/sci/ - Science & Math

[Anonymous No.6280652]

This is bullshit

http://www.youtube.com/watch?v=w-I6XTVZXww

These guys are drinking the Kool-Aid
>String Theory

[Anonymous No.6280670]

>math that hurts my feelings is wrong

[Anonymous No.6280673]

How do they justify 'moving over' the infinite series during subtraction?

If I've got S = 1 + 2 + 3 + ... , then S - S = 0, but with mathematical miracles, I can just move over the second S

1 + 2 + 3 + 4 + ...
-__1 + 2 + 3 + ...

and suddenly the answer is an infinite number of 1's

Can someone please tell me what the justification for this kind of thing is?

[Anonymous No.6280682]

This is when I stopped taking math seriously.

[Anonymous No.6280683]

So is this a proof string theory is wrong?

[Anonymous No.6280693]

>>6280673
Somebody?

[Anonymous No.6280701]

>>6280693
because one infinite series starts at 1 and the other starts at 1 because in the 1 + 1 - 1 + 1 ect they get .5.

So you do not know whether to start s2 at 0 or 1. So they start it at both and take the average again. they did a shitacualr job at explaining it in the video, but all this comes together and makes sense in the quantum world.

[Anonymous No.6280704]

>>6280701
*because one infinite series starts at 1 and the other starts at 0

[Anonymous No.6280714]

It's comedy, guys.

Though I think they should have saved it for April 1 like normal people.

[Anonymous No.6280716]

this is why pure math is for retards.

[Anonymous No.6280720]

Its still sounds like mathematical hocus pocus, and sleight of hand.

I don't know where he fucked up, or how, but I just have a feeling he fucked up.

For the same reason though that the best philosophical reason that death is defined as 'the inability to receive goods'. It makes sense but just feels wrong and unsatisfying.

[Anonymous No.6280727]

>>6280716
post your iq score

>>6280714
>>6280720

http://en.wikipedia.org/wiki/Zeta_function_regularization

[Anonymous No.6280733]

>>6280727
>post your iq score

145.

[Anonymous No.6280750]

>>6280733
this is why iq tests are for retards.

[Anonymous No.6280756]

>>6280727
So what we're talking about here is using an arbitrary method to derive a value from a series, and calling it the "sum" for no sane reason when one knows perfectly well that the series is divergent.

...and then presenting it to a pop-sci audience without telling them what you're actually doing.

Makes sense.

[Anonymous No.6280764]

>>6280750
>>6280727
Isn't IQ supposedly a terrible way to find 'intelligence' because its bias towards general western ways of thinking instead of 'objective intelligence'?

[Anonymous No.6280768]

Here is a better derivation with some explanation:
http://youtu.be/-I7PjKyCnI0?t=1h13m45s

basically you get
<div class="math"> \frac{1}{\epsilon^2} -\frac{1}{12} + \frac{\epsilon}{4} - \frac{\epsilon^2}{6} ... </div>

in which <span class="math"> \epsilon [/spoiler] goes to 0. which gives you an infinite part you don't care about, plus a finite part you can extract which is useful.

[Anonymous No.6280794]

>>6280750
retard detected.

[Anonymous No.6280808]

>>6280756
The reasoning process breaks down entirely at 2:19, when he says "We take the average of the two." and then he says that's the sum, and it just gets worse from there.

It's not the sum. At this point, a responsible presenter would explain that it's not the sum, in the sense that you'd understand a sum. It's something else entirely, which is called a "sum" for such and such reasons despite being a different thing.

But no, he just goes on about how he's "proving" that this is the "sum", as if calling it a "sum" isn't entirely arbitrary and in conflict with the conventions the audience is likely familiar with.

I can't stand people who communicate poorly and then say, "Isn't that delightfully unintuitive?" It's not unintuitive that some arbitrary mathematical process can associate the value -1/12 with the series 1+2+3+4..., it's only confusing that some mathematicians and physicists call it a "sum" and write it as if it were a sum, which is just lazy and imprecise communication.

[Anonymous No.6280828]

this is what string theory relies on, a flaw in math? sweet

[Anonymous No.6280830]

>>6280828
>flaw in math

Hurr.. I don't understand, so it must be bullshit!

[Anonymous No.6280843]

>>6280683
This is what I took from the video as well.

[Anonymous No.6280848]

>make false assumption
<lel look at all these awsum results xDDD!!!

Regards, your average physicist.

1-1+1-1+1-1+1-1.. does not equal 1/2. That has to be the dumbest shit I have ever heard. It's a divergent series.

Also, thanks for proving that string theory is bullshit, once and for all :^)

[Anonymous No.6280857]

>>6280701
>and makes sense in the quantum world.

Take note, young mathematicians; this is how you know that the physicist explaining mathematics to you is wrong.

[Anonymous No.6280860]

>>6280857
It can't be helped. Why don't you fuckers try explaining reality? You guys won't do a good job considering an orange is the same size as the sun in your world.

[Anonymous No.6280864]

>>6280860
>It can't be helped.

Yes it can. Realize that mathematics is not equal to the real world. Till then, live with the fact that mathematics is obviously beyond your heard.

>Why don't you fuckers try explaining reality?

"Why am I not a physicist?", is the question you wanted to ask. My answer to that is algebraic word problems are way too simple.

