In the End, It All Adds Up to -1/12 (1+2+3+4+ ··· ∞ = -1/12)

ElohimJD
reply to post by KrzYma

 

That video is exceptional thank you for the contribution.

you mean this Distinti guy ?
I like his way of thinking, I don't agree all the time with him, but... yeh, Thanks !

KrzYma
reply to post by Soylent Green Is People

 

The answer people are looking for in the real world is not based on an average, but on a real straightforward sum. The answer of "-1/12" is a function of the math itself, NOT a function of what really happens when I add whole things together.

YES, but if you watch the vids thy claim it is -1/12

Yeah, but as you indicated in your other post above, just because the video says that it is, that does not mean it is right.

Like I have said before, I understand WHY mathematicians say that the answer to 1+2+3+4+5+6...∞ could be said to be -1/12 when certain valid mathematical concepts are applied to the problem; however, (and as you seem to agree) that is not really the real-world answer.

Mathematicians working on more philosophical areas of math (such as attempting to work with the concept of ∞) could be said to be -1/12, but I still am logical enough to know that the cold hard reality of taking whole things (such as whole apples) and adding up how many I have will never ever result in a negative non-whole number.

reply to post by Soylent Green Is People


Professor Ed Copeland from Sixty Symbols said in the first 2 sec of the first video
" I'm going to give you an astounding result.. "

I think we all agree that the result of 1+2+3+4+5... is not -1/12

BTW: I like Sixty Symbols and their YouTube videos, very interesting, especially those "extra footage" versions of it.

Miniscuzz

The Physicist in the video showed that in a 2013 Textbook the answer is indeed -1/12

Physics doesn't deal with "Infinity" as a number....infinity can't even be a number.

In order to apply string theory in a mathematical formula, you must have some sort of constant variable. There was no "trickery" involved in the equation the Professor showed in the video. It was all basic Algebra even a 5th grader could understand.

Aww lil buddy prove it. When I say prove it, I mean using 5th grade algebra obviously. I mean a mathematical proof which is missing in this thread so far. I have studied calculus and different ways of using infinite numbers, but this doesn't follow even basic math laws.

Prove me wrong. I dare you.

Physics and math disagree, and physicists have no why.. If math agreed everything would add up to 0 and matter would not exist. Pure math does not describe reality, and the math used in the video is wrong. It supports string theory, but not math laws.

Basically this leans more to the universe not coming from 0 than anything else. Lets see it.


Summary of your post:

"Infinity is not a number, therefore infinity = -1/12
and 5th grade algebra says so?
String theory needs a number that can't be, so the number they make up is right in a theory that has no proof??? "

LOLZ...

reply to post by KnightLight


This uses basic differentiation of n(n+1) / 2 when n = -1 and the induction method to arrive at the answer - brush up on these and it'll make sense.

The second video provides a full, easy to understand proof of the problem and the logic behind it, the first video doesn't though and jumps through steps making it seem illogical to someone not familiar with the maths involved.

KnightLight

Basically this leans more to the universe not coming from 0 than anything else. Lets see it.

Best and most accurate sentence in this thread. This truly summarizes what was proved by the math.

Exceptional post in total, but this one simple to understand concept was excellently described.

God Bless,

bastion
reply to post by KnightLight

 

This uses basic differentiation of n(n+1) / 2 when n = -1 and the induction method to arrive at the answer - brush up on these and it'll make sense.

The second video provides a full, easy to understand proof of the problem and the logic behind it, the first video doesn't though and jumps through steps making it seem illogical to someone not familiar with the maths involved.

edit on 26-2-2014 by bastion because: (no reason given)

Correct me if I am wrong but: n(n+1)/2 when n=-1 is:

(-1+1) = 0
-1x0 = 0
0/2 = 0

0

What does your differentiation result in? Is it just 0? How does nothing (0) explain the sum of infinity?

KnightLight
Basically this leans more to the universe not coming from 0 than anything else. Lets see it.

ElohimJD
Best and most accurate sentence in this thread. This truly summarizes what was proved by the math.

Exceptional post in total, but this one simple to understand concept was excellently described.

God Bless,

That's fine, and I understand the concept of the maths involved, and I understand why these mathematical concepts are in fact valid and also are very useful in explaining advanced physics and explaining the virtually-impossible-to-define concept of infinity. I also understand how the answer to "1+2+3+4+5+6...∞" could be said to be -1/12 when these certain valid mathematical concepts are applied to the problem...

