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

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

#21

Post by andrewflnr »

inglor_cz wrote: post #3
andrewflnr wrote: post #2

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…

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…

> This is not the fault of the author. This is a fairly accurate description of the societal situation back then

The author is not giving a helpful description if they slip into the same mistakes as the people of the time.

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

#22

Post by inglor_cz »

aebtebeten wrote: post #20
inglor_cz wrote: post #3

Earlier quoted context omitted.

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…

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 w…

I like that perspective, but I believe the conflict was more about "old vs. new". Geometry was very old by that point, ancient, and it carried a lot of personal gravitas by being associated with Euclid, Archimedes, Thales etc. (Galenic theory of humors enjoyed similar ancient intellectual prestige, hence its long and bitter retreat from the scene at approximately the same time.) It was also "obviously right", in the sense of "everyone can look and see for themselves". Even uneducated peple can verify that a certain line touches both circles etc. No wonder it was an attractive safe haven for conservative minds.

Meanwhile, analysis was not yet particularly rigorous and it took several decades to converge on a standard apparatus and notation that could at least be understood coherently by other mathematicians. (Laymen tend to struggle with it until today.) Add the political dimensions of being seen friendly to the French into the mix, well...

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

#23

Post by bgilroy26 »

inglor_cz wrote: post #3
andrewflnr wrote: post #2

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…

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…

>Therefore, there was a certain tendency to RETVRN to the golden age of geometry

Echoed in the LaRouchians of the 2000s. I don't know what they're up to now

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

#25

Post by kazinator »

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.

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

#26

Post by aebtebeten »

pfdietz wrote: post #13

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 I wonder if the issues that this essay claims came up in Italy persisted in any way. I ask that, because…

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

(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

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

#28

Post by Blackthorn »

inglor_cz wrote: post #11
card_zero wrote: post #5

Earlier quoted context omitted.

> 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?

"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 se…

Very good reminder when it comes to thinking about that period of time. The famous apocryphal conversation between Napoleon and Laplace comes to mind here.

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

#29

Post by Terr_ »

inglor_cz wrote: post #11
card_zero wrote: post #5

Earlier quoted context omitted.

> 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?

"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 se…

> (But it wasn't always that cynical, plenty of the rulers themselves were quite pious.)

It's probably easy to believe in a God that pre-approved and delivered my life of wealth, power, and leisure. :p

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

#30

Post by angry_octet »

kazinator wrote: post #25

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.

Did you send this from an LLM?
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