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King of Loss View Drop Down
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Points: 16890 		Direct Link To This Post Posted: January 10 2014 at 14:28
Originally posted by Equality 7-2521 Equality 7-2521 wrote:

Originally posted by King of Loss King of Loss wrote:

I found this video watching Pat's video on the sum of 1+2+3+4+5+….=-1/12, I have found this video:

I think it's quite interesting because mathematics also affects our personal privacy!




Mathematics is our personal privacy in a digital age like this.

Mhmm.. It's very true. It's hard for most people to get that.. Maybe why we're heading towards a lovely serfdom-like existence.
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Points: 15784 		Direct Link To This Post Posted: January 10 2014 at 12:52
Cryptozology finds some scientific corroboration.
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Points: 15784 		Direct Link To This Post Posted: January 10 2014 at 12:00
Originally posted by King of Loss King of Loss wrote:

I found this video watching Pat's video on the sum of 1+2+3+4+5+….=-1/12, I have found this video:

I think it's quite interesting because mathematics also affects our personal privacy!




Mathematics is our personal privacy in a digital age like this.
"One had to be a Newton to notice that the moon is falling, when everyone sees that it doesn't fall. "
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Points: 65760 		Direct Link To This Post Posted: January 10 2014 at 00:23
I just started a course on cryptography on Coursera. It turns out cryptography is difficult.
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Points: 16890 		Direct Link To This Post Posted: January 09 2014 at 23:17
I found this video watching Pat's video on the sum of 1+2+3+4+5+….=-1/12, I have found this video:

I think it's quite interesting because mathematics also affects our personal privacy!
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Points: 16890 		Direct Link To This Post Posted: January 09 2014 at 23:08
Originally posted by Equality 7-2521 Equality 7-2521 wrote:

Originally posted by Padraic Padraic wrote:

I'd be interested in hearing the dialogue that Pat had with his students about it.


I'm not positive that I'm eloquent enough for it to have been that interesting. I tried to remind them about the dangers of conflating the colloquial meaning of words and the technical meaning of words ('the sum is'), how intuition and specifically usual arithmetic manipulations do not carry over to the infinite, and the fact that even really silly and recreational looking things in math tend to have profound ramifications on our world.

Maybe you can explain that mathematical effect to our politicians.
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Points: 15784 		Direct Link To This Post Posted: January 09 2014 at 15:00
Old mathematicians were pithy as hell. 
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Points: 31169 		Direct Link To This Post Posted: January 09 2014 at 14:58
Originally posted by Equality 7-2521 Equality 7-2521 wrote:

Pat: An elementary and sound explanation is given here if you would like to read it.

Ha!  This quote perfectly expresses how I feel about this!

"The divergent series are the invention of the devil,
and it is a shame to base on them any demonstration whatsoever."

LOL
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Points: 15784 		Direct Link To This Post Posted: January 09 2014 at 12:37
They are. However, addition is only a binary operation +: N x N -> N

Using the inductive principle, you can easily extend this to an operation on any finite number of inputs because of associativity. However, it cannot be extended to the infinite. With usual infinite summation, you're considering a limit of finite sums which can leave your closed Ring. This is how we deal with real numbers: as the limit of a sequence of rationals.
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Points: 31169 		Direct Link To This Post Posted: January 09 2014 at 12:30
Originally posted by Equality 7-2521 Equality 7-2521 wrote:

Originally posted by Padraic Padraic wrote:

I'd be interested in hearing the dialogue that Pat had with his students about it.


I'm not positive that I'm eloquent enough for it to have been that interesting. I tried to remind them about the dangers of conflating the colloquial meaning of words and the technical meaning of words ('the sum is'), how intuition and specifically usual arithmetic manipulations do not carry over to the infinite, and the fact that even really silly and recreational looking things in math tend to have profound ramifications on our world.

Maybe it's the infinite part, but:  aren't the natural numbers closed under addition?
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Equality 7-2521 View Drop Down
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Points: 15784 		Direct Link To This Post Posted: January 09 2014 at 12:26
Pat: An elementary and sound explanation is given here if you would like to read it.
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Points: 15784 		Direct Link To This Post Posted: January 09 2014 at 12:17
Originally posted by Padraic Padraic wrote:

I'd be interested in hearing the dialogue that Pat had with his students about it.


