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

KnightLight
reply to post by ChaoticOrder

 

It's just wrong. Every trick messes up the answer. And as for the actual addition of all POSITIVE numbers what do you think you get.. They already have an answer for it. It's called infinity.

True, and the wiki article for the series 1+1+1+1.... mentions infinity first, before going on to explain the zeta function regularization, which makes more sense as the y axis intercept in the drawings they show:

1 + 1 + 1 + 1 + ⋯

So it would make more sense to me if the parallel wiki article on 1 + 2 + 3 + 4 + ⋯ was written in more of a parallel fashion to explain infinity is the answer as with 1 + 1 + 1 + 1 + ⋯, but they seem to skip over that part.

reply to post by Arbitrageur


For someone claiming to be a physicists he sure has poor spelling and grammar. He uses lower cases i's and doesn't start his sentences with capital letters. I'm not saying he is wrong, but he certainly isn't a physicist with grammar skills that poor.

reply to post by Arbitrageur


On youtube it says "The sum of all natural numbers (from 1 to infinity) produces an "astounding" result." and this is misleading. I suspect the people involved are trying to sensationalize this to get publicity or something. It is not a 'sum' in the ordinary sense of the word because in this case they are using a different summability method. Of course if you carry out the regular summing method this series obviously continues to grow forever.

reply to post by ChaoticOrder


Its stupid, its wrong, its a trick.

aaaaarrrrggghhhh!!!! witchcraft!!!!



Ill see to this in more detail after i finish some beers later on

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. Without using this variable, Physics as a Science would cease to exist because you can't do physics based mathematics without constants.

I find it hard to believe that a Physics Professor at a very prestigious college would produce a YT video using shoddy mathematics principles and still have his career. This equation goes back at least a hundred years, perhaps further. To continue claiming "fake" is certainly being ignorant to the concept of Physics as a whole and is a slap in the face to people with IQ's that easily double ours at ATS.

Many of you are far too full of yourselves...the equation is indeed standard procedure no matter how many ATSers claim otherwise. In fact, Steven Hawking references this equation numerous times in his book "A Brief History of Time"....but I suppose Hawking isn't reliable when it comes to Physics huh ATS?

Site continues to go downhill with every visit....which is becoming less and less by the month.

reply to post by OpinionatedB


Obviously, you misunderstood me. In reality, 24 was a guesstimate obtained and that in reality, it may be 23, 25, or 37, since they are using a concise finite differential for infinity in their calculations. That being the case, religious synchronicity has no connection.

-1/12... hmmm

This just proves that advanced mathematics has no place in the scientific process. You can make the math say anything you want, just as the dude said about 3 minutes in this video.

Don't think too hard guys.

I watched the vid and did a little research on -1/12.. IMHO it seems to me that this guy had an answer, and used math magic to create a problem for that answer. It would be like inventing something then trying to figure out what it is for. Interesting concept though.

Infinity isn't a finite number therefore you cannot count "up to" infinity.

I'm far too stupid to understand this but if you count marbles in this way would you go from a universe filled with marbles then add more marbles and end up with less than 1 marble?

Is that even what they are saying or is it more an average for an infinite count going both positive and negative directions?

So let me get this straight...

If you give me $1, and someone else gives me $2, then another person gives me $3, and other people keep giving me money in the same pattern, forever (infinitely), and I don't spend any of it...

I would end up $-1/12 in debt?

That is the most idiotic thing anyone has ever postulated.

The problem with this video is that a physicist attempts to use logical deduction to prove a mathematical theorem and fails when he counters his own argument.

He begins by saying the 1-1+1-1... would have an "answer" of 1/2 because this is the average of the possible answers (0 or 1). The problem arises at the end of the video when he is asked by the speaker that if he put in 1+2+3+4... in his calculator until the end of time, the answer would be -1/12? The physicist quickly clarifies that by the definition of infinity, there would never be an end time to hit the "=" button.

If this is true then how can we know the final answer of 1-1+1-1+1...? We don't. We start with an "average" to "prove" that 1+2+3+4...=-1/12. The entire proof begins with an argument that is not valid and was even countered by the physicist himself.

reply to post by mandella1099

The problem arises at the end of the video when he is asked by the speaker that if he put in 1+2+3+4... in his calculator until the end of time, the answer would be -1/12? The physicist quickly clarifies that by the definition of infinity, there would never be an end time to hit the "=" button.

