and logic. This is a cultural bias. Mathematics is about what comes from taking certain distinctions and imagining that they can become a currency for discussion and exploration. Mathematics is about the exploration of distinctions. Once this is understood then it becomes possible to see how mathematical reasoning can arise without formalisms and axioms because certain distinctions are sufficiently vivid and sufficiently shared. We do not teach young children the Peano Axioms for arithmetic but they learn the essence of then in learning how to count and work with discrete patterns. We can show the proof that THE SUM OF THE FIRST N ODD NUMBERS IS EQUAL TO THE SQUARE OF N  without any induction or other formalization by arranging pebbles in the form of a square. 
  Consider striking examples that work well in teaching. We say to a class: “There are 25 of you. The chances are better than 1/2 that two of you have the same birthday.”  This bit of probability is striking because of the sharp cultural and personal resonance with the day of birth. In other cultural situations there will be other examples that have a similar resonance. It is worth searching them out. 
  We forget how culturally bound we are. Gutenberg press and moveable type led us all to converge on mathematical formal systems as fundamentally typographical. Witness Doug Hofstadter’s  TNT (Typographical Number Theory) in his book Goedel Escher Bach. The book is actually a plea for getting mathematics off the typographical page, but it is bound by the logic of the author’s origins. 
  A possible right attitude is to be as curious as possible about what mathematics might come from structures in any human culture. Included here are papers of mine with some hints of how modern knot theory is indebted to the vast cultural precedence of weaving and knotting in world culture. 
  Very best, Lou Kauffman ----------------------------------------------- (>From Baars) 
    The post-modern assault on mathematics is destructive nonsense, intended to destroy Western culture.  To be nice and understanding about it is very kind, but it's a failure to understand a deadly cultural threat.  If you want to understand this dangerous cancer running through our schools and universities you have to look to the most determined enemies of the civilization that mostly produced mathematics - Europe and its offspring, and then it's wise to notice how many other cultures have joined the great stream of mathematics - Russians, Chinese, Japanese, many others that did not cultivate high mathematics as a public good are now doing it. The Mandarins and the Indians were perfectly capable of doing it, and they very often loved it passionatetly, but they kept it in protected societies, guilds, priesthoods and bureaucracies that acted the way unions and corporations do today - they shut out most of their own populations and certainly foreigners. 
  
  Asian peoples discovered all kinds of arts and crafts, some extremely beautiful and clever, for their own inner circles. Europe tried that too, of course, but by the time of the Gutenberg Bible expert knowledge escaped out of control. Probably much earlier, but I would have to study the history more than I have. The Egyptians may have discovered the Pythagorean Theorem for purposes of building and land management (for taxation?). The most abstract forms of the theorem were probably stated very early on, maybe the Late Bronze Age, which was discovered by the ancient Greeks and related Mediterranean cultures around the same time. You could not build Pericles' fabulous buildings without a deep practical knowledge of geometry. So basic geometry had be available at that time, based on the Bronze Age collapse of 1178 BCE, I believe. But it wasn't just the Greeks (who had the best PR because they used the easiest non-tech writing system, the alphabet, with its Phoenician/Hebrew/Egyptian/Canaanite roots. Sanskrit alphabet popped up around the same time, and we know that the Indus Civilization carried on the soft metal trade to the Med and to China. These peoples were just as smart and ambitious then and now. 
  
  The PoMo/Woke attack on math and STEM fields violates all the rules of logic and math, particularly the importance of deductive proof and rigorous certainty. Plato's Academy required 10 years of geometry as a condition of entry, and Greek geometry required a confrontation with infinite series, with PI, and with the idea of "compelling proof" - one that forced any rational student of philosophy to assent.  I do not believe the famous places of origin were the ONLY places of origin, because we know that basic math is invented over and over again, just as music and dance, and warfare and peacemaking are invented over and over again. Math early in life (especially for both) has a compelling esthetic quality. It "HAS" to be done by those who fall under its spell. 
  
  This looks like an epigenetic switch on normal intellectual development, not even in Piaget's highest stage, but much earlier. It tends to be boys, because "little girls are interested in people, little boys play with THINGS,' according to the basic developmental observation. These are temperamental tendencies first manifesting in infancy. 
  Mozart became deeply enamored of music very early in life, my guess is long before age six, because his father Leopold was a famous violin teacher and lived that life. At the time in Vienna dancing and music making was a popular pastime, and the Catholic Church encouraged it, the aristocracy supported it, etc. But then you had spectacular chilhood geniuses popping up.  Math seems to be similar, and no doubt other talents are like that. 
  
  The PoMo/Woke story is a political movement driven by envy and get-even-with-them-ism.  They WILL kill off budding talents and differences between boys and girls, blacks and whites, and the excellent performance of many Asians. There will be fanatical propaganda and probably warfare over this. It's not the first time that "idealistic fanatics" have tried to coerce nature to fit their Procrustean beds. It's bound to end badly, which is why plausibly the smarter Chinese and other hostile powers are sponsoring, via Lenin's "useful fools." The aim is to kill off the goose that laid the golden egg, even as China (and Russia) are ruthlessly educating and training their own most talented people to take over. The West - or more generally, the rational cultures and subcultures of the world now seem happy to surrender, just as Americans are surrending to those Chinese espionage balloons driving over our major nuclear missile fields. Stupid is as stupid does. Under Mao, China went through exactly these mad gyrations, killed off their own most talented people, broke up families with the one-child rule, cut their population growth, all based on coercive lies. 
  
  By now they think we deserve our turn with suicidal educational policies, and apparently nobody really minds.  Hitler hated Einstein because he produced "Jewish science." That's one reason why Hitler lost the war. The Democrats are now pursuing a similar policy against "White science." But it's horseshit and there is no excuse for it.  :)b   ---------------------------------------------------------
 
   

 
 

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