Taming Infinity
How does physics deal with infinity? Tweet it - http://bit.ly/r7EwHK Facebook it - http://on.fb.me/n4pShU minutephysics is now on Google+ - http://bit.ly/qzEwc6 And facebook - http://fac...
==========
There's been some discussion about the video where I claimed that 1+2+4+8+16 and so onis equal to negative one - apparently I'm on my way to math jail. But actually, addingup divergent series is an old topic in math, and more importantly, it's actually relevantto physics! In physics, there are a lot of hard problems where we can't find the wholeanswer - but we can find the answer to a simplified version of the problem, and then correct itstep by step so we get closer and closer to the real answer.Check it out: we can approximate this hyperbola by starting with a line, adding a curve, awiggle, and onwards… except that our step-by-step process only works for a little part of thecurve! Outside this "area of convergence", we&...
==========
There's been some discussion about the video where I claimed that 1+2+4+8+16 and so onis equal to negative one - apparently I'm on my way to math jail. But actually, addingup divergent series is an old topic in math, and more importantly, it's actually relevantto physics! In physics, there are a lot of hard problems where we can't find the wholeanswer - but we can find the answer to a simplified version of the problem, and then correct itstep by step so we get closer and closer to the real answer.Check it out: we can approximate this hyperbola by starting with a line, adding a curve, awiggle, and onwards… except that our step-by-step process only works for a little part of thecurve! Outside this "area of convergence", we&...
