[ﮎingulaЯiτy]

I might as well post this on the forum where I still know some of the people.

Analytic continuation allows us to approximate an infinite series as a function. The more terms you add to the series, the more accurately you describe the function. So at the limit, when you have all the terms, that series can be considered equal to that function.

This allows us to assign meaningful numerical values to infinite series, even divergent ones.

For example, the infinite series "1 + 2 + 3 + 4 + 5... " can be evaluated. However, the result is disturbingly counter-intuitive. If you stop adding terms at any finite point, you'll have a larger and larger number as the result. However, if you "evaluate this after an infinite number of terms, you'll find the sum to actually be -1/12.

There are a variety of proofs for this, and this number is demonstrably a meaningful . This result is actually seen in physics. Furthermore this result is a foundation in string theory for the number of required dimensions.

[Pete Svarrior]

But Singy, infinity isn't even a real number. Why do you bother with things that don't exist?

[Ghost of V]

Are you asking us a question or just showing off? 

[Shane]

Interesting.

[Blanko]

Hey I watched that episode of Numberphile as well 

[fappenhosen]

http://www.numberphile.com/videos/analytical_continuation1.html

Cool.

[spoon]

Are you asking us a question or just showing off? 

Neither really.

[Rushy]

But Singy, infinity isn't even a real number. Why do you bother with things that don't exist?

This. Numbers aren't real. A smart guy once told me so. Nothing made out of numbers actually exists.

[ﮎingulaЯiτy]

Are you asking us a question or just showing off? 

Sharing something I found interesting, and leaving it open for questions/discussion. I expected for "no's" and "wtf's" like I did when I first came across it. I feel like I would have had to discover the proof to be a show off. Instead I'm reading other people's life work.

[ﮎingulaЯiτy]

But Singy, infinity isn't even a real number. Why do you bother with things that don't exist?

This. Numbers aren't real. A smart guy once told me so. Nothing made out of numbers actually exists.

Please send me a pm of your checking/banking account numbers and pins. Sounds like you wont miss them. <3

[Eddy Baby]

Shouldn't there be some minuses in there somewhere

[Pete Svarrior]

Shouldn't there be some minuses in there somewhere

No, it's meant to be counter-intuitive

[EnigmaZV]

Well, if string theory needs it, then it must be important.

[Rama Set]

Nothing made out of numbers actually exists.

So Nothing usually does not exist but when you make nothing from numbers it actually does exist?

My brain hurts.

[Rushy]

Please send me a pm of your checking/banking account numbers and pins. Sounds like you wont miss them. <3

I can't do that, they're not real. How am I supposed to send you numbers? You can't hold numbers in your hand, stupid.

[Ghost of V]

Please send me a pm of your checking/banking account numbers and pins. Sounds like you wont miss them. <3

I can't do that, they're not real. How am I supposed to send you numbers? You can't hold numbers in your hand, stupid.

Fucking magnets, how do they work?

[sandokhan]

"Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality."

(Nikola Tesla)


The two scientists in the video are not mathematicians, but physicists; no mathematician who knows the theory of divergent series is going to tell you that Σ n (1 from infinity) = -1/12.

The physicists in the video have no idea or knowledge about Ramanujan summation, or the constant term of a divergent series, or the dangers/pitfalls in applying summation methods to divergent series.


For those who want to get an idea why Ramanujan is still considered the greatest mathematician who ever lived, here is the work, Collected Papers:

http://www.imsc.res.in/~rao/ramanujan/collectedindex.html

One of his most famous papers is "On the number of divisors of a number", article #8

[sandokhan]

Now, let us carefully examine the colossal mistakes committed by the two physicists in obtaining the preposterous result:



The most that can be said, within the context of Ramanujan summation (a highly abstract mathematical setting) is that c, the constant of the series employed by Ramanujan (his "center of gravity" of a series), will equal -1/12.

By using the same reasoning, on the sum Σ1 (1 to infinity), c will equal -1/2.

However, the Abel and Cesaro sums of Σ1 are both infinity.

You cannot operate with highly divergent infinite series using the rules of convergent series: the results will be spurious.

Certain divergent series, like asymptotic series, can added/substracted, but under very strict rules.


Also, when using analytic continuation, you are actually substracting infinity from infinity to get something finite: again, an abstract mathematical operation with no connection to the real world.


There is no such thing as bosonic string theory in multiple dimensions, or the derivation of Casimir effect assuming zeta regularization:

https://web.archive.org/web/20120128042636/http://www.scientificexploration.org/journal/jse_09_4_phillips.pdf

[Ayowindip]

Whoa. I expected multiple and non-stop discussions about how flat the earth is. But I found something better. That feeling of home. I really do feel as though I can really relate to this society. After all these years... I am home!!!

[Charming Anarchist]

For example, the infinite series "1 + 2 + 3 + 4 + 5... " can be evaluated. However, the result is disturbingly counter-intuitive.

It seems flawed too. 

Right from the get-go, that Grundi series sounds like MyThButhterth-style rhetorical hypnotizm to confuse the masses.  The Grundi series calculation assumes that you stop the series at some point.  You can not do that.  You are looking at the concept of infinity backwards. 






Infinity exists.  Notice the symbol for infinity is the same as the trajectory of the sun. 

Notice how the number 8 is an infinity sign which accurately depicts the path of the sun going up and down as well as wide and small. 

Notice how the 8th step of a musical scale takes you back to the fundamental leading the scale to infinity. 





I reckon life for mankind would be a lot more peaceful if we adopted a base-8 numbering system.