The h Bar

Obliv

21:18

how can mathematicians actually believe that the sum of the natural numbers is NEGATIVE..

like if $1+1+1...$ is infinite then how could $1+2+3...$ be finite not to mention negative. Makes no sense man

Bernard Meurer

@Obliv Because they proved it :)

Obliv

actually wait it says the sum is divergent but they somehow assigned a value to the sum anyway

Bernard Meurer

@ACuriousMind

You can prove by using analytical continuation

even with the series being divergent

ACuriousMind

@BernardMeurer lol...what's up?

Obliv

sounds like an incredibly useful/insane concept I want to learn now..

assigning values to divergent sums o.o

Bernard Meurer

21:26

@ACuriousMind You had a link for a nice proof of this, do you still have that laying around?

ACuriousMind

Terry Tao on analytical continuation/zeta functions

Damn it

Bernard Meurer

What did I just download O.o

ACuriousMind

Copy-paste didn't work right the first time

Obliv

was that not the right link?

ACuriousMind

You probably now have my notes for a course on constructive field theory :D

@Obliv It's the right link now

Bernard Meurer

21:28

@ACuriousMind I bet they'll be useful some day hahaha

Are these your notes?

ACuriousMind

@BernardMeurer It's what I personally copied from the blackboard, if that's what you mean

Bernard Meurer

Why is it not in German?

ACuriousMind

Because the teaching language in our master is English, only a few lectures are in German, and only if no international student is taking them

Obliv

When did you start learning english? I'm always amazed when non-native english speakers can speak so fluently..

ACuriousMind

Around third grade, I think

skill patrol

21:34

what language do you speak most often?

other than math :P

ACuriousMind

Aloud? German. I write more English than German though, I think

Obliv

is it correct to call it german, deutsche or both?

skill patrol

yup, aloud

user507974

hey guys, how did i write down the right BC for this again:

ACuriousMind

@Obliv What do you mean? The language is called Deutsch in German, and, well, "German" in English

user507974

21:36

(on an infinite domain and evolving in time)

Obliv

don't europeans call it deutsche even if they don't speak german though?

ACuriousMind

@user507974: Uh, what do you mean by "writing the right BC"?

user507974

@ACuriousMind basically you do seperation of variables (sinusoidal answer in x and exponential in t) then you use BC to find coefficients right?

ACuriousMind

@Obliv No, they use their own names. It's awkward to switch to the native name right in the middle of a sentence

@user507974 You will have to be a bit more explicit for me to understand what you're doing. What is that picture? A potential?

user507974

@ACuriousMind concentration, diffusion problem

ACuriousMind

21:40

Why do you need boundary conditions? Can you not just feed it as initial condition into the evolution equation?

user507974

so you start with a concentration that is 0 for all x except here at t=0 and it diffuses out

Obliv

is $a|b$ true if $b$ is $0$?

user507974

my bad, i meant to say initial condition

ACuriousMind

@user507974 And your question is? What function describes that concentration?

user507974

@ACuriousMind yep, im kind of in a bit of a thinking blank and even though i should know this im forgetting

ACuriousMind

21:50

@user507974 It's the difference of two Heaviside functions: $f(x) = C_0 \left(\theta(x-a) - \theta(x-b)\right)$

user507974

@ACuriousMind i know its a heaviside but how did I write that out, fourier transform the heavisides and sum them together?

ACuriousMind

What do you mean "write it out"?

You can determine the Fourier transform, it'll be a scaled $\frac{\sin(x)}{x}$ with some phase in front

user507974

@ACuriousMind its a bit different than a sinc from these starting points isnt it?

ACuriousMind

That's why I said "scaled" and "some phase in front". The Fourier transform of the height 1, width 1 rectangle centered at 0 is the sinc, and you have relations like $F(f(x-a))(\omega) = \exp(\mathrm{i}\omega a)F(f)(\omega)$ and $F(f(ax)) = \frac{1}{a}F(f)(\omega/a)$.

Check carefully what the $2\pi$ prefactors are in your Fourier convention

I.e. a shift becomes a phase, and a scaling, well, an inverse scaling.

user507974

thanks

Obliv

22:28

what does $a\equiv b~ (mod~n)$ mean? is it saying (mod n) is the same thing as saying $a \equiv b$?

vzn

@kevinTahN. plz drop by here for all the gory details

Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli). The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801. A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00. Usual addition would suggest that the later time should be 7 + 8 = 15, but this is not the answer because clock time "wraps...

Obliv

thanks @vzn

vzn

@Obliv cybersynchronicity, just finished bostroms 2014 book on AI... whew o_O

Obliv

how was it :D?

I never read any of his material just listened to his talks

vzn

@Obliv hyperintelligent but also kind of "academic"... "jargony"

Obliv

22:35

I feel like he is an A.I. sometimes. The way he quantifies 'value' is comical but persuasive

vzn

@Obliv do you know what Secret was referring to, "Q3"?

are you a student? undergrad? US, elsewhere?

Obliv

a student in undergraduate ya

in the U.S.

vzn

Bostrom is one of the "big thinkers"/ philosophers of our time...

@Obliv what major?

Obliv

physics :p

vzn

amazon.com/…

@Obliv what area you want to specialize in?

Obliv

22:38

@vzn by Q3, I think he was referring to questions that lead to the discovery of something.

I don't know man physics is a very large field. Probably something theoretical rather than experimental. Not sure though

vzn

what talks of Bostrom have you listened to?

Obliv

I listened to an interview by someone (i forgot), a ted talk, and a talk at google (I think?)

I even emailed him over the summer and he responded lol

vzn

cool

Obliv

he had a big impact on me

how about you?

vzn

have heard of him over the years, he seems more active lately, or higher profile, or both

Obliv

22:42

are you a student?

Bernard Meurer

@Obliv What are you majoring in again?

ACuriousMind

@BernardMeurer Dude, just scroll a little bit up :P

vzn

@Obliv BS software engr, work in industry. re "Q3," oh now see the definition that Secret gave. nice framework. most ppl dont care about Q3 level questions and they are not necessarily relevant to daily life, making money, etc, many are not. eg relativity, evolution, heliocentric universe, quantum mechanics etc....!

Bernard Meurer

@ACuriousMind Oh, didn't see someone had asked that :p

Obliv

On my phone now.@vzn most people don't care about things outside of their lives and community. I have little clue of how bostrom became so motivated to undertake the questions he has and dedicate his time to them

They seem totally irrelevant to his own life which leads me to believe he's an a.i.

I mean to be fair many string theorists and cosmologists study concepts that are not clearly significant to our lives either.

vzn

23:22

@Obliv AI is a "big question" of our time & Bostrom has a lot of strong philosophical inclinations. you can see in his book wrt AI wrestle with theories of morality, a philosophy specialty. if you look at his history of writing one can see a thread. AI is increasingly relevant in our daily lives. tend to think/ feel myself, superintelligence on other hand is decades away... but even human level intelligence would be revolutionary so the term "superintelligence" may be some misnomer...

Sir Cumference

@vzn Hey Smithy, can you do me a favor?

Check over this code

Obliv

23:46

@vzn yes that is true a.i. is potentially extremely beneficial to our lives. I meant more so his wanting to minimize existential risk than a.i. though. I feel like that is not directly relevant to our lives but relevant to people of the future which is very selfless in a way.

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