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New evidence that Cantor plagiarized Dedekind?

quantamagazine.org

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Re: New evidence that Cantor plagiarized Dedekind?

#11

Post by tgv »

dang wrote: post #5

I think we can do without the baity title since most HN readers should know who Cantor and Dedekind are. Edit: okay, maybe not Dedekind. If someone wants to suggest a better title (i.e. more accurate and neutral, and preferably using representative language from the article itself), we can change it again.

I'm here for the 19th century drama. Imagine the head lines!

    Cantor's Continuity Credentials Cancelled: Clear Cut Copy Cat Case!
Millions of views for Tiktoks about homomorphisms and aleph numbers. Just the news we need right now.

Re: New evidence that Cantor plagiarized Dedekind?

#12

Post by pfortuny »

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…

The continuum. Connectedness.

Re: New evidence that Cantor plagiarized Dedekind?

#13

Post by collabs »

dang wrote: post #5

I think we can do without the baity title since most HN readers should know who Cantor and Dedekind are. Edit: okay, maybe not Dedekind. If someone wants to suggest a better title (i.e. more accurate and neutral, and preferably using representative language from the article itself), we can change it again.

This comment made me think of this xkcd 2501

https://xkcd.com/2501

There really is an xkcd for everything

Re: New evidence that Cantor plagiarized Dedekind?

#15

Post by zeroonetwothree »

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…

Complete just means the limit of every sequence is part of the set. So there’s no way to “escape” merely by going to infinity. Rational numbers do not have this property.

How to construct the real numbers as a set with that property (and the other usual properties) formally and rigorously took quite a long time to figure out.

Re: New evidence that Cantor plagiarized Dedekind?

#16

Post by zeroonetwothree »

mymacbook wrote: post #3
leephillips wrote: post #2

“Noether, who was Jewish, fled from Germany to the U.S., where she died two years later from cancer” It wasn’t two years, and it wasn’t cancer. These details are unimportant to the (quite interesting) story, but the error is a sign that the author copies information from unreliable secondary sources, which puts the other facts in the article in doubt. I wrote to him about the error when the article first appeared, bu…

Thank you! After Benj Edwards and Kyle Orland's Ars Technica article they published using AI (while saying they didn't), and all the while their article was about an AI agent publishing a hit piece on Scott Shambaugh (matplotlib maintainer), I feel like I now assume journalists are using AI and things need to be fact-checked just as we do for our AI interactions. I appreciate hearing about details like this and getti…

It’s not like journalists were very accurate before AI. Classic Gell-Mann amnesia

Re: New evidence that Cantor plagiarized Dedekind?

#17

Post by QuesnayJr »

leephillips wrote: post #2

“Noether, who was Jewish, fled from Germany to the U.S., where she died two years later from cancer” It wasn’t two years, and it wasn’t cancer. These details are unimportant to the (quite interesting) story, but the error is a sign that the author copies information from unreliable secondary sources, which puts the other facts in the article in doubt. I wrote to him about the error when the article first appeared, bu…

Are you citing your own book?

Re: New evidence that Cantor plagiarized Dedekind?

#18

Post by markisus »

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…

> Before their papers, mathematicians had assumed that even though the number line might look like a continuous object, if you zoomed in far enough, you’d eventually find gaps.

I'll try to interpret this sentence.

We all have some mental imagery that comes to mind when we think about the number line. Before Cantor and Dedekind, this image was usually a series of infinitely many dots, arranged along a horizontal line. Each dot corresponds to some quantity like sqrt(2), pi, that arises from mathematical manipulation of equations or geometric figures. If we ever find a gap between two dots, we can think of a new dot to place between them (an easy way is to take their average). However, we will also be adding two new gaps. So this mental image also has infinitely many gaps.

Dedekind and Cantor figured out a way to fill all the gaps simultaneously instead of dot by dot. This method created a new sort of infinity that mathematicians were unfamiliar with, and it was vastly larger than the gappy sort of infinity they were used to picturing.

Re: New evidence that Cantor plagiarized Dedekind?

#19

Post by wrsh07 »

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…

You can construct sequences of rational numbers where the limit is not rational (eg it's sqrt 2)

Trivially, the sequence of numbers who are the truncated decimal expansion of root 2 (eg 1.4, 1.41. 1.414, ...) although I find this somewhat unsatisfying.

With the real numbers there are no gaps. There are no sequences of reals where the limit of that sequence is not a real number

Re: New evidence that Cantor plagiarized Dedekind?

#20

Post by ajkjk »

lich_king wrote: post #10
leephillips wrote: post #2

“Noether, who was Jewish, fled from Germany to the U.S., where she died two years later from cancer” It wasn’t two years, and it wasn’t cancer. These details are unimportant to the (quite interesting) story, but the error is a sign that the author copies information from unreliable secondary sources, which puts the other facts in the article in doubt. I wrote to him about the error when the article first appeared, bu…

I have an opinion about the editorial style of Quanta that I don't think it's popular here (judging by how often they get upvoted), but I think it's a symptom of that. They cover science, but the template they consistently follow is a vague title that oversells the premise and then an article filled with human-interest details and appeals to implications. This makes it easy for everyone to follow along and have an op…

I think your opinion is popular here. Quanta is, while better than nothing, universally disappointing. It seems like it would be much easier for them to do a better job -- write less vaguely, fact-check more, assume the reader is a bit more intelligent.
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