Just because something cannot be done physically doesn't mean it cannot be done mathematically. There is a response article by Tony Padilla in which he states:

What do we get if we sum all the natural numbers? This was the question we asked in our recent Numberphile video. The answer we gave was, to the surprise of many I'm sure, -1/12. It's by no means obvious, but this is the only sensible value one can attach to this divergent sum. Infinity is not a sensible value. In my opinion, as a physicist, infinity has no place in physical observables, and therefore no place in Nature. David Hilbert, one of the founding fathers of quantum mechanics, described infinity as "a mathematical abstraction that does not have a physical content". I think most physicists would firmly agree with this sentiment. The trouble is that divergent sums like the one we discuss in the video do appear in calculations of physical observables, such as the Casimir energy, or in the dimensionality of the Universe in bosonic string theory. Therefore, only a very brave individual would dream of attaching the value infinity to sums like this. Minus a twelfth is far less crazy a value when you start talking about Physics.

He says that "infinity is not a sensible value" because it "has no place in physical observables". It seems he is trying to justify his conclusion with a similar argument. What makes him think that mathematical results must perfectly comply with the physical world? Infinity is a perfectly acceptable answer from a purely mathematical perspective.

As noted by Arbitrageur at the top of this page, the Wikipedia page titled 1 + 1 + 1 + 1 + ⋯ says that the answer to 1+1+1+... is infinity, however if it's manipulated through zeta function regularization then the answer becomes -1/2. The Wikipedia page titled 1 + 2 + 3 + 4 + ⋯ isn't so clear about that, but it's basically saying the same thing. It's saying that the answer is infinity but it also notes that "although the series seems at first sight not to have any meaningful value at all, it can be manipulated to yield a number of mathematically interesting results".

So my conclusion would be that the mathematically correct answer would be infinity for both those equations, however using a special type of mathematical tool to solve the problem can give a finite result which is useful for physical applications. The best way of understanding it might be to imagine that if you take the equation all the way to infinity it essentially loops around and comes right back to where it started, which is to say it converges on the y-intercept. The equations used are essentially a method of calculating the y-intercept more than they are a method of calculating the true sum.

ChaoticOrder
So my conclusion would be that the mathematically correct answer would be infinity for both those equations, however using a special type of mathematical tool to solve the problem can give a finite result which is useful for physical applications.

Is that "special mathematical tool" a balding guy scribbling nonsense on a napkin with a marker by any chance?

reply to post by WeAre0ne


Lol, no, I was referring to zeta function regularization.

darrellabbott
This just proves that advanced mathematics has no place in the scientific process. You can make the math say anything you want, just as the dude said about 3 minutes in this video.

Don't think too hard guys.

It's actually quite the opposite. These bizzare asymptotic techniques ended up being important for doing computations in quantum field theory, dozens to hundreds of years later.

WeAre0ne

ChaoticOrder
So my conclusion would be that the mathematically correct answer would be infinity for both those equations, however using a special type of mathematical tool to solve the problem can give a finite result which is useful for physical applications.

Is that "special mathematical tool" a balding guy scribbling nonsense on a napkin with a marker by any chance?

Yes! Occasionally they have hair, and nearly always they have caffeine injectors nearby.

Some people recognize the difference between a genius mathematician and a schizophrenic nut bar.

ChaoticOrder
He says that "infinity is not a sensible value" because it "has no place in physical observables". It seems he is trying to justify his conclusion with a similar argument. What makes him think that mathematical results must perfectly comply with the physical world? Infinity is a perfectly acceptable answer from a purely mathematical perspective.

Yes, at one level, but the point is to generalize the mathematics to be more useful for other cases in which it is not.
It usually means redefining subtly what "x + y + ... " means because that is, as it turns out, far more complicated than "x + y".

www.sciencedirect.com...

mbkennel

darrellabbott
This just proves that advanced mathematics has no place in the scientific process. You can make the math say anything you want, just as the dude said about 3 minutes in this video.

Don't think too hard guys.

It's actually quite the opposite. These bizzare asymptotic techniques ended up being important for doing computations in quantum field theory, dozens to hundreds of years later.

Why is the answer not -1/any other number? why 12? I saw the video and it seemed like he stopped at an arbitrary number to use which ended up yielding the 12.