The h Bar

AccidentalFourierTransform

00:00

I mean, am familiar with what you've said so far

Ben Niehoff

actually, I hate the word "spin connection", too :P

I always just call it the connection 1-form

AccidentalFourierTransform

I guess my point is that I dont know why they are useful

we need them because its the only way to treat fermions on a curved background?

Ben Niehoff

the spin connection is technically the connection on the spin bundle, which is a contraction of the connection 1-form with some gamma matrices

ACuriousMind

@BenNiehoff Well, the Christoffels are also a connection 1-form, so that's not very specific :P

dmckee

@0celo7 Who knows the way the sprout like toadstools these days.

Bernardo Meurer

00:01

@dmckee My CPU is attacking everything

Ben Niehoff

@ACuriousMind True! And if the connection is the Levi-Cività one, then they are really the same connection, in different bases :)

and people have been known to write down "coordinate-dependent gamma matrices", which I think is insane, but there you go

@AccidentalFourierTransform The main point of frames is actually the co-frames; the dual basis of 1-forms

with co-frames, you can construct the Riemann tensor just like a non-Abelian gauge field: R = d\omega + \omega \wedge \omega

AccidentalFourierTransform

oh I remember that formula!

or I think I do

ACuriousMind

The day I realized the Christoffels are basically just a $\mathrm{GL}(n)$ gauge field I was like "Why didn't anyone tell me this?"

And I've ranted in this chat before about that

AccidentalFourierTransform

and now that we are at it, can anyone tell me what a twistor is?

Ben Niehoff

yes, and using orthonormal frames just means that in Riemannian geometry, you can always reduce them to an O(n) gauge field :P

@AccidentalFourierTransform I'm not so clear on twistors, unfortunately...I understand it's some neat way of encoding null lines, or something

but that's about all

but anyway, the real power of frames (or co-frames) comes when you have continuous isometries

for example, say your metric is SU(2)-invariant

then it must have 3 linearly independent vector fields that generate that SU(2)

and whose commutators are the SU(2) algebra

likewise, there must be three 1-forms which satisfy the Maurer-Carten relations

d\sigma_1 = \sigma_2 \wedge \sigma_3, and cyclic

*Cartan

so, choose these three 1-forms as your co-frame basis!

AccidentalFourierTransform

00:12

(why dont you use mathjax?)

Ben Niehoff

no need to write down coordinates on a 3-sphere

none of the equations display for me

ACuriousMind

@BenNiehoff In the upper right corner of the chat there's a link to some scripts that make MathJax display in chat

Ben Niehoff

I don't want to go through a bunch of extra steps every time I enter the chatroom

heather

all you have to do is click on a bookmark

and that only when you're using math

it's not too bad.

AccidentalFourierTransform

ok, you convinced me

tetrads are indeed useful

tetrads ;-)

Ben Niehoff

00:17

shudder

@heather My preferred solution is to minimize my use of math :)

AccidentalFourierTransform

anyways, I dont think my mathematica code will converge today

its been running for several hours already

so I better go to sleep

bye for now peeps

Bernardo Meurer

@AccidentalFourierTransform Bah, that's silly

heather

@BenNiehoff lol, fair enough

@AccidentalFourierTransform, good night =)

Ben Niehoff

@AccidentalFourierTransform what is your code doing?

AccidentalFourierTransform

@BernardoMeurer huh?

@BenNiehoff integrating hypergeometric functions

long story, Im a lazy fuck and I dont want to integrate them myself

Bernardo Meurer

00:20

@AccidentalFourierTransform It's silly because me and my labmate are still trying to contain my code from destroying the devboard :P

@AccidentalFourierTransform Mathematica? Free yourself from this proprietary malware that doesn't respect you!

AccidentalFourierTransform

wtf is a devboard?

Bernardo Meurer

Break thy shackles!

AccidentalFourierTransform

maple is free IIRC

Bernardo Meurer

It's something you use to develop CPU designs on, an FPGA

It's not free as in gratis

it's free as in FREEDOM

gnu.org/philosophy/free-sw.en.html

AccidentalFourierTransform

also, no, maple is not free

Bernardo Meurer

00:22

GNU Octave

GNU Octave is software featuring a high-level programming language, primarily intended for numerical computations. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with Matlab. It may also be used as a batch-oriented language. Since it is part of the GNU Project, it is free software under the terms of the GNU General Public License. Octave is one of the major free alternatives to Matlab, others being FreeMat and Scilab. Scilab, however, puts less emphasis on (bidirectional) syntactic ...

