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<div class="moz-cite-prefix">Dear FISers, <br>
</div>
<div class="moz-cite-prefix">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:</div>
<div class="moz-cite-prefix"><a href="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://www.nature.com/articles/d41586-023-00223-w?utm_campaign=nature-careers-newsletter&utm_medium=email&utm_edition=202302030500&utm_source=newsletter</a></div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">I copy below interesting responses from
Lou Kauffman and Bernard Baars. <br>
</div>
<div class="moz-cite-prefix">They make an interesting read.</div>
<div class="moz-cite-prefix">Best--Pedro<br>
</div>
<div class="moz-cite-prefix">
<div class="moz-text-html" lang="x-unicode">----------------------------</div>
<div class="moz-text-html" lang="x-unicode">Dear Plamen,
<div class="">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,</div>
<div class="">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. </div>
<div class=""><br class="">
</div>
<div class="">In teaching mathematics it is important to bring
examples that students can understand. Backgrounds vary. </div>
<div class=""><br class="">
</div>
<div class="">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.</div>
<div class=""><br>
</div>
<div class="">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.”</div>
</div>
<div class="">This bit of probability is striking because of the
sharp cultural and personal resonance with the day of birth.</div>
<div class="">In other cultural situations there will be other
examples that have a similar resonance.</div>
<div class="">It is worth searching them out.</div>
<div class=""><br class="">
</div>
<div class="">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 </div>
<div class="">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.</div>
<div class=""><br class="">
</div>
<div class="">A possible right attitude is to be as curious as
possible about what mathematics might come from structures in
any human culture.</div>
<div class="">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.</div>
<div class=""><br class="">
</div>
<div class="">Very best,</div>
<div class="">Lou Kauffman</div>
<div class="">-----------------------------------------------</div>
<div class="">(From Baars)</div>
<div class=""><br>
</div>
<div class="">
<div dir="ltr">
<div class="gmail_default" style="font-family:comic sans
ms,sans-serif;font-size:xx-large"><font size="-1">The
post-modern assault on mathematics is destructive
nonsense, intended to destroy Western culture. </font></div>
<div class="gmail_default" style="font-family:comic sans
ms,sans-serif;font-size:xx-large"><font size="-1">To be nice
and understanding about it is very kind, but it's a
failure to understand a deadly cultural threat. </font></div>
<div class="gmail_default" style="font-family:comic sans
ms,sans-serif;font-size:xx-large"><font size="-1">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. <br>
</font></div>
<div class="gmail_default" style="font-family:comic sans
ms,sans-serif;font-size:xx-large"><font size="-1"><br>
</font></div>
<div class="gmail_default" style="font-family:comic sans
ms,sans-serif;font-size:xx-large"><font size="-1">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. <br>
</font></div>
<div class="gmail_default" style="font-family:comic sans
ms,sans-serif;font-size:xx-large"><font size="-1"><br>
</font></div>
<div class="gmail_default" style="font-family:comic sans
ms,sans-serif;font-size:xx-large"><font size="-1">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. </font></div>
<div class="gmail_default" style="font-family:comic sans
ms,sans-serif;font-size:xx-large"><font size="-1">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. <br>
</font></div>
<div class="gmail_default" style="font-family:comic sans
ms,sans-serif;font-size:xx-large"><font size="-1"><br>
</font></div>
<div class="gmail_default" style="font-family:comic sans
ms,sans-serif;font-size:xx-large"><font size="-1">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.</font></div>
<div class="gmail_default" style="font-family:comic sans
ms,sans-serif;font-size:xx-large"><font size="-1"><br>
</font></div>
<div class="gmail_default" style="font-family:comic sans
ms,sans-serif;font-size:xx-large"><font size="-1">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. </font></div>
<div class="gmail_default" style="font-family:comic sans
ms,sans-serif;font-size:xx-large"><font size="-1">Math seems
to be similar, and no doubt other talents are like that. <br>
</font></div>
<div class="gmail_default" style="font-family:comic sans
ms,sans-serif;font-size:xx-large"><font size="-1"><br>
</font></div>
<div class="gmail_default" style="font-family:comic sans
ms,sans-serif;font-size:xx-large"><font size="-1">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. <br>
</font></div>
<div class="gmail_default" style="font-family:comic sans
ms,sans-serif;font-size:xx-large"><font size="-1"><br>
</font></div>
<div class="gmail_default" style="font-family:comic sans
ms,sans-serif;font-size:xx-large"><font size="-1">By now
they think we deserve our turn with suicidal educational
policies, and apparently nobody really minds. </font></div>
<div class="gmail_default" style="font-family:comic sans
ms,sans-serif;font-size:xx-large"><font size="-1">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. </font></div>
<div class="gmail_default" style="font-family:comic sans
ms,sans-serif;font-size:xx-large"><font size="-1">:)b</font></div>
</div>
</div>
<div class="">---------------------------------------------------------<br
class="">
<br>
</div>
</div>
<p><br>
</p>
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