foundational crises: notes

[Joseph Tracy]

Crisis in Mathematics in ATD : notes

I decided to look up the original quote from ATD that was used for  
the Nina Engelhardt abstract, then kinda bounced around the net.  I  
left out  a lot, but I hope the notes  below give a little more  
context for an interesting topic. Besides some of what I list, the  
life of Bertrand Russell is also an interesting reference: Anti-war  
enough to be jailed during WW1, sexually libertarian, friend of  
Wittgenstein, went to Russia early after revolution and was  
disenchanted, challenged Christianity with logic, part of attempt to  
provide a logical foundation for mathematics, but also undermined  
same. Thanks Ray for provoking a look into a topic and people that is  
not my natural element.

Selections from page 594 for context, with complete quote on crisis

	One evening he( Kit) happened to be walking along the promenade on  
top of the old fortifications, and near the statue of Gauss passing  
to Weber a remark forever among the pages of silence….

	…Whenever I see one( Zeta function) it reminds me of you (Yashmeen).  
The charmer part anyway”

	Aaah! Even more trivial. Do none of you ever think beyond these  
walls? There is a crisis out there” She scowled into the stained  
orange 	glow of the just vanished sun, the smoke rising from hundreds  
of chimneys. “ And Gottingen’s no more exempt than it was in  
Reimann’s 	day, in the war with Prussia. The political crisis in  
Europe maps into the crisis in mathematics. Weierstrass functions,  
Cantor’s continuum, 	Russell’s equally inexhaustible capacity for  
mischief - once, among nations, as in chess, suicide was illegal.  
Once among mathematicians, the infinite was all but a conjuror’s  
convenience. The connections lie there, Kit - hidden and poisonous.  
Those of us who must creep among them do so at our peril”

	“Come on,” Kit said,” let a trivial fellow buy you a beer.”


national suicide …connected to (=)…the infinite ( some infinities  
being larger than others, according to Cantor)  One of the problems  
with capitalism is the Ponzi–style reliance on constant growth 
( implied infinity) in a world of limited resources, widespread  
resource competition.

the statue of Gauss and Weber reinforces the connections between  
mathematics and  practical uses of electromagnetism and also between  
academia and technology

 From Wikipedia
...at one time, the Greeks held the opinion that 1 (one) was not a  
number, but rather a unit of arbitrary length. A number was defined  
as a multitude. Therefore 3, for example, represented a certain  
multitude of units, and was thus not "truly" a number. At another  
point, a similar argument was made that 2 was not a number but a  
fundamental notion of a pair. These views come from the heavily  
geometric straight-edge-and-compass viewpoint of the Greeks: just as  
lines drawn in a geometric problem are measured in proportion to the  
first arbitrarily drawn line, so too are the numbers on a number line  
measured in proportional to the arbitrary first "number" or "one."
These earlier Greek ideas of numbers were later upended by the  
discovery of the irrationality of the square root of two. Hippasus, a  
disciple of Pythagoras, showed that the diagonal of a unit square was  
incommensurable with its (unit-length) edge: in other words he proved  
there was no existing (rational) number that accurately depicts the  
proportion of the diagonal of the unit square to its edge. This  
caused a significant re-evaluation of Greek philosophy of  
mathematics. According to legend, fellow Pythagoreans were so  
traumatized by this discovery that they murdered Hippasus to stop him  
from spreading his heretical idea.

Seems like maths related politics and killing have precedent even  
among the pacifist Pythagoreans.

Wikipedia on Frege( taught at Gottingen)

Gottlob Frege wanted to show that mathematics grew out of logic, but  
in so doing devised techniques that took him far beyond the  
Aristotelian syllogistic and Stoic propositional logic that had come  
down to him in the logical tradition. In effect, he invented  
axiomatic predicate logic, in large part thanks to his invention of  
quantified variables, which eventually became ubiquitous in  
mathematics and logic, and solved the problem of multiple generality.
He was anti-semitic, anti- catholic and died in 1925, an ardent  
admirer of Adolph Hitler, He also taught Jewish historian and  
Kabbalist Gershom Scholem.
He shared  philosophical communication and accord with the very  
politically different Bertrand Russell.

I feel there is a consistent historical connection between axiomatic  
predicate logic, which sounds  a lot like the basis of Calvinist  
Theology, and the logic of ethnic cleansing, purification of the  
party/race/faith/nation?

multiple universes, digital machinery, world wide communication,  
subatomic energy, limits, chemistry, penises ascending into the great  
blue yonder-

Mathematics leads in many directions. The sense I got as I read more  
about the foundational crisis is about the uncanny power of  
disciplined thought, the importance of foundational ideas, and the  
difficulty of knowing anything or of finding even  enough common  
ground to avoid spite, fear, mistrust and violence.