[Fis] Tough question: Decolonizing mathematics?

[Pedro C. Marijuán]

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!SntPyaSYtntTddsh_b-b4yYZqLRzIehRczCfgjUIVXQiro3Ll0jjFtCncoqw8JgpGoahAqw_NPqcM_Moe3z-dp5FYtd-$  
<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!SntPyaSYtntTddsh_b-b4yYZqLRzIehRczCfgjUIVXQiro3Ll0jjFtCncoqw8JgpGoahAqw_NPqcM_Moe3z-dp5FYtd-$ >

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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