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The issue with physics isn't that they're hand-wavy, it's that they teach their students demonstrably false things. Such as, an infinite point-impulse is a func

by j2kun 12y ago

The issue with physics isn't that they're hand-wavy, it's that they teach their students demonstrably false things. Such as, an infinite point-impulse is a function with integral 1, and the sum of all positive integers is -1/12, and other such nonsense about "convergent" sequences. They balk at the nuance of mathematics when it actually matters to us.

nilkn 12y ago
The nuances of mathematics are really extremely important in modern theoretical physics, too, given that most problems in quantum field theory have historically involved divergent integrals that physicists need to converge. (This is also what's preventing a quantum theory of gravity.) Physics today does have some remarkably talented mathematical thinkers, like Edward Witten, but most of them are involved in very fanciful theories like string theory.
tjradcliffe 12y ago
I've never heard a physicist claim the sum of all positive integers is -1/12. Such people may exist, but they are extremely rare. And the Dirac delta is the limit of a function with integral 1, not a function. Maybe you need to hang out with a better class of physicists? There are certainly plenty of mathematicians who believe odds things, but I'd be leery of tarring the whole lot with the same brush.
- jdpage 12y ago
  The sum of all positive integers can actually be considered to be -1/12 in a self-consistent fashion. It isn't equal in the same sense that 2+2=4, and it's still true that the limit at infinity of the partial sum of the positive integers doesn't exist. On the other hand, it really is a useful result. The negative part is, for example, why the Casimir force is attractive. Here's an article about the whole thing, with links to the various Numberphile videos and Phil Plait articles that have been done about it: http://physicsbuzz.physicscentral.com/2014/01/does-1234-112.html http://physicsbuzz.physicscentral.com/2014/01/does-1234-112....
  - j2kun 12y ago
    Forgetting for a moment that the entire post is an appeal to authority (in other words, ignoring all logic) here's the culprit quote from the post: > In the Wikipedia article, they have an equation that looks like this \zeta(-3)=1/120, but the stuff on the left hand side is just another way of writing 1^3+2^3+3^3 +4^3+... If you can't explain why the above claim is screwy, then every time you claim, "the sum of all positive integers is -1/12," you need to qualify it with "I have no idea why, but I know there's some complicated mathematics that removes the word 'sum' and 'positive integers' and replaces them with more complicated concepts I'm don't have the time to learn about, and we physicists abuse it to say what I just said."
  - j2kun 12y ago
    He also says things like > If QED is correct ... then I would argue that the things that go into QED calculations must be just as correct. Also not how logic works.
gone35 12y ago
the sum of all positive integers is -1/12, and other such nonsense Sure sure, but do know that a lot of all that hacky regularization stuff can be made mathematically sound after all --see for instance [1,2]. [1] http://www.maths.qmul.ac.uk/~tp/talks/casimir.pdf#page55 http://www.maths.qmul.ac.uk/~tp/talks/casimir.pdf#page55 [2] http://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation/ http://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin...
- j2kun 12y ago
  Of course I know (I'm a mathematician, I'm the one who cringes at all that). The abuse doesn't stop there though... :(

by j2kun 12y ago

nilkn 12y ago

The nuances of mathematics are really extremely important in modern theoretical physics, too, given that most problems in quantum field theory have historically involved divergent integrals that physicists need to converge. (This is also what's preventing a quantum theory of gravity.) Physics today does have some remarkably talented mathematical thinkers, like Edward Witten, but most of them are involved in very fanciful theories like string theory.

tjradcliffe 12y ago

I've never heard a physicist claim the sum of all positive integers is -1/12. Such people may exist, but they are extremely rare. And the Dirac delta is the limit of a function with integral 1, not a function. Maybe you need to hang out with a better class of physicists? There are certainly plenty of mathematicians who believe odds things, but I'd be leery of tarring the whole lot with the same brush.

jdpage 12y ago
The sum of all positive integers can actually be considered to be -1/12 in a self-consistent fashion. It isn't equal in the same sense that 2+2=4, and it's still true that the limit at infinity of the partial sum of the positive integers doesn't exist. On the other hand, it really is a useful result. The negative part is, for example, why the Casimir force is attractive. Here's an article about the whole thing, with links to the various Numberphile videos and Phil Plait articles that have been done about it: http://physicsbuzz.physicscentral.com/2014/01/does-1234-112.html http://physicsbuzz.physicscentral.com/2014/01/does-1234-112....
- j2kun 12y ago
  Forgetting for a moment that the entire post is an appeal to authority (in other words, ignoring all logic) here's the culprit quote from the post: > In the Wikipedia article, they have an equation that looks like this \zeta(-3)=1/120, but the stuff on the left hand side is just another way of writing 1^3+2^3+3^3 +4^3+... If you can't explain why the above claim is screwy, then every time you claim, "the sum of all positive integers is -1/12," you need to qualify it with "I have no idea why, but I know there's some complicated mathematics that removes the word 'sum' and 'positive integers' and replaces them with more complicated concepts I'm don't have the time to learn about, and we physicists abuse it to say what I just said."
- j2kun 12y ago
  He also says things like > If QED is correct ... then I would argue that the things that go into QED calculations must be just as correct. Also not how logic works.

gone35 12y ago

the sum of all positive integers is -1/12, and other such nonsense Sure sure, but do know that a lot of all that hacky regularization stuff can be made mathematically sound after all --see for instance [1,2]. [1] http://www.maths.qmul.ac.uk/~tp/talks/casimir.pdf#page55 http://www.maths.qmul.ac.uk/~tp/talks/casimir.pdf#page55 [2] http://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation/ http://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin...

j2kun 12y ago
Of course I know (I'm a mathematician, I'm the one who cringes at all that). The abuse doesn't stop there though... :(