5 ms·

Naples' 1790s civil war was intensified by moral panic over Real Analysis (2023)

124 points by OgsyedIE 9mo ago

deleted 9mo ago
[deleted]
kazinator 9mo ago
Since the dawn of electronics, mathematics has entangled with politics indirectly, via technological change. The article describes a de facto technological change (emergence of Real Analysis), a kind of technology with many practical applications with economic implications.
- angry_octet 9mo ago
  Did you send this from an LLM?
  - kazinator 9mo ago
    Absolutely not.
boothby 9mo ago
Ye gods, we're truly in the stupidest timeline.
andrewflnr 9mo 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.
- inglor_cz 9mo 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.
  - deleted 9mo ago
    [deleted]
  - aebtebeten 9mo ago
    I'd always kind of imagined the reactionary geometers were defending an order in which their tools were imperfect finite approximations that yielded insights into perfect infinite truths, where the original sin of the revolutionary analysts was in saying that "yes, and with compactness and continuity, many of these problems have their α-and-ω in finite descriptions". Is that a fair take? Would it be one, even if it were ahistorical?
arduanika 9mo ago
War often pushes people to the limit
bawolff 9mo 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 9mo 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.
zozbot234 9mo 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: https://ncatlab.org/nlab/show/synthetic+mathematics https://ncatlab.org/nlab/show/synthetic+mathematics https://en.wikipedia.org/wiki/Synthetic_mathematics https://en.wikipedia.org/wiki/Synthetic_mathematics . There's nothing wrong with wishing to pursue a "coordinate-free" approach to any mathematical field: the old geometers were quite right about this.
- DangitBobby 9mo ago
  I don't understand how you got that at all. The impression I got was the synthetic mathematicians were wary of applying the new "analysis" methods because lack of rigor made them question how safe and valid it was to use. > Using another set of metaphors: Analysts followed the fast flights of their feverish and uncontrolled imagination, while synthetics kept their feet on the ground. Their procedures were slow but safe.
  - zozbot234 9mo ago
    > I don't understand how you got that at all. The word "reactionary" appears multiple times on that page, in association with either synthetic mathematics itself or the politics that's said to be closely connected to it. I'd say that's by far the most unambiguous part of my argument about this text.
    - freehorse 9mo ago
      Maybe because the title of the book this is a review of is “Reactionary Mathematics: A Genealogy of Purity”. This does not mean that coordinate free geometry is reactionary per se, but considering the coordinate system as spoiling the purity of geometry is.
      - zozbot234 9mo ago
        > considering the coordinate system as spoiling the purity Isn't that one of the main arguments for "coordinate free" or "synthetic" anything? It's about a pursuit of elegance and increased generality, not necessarily of obnoxious real-world politics; so it seems especially weird to inherently conflate these things.
pfdietz 9mo 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. https://en.wikipedia.org/wiki/The_Analyst https://en.wikipedia.org/wiki/The_Analyst 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. https://en.wikipedia.org/wiki/Italian_school_of_algebraic_geometry https://en.wikipedia.org/wiki/Italian_school_of_algebraic_ge... History doesn't repeat but it sometimes rhymes.
- aebtebeten 9mo ago
  From a contemporary viewpoint, Berkeley seems to have been a bit of an edgelord in his defense of faith: https://en.wikipedia.org/wiki/Appeal_to_the_stone#Origin https://en.wikipedia.org/wiki/Appeal_to_the_stone#Origin (or am I doing him an injustice and he was running with the whole Cartesian Demon thing to see just how far he could take it?) Mumford (a grand-advisee of Castelnuovo's) on the infamous school: https://ftp.mcs.anl.gov/pub/qed/archive/209 https://ftp.mcs.anl.gov/pub/qed/archive/209
  - gsf_emergency_6 9mo ago
    Fwiw, (exotericised) Accidentally self-awakened patriotic^W self-reliant cynic Seems like it could be somewhat ticklish, and Accidentally self-(right-)radicalising marginally-woke Could almost be. Btw, JD Vance claimed his wife is his spirit animal, so if he's a racist, he is at best the kind of racist who'd find it morally imperative that animals try and become human? PS: have you figured out what math pros would call the satirical functor? It's alright to ask your kith kin or kollegen for help :)
    - aebtebeten 9mo ago
      Unless it be one of the functors from Mathematics Made Difficult (1971) I shall have to ask my kith for counsel...
rm30 9mo 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.
amelius 9mo ago
This is so far removed from today's politics where the electorate seems to have switched off their brains.

