The most counterintuitive result ever!!!!

[bcp]

I think that string theory has evolved into plane theory for anyone who is interested. That stuff is so far out there that it twists the mind. Mr. Hawking is pretty dam impressive what he comes up with in his mind and I'm always fascinated when I read anything he writes about. Look into the theory about black holes. That gets into some trippy math as well!!

I think they are now gray holes.

Check the news.

Bruce

 

[buickanddeere]

I would say the welfare system. The more you help somebody the more helpless and dependent they become.

 

[SPYDERLK]

Not counterintuitive. Wrong. For any progress to ever be made the distinction between "not readily evident w/o explanation", and incorrect, must be recognized. Otherwise the flawed rules that led to the false truth are not critically inspected and fixed. ... If this result is actually used in string theory then string theory is also wrong from the point at which it was used forward.
larry

 

[smstonypoint]

Not counterintuitive. Wrong. For any progress to ever be made the distinction between "not readily evident w/o explanation", and incorrect, must be recognized. Otherwise the flawed rules that led to the false truth are not critically inspected and fixed. ... If this result is actually used in string theory then string theory is also wrong from the point at which it was used forward.
larry

There is an earlier mathematical proof due to Euler according to Astounding Result - Numberphile - Videos about Numbers and Stuff.

A point I took away from the videos is that while "infinity" is a useful concept in math, "physics" solutions don't involve infinity. The videos also mention another area in which the -1/12 result is useful. If I understood correctly, it is the "Casimir effect" (Casimir effect - Wikipedia, the free encyclopedia).

As I understand it, the physicists who question/reject string theory do so on the basis that the theory does not provide "novel experimental predictions at accessible energy scales" (String theory - Wikipedia, the free encyclopedia, rather than flaws in the mathematical underpinnings of the theory. If the math was wrong, the theory would be dismissed out of hand.

Steve

 

[SPYDERLK]

The point is, the math is wrong if it accepts the -1/12 sum. If they would endeavor to find out what mathematical rule is being applied incorrectly, or is not developed enuf to be fully coherent with the calculation, then they would get somewhere.
larry

 

[Loren49]

Rondam Ramblings: No, the sum of all the positive integers is not -1/12

" About a week ago, two British mathematicians named Tony Padilla and Ed Copeland, who produce a video blog called Numberphile, posted a video that purports to prove that the sum of all the positive integers is -1/12. It was making the usual geek rounds where I would have been content to let it circulate, but today the story was picked up by a naive and credulous reporter at Slate, where the story stands to do some real damage if not challenged."

....explanation and equation at referenced site....

"The flaw in both cases is the same: the algebraic rules that apply to regular numbers do not apply to infinity. Actually, it's more general than that: the algebraic rules that apply to regular numbers do not apply to non-converging infinite sums. All of the sums above are non-converging infinite sums, so regular algebraic rules to not apply. It is no different from using regular algebra when dividing by zero. It doesn't work.

Now, there are ways to define the sums of non-converging infinite series so that they do not lead to contradictions. The one that leads legitimately to the conclusion that 1 + 2 + 3 + 4 ... = -1/12 is called Ramanujan summation, which in turn is based on something called an analytic continuation. But the problem is that the Numberphile video makes no mention of this. They present the result as if it is legitimately derivable using high school algebra, and it isn't. Telling people that it is does a grave disservice to the cause of numerical literacy."

Here is another informative explanation:

Does 1+2+3

Arithmetic - Wikipedia, the free encyclopedia
Arithmetic or arithmetics (from the Greek word ἀριθμός, arithmos "number") is the oldest[1] and most elementary branch of mathematics, used very popularly, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of operations that combine numbers. In common usage, it refers to the simpler properties when using the traditional operations of addition, subtraction, multiplication and division with smaller values of numbers.

I'm an old farmer with a degree in Mathematics
Loren

 

[smstonypoint]

Now, there are ways to define the sums of non-converging infinite series so that they do not lead to contradictions. The one that leads legitimately to the conclusion that 1 + 2 + 3 + 4 ... = -1/12 is called Ramanujan summation, which in turn is based on something called an analytic continuation. But the problem is that the Numberphile video makes no mention of this. They present the result as if it is legitimately derivable using high school algebra, and it isn't. Telling people that it is does a grave disservice to the cause of numerical literacy."

Loren,

Thanks for posting the links. I do not know whether it absolves the Numberphile boffins, but their second video (Astounding Result - Numberphile - Videos about Numbers and Stuff) does mention analytic continuation.

I had not heard of Ramanujan summation, but I had heard of Ramanujan, thanks to a PBS documentary (Nova?) a few years ago.

Steve

 

[SPYDERLK]

That error really needs to be found. As is it will contaminate everything based upon it.
larry

 

[DarkBlack]

What made Einstein so great compared to modern day wanabee's is that his theories were most often, able to be proven, put to good use.

-1/12, or -.083333... in itself is at odds with the concept of "infinity" since infinity is the concept of "endless, without limits". Posturing the "cracking" a pre-calculated limit "ending" answer of "-.08333..." is in direct opposition to the initial concept. This would of course.. would have to put the math used to "prove" it into as much question, as the disregard of the "infinite" concept.

 

[Loren49]

What made Einstein so great compared to modern day wanabee's is that his theories were most often, able to be proven, put to good use.

-1/12, or -.083333... in itself is at odds with the concept of "infinity" since infinity is the concept of "endless, without limits". Posturing the "cracking" a pre-calculated limit "ending" answer of "-.08333..." is in direct opposition to the initial concept. This would of course.. would have to put the math used to "prove" it into as much question, as the disregard of the "infinite" concept.

