One minus one plus one minus one - Numberphile

Discussing the brain-bending Grandi's Series and Thomson's Lamp - featuring Dr James Grime.
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NUMBERPHILE

Videos by Brady Haran

[pilotandy_com]

An infinite number of mathematicians walk into a bar. The first one orders a beer. The second one orders half a beer. The third one orders a fourth of a beer. The bartender stops them, pours two beers and says, "You guys should know your limits."

[WhiteSleevedStu]

"This is weird. " - Guido Grandi, Italian Mathematician

[bubbleworld]

Look at his pupils. He's clearly on crystal math.

[ECopas]

I love how much this dude genuinely loves math; he couldn’t hide it if he tried

[enochromeropress]

3:33 the best dramatic zoom of all time

[anastasissfyrides]

its like asking whether infinity is even or odd

[moniquemauleon]

When you try to balance the light switch between on and off

[srquint]

No mystery here! The answer to this question is that the problem is improperly (or incompletely) defined. Therefore, as approached in this presentation, the answer is dependent on additional constraints on the problem imposed by the solution which is applied. Moving the parentheses about depending on the method used is actually adding constraints to the posed question and in so doing CHANGING the posed question. For example, placing the parentheses as (1-1) for ALL summed terms assures that the answer will be zero at infinity. This is a DIFFERENT problem than starting a 1 and then adding (-1+1) terms, assuring that the starting 1 always has a 0 added at each step to infinity. Thus, the answer is INDETERMINATE due to an incompletely defined problem.

[jasoncdebussy]

"Grandi... was a monk, he was a mathematician, he was one one of those types" - lol!

[NWOltdZweigbueroLissabon]

_"And I'm hoping it will cause a little bit of debate on the comments, 'cause I know YouTube is the home of rational and informed debate. So I look forward to that."_

That's exactly my kind of humour. ^^

[pte]

I've never seen mathematics explained in such an exciting way. If I only have had this guy teaching me mathematics 50 years ago.

[mymy]

Love his confidence as he writes with a sharpie 🌞

[July-gjst]

I remember watching this video when I was in high school and thinking “man this is amazing”, now I’m a maths major ending his first course of real analysis and boy, this is the stuff of nightmares.

[weebaldfella]

So if you turn a light on and off really fast .. you just invented a dimmer switch and set the light to half brightness

[elbowsup]

I know this is an old video, but if anyone is interested, the idea of taking the average partial sums is known as "Cesaro summation". And it's just one way of "summing" divergent series.

[jonandmoni]

I'm not a mathematician, but a lot of these questions just seem to be treating infinity as a really big number. If you add 1+½+¼+⅛, then by infinity you reach 2. Well, you don't reach infinity at all, by definition, so you're always a little short of 2. The sum 1-1+1-1... is ½. No, it's either 1 or 0 if you ever reach a point where you can answer the question, depending on whether the last number is 1 or -1. If the sum is infinite, then the answer keeps switching between 1 and 0 forever. If you switch a light on and off progressively faster for 2 minutes, is it on or off at the 2 minute mark? If you're moving the switch at infinite speed then it's probably broken and you may not need a light at that point anyway.

A lot of the paradoxes leave me thinking either "I don't think that's how reality works" or "I don't think that's how infinity works".

[callumrowley]

YouTube strikes again. Where am I? I'm up in 6 hours for work and I'm here watching a random mathematical equation /show/mind boggle. Love it.

[timelinedifferential]

The answer" You discovered quantum mechanics and the light is in a superposition of on and off. :)

[DS-Akin]

I swear, that in personal journal writing I wrote and 'started seeing' something like 0:23-0:43 once but everything from 0:43+ is where it's 'starts becoming it's own thing'--the nice feeling of validation when you find words to an experience might sort of apply here now that I know of 'Grandi series'

[InstaSound]

My parents never let me turn the light on and off very quickly. Today I learned why.