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on Gopher (inofficial)
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URI Naples' 1790s civil war was intensified by moral panic over Real Analysis (2023)
rm30 wrote 6 min ago:
If we review the history we can notice that there was always an
influence from politics/religion to science, literature, arts,
philosophy and the use of them by politics, maybe to justify some
decision and state of facts.
It helps to empower control over population and fits perfectly in the
social and historical context: the emperor blessed by God, the
evolution theory, the epic poems, theory of race, the industrial
revolution, and modern times don't escape these patterns too, we just
suppose to be neutral.
pfdietz wrote 14 min ago:
The critique of calculus as lacking in rigor goes much further back
than that. Bishop Berkeley famously argued calculus was no more
dependable than theology. It was only with Cauchy and the
formalization of analysis in the 19th century that this issue would be
put to bed.
I wonder if the issues that this essay claims came up in Italy
persisted in any way. I ask that, because there was later (1885-1935)
an infamous breakdown in Italian mathematics (the "Italian School of
Algebraic Geometry") due to foundational issues. [1] History doesn't
repeat but it sometimes rhymes.
URI [1]: https://en.wikipedia.org/wiki/Italian_school_of_algebraic_geom...
zozbot234 wrote 2 hours 7 min ago:
Hot take: the author sneaks in a premise that synthetic mathematics is
per se "reactionary", but this is itself pure reactionary copium for
not getting it: [1] [2] . There's nothing wrong with wishing to pursue
a "coordinate-free" approach to any mathematical field: the old
geometers were quite right about this.
URI [1]: https://ncatlab.org/nlab/show/synthetic+mathematics
URI [2]: https://en.wikipedia.org/wiki/Synthetic_mathematics
bawolff wrote 3 hours 33 min ago:
> The Neapolitans did not reject modern analysis simply because they
considered it French.
And yet after reading the article, it sounds like that is exactly what
happened. They took some minor philosophical dispute in math and blew
it up for cultural reasons to stick it to the invader. It doesn't sound
like it ever really was about the math for most people in that context.
2b3a51 wrote 1 hour 18 min ago:
I think it depends on what one regards as a minor dispute. The
Newton/Leibniz calculus dispute a generation or so earlier was pretty
major, with Newton defending his deductive geometrical method of
fluxions against Leibniz's more algebraic concepts. Leibniz was also
much into his universal calculus. I was wondering what this Fergola
would have thought about Newton and his geometrical method
(fluxions)!
The Naples state at that time was around 5 million people. You had
the landowners (I imagine) looking around at the 'enclosures' of
common land in Britain and other parts of Europe and thinking about
rents. You had the engineers and Jacobins thinking about new roads
and canals and all. The ones who lost out appear to have been the
peasants as they lost the feudal protections and access to common
lands. And so it goes.
arduanika wrote 3 hours 50 min ago:
War often pushes people to the limit
andrewflnr wrote 4 hours 48 min ago:
I really want to read an essay on this topic by someone I'm more
confident actually understands what math is. Or truth, for that matter.
The author smears the boundary between what people believe and what is
logically entailed, and between mathematical techniques and the way
they are applied in modelling the real world. They persist in phrasing
their statements about how people conceptualize math in terms of "is"
and "are", which I tend to assume is a stylistic choice to speak in the
perspective of their subjects, but they're so sloppy about perception
and truth and "reason" in the rest of the piece that I can't be sure.
rtpg wrote 21 min ago:
> The author smears the boundary between what people believe and what
is logically entailed, and between mathematical techniques and the
way they are applied in modelling the real world.
I think the clue here is the section mentioning Cauchy and rigor.
Without a certain flavor of rigor, "proofs" given by people,
_especially in analysis_, can feel unsatisfying and can outright be
incorrect, even if the thing they are trying to prove is true!
Imagine a proof of the intermediate value theorem like: well if you
try to go from point A to point B you _have_ to pass through C in
between eventually or else you'll never get to B.
This might be a sketch of a proof, vaguely. And it's not like the IVT
is _wrong_, right? But a non-rigorous proof is not convincing. A
non-rigorous proof might leave out details that would otherwise
guarantee that a proof isn't left up to interpretation.
