The most counterintuitive result ever!!!!

[smstonypoint]

Even if you are math-phobic, you should be able to answer this question.

Suppose you sum all the positive integers from 1 through infinity (1+2+3+............... ).

The answer is a really, really, really, really big number, right?

Well, no. I still haven't wrapped my mind around the idea, but the answer is -1/12.:confused2::confused2::confused2:

The proof is here:

[video]http://www.numberphile.com/videos/analytical_continuation1.html[/video]

Steve

 

[xtn]

Proof? Hardly.

Conceptual Flaw: Infinity is a concept. Sum equations meant to go all the way to infinity are also a concept. They can't actually have a definitive answer, because one can never stop calculating them. Duh.

Math Flaw: that 1+1-1+1-1+1-... somehow equals 0.5. That's fake. The excuse is basically that it must equal 1 or 0 depending where you stop, and since we don't know where to stop we just average the two possible answers. Firstly, the equation requires, through the three little dots, that we don't ever finish it. It therefore does not have an answer. See "Conceptual Flaw" above. And even if it did, deciding to arrive at it just by averaging the two possibilities is completely arbitrary.

Proof Flaw: Everything he did afterwards to arrive at -1/12 is based off of the flawed 0.5 value.

 

[smstonypoint]

Proof? Hardly.

Conceptual Flaw: Infinity is a concept. Sum equations meant to go all the way to infinity are also a concept. They can't actually have a definitive answer, because one can never stop calculating them. Duh.

Math Flaw: that 1+1-1+1-1+1-... somehow equals 0.5. That's fake. The excuse is basically that it must equal 1 or 0 depending where you stop, and since we don't know where to stop we just average the two possible answers. Firstly, the equation requires, through the three little dots, that we don't ever finish it. It therefore does not have an answer. See "Conceptual Flaw" above. And even if it did, deciding to arrive at it just by averaging the two possibilities is completely arbitrary.

Proof Flaw: Everything he did afterwards to arrive at -1/12 is based off of the flawed 0.5 value.

The video presents an informal proof -- there is apparently a formal proof that the 0.5 value holds.

As the video indicates, the proof has implications that are important for "string theory." I have read a small amount about that theory -- enough that my brain aches when I even hear the term "string theory."

Steve

 

[2LaneCruzer]

Proof? Hardly.

Conceptual Flaw: Infinity is a concept. Sum equations meant to go all the way to infinity are also a concept. They can't actually have a definitive answer, because one can never stop calculating them. Duh.

Math Flaw: that 1+1-1+1-1+1-... somehow equals 0.5. That's fake. The excuse is basically that it must equal 1 or 0 depending where you stop, and since we don't know where to stop we just average the two possible answers. Firstly, the equation requires, through the three little dots, that we don't ever finish it. It therefore does not have an answer. See "Conceptual Flaw" above. And even if it did, deciding to arrive at it just by averaging the two possibilities is completely arbitrary.

Proof Flaw: Everything he did afterwards to arrive at -1/12 is based off of the flawed 0.5 value.

I don't buy it either. Seems like they are using real numbers to solve an unreal problem...or something...

 

[nwltruck]

This is why theoretical physicist gets disproven. You can't just run the math in any direction to get the answer you want.

 

[/pine]

The video presents an informal proof -- there is apparently a formal proof that the 0.5 value holds.

As the video indicates, the proof has implications that are important for "string theory." I have read a small amount about that theory -- enough that my brain aches when I even hear the term "string theory."

Steve

I find the string theory quite intriguing...on a basic layman's scale it is not difficult to comprehend...

Here is a page that gives some basics on just how small a "string" is...
NOVA | A Sense of Scale: String Theory

If an atom were magnified to the size of the solar system, a string would be the size of a tree

launch the interactive slideshow...

 

[kevin37b]

Do you want 10,000 or a start with a penny and double everyday for 30 days ?

 

[ddb123]

I'm good at math until it starts to lose all correspondence to reality. If you want to disprove the "proof," just add one golf ball to another forever, and see if at any point you have one twelfth of a golf ball.

 

[CobyRupert]

I'm good at math until it starts to lose all correspondence to reality. If you want to disprove the "proof," just add one golf ball to another forever, and see if at any point you have one twelfth of a golf ball.

You'd have negative 1/12 of a golf ball. Do that 12 times and you owe me a golf ball. Should I send you my address?

 

[ddb123]

You'd have negative 1/12 of a golf ball. Do that 12 times and you owe me a golf ball. Should I send you my address?

Yes. I'll send it in 12 separate negative packages.

 

[Daver1963]

I thought this thread would somehow explain the government spending deficit. Seems like they are trying for infinity!

 

[smstonypoint]

I thought this thread would somehow explain the government spending deficit. Seems like they are trying for infinity!

Funny that you should mention that. I stumbled upon this result in the context of a blog discussion of deficit spending

Political Calculations: Government Budget Math.

I hope that this doesn't turn into a political discussion in which the Johnny One Notes (of both factions) start exchanging talking points like they do in the "Unfriendly Politics" forum.

Steve

 

[/pine]

I hope that this doesn't turn into a political discussion in which the Johnny One Notes (of both factions) start exchanging talking points like they do in the "Unfriendly Politics" forum.

There seems to be an echo in here...

At any rate I think this thread and the climate change thread(s) should be combined...both offer about the same merit when it comes down to actual science and the relative data used to compile the subsequent theories...

 

[smstonypoint]

There seems to be an echo in here...

Guilty as charged -- but I think my point is valid.

Steve

 

[MoKelly]

Interesting. Calculate this test for any number other than infinity and you get an intuitive answer. Try it using infinity and you get the non-intuitive number. Why? Because the math formula required to solve the equation requires dividing by the largest number in the test. Anything divided by infinity is close to zero.

What real world use dividing anything by infinity has is beyond me.

Bottomline, if anyone really believes adding all positive numbers together forever really results in a number close to zero, I have oceanfront property in Arizona to sell you.

MoKelly

 

[stuckmotor]

About this string theory. Is the string made out of cotton or man made fiber?

 

[smstonypoint]

About this string theory. Is the string made out of cotton or man made fiber?

100% natural.

Steve

 

[timswi]

Math is hard. Coming from an Economics major...Just don't have the energy in my off time.

 

[LD1]

Bottomline, if anyone really believes adding all positive numbers together forever really results in a number close to zero, I have oceanfront property in Arizona to sell you.

MoKelly

Actually, BELOW zero....

 

[nickc]

GREEN OR ORANGE????