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to the server to view the underlying object.
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"id": "https://infosec.exchange/users/sophieschmieg/statuses/113320184377876816",
"type": "Note",
"summary": "Physicists wielding ignorance as a super power",
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"published": "2024-10-17T01:33:09Z",
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"content": "<p>A rant, brought to you by me being jet-lagged and awake at 3am.</p><p>You might have heard about how the sum of all positive integers is equal to -1/12. It is not. The Riemann zeta function, for complex numbers with a real part bigger than one can be written as a series, and that series converges and forms a complexly differentiable (aka holomorphic) function. Holomorphic functions, defined on an open set, can be extended further. It doesn't always work, but when it does (and in the case of the Riemann zeta function it does), that extension is unique, so you can discuss the value of the Riemann zeta function at places that have a real part smaller than 1, like for example -1. We can calculate what the value the function takes there is, it happens to be -1/12. But, and the math is very clear on this, that value has absolutely, definitely, positively nothing to with the series we used on the right half plane.<br />So what do quantum physicists do, when their little theory runs into the sum of all positive integers? They just ignore that fact and replace the sum by -1/12. So far, that would just be a cautionary tale of how you shouldn't ignore preconditions, but they then go ahead, go to their experimental physicist colleagues, and ask them to run an experiment. And nature, which, at this point has to be assumed to be in on the conspiracy to drive mathematicians mad, makes it so that the result of the experiment is -1/12 to some ridiculously low tolerance.</p>",
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"en": "<p>A rant, brought to you by me being jet-lagged and awake at 3am.</p><p>You might have heard about how the sum of all positive integers is equal to -1/12. It is not. The Riemann zeta function, for complex numbers with a real part bigger than one can be written as a series, and that series converges and forms a complexly differentiable (aka holomorphic) function. Holomorphic functions, defined on an open set, can be extended further. It doesn't always work, but when it does (and in the case of the Riemann zeta function it does), that extension is unique, so you can discuss the value of the Riemann zeta function at places that have a real part smaller than 1, like for example -1. We can calculate what the value the function takes there is, it happens to be -1/12. But, and the math is very clear on this, that value has absolutely, definitely, positively nothing to with the series we used on the right half plane.<br />So what do quantum physicists do, when their little theory runs into the sum of all positive integers? They just ignore that fact and replace the sum by -1/12. So far, that would just be a cautionary tale of how you shouldn't ignore preconditions, but they then go ahead, go to their experimental physicist colleagues, and ask them to run an experiment. And nature, which, at this point has to be assumed to be in on the conspiracy to drive mathematicians mad, makes it so that the result of the experiment is -1/12 to some ridiculously low tolerance.</p>"
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"updated": "2024-10-17T05:27:09Z",
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