I'm not positive that I'm eloquent enough for it to have been that interesting. I tried to remind them about the dangers of conflating the colloquial meaning of words and the technical meaning of words ('the sum is'), how intuition and specifically usual arithmetic manipulations do not carry over to the infinite, and the fact that even really silly and recreational looking things in math tend to have profound ramifications on our world.
"One had to be a Newton to notice that the moon is falling, when everyone sees that it doesn't fall. "
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Points: 15784 		Direct Link To This Post Posted: January 09 2014 at 12:14
Originally posted by Padraic Padraic wrote:

Originally posted by Equality 7-2521 Equality 7-2521 wrote:

I showed this video to my students this morning to teach a few meta-mathematical things and give them an example of a series.

 1+2+3+...=-1/12

It garnered more interest than I expected so I thought I'd post it here.

Very cool, interesting paradox which starts with the Grandi's series (1, -1, 1, ...).  Although I don't like the manipulations that led to it's sum = 1/2.


The manipulation is not valid. It's the right intuition that would lead you to proving the result rigorously using Ramanujan summation.
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Points: 31169 		Direct Link To This Post Posted: January 09 2014 at 11:20
I'd be interested in hearing the dialogue that Pat had with his students about it.
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Points: 37575 		Direct Link To This Post Posted: January 09 2014 at 11:19
Originally posted by Padraic Padraic wrote:

Originally posted by Dean Dean wrote:

Originally posted by Padraic Padraic wrote:

Originally posted by Equality 7-2521 Equality 7-2521 wrote:

I showed this video to my students this morning to teach a few meta-mathematical things and give them an example of a series.

 1+2+3+...=-1/12

It garnered more interest than I expected so I thought I'd post it here.

Very cool, interesting paradox which starts with the Grandi's series (1, -1, 1, ...).  Although I don't like the manipulations that led to it's sum = 1/2.

He could have done S-(-S) = 2S = 1
 
1-1+1-1+... and 1+2+3+4+... are still a divergent series.

That's what he did do.  And indeed they are.
Yeah,  I meant he could have shown that's what he did, he just said it averages at ½.
What?
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Points: 31169 		Direct Link To This Post Posted: January 09 2014 at 11:07
Originally posted by Dean Dean wrote:

Originally posted by Padraic Padraic wrote:

Originally posted by Equality 7-2521 Equality 7-2521 wrote:

I showed this video to my students this morning to teach a few meta-mathematical things and give them an example of a series.

 1+2+3+...=-1/12

It garnered more interest than I expected so I thought I'd post it here.

Very cool, interesting paradox which starts with the Grandi's series (1, -1, 1, ...).  Although I don't like the manipulations that led to it's sum = 1/2.

He could have done S-(-S) = 2S = 1
 
1-1+1-1+... and 1+2+3+4+... are still a divergent series.

That's what he did do.  And indeed they are.


Edited by Padraic - January 09 2014 at 11:07
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Dean View Drop Down
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Points: 37575 		Direct Link To This Post Posted: January 09 2014 at 11:05
Originally posted by Padraic Padraic wrote:

Originally posted by Equality 7-2521 Equality 7-2521 wrote:

I showed this video to my students this morning to teach a few meta-mathematical things and give them an example of a series.

 1+2+3+...=-1/12

It garnered more interest than I expected so I thought I'd post it here.

Very cool, interesting paradox which starts with the Grandi's series (1, -1, 1, ...).  Although I don't like the manipulations that led to it's sum = 1/2.

He could have done S-(-S) = 2S = 1
 
1-1+1-1+... and 1+2+3+4+... are still a divergent series.
What?
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Points: 34083 		Direct Link To This Post Posted: January 09 2014 at 10:50
Its the ofdest time sig coveyed in music
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Padraic View Drop Down
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Points: 31169 		Direct Link To This Post Posted: January 09 2014 at 10:50
Originally posted by Equality 7-2521 Equality 7-2521 wrote:

I showed this video to my students this morning to teach a few meta-mathematical things and give them an example of a series.

 1+2+3+...=-1/12

It garnered more interest than I expected so I thought I'd post it here.

Very cool, interesting paradox which starts with the Grandi's series (1, -1, 1, ...).  Although I don't like the manipulations that led to it's sum = 1/2.
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Equality 7-2521 View Drop Down
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Points: 15784 		Direct Link To This Post Posted: January 09 2014 at 09:56
I showed this video to my students this morning to teach a few meta-mathematical things and give them an example of a series.

 1+2+3+...=-1/12

It garnered more interest than I expected so I thought I'd post it here.
"One had to be a Newton to notice that the moon is falling, when everyone sees that it doesn't fall. "
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