Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

New evidence that Cantor plagiarized Dedekind?

quantamagazine.org

Post reply on HN
Print view View original

51–60 of 96 posts

Re: New evidence that Cantor plagiarized Dedekind?

#51

Post by AndrewKemendo »

dkarl wrote: post #48
AndrewKemendo wrote: post #35

Earlier quoted context omitted.

> If Dedekind and Cantor only changed how we visualize infinity, I don't understand why it would cause a stir. Because scientific progress is explicitly the process of changing the general mental model of how people approach a problem with a more broadly capable and repeatable set of operations This is philosophy of science 101

I should have been more specific; I understand why it was a mathematical breakthrough. What I don't understand is why it would have triggered some kind of psychological horror or philosophical crisis. It was a new way of understanding numbers, but it didn't reveal numbers to be acting any differently than we had always assumed. If anything, it seems like it would have been comforting to finally have mathematical cons…

History only seems obvious in retrospect

I would invite you to be more open to the idea that people don’t live in a world where they operate inside a theoretical framework with localized test actions

major breakthroughs tend to cause existential crises because most people don’t have full scope of their work in order to understand where it is broken

Re: New evidence that Cantor plagiarized Dedekind?

#52

Post by readthenotes1 »

renewiltord wrote: post #14

This whole plagiarism thing is too overwrought these days. People discuss stuff and the idea forms in the discussion between the two. Then one writes it up. Oh he plagiarized the other. I don’t know man.

Try reading the article?

And you don't like giving credit to people that help you? You may be successful by some measures, but not by the more important ones

Re: New evidence that Cantor plagiarized Dedekind?

#53

Post by dkarl »

antasvara wrote: post #33
dkarl wrote: post #4

> In their 1872 papers, though, Cantor and Dedekind had found a way to construct a number line that was complete. No matter how much you zoomed in on any given stretch of it, it remained an unbroken expanse of infinitely many real numbers, continuously linked. > Suddenly, the monstrosity of infinity, long feared by mathematicians, could no longer be relegated to some unreachable part of the number line. It hid within…

Take something like the integers (1,2,3,etc.). They are infinite; given an integer, you can always add 1 and get a new integer. However, there are "gaps" in that number line. Between 1 and 2, there are values that aren't integers. So the integers make a number line that is infinite, but that has gaps. Then we have something like the rational numbers. That's any number that can be expressed as a ratio of 2 integers (s…

I just don't understand why this was disturbing. Prior to the construction of the reals, the existence of irrational and transcendental numbers was disturbing, because they showed that previous constructions (rational numbers and algebraic numbers) were incomplete. If those gaps were disturbing, a construction without gaps should have been satisfying, reassuring, a resolution of tension. Was there some philosophical or theological theory that required the existence of gaps, that claimed that a complete construction of the number line was mathematically impossible, because of some attribute of God or the cosmos?

Re: New evidence that Cantor plagiarized Dedekind?

#54

Post by littlestymaar »

lupire wrote: post #36
antasvara wrote: post #33

Earlier quoted context omitted.

Take something like the integers (1,2,3,etc.). They are infinite; given an integer, you can always add 1 and get a new integer. However, there are "gaps" in that number line. Between 1 and 2, there are values that aren't integers. So the integers make a number line that is infinite, but that has gaps. Then we have something like the rational numbers. That's any number that can be expressed as a ratio of 2 integers (s…

Right, but that's the opposite of what the Quanta article says. The article says that Cantor and Dedekind discovered infinity in bounded intervals. What they discovered (really, what they concocted) was uncountable infinity.

Quanta messing things up isn't a particularly rare occurrence, unfortunately.

Re: New evidence that Cantor plagiarized Dedekind?

#56

Post by Exoristos »

dkarl wrote: post #48
AndrewKemendo wrote: post #35

Earlier quoted context omitted.

> If Dedekind and Cantor only changed how we visualize infinity, I don't understand why it would cause a stir. Because scientific progress is explicitly the process of changing the general mental model of how people approach a problem with a more broadly capable and repeatable set of operations This is philosophy of science 101

I should have been more specific; I understand why it was a mathematical breakthrough. What I don't understand is why it would have triggered some kind of psychological horror or philosophical crisis. It was a new way of understanding numbers, but it didn't reveal numbers to be acting any differently than we had always assumed. If anything, it seems like it would have been comforting to finally have mathematical cons…

Because painting those who objected to these definitions of mathematical infinity as "horrified" and "disturbed" was a form of character assassination, which was not uncommon at the time. The high moderns didn't play.