-1/12 is a rational number. When -1 is divided by 12 the result is the repeating decimal -.08333... which equals -1/12 if the 3s go on forever. No reason to make the -1/12 look confusing. There is no math problem here.

Loren

 

[Alan L.]

Multiplication, division, adding and subtracting. In order to end up with a negative result a negative number has to be introduced into the computation somewhere. And that would never happen if all you are doing is adding positive integers.

 

[orezok]

Don't anyone take this personally, but when I was in college in a previous century, my calculus professor told me that "Figures never lie, but liars figure!".

 

[AgriStoreUSA]

I'll risk my meager reputation to say that I watched all of the related videos and was able to follow. It's an interesting thought experiment using high level mathematics that I'm sure I wouldn't understand, but the video demonstrated the theories correctly.

Thanks for posting

 

[xtn]

Yes, except for the assumption that 1-1+1-1+1-1+1-... = 0.5 or 1/2. "Because we don't know whether to stop after a +1 or after a -1, we just average the two possible answers," is just a completely arbitrary solution. The little three dots, indicating that the equation goes on forever, mean that the equation must be conceptual only, because one must NEVER STOP calculating it. The idea that we must pick either a +1 or a -1 to stop at ruins the whole thing. Then arbitrarily deciding just to average the two possible answers ruins it again. It's ruined squared.

And 1+2+3+4+5+6+... is also conceptual only for the same reason. It cannot actually have any concrete answer, much less -1/12. So they can write proofs until the cows come home, but it's all meaningless. In fact they hint at this themselves without ever realizing it. They point out that in physics, we can not actually deal with infinite measurements. Well no duh. The same applies to these conceptual equations. We cannot actually answer them. The whole premise that we can assign a finite answer to a never-ending calculation is flawed right out of the gate.

The only examples of never-ending equations that can be answered are ones that could be restated as equations that end. Such as 1*1*1*1*1*... because obviously its value is the same as 1*1. Continuing to carry out additional operators never changes the value. Or 0+0+0+0+0+... has the same property.

 

[Marveltone]

Yes, except for the assumption that 1-1+1-1+1-1+1-... = 0.5 or 1/2. "Because we don't know whether to stop after a +1 or after a -1, we just average the two possible answers," is just a completely arbitrary solution. The little three dots, indicating that the equation goes on forever, mean that the equation must be conceptual only, because one must NEVER STOP calculating it. The idea that we must pick either a +1 or a -1 to stop at ruins the whole thing. Then arbitrarily deciding just to average the two possible answers ruins it again. It's ruined squared.

And 1+2+3+4+5+6+... is also conceptual only for the same reason. It cannot actually have any concrete answer, much less -1/12. So they can write proofs until the cows come home, but it's all meaningless. In fact they hint at this themselves without ever realizing it. They point out that in physics, we can not actually deal with infinite measurements. Well no duh. The same applies to these conceptual equations. We cannot actually answer them. The whole premise that we can assign a finite answer to a never-ending calculation is flawed right out of the gate.

The only examples of never-ending equations that can be answered are ones that could be restated as equations that end. Such as 1*1*1*1*1*... because obviously its value is the same as 1*1. Continuing to carry out additional operators never changes the value. Or 0+0+0+0+0+... has the same property.

I don't even understand advanced maths, and really only have a very tenuous grasp on the most basic arithmetic, but even I can understand that adding infinite pluses can't equal a negative. It seems some mathematicians get so full of themselves and their higher knowledge of conceptual theories and formulas that they tend to lose all sense of reality.

Reminds me of a limerick. It's about vocabulary, but the same idea seems to apply:

A man of utter verbosity
Loved words with such ferocity,
Waxing profound,
He fell to the ground,
Knocked down by hes own pomposity.

Joe

 

[kevin37b]

Actually math is no different than a fiction novel . Who says 2+2 = 4 .That is just an opinion .What happens when those aliens come to pick up those pallets and tell you that 2x2 =0 . Are you going to file a grievance ?

 

[Marveltone]

Actually math is no different than a fiction novel . Who says 2+2 = 4 .That is just an opinion .What happens when those aliens come to pick up those pallets and tell you that 2x2 =0 . Are you going to file a grievance ?

No... If I file a grievance, the lawyers will show up, then things get really messy!

Joe

 

[Dr_Zinj]

...
If you wake up and the instructor is saying, "If this had worked the way it was supposed to, .......," you're in physics lab.

Nah. You're in a Politics 354 class.

 

[Dr_Zinj]

Steve, a lot of physics solutions involve infinity, usually as a limit in a calculus equation. For instance, the energy needed to accelerate a mass increases geometrically as the velocity increases. The energy requirement approaches infinity as the velocity approaches the speed of light in a vacuum. Which is why they say you can never reach light speed, as the energy required would be infinite, but infinity is never actually reachable.

 

[smstonypoint]

Steve, a lot of physics solutions involve infinity, usually as a limit in a calculus equation. For instance, the energy needed to accelerate a mass increases geometrically as the velocity increases. The energy requirement approaches infinity as the velocity approaches the speed of light in a vacuum. Which is why they say you can never reach light speed, as the energy required would be infinite, but infinity is never actually reachable.

I don't think we are in disagreement, it's just a matter of semantics. I know more about statistics than physics, and statistics often require using +/- infinity as limits of integration. What I understood the physicist was saying is that we don't "observe" infinity in the physical world.

Steve

Edit: Here's another physicist's take on infinity: http://www.edge.org/response-detail/25344.