However, the answer of "-1/12" is still just a function of the maths itself (due to the attempt by the maths being used to define the virtually-impossible-to-define concept of infinity) rather than being what is truly there in the real world. I say this because in the real world, if I start putting apples in bushels, and even if I can conceptually do it for eternity, there will be no way that I will ever have -1/12 apples.

The answer is being contaminated by the maths attempt at defining the undefinable -- i.e., "infinity".

Soylent Green Is People

However, the answer of "-1/12" is still just a function of the maths itself (due to the attempt by the maths being used to define the virtually-impossible-to-define concept of infinity) rather than being what is truly there in the real world. I say this because in the real world, if I start putting apples in bushels, and even if I can conceptually do it for eternity, there will be no way that I will ever have -1/12 apples.

This work is not applicable to counting apples - it applies to quantum mechanics etc. Its not about the reality of counting apples its about the reality of string theory etc.

reply to post by ElohimJD


That's precisely why -1 i chosen

You need to differentiate the function first (i.e 2n/2+ 1/2) as explained in the second video.

Continuing this process causes the S,..Sn, +/- alternating series which tends to -1/12.


What the first video skips out is the letting n = -1 which is the crucial step made here as it's the only integer that makes the series converge (otherwise it tends to infinity).

saneguy

Soylent Green Is People

However, the answer of "-1/12" is still just a function of the maths itself (due to the attempt by the maths being used to define the virtually-impossible-to-define concept of infinity) rather than being what is truly there in the real world. I say this because in the real world, if I start putting apples in bushels, and even if I can conceptually do it for eternity, there will be no way that I will ever have -1/12 apples.

This work is not applicable to counting apples - it applies to quantum mechanics etc. Its not about the reality of counting apples its about the reality of string theory etc.

And that's what I said in my first paragraphs in my response -- i.e., that the maths used are both valid and are also useful to help explain other concepts.

However, there are people who think the guys in this video are taking it literally -- i.e., that a sum of things being counted eventually ("at infinity", whatever that means to them) will be "-1/12". That's not what is being said here, but the first video is not clear on that. The implication of the first video is that it is a reality that infinitely summing together numbers (or things) with result in a sum of "-1/12".

They didn't really explain the point that because infinity cannot be truly defined, the answer is only a mathematical construct (a function of the maths used). It is "infinity" that is causing the problem here, because as soon as with put a finite end to this mathematical series, the sum collapses into a positive integer.

reply to post by Soylent Green Is People


I agree that there was a certain amount of sensationalism present in the videos. I think they are merely trying to create interest about mathematics but unfortunately it may be backfiring somewhat.

bastion
reply to post by ElohimJD

 

That's precisely why -1 i chosen

You need to differentiate the function first (i.e 2n/2+ 1/2) as explained in the second video.

Continuing this process causes the S,..Sn, +/- alternating series which tends to -1/12.

edit on 26-2-2014 by bastion because: (no reason given)

What the first video skips out is the letting n = -1 which is the crucial step made here as it's the only integer that makes the series converge (otherwise it tends to infinity).

edit on 26-2-2014 by bastion because: (no reason given)

edit on 26-2-2014 by bastion because: (no reason given)

Thank you for this explanation, I understand your initial point far better now.

I also understand why my original claim of "magic trick" in S2 was in error as well; this reply makes that sum understandable as a proof in math, once n=-1 is applied.

God Bless,

Soylent Green Is People

They didn't really explain the point that because infinity cannot be truly defined, the answer is only a mathematical construct (a function of the maths used). It is "infinity" that is causing the problem here, because as soon as with put a finite end to this mathematical series, the sum collapses into a positive integer.

This to me appears to be the most likely explanation of the confusion in this thread.

By adding this clear explanation to the replies from Bastion regarding the mathematical construct used and why it was used; I can now agree that while infinity remains infinite the sum remains -1/12; once infinity become finite the concept collapses into a positive large whole integer.

Great posts guys.

Thanks,

reply to post by ChaoticOrder


If interested, I have plenty to share regarding number theory, abstract geometry, numeral linguistics, the history regarding these topics and more. It's funny, my last thread I referenced -1 / 12, but nobody really caught on... lol.