Octave is your friend

Ben Niehoff

Maple locks down their site licenses more than Mathematica does

AccidentalFourierTransform

why this new obsession with libre shit?

who cares

Bernardo Meurer

It's Libre

Because you are all being abused by corporate shills and their proprietary malware

Ben Niehoff

shills

Bernardo Meurer

And you must choose freedom

AccidentalFourierTransform

00:23

I like being abused

Ben Niehoff

although shrills was funny

heather

i'm mostly libre or whatever

Bernardo Meurer

stallman.org/saint.html

There is no system but GNU, and Linux is one of its kernels!

@heather You still have shackles to break young one

Ben Niehoff

and its other kernels are barely functional!

AccidentalFourierTransform

kbye

Bernardo Meurer

00:25

@BenNiehoff Not true, GNU Hurd is perfectly working

heather

@Bernardo such as...?

Bernardo Meurer

@AccidentalFourierTransform May your dreams be blessed by GNU

@heather DRM, Codecs

Ben Niehoff

I do notice you said perfectly working, not working perfectly ;)

Bernardo Meurer

@BenNiehoff You caught me there :P

heather

@Bernardo what are those...?

Ben Niehoff

00:26

GNU HURD: working as designed!

but actually, I love free software and even ran Arch Linux on a laptop for a while

Bernardo Meurer

@heather Non-free software

MP3 for example is a non-free codec

Don't use it

use FLAC, OGG, Opus

peterh

@BenNiehoff It is so wonderful, although their microkernel is far from the linux and it is also a little bit... big.

Bernardo Meurer

@BenNiehoff I use Arch, but do note it's not Free Software. There is an Arch Linux analogue that is free software called Parabola

Ben Niehoff

but I don't use it much anymore, because I use a Surface Pro 4 and Linux just doesn't agree with it

peterh

@BenNiehoff I think, hurd would be the best if it would use a very mutilated Linux as microkernel.

Ben Niehoff

00:31

oh, ok, then I don't care about Free Software, only free software ;)

Bernardo Meurer

The Linux kernel is just a mess nowadays

peterh

@BenNiehoff For example, it the case of the USB drivers, I can't see any reason why they should be in kernel space. Communicating on an usb channel is exactly like communicating on a TCP socket. The same is for the filesystem, they are essentially demons providing a dav-like directory API using a block device.

Bernardo Meurer

Microkernels are the future, but they're just that; the future

Ben Niehoff

there is one thing that I can't stand about the FOSS movement, though

and I think it's a result of removing money, and thus customers, from the equation

Bernardo Meurer

That is indeed a problem

Ben Niehoff

00:35

a lot of developers get arrogant and leave bugs unfixed and features unimplemented, by saying that the user shouldn't want those things

peterh

@BernardoMeurer The Linux modules should be userspace daemons. It wouldn't be very hard to make them working from user space. It shouldn't be the future, it should be real in the present.

Bernardo Meurer

@peterh Yeah, well, I don't know about that (how hard it would be)

Ben Niehoff

oh, the other thing I can't stand is people focusing way too much on the elegance of the design, even on the language it's written in, rather than the end-user experience and whether it does what someone needs

Bernardo Meurer

@BenNiehoff Elegance of the design has a direct impact on the user experience

Ben Niehoff

like I don't give a shit whether it's written in Fortran or cuneiform, but does it work?

peterh

00:38

@BernardoMeurer All of the drivers see an interface on which they are talking with the rest of the kernel, partially with other modules. They call eachother by call instructions. These call instructions should be changed to some IPC mechanism. Even source modifications wouldn't be needed.

Ben Niehoff

@BernardoMeurer To a degree, yes, of course. But it's not something to obsess over.

Bernardo Meurer

@peterh I mean, I know how drivers work, but I also know that many of them are hackish as hell and easy to break

And, "we never break userspace"

Ben Niehoff

You can't future-proof anything, ever

Bernardo Meurer

@BenNiehoff Hm, I disagree, I think it's the one thing to obsess over. A good design will stand the test of time

and save you from refactoring everything every 6 months

Ben Niehoff

but it all gets refactored every 6 months anyway :P

because FOSS is a developer's hobby

Bernardo Meurer

00:41

Meh, it's not necessarily a hobby

I know plenty of people who work in FOSS

Heck I've worked in FOSS

Ben Niehoff

yes, I know people get paid to do it

peterh

@BernardoMeurer Yes, the bad drivers wouldn't work.

