12:00 AM
I mean, am familiar with what you've said so far

actually, I hate the word "spin connection", too :P
I always just call it the connection 1-form

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?

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

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

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

12:01 AM
@dmckee My CPU is attacking everything

@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

oh I remember that formula!
or I think I do

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

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

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 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!

12:12 AM
(why dont you use mathjax?)

no need to write down coordinates on a 3-sphere
none of the equations display for me

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

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

all you have to do is click on a bookmark
and that only when you're using math

ok, you convinced me

12:17 AM
shudder
@heather My preferred solution is to minimize my use of math :)

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

@AccidentalFourierTransform Bah, that's silly

@BenNiehoff lol, fair enough
@AccidentalFourierTransform, good night =)

@AccidentalFourierTransform what is your code doing?

@BernardoMeurer huh?
@BenNiehoff integrating hypergeometric functions
long story, Im a lazy fuck and I dont want to integrate them myself

12:20 AM
@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!

wtf is a devboard?

Break thy shackles!

maple is free IIRC

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

also, no, maple is not free

12:22 AM
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 ...

Maple locks down their site licenses more than Mathematica does

why this new obsession with libre shit?
who cares

It's Libre
Because you are all being abused by corporate shills and their proprietary malware

shills

And you must choose freedom

12:23 AM
I like being abused

although shrills was funny

i'm mostly libre or whatever

There is no system but GNU, and Linux is one of its kernels!
@heather You still have shackles to break young one

and its other kernels are barely functional!

12:25 AM
@BenNiehoff Not true, GNU Hurd is perfectly working

@Bernardo such as...?

@AccidentalFourierTransform May your dreams be blessed by GNU
@heather DRM, Codecs

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

@BenNiehoff You caught me there :P

@Bernardo what are those...?

12:26 AM
GNU HURD: working as designed!
but actually, I love free software and even ran Arch Linux on a laptop for a while

@heather Non-free software
MP3 for example is a non-free codec
Don't use it
use FLAC, OGG, Opus

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

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

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

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

12:31 AM
oh, ok, then I don't care about Free Software, only free software ;)

The Linux kernel is just a mess nowadays

@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.

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

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

That is indeed a problem

12:35 AM
a lot of developers get arrogant and leave bugs unfixed and features unimplemented, by saying that the user shouldn't want those things

@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.

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

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

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

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

12:38 AM
@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.

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

@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"

You can't future-proof anything, ever

@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

but it all gets refactored every 6 months anyway :P
because FOSS is a developer's hobby

12:41 AM
Meh, it's not necessarily a hobby
I know plenty of people who work in FOSS
Heck I've worked in FOSS

yes, I know people get paid to do it

@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.

when I call it a hobby, I mean that the focus is usually on the developing
it's fun to design and write software!

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

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

12:46 AM
make it POSIX and it should still be compatible with Linux for the most part

1:11 AM
@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?

@0celo7 I need to meet bob

1:30 AM
hi @bernard @0celo7

@Obliv hey man! You're back!
Just in time for the post-mortum of my CPU
what have we learned?

lol what happened

omg

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

obliv sup

1:32 AM
@BernardoMeurer Programming close to the metal always allows you to shoot yourself in the foot. The closer to the metal the larger the caliber.

whats up @obe lookin blue like usual i see

FPGA are the metal. You figure it out.

@Obliv, hello, how've you been?

I've been good, how about u @heather

pretty good.

1:33 AM
@obliv how did your transfering work out? are you applying this year or did you apply already?

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

Yep.

@Obliv hey

@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

i forget if you posted it
the one where you explained tensors properly

1:39 AM
@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

@Obliv I got married
@OBE no, it was too long
Why?

or did you delete it

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

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.

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

1:43 AM
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..

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

Tensors are pretty easy, what do you want to know

I just wanted to learn them properly
I only know carroll level tensors
and idk which book to use
brb

There's only one book

1:50 AM
back which book?

@OBE there's only one book.
@OBE I'm very disappointed

wait
not hawking and ellis
is that what you're referencing?

No

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

@heather did you understand my proof earlier

2:02 AM
sort of
i have to go to bed now
good night everyone

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

@Obliv Apparently I do
square brackets and round brackets go the other way round for links in text

ah okay thought it was something like that

@Obliv ping me an email at hello@artofcode.co.uk, I'll send it back to you

this is illegal

2:17 AM
...that was the point of the whole email thing

@0celo7 flag me
(don't actually, because i know you will)

2:59 AM
@ArtOfCode I don't see any difference between this an planning a murder
I don't think that would be allowed in the chat

3:18 AM
@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

What is that

@BernardoMeurer uh... Why?

@0celo7 Boolean algebra
@ArtOfCode 'Cause you're mean

@ArtOfCode you have a bad habit of banning people

3:24 AM
Not unless they're doing something ban worthy

No such thing

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

@ArtOfCode Do you happen to speak Portuguese?

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

3:25 AM
@BernardoMeurer Spanish.

Same thing.

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

i don't suppose it happens to be the same one I've just done?
Probably unlikely, but hey

Boolean logic I can do, if that helps

3:27 AM
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

@BernardoMeurer Apparently Birdman tried to take out Khaled
Didn't work

It's some black magic for doing arithmetic with numbers that use up to 8 bits of the 16 available bits
@0celo7 What?

Like...everything

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

@ArtOfCode "ing"?

3:30 AM
thing

Ah
Yes, to me neither
I have no clue what he's asking

shrug

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

2 hours later…

1 hour later…
user228700
6:51 AM
@JohnR: I have done you a great injustice by not sharing this video with you:

user228700
Enjoy!

:-) 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!

7:18 AM
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

2 hours later…
9:06 AM
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

1 hour later…
10:11 AM
Hello @JohnRennie

Naming yourself after a famous scientist is a bit conceited

Why do you think so?

just an opinion :p

10:36 AM
Oh. But I don't think so

10:58 AM
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:

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

11:32 AM
General form of any exponential integrands with bounded derivatives $i.e. a^{(k)}(x)< \infty, \forall k \in \Bbb{N}$, and $n > 1$

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

12:11 PM
christ
too many integrals

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...

12:50 PM
@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 $f \ast f^{-1}$, $f(0) = x$

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

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

@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

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

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

12:56 PM
It is based at a point, yes
$\tau_q(L, x)$

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

I don't think so?
It's specifically mentionned as an addition to the space of loops

going back and forth is indeed a loop

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

stings?
what do the authors actually call it

12:57 PM
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.

A sting based at $x$.

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