[Anonymous No.6280866]

>>6280843
>>6280828
>>6280652
what the fuck does this even have to do with string theory? QFT used it long before string theory was a thing. this is fucking retarded

[Anonymous No.6280920]

>1 - 1 + 1 - 1 + ... = 1/2
Cesaro sum of that sequence. This is an entirely reasonable way of defining infinite sums; you just take the averages of the partial sums, and take the limit of the resulting sequence. (this coincides with the definition of finite sums)

>1 - 2 + 3 - 4 + ... = 1/4
Idk about this one. Certainly not Cesaro summable. Analytic continuation probably works.

>1 + 2 + 3 + 4 + ... = -1/12
Is the analytic continuation of the function s -> 1^{-s} + 2^{-s} + ... at -1. Again an entirely reasonable way of defining infinite sums, as it coincides with the definition of finite sums.

Why do you popsci faggots always complain about completely acceptable ways of dealing with the infinite?

[Anonymous No.6280935]

>>6280652

if you sum up all POSITIVE NATURAL numbers, you not only get a NEGATIVE number but a fucking fraction!

HAHAH HAHAHA HAHAH HAAHHAHAHAH HAHAHAHAHHAHAHAHAHAHAH

>MUH DIVERGENT SERIES
>NO INFINITE SERIES IN NATURE

hahahaha… fucking pure math fаgs always try to justify their mental illness.

[Anonymous No.6280941]

>>6280935
>getting this upset

[Anonymous No.6280949]

>I can see the sun moving in the sky! Obviously the earth doesn't rotate around it!
>We're so perfect we're totally different from animals!
>Matter isn't full of void! This shit is stupid and doesn't make sense!

[Anonymous No.6280956]

>>6280941
>>upset

I'm LAUGHING my ass off while you're the one who's projecting. why are you so butthurt? did my post make you suicidal or something?

AHAHH HAHAHAHAHAH

[Anonymous No.6280961]

>>6280956

Wow your anal frustration is overwhelming.

[Anonymous No.6280967]

>>6280961
so much butthurt from a pure math idiot.

aren't you late for you Subway shift? hurry up and make me a sammich.

HAHAH HAHAHAHAHHAHA

[Anonymous No.6280992]

>>6280652
But I can disprove that 1-1+1-1+1-1+1-1+1-... = 1/2
quite easily.

Or at least I can show that one of the steps they used to derive it in the video is wrong, perhaps there is another way to reach the result, but they way they did it has a problem.

The trick they do about placing parenthesis over all terms but the first one is hard to refute when you are already taking the sum S as going out to infinity. But that's not how you are supposed to do it. The sum S should be found going out to some arbitrary number N and then you take the limit as N goes to infinity. So let's do that and see if it works, their sums were:

<span class="math">\sum_{n=0}^{N}(-1)^{n}[/spoiler]
and <span class="math">1+\sum{n=0}^{N}(-1)^{n}[/spoiler]

Again, if you take N as going to infinity and write both of them out they indeed look equal, so they set them as equal to each other giving S = 1-S and they arrive at S=1/2
However, those two sums ARE NOT EQUAL for any N. The value of the first sum for N=1 is 1, the value of the second sum for N=1 is 0.
If you write them all out it looks like this

S for first sum at different values of N:
1 0 1 0 1 0 1 0 1 0 1.....
S for second sum at different values of N:
0 1 0 1 0 1 0 1 0 1 0....

They are different.

Now, I'm sure doing things like this might not have problems in physical situations in which things are actually oscillating and taking the average of the series "just works" but setting them equal to each other is wrong

isn't it? Or am I mistaken?

[Anonymous No.6280994]

>>6280992
sorry that second sum was supposed to have a minus after the 1, not a plus:

<span class="math">1-\sum_{n=0}^{N}(-1)^{n}[/spoiler]

[Anonymous No.6281000]

Wow, this is pretty interesting OP.

Even though the manipulations done in the video are complete bogus, they still agree with "reasonable" definitions for those sums via the Riemann Zeta function. Has there been any investigation into making these techniques rigorous? It reminds me of umbral calculus a lot.

[Anonymous No.6280997]

>>6280992
>I can disprove that 1-1+1-1+1-1+1-1+1-... = 1/2
That depends on what the meaning of the symbol = is.

[Anonymous No.6281019]

That skim over of Grandi's series was awful.

[Anonymous No.6281023]

>>6281019
that autistic redheaded idiot makes me puke. he's THE WORST person they have on that channel. guy's so fucking creepy and disgusting and can't explain anything even if his life depended on it.

[Anonymous No.6281027]

>>6281023
I kinda likes him actually,
but that's probably just because he reminds me or Fred and George Weasley

[Anonymous No.6281028]

>>6281019
They skipped it because they already have a whole video on it.

[Anonymous No.6281026]

>>6280967
>dat asspain

[Anonymous No.6281033]

>>6281026
asspain from from? from laughing so hard at you that my sides are hurting? hahaha… stay mad, kid, stay mad… and keep on studying this pointless bullshit. maybe by the time you're done you'll be able to explain to your shift manager how summing up all positive numbers ends up in a negative fraction.

[Anonymous No.6281035]

>>6280808
>communication

I feel this is a significant barrier for many mathematicians.

But I mean, 2 mins going through wikipedia explained it for me.

[Anonymous No.6281041]

im a physicist, i know whats going on in the vid and how its perfectly reasonable and i can live with it.

[Anonymous No.6281052]

>>6281041
Can you or someone else explain how this comes up naturally in physics to a pleb? I'm genuinely curious as a mathfag here who has only seen this as being used to troll others using the Riemann zeta function.

[Anonymous No.6281055]

http://en.wikipedia.org/wiki/Ramanujan_summation

It's not REALLY -1/12 but it kinda is :^)