@BernardoMeurer I've just compiled a latest 4.10.4 kernel with make allnoconfig, the result is an 570kB bzImage. It would be a good start for a new microkernel.

Ben Niehoff

when I call it a hobby, I mean that the focus is usually on the developing

it's fun to design and write software!

Bernardo Meurer

@peterh I just think if you're going to go through the trouble of making a microkernel just make it a new design

Ben Niehoff

it's a bit less fun to do good research on what the user wants or needs, and good testing to make sure everything works well

Bernardo Meurer

00:46

make it POSIX and it should still be compatible with Linux for the most part

0celo7

01:11

@BernardoMeurer I just spent 1.5 hours explaining measure theory to bob

@BenNiehoff I know of a German book that uses tetrad. I don't really understand the logic there :P

@AccidentalFourierTransform You've never seen a good proof in a class that you've never seen anywhere else?

Bernardo Meurer

@0celo7 I need to meet bob

Obliv

01:30

hi @bernard @0celo7

Bernardo Meurer

@Obliv hey man! You're back!

Just in time for the post-mortum of my CPU

what have we learned?

Obliv

lol what happened

OBE

omg

Bernardo Meurer

DO NOT, I repeat, DO NOT, write to the wrong memory buffers in loop while walking through the addresses

OBE

obliv sup

dmckee

01:32

@BernardoMeurer Programming close to the metal always allows you to shoot yourself in the foot. The closer to the metal the larger the caliber.

Obliv

whats up @obe lookin blue like usual i see

dmckee

FPGA are the metal. You figure it out.

heather

@Obliv, hello, how've you been?

Obliv

I've been good, how about u @heather

heather

pretty good.

OBE

01:33

@obliv how did your transfering work out? are you applying this year or did you apply already?

Bernardo Meurer

@dmckee So it's like turning my foot into a bazooka and shooting while standing?

dmckee

Yep.

0celo7

@Obliv hey

Obliv

@obe no

@bernard do you know much about charles babbage's difference engine? like how he could mechanically approximate differential equations?

@0celo7 whats up dude anything insane happen while i was gone

OBE

@0celo7 do you still have your super detailed tensor answer?

i forget if you posted it

the one where you explained tensors properly

Bernardo Meurer

01:39

@Obliv All I know about Babbage's contraption was:
1. It never worked
2. The plans were perfect though
3. His notation is absolutely nuts and we're still trying to make heads and tails of it
4. With today's machining precision we could build a working Difference Engine

0celo7

@Obliv I got married

@OBE no, it was too long

Why?

OBE

I want to read it

dropbox link?

or did you delete it

Obliv

@bernard we already have two in the world I thought.

0celo7

It's in a series of .tex files on my hard drive

It's not something I care to put together

I encourage specific, intelligent questions.

OBE

okay whenever you have time if you could link it it would be helpful

since i couldn't appreciate it back then

but i can appreciate it more now

Obliv

01:43

I know that he used the idea of finite differences of polynomial approx of differential equations but I can't figure out how he mechanically designed this.. I figure it's similar to the differential analyzer (which is wayyy simpler) but Im too curious..

just look at it..

0celo7

@OBE just ask questions

Obliv

how could that thing possibly determine finite differences using $f_{k+1} = (1+h)f_k$ and outputting the result in a result column

0celo7

Tensors are pretty easy, what do you want to know

OBE

I just wanted to learn them properly

I only know carroll level tensors

and idk which book to use

brb

0celo7

There's only one book

OBE

01:50

back which book?

link

0celo7

@OBE there's only one book.

@OBE I'm very disappointed

heather

wait

not hawking and ellis

is that what you're referencing?