124 points by OgsyedIE 9mo ago

deleted 9mo ago

[deleted]

Since the dawn of electronics, mathematics has entangled with politics indirectly, via technological change. The article describes a de facto technological change (emergence of Real Analysis), a kind of technology with many practical applications with economic implications.

angry_octet 9mo ago
Did you send this from an LLM?
- kazinator 9mo ago
  Absolutely not.

boothby 9mo ago

Ye gods, we're truly in the stupidest timeline.

andrewflnr 9mo 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.

inglor_cz 9mo 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.
- deleted 9mo ago
  [deleted]
- aebtebeten 9mo ago
  I'd always kind of imagined the reactionary geometers were defending an order in which their tools were imperfect finite approximations that yielded insights into perfect infinite truths, where the original sin of the revolutionary analysts was in saying that "yes, and with compactness and continuity, many of these problems have their α-and-ω in finite descriptions". Is that a fair take? Would it be one, even if it were ahistorical?

arduanika 9mo ago

War often pushes people to the limit

bawolff 9mo 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 9mo 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.

zozbot234 9mo 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: https://ncatlab.org/nlab/show/synthetic+mathematics https://ncatlab.org/nlab/show/synthetic+mathematics https://en.wikipedia.org/wiki/Synthetic_mathematics https://en.wikipedia.org/wiki/Synthetic_mathematics . There's nothing wrong with wishing to pursue a "coordinate-free" approach to any mathematical field: the old geometers were quite right about this.

DangitBobby 9mo ago
I don't understand how you got that at all. The impression I got was the synthetic mathematicians were wary of applying the new "analysis" methods because lack of rigor made them question how safe and valid it was to use. > Using another set of metaphors: Analysts followed the fast flights of their feverish and uncontrolled imagination, while synthetics kept their feet on the ground. Their procedures were slow but safe.
- zozbot234 9mo ago
  > I don't understand how you got that at all. The word "reactionary" appears multiple times on that page, in association with either synthetic mathematics itself or the politics that's said to be closely connected to it. I'd say that's by far the most unambiguous part of my argument about this text.
  - freehorse 9mo ago
    Maybe because the title of the book this is a review of is “Reactionary Mathematics: A Genealogy of Purity”. This does not mean that coordinate free geometry is reactionary per se, but considering the coordinate system as spoiling the purity of geometry is.
    - zozbot234 9mo ago
      > considering the coordinate system as spoiling the purity Isn't that one of the main arguments for "coordinate free" or "synthetic" anything? It's about a pursuit of elegance and increased generality, not necessarily of obnoxious real-world politics; so it seems especially weird to inherently conflate these things.

pfdietz 9mo 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. https://en.wikipedia.org/wiki/The_Analyst https://en.wikipedia.org/wiki/The_Analyst 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. https://en.wikipedia.org/wiki/Italian_school_of_algebraic_geometry https://en.wikipedia.org/wiki/Italian_school_of_algebraic_ge... History doesn't repeat but it sometimes rhymes.

aebtebeten 9mo ago
From a contemporary viewpoint, Berkeley seems to have been a bit of an edgelord in his defense of faith: https://en.wikipedia.org/wiki/Appeal_to_the_stone#Origin https://en.wikipedia.org/wiki/Appeal_to_the_stone#Origin (or am I doing him an injustice and he was running with the whole Cartesian Demon thing to see just how far he could take it?) Mumford (a grand-advisee of Castelnuovo's) on the infamous school: https://ftp.mcs.anl.gov/pub/qed/archive/209 https://ftp.mcs.anl.gov/pub/qed/archive/209
- gsf_emergency_6 9mo ago
  Fwiw, (exotericised) Accidentally self-awakened patriotic^W self-reliant cynic Seems like it could be somewhat ticklish, and Accidentally self-(right-)radicalising marginally-woke Could almost be. Btw, JD Vance claimed his wife is his spirit animal, so if he's a racist, he is at best the kind of racist who'd find it morally imperative that animals try and become human? PS: have you figured out what math pros would call the satirical functor? It's alright to ask your kith kin or kollegen for help :)
  - aebtebeten 9mo ago
    Unless it be one of the functors from Mathematics Made Difficult (1971) I shall have to ask my kith for counsel...

rm30 9mo 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.

amelius 9mo ago

This is so far removed from today's politics where the electorate seems to have switched off their brains.