Re: New evidence that Cantor plagiarized Dedekind?

#57

Post by renewiltord »

readthenotes1 wrote: post #52
renewiltord wrote: post #14

This whole plagiarism thing is too overwrought these days. People discuss stuff and the idea forms in the discussion between the two. Then one writes it up. Oh he plagiarized the other. I don’t know man.

Try reading the article? And you don't like giving credit to people that help you? You may be successful by some measures, but not by the more important ones

Haha, the sanctimony is really too much.

Re: New evidence that Cantor plagiarized Dedekind?

#58

Post by QuesnayJr »

cls59 wrote: post #42
QuesnayJr wrote: post #25

From the article it's hard to tell if Cantor really did plagiarize (though it seems Dedekind thought he did). According to the article, Cantor proved the theorem first and sent it to Dedekind. Dedekind suggested a simplification of the proof, which Cantor used when he wrote it up. The story doesn't make Cantor look good, but if the original proof by Cantor is correct, then the credit for the theorem still basically b…

If I understand the article correctly, that second proof was published as a rider on a first proof that was entirely Dedekind's. So, there was definitely a credit owed at time of publishing. I came away with the impression that the biggest villain in this story was Kronecker. Without the need to tiptoe around his ego and gatekeeping, these results may have been published as a paper with joint authorship.

I read it the other way. Here's the quote from the article:

On December 7, 1873, he wrote to Dedekind that he thought he’d finally succeeded: “But if I should be deceiving myself, I should certainly find no more indulgent judge than you.” He laid out his proof. But it was unwieldy, convoluted. Dedekind replied with a way to simplify Cantor’s proof, building a clearer argument without losing any rigor or accuracy. Meanwhile Cantor, before he’d received Dedekind’s letter, sent him a similar idea for how to streamline the proof, though he hadn’t worked out the details the way Dedekind had.

Re: New evidence that Cantor plagiarized Dedekind?

#59

Post by dvt »

wizzwizz4 wrote: post #27
leephillips wrote: post #22

Earlier quoted context omitted.

It won’t be the last time.

It's best practice to say something like "Noether's real story is recounted in my book [link]". This both establishes you as a subject matter expert, and stops your comments looking like disingenuous grift.

It's literally cited in his bio, and he's using his real name on HN. It's about as far as grift as it could be. If he's being curt, he's probably (rightfully) frustrated that "journalists" are getting such bottom-of-the-barrel facts wrong.

Re: New evidence that Cantor plagiarized Dedekind?

#60

Post by AdAbsurdum »

QuesnayJr wrote: post #58
cls59 wrote: post #42

Earlier quoted context omitted.

If I understand the article correctly, that second proof was published as a rider on a first proof that was entirely Dedekind's. So, there was definitely a credit owed at time of publishing. I came away with the impression that the biggest villain in this story was Kronecker. Without the need to tiptoe around his ego and gatekeeping, these results may have been published as a paper with joint authorship.

I read it the other way. Here's the quote from the article: On December 7, 1873, he wrote to Dedekind that he thought he’d finally succeeded: “But if I should be deceiving myself, I should certainly find no more indulgent judge than you.” He laid out his proof. But it was unwieldy, convoluted. Dedekind replied with a way to simplify Cantor’s proof, building a clearer argument without losing any rigor or accuracy. Mea…

I think the relevant quotes are these:

"Dedekind quickly replied that...he’d worked out a proof that the algebraic numbers (the numbers you get as solutions to algebra problems) could be counted.

[...]

Weierstrass had been most excited about the proof that algebraic numbers are countable. (He would later use that result to prove a theorem of his own.) So Cantor chose a misleading title [for his paper] that only mentioned algebraic numbers.

[...]

Writing his paper, Cantor put the proof about algebraic numbers first. Below it, he added his own proof that the real numbers cannot be counted — Dedekind’s simplified version of it, that is."

So the first proof -- the one the article was titled after -- was completely created by Dedekind.

Post reply on HN