0celo7

No

heather

phew

i remember looking at that and thinking it was crazy (hard)

0celo7

@heather did you understand my proof earlier

heather

02:02

sort of

i have to go to bed now

good night everyone

Obliv

o/

anyone have an institutional login at this (website)[ieeexplore.ieee.org/document/1498720/]

i forgot how to embed links in text LOL it's been too long

ArtOfCode

@Obliv Apparently I do

square brackets and round brackets go the other way round for links in text

Obliv

:O could you share this document with me pretty please @artofCode

ah okay thought it was something like that

ArtOfCode

@Obliv ping me an email at [email protected], I'll send it back to you

0celo7

this is illegal

please stop discussing in chat

ArtOfCode

02:17

...that was the point of the whole email thing

Obliv

@0celo7 flag me

(don't actually, because i know you will)

0celo7

02:59

@ArtOfCode I don't see any difference between this an planning a murder

I don't think that would be allowed in the chat

Bernardo Meurer

03:18

@ArtOfCode Shoo, go away

Unless you can help me with VHDL

otherwise, shoo

Is $A\cdot B + \overline{A}\cdot\overline{B} = A\bigoplus B$?

Hm

nope

Screw this class really

0celo7

What is that

ArtOfCode

@BernardoMeurer uh... Why?

Bernardo Meurer

@0celo7 Boolean algebra

@ArtOfCode 'Cause you're mean

0celo7

@ArtOfCode you have a bad habit of banning people

Bernardo Meurer

^

ArtOfCode

03:24

Not unless they're doing something ban worthy

0celo7

No such thing

Bernardo Meurer

^

ArtOfCode

Which nobody was, until I was pinged out of the blue at 3:30AM by someone telling me to go away.

Bernardo Meurer

@ArtOfCode Do you happen to speak Portuguese?

0celo7

@BernardoMeurer Wonder if Fantano will like Rozay's new album

ArtOfCode

03:25

@BernardoMeurer Spanish.

0celo7

Same thing.

Bernardo Meurer

If so I will forgive your sins if you help me with my Computer Architecture lab project

ArtOfCode

i don't suppose it happens to be the same one I've just done?

Probably unlikely, but hey

Bernardo Meurer

fenix.tecnico.ulisboa.pt/downloadFile/1970943312289270/…

ArtOfCode

Boolean logic I can do, if that helps

Bernardo Meurer

03:27

Page 3, question 2

Boolean algebra I can do too :P

I just don't get what he's asking me to change in my CPU design

0celo7

@BernardoMeurer Apparently Birdman tried to take out Khaled

Didn't work

Bernardo Meurer

It's some black magic for doing arithmetic with numbers that use up to 8 bits of the 16 available bits

@0celo7 What?

0celo7

@BernardoMeurer watch DJ akademiks

Like...everything

ArtOfCode

@BernardoMeurer yeah, I can read most of those words, but the ing as a whole makes no sense to me.

Bernardo Meurer

@ArtOfCode "ing"?

ArtOfCode

03:30

thing

Bernardo Meurer

Ah

Yes, to me neither

I have no clue what he's asking

ArtOfCode

shrug

Bernardo Meurer

Like, I think I get what he's asking

but it seems pointless

He wants me to add something in my ALU that detects when a number is "small" and we define small as >=8bits on the 16 bit bus

in this case we activate a signal small_num and replace all it's 8 signal bits to 0 (two's complement is used here)

we then do the ops normally and flip the 8 bits back if needed

now why I dunno

Secret

05:28

42 is the answer to life, the universe and everything. The following might be one tiny slice of that question

user228700

06:51

@JohnR: I have done you a great injustice by not sharing this video with you:

user228700

Eating Weird Food from the 50s (with Katherine)

►

user228700

Enjoy!

John Rennie

:-) I'm a little tied up with recalcitrant servers at the moment, but I will watch it later. British food in the 50s was notoriously bad!!!

user228700

:-) Wokay. Have fun fixing them servers!

Secret

07:18

Time is what nature use to prevent everything to happen all at once
Money and price are really means to control and regulate the distribution of resources

If you managed to control both, you control everything in a civillisation
https://en.wikipedia.org/wiki/PyMOL

Why is that? Because infnite cardinals don't physically exist and resources are finite

Slereah

09:06

So this paper defines a class of loops for timelike curve, but it also includes "stings", which are sort of path wangs sticking out of the form $f \ast f^{-1}$, $f(0) = x$

And you can insert stings on timelike curves by $g \to g_+ f f^{-1} g_-$

But nowhere does he really say really why we need stings

some vague thing about needing them to complete the group structure of the loop space, but then again every curve is $\approx$ a curve without any stings, and also the constant curve $f(\lambda) = x$ is also in the space of generalized timelike loops

So I don't have a clue why you'd need them

Leonhard Euler

10:11

Hello @JohnRennie

Slereah

Naming yourself after a famous scientist is a bit conceited

Leonhard Euler

Why do you think so?

