5 ms·

If they make the limit infinite, you'd end up being paid -1/12 of a cent. https://www.youtube.com/watch?v=w-I6XTVZXww https://www.youtube.com/watch?v=w-I6XTVZX

If they make the limit infinite, you'd end up being paid -1/12 of a cent. https://www.youtube.com/watch?v=w-I6XTVZXww https://www.youtube.com/watch?v=w-I6XTVZXww

barsonme 11y ago
Good Lord, I watched the second video -- the one featuring Ed Copeland -- and I think I just fried my brain for the rest of the day. (Also, he has fantastic penmanship.)
serge2k 11y ago
Only if you're an Indian Mathematician. or a physicist.
owenversteeg 11y ago
Nope! http://goodmath.scientopia.org/2014/01/17/bad-math-from-the-bad-astronomer/ http://goodmath.scientopia.org/2014/01/17/bad-math-from-the-...
- openasocket 11y ago
  Incorrect, there is actually some well-established mathematics dealing with divergent series as summing to finite values via analytic continuation. These results have to be treated with care, because they are inconsistent under certain algebraic manipulations, but the techniques are "real" enough that their results are used in particle physics. https://en.wikipedia.org/wiki/Regularization_(physics) https://en.wikipedia.org/wiki/Regularization_(physics)
  - owenversteeg 11y ago
    "The sum of the series 1+2+3+4+5+6... = -1/12" is patently false, without a previous assertion that we have assumed the Cesàro sum of a series is equal to the series. Even mathematicians working with Cesàro sums surround such statements with "this holds only if we interpret the infinite sum defining Z to be the Cesàro sum..." [0] Precisely none of the times I've heard the "1+2+3+4...=-1/12" bullshit has the person stating it prefaced their statement with "this holds only if we interpret the infinite sum defining Z to be the Cesàro sum..." If you say that "1+2+3+4...=-1/12" without stating your prior assumptions, you suddenly allow anyone to make any assumption whatsoever, no matter how obscure it is. In your imaginary world, someone could walk into a store and claim that "this 95 cent pack of gum is free" because they just made the unstated assumption that all non-integers do not exist, and seconds later they could return it for a full refund of $0.95 after making the unstated assumption that in fact the rational numbers do exist. Numbers, and in fact the entire system of mathematics fail to work at all once you allow arbitrary, unstated assumptions no matter their obscurity. And in fact, the assumption that non-integer numbers do not exist is made far, far more frequently than the assumption that the infinite sum defining the sequence is the Cesàro sum. The only difference is that assuming the non-integer numbers do not exist is a defensible assumption in many, many scenarios... but Cesàro summations are only invoked about twelve times a year, in pure math or advanced physics papers. [0] Madras, Neal. "A Note on Diffusion State Distance." arXiv preprint arXiv:1502.07315 (2015).
rdancer 11y ago
Tony Padilla sure can sell that sleight of hand :-)

If they make the limit infinite, you'd end up being paid -1/12 of a cent. https://www.youtube.com/watch?v=w-I6XTVZXww https://www.youtube.com/watch?v=w-I6XTVZXww

barsonme 11y ago

Good Lord, I watched the second video -- the one featuring Ed Copeland -- and I think I just fried my brain for the rest of the day. (Also, he has fantastic penmanship.)

serge2k 11y ago

Only if you're an Indian Mathematician. or a physicist.

owenversteeg 11y ago

Nope! http://goodmath.scientopia.org/2014/01/17/bad-math-from-the-bad-astronomer/ http://goodmath.scientopia.org/2014/01/17/bad-math-from-the-...

openasocket 11y ago
Incorrect, there is actually some well-established mathematics dealing with divergent series as summing to finite values via analytic continuation. These results have to be treated with care, because they are inconsistent under certain algebraic manipulations, but the techniques are "real" enough that their results are used in particle physics. https://en.wikipedia.org/wiki/Regularization_(physics) https://en.wikipedia.org/wiki/Regularization_(physics)
- owenversteeg 11y ago
  "The sum of the series 1+2+3+4+5+6... = -1/12" is patently false, without a previous assertion that we have assumed the Cesàro sum of a series is equal to the series. Even mathematicians working with Cesàro sums surround such statements with "this holds only if we interpret the infinite sum defining Z to be the Cesàro sum..." [0] Precisely none of the times I've heard the "1+2+3+4...=-1/12" bullshit has the person stating it prefaced their statement with "this holds only if we interpret the infinite sum defining Z to be the Cesàro sum..." If you say that "1+2+3+4...=-1/12" without stating your prior assumptions, you suddenly allow anyone to make any assumption whatsoever, no matter how obscure it is. In your imaginary world, someone could walk into a store and claim that "this 95 cent pack of gum is free" because they just made the unstated assumption that all non-integers do not exist, and seconds later they could return it for a full refund of $0.95 after making the unstated assumption that in fact the rational numbers do exist. Numbers, and in fact the entire system of mathematics fail to work at all once you allow arbitrary, unstated assumptions no matter their obscurity. And in fact, the assumption that non-integer numbers do not exist is made far, far more frequently than the assumption that the infinite sum defining the sequence is the Cesàro sum. The only difference is that assuming the non-integer numbers do not exist is a defensible assumption in many, many scenarios... but Cesàro summations are only invoked about twelve times a year, in pure math or advanced physics papers. [0] Madras, Neal. "A Note on Diffusion State Distance." arXiv preprint arXiv:1502.07315 (2015).

rdancer 11y ago

Tony Padilla sure can sell that sleight of hand :-)