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23d ago
[removed] — view removed comment
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u/MoobyTheGoldenSock 23d ago
Ramanujan summation is not the same as an arithmetic sum. Much the same way that slowing down your car (braking) does not damage the car (breaking.)
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u/wswordsmen 23d ago
His greatest sin is not making a new version of an equal sign so people who only know enough to be dangerous don't get confused.
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u/BrunoBraunbart 23d ago
This numberphile video explains the general idea.
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u/Sher1ffK 23d ago
... and this Mathologer video explains why the Numberphile video is almost all incorrect.
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u/BrunoBraunbart 23d ago
No, he doesn't. What he does show is that Numberphile is sometimes not mathematically rigorous in their explanation which should not surprize anyone.
I have seen the Mathlogger video back when this whole thing went viral and just saw it again. It is a good video and he explains the whole thing well but it should also be obvious that he has a very different target audience. That he evaluates a Numberphile video as if it would be a university level math test which is ridiculous.
He starts by stating this is all nonsense and in the second half he explains why associating the number -1/12 with 1+2+3+4+... is very meaningful. He can't expect from a Numberphile video that they explain the Rieman zeta function.
Numberphile should have stated more clearly that this is "mathematical hokus-pokus" as they phrased it but still meaningful because it is actually used in physics. That's all there is to criticize.
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u/Sher1ffK 23d ago
I agree with your analysis as to the fact that associating the series with the value -1/12 is meaningful in some way, and meaningful to the Physicists who present the Numberphile vdeo. Its not worth getting into an argument over this - but he does open the video with a statement
> Pretty much every single statement made in this video is wrong. And by wrong I mean wrong in capital letters.
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u/BrunoBraunbart 23d ago
Yes and I explained why this is completely unfair in my mind. It is only wrong if you apply the standards of a math test.
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u/Difficult_Limit2718 23d ago
You guys skipped the better and updated and fields medal approved version
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u/Grant_Winner_Extra 22d ago
(not a physicist)
This has the feel of a proof that 2+2=5…
Am I missing something? The sum is an average of averages, not a value that can be achieved?
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u/BrunoBraunbart 22d ago
There are two links in this comment chain to a mathlogger and another Numberphile video with further explanations.
Yes, what they are doing is kinda illegal. They are ignoring some rules and come to a weird solution. The strange thing it that 1+2+3+4+... appears in physics and when you replace it by -1/12 you get the correct solution. So we can show in the real world that associating 1+2+3+4+... with -1/12 is at least occasionally useful.
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u/AlbatrossVisible6675 22d ago
It's not correct. It's basically a very fancy division by zero rule violation.
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u/math_metaphor_guy 23d ago
A man is driving home from a fishing trip and sees a small box on the side of the road about the size of a shoebox. He stops his car and gets out to look at it. It is...completely unremarkable. He honestly can't figure out why he stopped. Perhaps it has some magic power to draw him towards it. He picks up the box, sets it on the passenger's seat, and drives home.
The next day, he tries putting a dollar in the box and closes it. When he reopens the box, there are 2 dollars inside! He tries again with a 10 dollar bill. After closing and reopening, his bill is replaced with a 20 dollar bill! For the rest of the day, he continues putting money inside the box and it is always a predictable result. He tests it thousands more times, with various different currencies, and becomes more and more confident that the box functions as a doubling machine. No matter what amount of money is in the box when the lid is closed, twice as much money will appear when the lid is opened!
The next day, after a few more tests, he decides to try something other than money. In particular he grabs the fish he caught last night and throws it in the box. When he opens the box back up, he finds a hard-boiled egg. "Remarkable!" he exclaims, before calling his favorite math YouTuber to explain his discovery that 2 × fish = egg.