All of this has been known for a long long time now... and there's soooo much more that applies to every single aspect of our lives. It's truly the most amazing rabbit hole ever devised.

btw...

retirednature
It's truly the most amazing rabbit hole ever devised.

btw...

I watched the first video and it makes me cringe that the guy with the PhD in math doesn't seem as smart as the guy doing the interview who doesn't know math as well, yet seems smarter.

The interviewer is spot on and he freaked out the mathematician a little bit. Here's what the video describes:

-create abstract concepts that don't match reality, like points on a number line.
-discover that the abstract concepts are abstract and don't match reality

The mathematician is freaking out and calling it a rabbit hole. The interviewer is asking why he didn't know these representations were abstract to begin with. Math guru is stumped.

Engineers don't seem to have these problems with maths because they try to connect their models to reality somehow...it's what they do, while mathematicians are under no such constraints.

As George Box said:

"All models are wrong. Some are useful."

Coming up with abstract concepts like points on a number line and infinities may be useful in some ways, but it's certainly no rabbit hole that abstract concepts don't match reality. By the way this idea of models as flawed representations of reality applies to not just number lines, but every single model I've ever seen. Even the supposedly undeniable second law of thermodynamics has been violated, but only a drama queen would call it a rabbit hole, it's an expected consequence of the simpler models not matching reality just as it should be an expected consequence of using abstract concepts like points and infinities that don't match reality, because, they are abstractions, not real.

What people do not understand is that infinity don't necessarily apply to real world.

That infinity sum? It can be said to be the "WHOLE" thing and not summing it up infinitely.
Infinity is a hard thing to explain.

en.wikipedia.org...

As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.

Mathematical abstractions are based on definitions with all particulars included and so we create exact structures. Physical abstractions cannot be exact because of unknown variables which are always present. As physics progresses we can can increase the accuracy of our calculations but we can never achieve perfection - this is the realm of mathematics.

reply to post by Arbitrageur


You should have watched the entire video and then the second part which I provided latter the former.

Maybe maths aren't your thing, or you just dont get excited over the stuff.... but the fundamental principal being presented here is fairly significant.

Consider the following...

Maths and Geometry are essentially the foundation of:
Logic, Computation, Physics, Religion, Navigation, Economics, and our overall paradigm that governs the very means through which we interact with the natural world and one another. I think there's a lot more to what is behind his sentiment being displayed than what he's saying, once the totality is considered. From sociolinguistics and the role of semiotics, music theory, graph theory, set theory, etc etc etc... quantitative analysis' to ..perceptual organization, logistics, infrastructures, culture and conceptual metaphors, to even how an individual values themselves and so forth...

A world dictated by numbers over form...



What if numbers are real? That means a singularity exists? Does that mean God exists? Or.... does it.(see previous post w/ video 'god leaves of grass')

retirednature
reply to post by Arbitrageur

 

You should have watched the entire video and then the second part which I provided latter the former.

At the end of the first video there was a link to more and I clicked that link, then there was a link to more at the end of that video and I watched that. I checked that third video against your third video and they didn't match, but the second video did which I didn't check until reading your reply, so yes I watched it.

The statements the mathematician makes sound pretty stupid to me frankly. He says if you remove 3.5 from the number line you'd expect to see a little sliver of space missing where you removed it, but as the interviewer already pointed out, no you wouldn't expect that because the point you removed has no dimensions.

So the math guy seems baffled by a problem he's created in his own mind that even the non-math expert realizes isn't really a problem. Or maybe there really was one but the mathematician is such a terrible communicator he can't explain it.

Maybe maths aren't your thing, or you just dont get excited over the stuff.... but the fundamental principal being presented here is fairly significant.

I love math, because we can do practical things like this with it:

Boeing 777 Wing Test


Engineers wanted the wings to withstand just over 150% in the wing stress test and the wings broke at 154%.

They don't show all the math that went into their models but this is really harder to do than it looks because there are so many variables and error bars stacking up. So instead of freaking out about abstract concepts being abstract like the mathematician did when he looked like this (ok maybe not quite this bad, but close):



The engineers used finite element analysis (instead of "infinite" element analysis ) so they didn't have to freak out when they tried to use an abstraction like infinity in their calculations, and they did a fine job too.

To me that video is a nice illustration of the power of applied mathematics.