If your proof hand waves away some cases that feel trivial to you, to
others that might look like a hole in your proof! Or you might think
it's trivial, and actually it's not trivial.. but you haven't done
it.
Anyways this is, I think, the core here. A new style of mathematics
with new foundations... that haven't quite been smoothed out yet. The
conclusions being reached are all kinda mostly right, but the reasons
the conclusions are correct have not been actually properly set up.
So skeptics can drive a truck through that contradiction.
Knowledge is about knowing the right thing for the right reasons...
and in its infancy I could see a universe where a lot of
mathematicians are running around using its tooling without having
the right foundations for it.
We are lucky to live downstream of all this hard work. In the moment
things were messier (see also calculus' initial growing pains)
card_zero wrote 4 hours 11 min ago:
> statements about how people conceptualize math in terms of "is" and
"are"
What do you mean? I searched the page for "are", it doesn't appear
much at all, I'm ruling that one out. So do you mean for instance
this statement - ?
"This zealous quest for universal problem-solving algorithms is
precisely what made the synthetics uneasy."
What's wrong with that?
inglor_cz wrote 23 min ago:
"What's wrong with that?"
Political context. Rationalism was associated with atheism, which,
for the first time in European history, started making visible
inroads into the intellectual class. If you can solve all your
problems using your reason, do you really need a God? And plenty of
French philosophers hinted that the answer could be "no".
It wasn't just a religious question. Atheism or suspicion of
thereof was seen as politically subversive, in the age when most
ruling feudal dynasties still relied on God's grace as the ultimate
fount of their power - at least in their eyes of the subjects. (But
it wasn't always that cynical, plenty of the rulers themselves were
quite pious.)
gilleain wrote 4 hours 16 min ago:
Oh! I really liked the essay - the idea that French 'analysis' was
seen as a dangerous modern invention and contrasted with 'synthetic'
geometric understanding of the world had political implications is
fascinating. There could be parallels with the present day use of
computer modelling (and now AI) being seen as a risky way to organise
and run societies.
I agree that there is a lot of vague language around the practice of
mathematics as a social and philosophical construct ('analysts' vs
'synthetics') but I'm not sure how that indicates the author does not
understand what truth is. My understanding of the history of
mathematics and science is that these areas of knowledge were much
more intertwined with philosophy and religion than they are
considered to be today.
So Newton saw no issue with working on the calculus at the same time
as being an alchemist and a non-trinitarian. Understanding the world
was often a religious activity - by understanding Nature, you
understood God's creation - and in Naples it seems that understanding
analysis was tied to certain political and nationalist ideas.
inglor_cz wrote 4 hours 29 min ago:
I studied math (Algebra and Number Theory) and I am also quite
interested in history, and while I cannot write you a whole essay,
this is what I would like to react to:
"The author smears the boundary between what people believe and what
is logically entailed"
This is not the fault of the author. This is a fairly accurate
description of the societal situation back then, and the article is
more about societal impacts of math than math itself. Revolutionary,
and later Napoleonic France had very high regard for science, to the
degree that Napoleon took a sizeable contingent of scientists
(including then-top mathematicians like Gaspard Monge) with him to
Egypt in 1799. The same France also conquered half of the continent
and upended traditional relations everywhere.
This caused some political reaction in the, well, more reactionary
parts of the world, especially given that the foundations of modern
mathematics were yet incomplete. Many important algebraic and
analytic theorems were only discovered/proven in the 19th century
proper. Therefore, there was a certain tendency to RETVRN to the
golden age of geometry, which also for historical reasons didn't
involve any French people (and that was politically expedient).
If I had to compare this situation to whatever is happening now, it
would be politicization of biology/medicine after Covid. Another
similarity is that many scientists were completely existentially
dependent on their kings, which didn't give them a lot of
independence, especially in bigger countries, where you could not
simply move to a competing jurisdiction 20 miles away.
If your sovereign is somewhat educated (which, at that time, was
already quite normal; these aren't illiterate chieftains of the
Carolingian era) and hates subversive French (mathematical or
otherwise) innovations with passion, you won't be dabbling with them
openly.
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