Slereah

just an opinion :p

Leonhard Euler

10:36

Oh. But I don't think so

Secret

10:58

Here is why integrals are hard. In general, they have no nice infinite series representations:

\begin{align}
I_1(0,x,n)=\int a^{(0)}(x)e^{-nx}dx & = a(x)\left(\int e^{-nx} dx\right)-a'(x)\left(\iint e^{-nx} d^2x\right)+a''(x)\left(\iiint e^{-nx} d^3x\right)-+a'''(x)\left(\iiiint e^{-nx} d^4x\right)+\cdots +(-1)^{R+1}\int a^{(R+1)}(x)\left(e^{-nx}\right)^{(-(R+2))}dx\\
& =\sum_{k=0}^{R}(-1)^ka^{(k)}(x)\left(e^{-nx}\right)^{(-(k+1))} +(-1)^{R+1}\int a^{(R+1)}(x)\left(-\frac{1}{n}\right)^{R+2}e^{-nx}dx\\
& =\sum_{k=0}^{R}(-1)^ka^{(k)}(x)\left(-\frac{1}{n}\right)^{k+1}e^{-nx} -\int a^{(R+1)}(x)\left(\frac{1}{n^{R+2}}\right)e^{-nx}dx\\

NB feel free to let $R,S \to \infty$. Then that final term has to go to zero else the integral will diverge as you will be effectively summing countable number of constants

Also this 'formula' only works if $a(x) \in \mathcal{C}^{\infty}$, otherwise anywhere there is cusp in the kth derivative it will be undefined at those points

As long these conditions are met, then the "indefinite Laplace transform" has a infinite series representation as the exponential function times a series of derivatives of $a(x)$

That is, given some $a(x)$ that satisfy the above conditions, then:

$\int a(x)e^{-x}dx=-e^{-x}\sum_{k=0}^{\infty}a^{(k)}(x)$

Secret

11:32

General form of any exponential integrands with bounded derivatives $i.e. a^{(k)}(x)< \infty, \forall k \in \Bbb{N}$, and $n > 1$

$$\int a(x)e^{-nx}dx=-e^{-nx}\sum_{k=0}^{\infty}\frac{a^{(k)}(x)}{n^{k+1}}$$

0celo7

12:11

christ

too many integrals

Secret

Treatingin integrals and sums as linear functionals does make them less headache because it turns an analysis problem into an abstract algebra problem, which I am slightly more comfortable at

but anyway...

Slereah

12:50

@0celo7 any clue why someone would need those stings

cf this and below

4 hours ago, by Slereah

So this paper defines a class of loops for timelike curve, but it also includes "stings", which are sort of path wangs sticking out of the form $f \ast f^{-1}$, $f(0) = x$

0celo7

@Slereah I saw that, no I don't know

can you provide more information?

Jim

"path wangs" there's a scientific description if I ever saw one

0celo7

@BernardoMeurer New D R A K E A L B U M

@Jim @OBE

@Slereah what is a path wang anyway

and what kind of group are you trying to get here

Usually the fundamental group is based at a point

Slereah

I call it thusly because it's basically just a big line sticking out awkwardly from a timelike curve

0celo7

If you want some sort of generalization you need tentacles that allow you to get to other base points I guess

Slereah

12:56

It is based at a point, yes

$\tau_q(L, x)$

ACuriousMind

@Slereah Those stings are just a special case of the loops, no?

Slereah

I don't think so?

It's specifically mentionned as an addition to the space of loops

0celo7

going back and forth is indeed a loop

Slereah

And I don't think the stings are required to be timelike

0celo7

stings?

what do the authors actually call it

ACuriousMind

12:57

But...for any path $\gamma$, $\gamma\ast\gamma^{-1}$ is a loop, by definition - since it is a path that starts and ends at the same point.

Slereah

A sting based at $x$.

0celo7

...

so your loops are timelike

but you can have this stings too?

Slereah

Defined by $f f^{-1}$, with $f(0) = x$

yeah

I'm not sure why

I suspect it might be to simplify some proofs?

but he seems to imply that it's to make the loop composition into a group

Which doesn't seem to make sense

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