<whitequark>
ocaml has one but imo it sucks, and I think there could not really be a formal definition.
<whitequark>
module is something you reuse.
<alexgordon>
well I'm happy having all top level functions explicitly typed. I don't think that's a bad thing, I think it actually should be required anyway
<whitequark>
so, you separate your concerns into modules, and reason about every module locally, and then you assemble them on a higher level, and this will be sort of local too
<whitequark>
you don't have to span too much levels of abstraction, that's the point
<alexgordon>
yeah, module systems are completely out of the scope of this discussion :P
<whitequark>
module systems in "real world" often solve a different problem anyway
<alexgordon>
designing a good module system is far harder than designing a good programming lang
<whitequark>
like "my dependency maintainers are all morons, how do i still have working software"
<whitequark>
aka why bundler exists
<whitequark>
disagree on "far harder" but i see your point
<incomprehensibly>
i seriously no longer have the attention span for irc
<incomprehensibly>
especially language design irc
<whitequark>
incomprehensibly: eh?
<whitequark>
too short?
* whitequark
is translating ruby into ocaml in the background. the things you have to do...
<ec>
incomprehensibly: that's because of the place you are in your life
<ec>
incomprehensibly: been there. many times. I tend just drift away for a few months.
<whitequark>
ec: you seem to understand him
<whitequark>
i don't really
<whitequark>
explain pls
<ec>
understand who?
<whitequark>
incomprehensibly
<whitequark>
well, not explain, name it
<ec>
what 'bout 'im?
<ec>
incomprehensibly is micahjohnston
* whitequark
sighs
<whitequark>
nevermind
<incomprehensibly>
whitequark: yeah attention span is too short
<incomprehensibly>
is what i mean
<alexgordon>
so
<alexgordon>
TYPE SYSTEM
<whitequark>
YEAH
<incomprehensibly>
ec: yeah I barely go on the computer nowadays except to watch shows
<alexgordon>
the problem I have is how to merge dynamic and static typing
<ec>
been there.
<alexgordon>
like I know I want to be able to do
<ec>
everyone burns out, incomprehensibly
<ec>
if you want to stay sane, even *several* times.
<incomprehensibly>
mhm
<whitequark>
alexgordon: I totally get what you want
<alexgordon>
j = json.read(somefile); j["foo"]
<ec>
don't fight it, and don't pretend it's consistent. Just live. (=
<whitequark>
and in fact I've been thinking about it too
<incomprehensibly>
i just feel kinda dumb about producing little or no creative output for my last summer before college
<incomprehensibly>
:p
<ec>
yes. I know.
<ec>
I just spent two *months* playing Minecraft instead of doing anything valuable.
<incomprehensibly>
gotta make some fuckin hip hop beats
<ec>
Last year, I spent six months throwing parties.
<alexgordon>
I want the maximal benefits from static typing, but the convenience of dynamic typing
<ec>
Year before that, two seperate two/three month periods, playing World of Warcraft.
<ec>
Two years before *that*, six months traveling.
<alexgordon>
objc is pretty good, but the static typing is kinda weak (getting stronger)
* ec
shrugs
<purr>
¯\(º_o)/¯
<ec>
life's not programming.
<incomprehensibly>
so last year you turned into jesse
<incomprehensibly>
wait how far have you seen
<ec>
programming, conversely, is life.
<alexgordon>
oh and it shouldn't be slow
<ec>
incomprehensibly: Oh, idk. Which season has the title-card where he's a king in a chair?
<ec>
I think I saw the first episode of that season.
<alexgordon>
that's the other problem with dynamic typing: too. much. malloc()
<incomprehensibly>
uh i don't think i have seen that
<ec>
so, maybe a season and a half, or maybe two, behind?
<whitequark>
alexgordon: dynamic, monstrous, slow: pick any two
<alexgordon>
whitequark: dynamic, monstrous.
<whitequark>
v8.
<alexgordon>
if I can't build a game in it, it's not worth my time ;)
<whitequark>
fuck all about that.
<whitequark>
first we make a shitty language, then we turn it into a non-shitty language under the hood, but don't say the user how to avoid the shitty bits
<whitequark>
and change them all the time to make the output even less predictable
<incomprehensibly>
ec: do you remember the state of affairs regarding skyler, or regarding gus?
<ec>
fuck if I remember *shrug*
<purr>
¯\(º_o)/¯
<incomprehensibly>
ec: yeah uh i think season 5 is king in a chair
<alexgordon>
whitequark: hahaha
<alexgordon>
whitequark: yes
<incomprehensibly>
so you've seen more than me
<incomprehensibly>
ok
<incomprehensibly>
so yeah remember after he shot gale
<incomprehensibly>
and broke down
<incomprehensibly>
and turned his house into a crackhouse
<ec>
okay not sure I remember that D:
<ec>
wait, gale isn't his wife, who the fuck is gale
<ec>
I don't remember shit about this shit. >:
<incomprehensibly>
gale is nerdy assistant
<ec>
Lots of tweets I agree with today.
<incomprehensibly>
skyler is wife
<ec>
ah yes
<ec>
I wish I could save tabsets to to-do entries.
<incomprehensibly>
seriously computers are feeling like more of a bottleneck to communication right now
<incomprehensibly>
typing and reading are nowhere near as good as talking
<ec>
and *this* is why every. single. resource. needs a URL.
<incomprehensibly>
or watching tv shows lol
<purr>
lol
<ec>
even amongst desktop apps, the thing that iOS taught us, is that things:list/686228 is a USEFUL THING TO PROVIDE.
<whitequark>
typing and reading have the advantage of being *permanent* and *indexable*
<whitequark>
so it's only nowhere as good if you have nothing interesting to say
<ec>
and the ubiquity of the web can only assist with that
<whitequark>
which (tv shows yeah) seems to be the case here :p
<whitequark>
so: voice for transient matters, text for permanent ones
<incomprehensibly>
whitequark: how much do you talk to real life people
<whitequark>
incomprehensibly: "it depends"
<whitequark>
I don't think there can ever be an average measurement of how much do I talk to real life people. it's like average temperature in the hospital: 36.6°C
<ec>
incomprehensibly: not much
<ec>
incomprehensibly: but he's smart, so that's okay
<incomprehensibly>
haha aight
<ec>
I've always felt that there's some “average measurement” of people-skills, inherent intelligence, and knowledge-base
<ec>
that if you average all three out, you get a “quality of this person” result.
<ec>
You can have somebody worth including in your life, if they're dumb, but kind and fun and make-you-feel-good-peopleness-y
<ec>
or, you can deal with somebody being an incompetent asshole if they're just blazing genius smart,
<incomprehensibly>
haha
<ec>
or they can be dumb-with-people, *and* rather slow, if they're the aspie type who's obsessively learned EVERYTHING in all their lonely time, and thus can answer lots of questions
<ec>
I retain all three types within the bounds of my monkeysphere.
<whitequark>
ec: you know
<whitequark>
dealing with assholes isn't worth it
<whitequark>
don't. just don't.
<whitequark>
[cue "that coworker" story which is not about to be told]
<ec>
lol.
<purr>
lol
<incomprehensibly>
6:23 PM <•ec> or they can be dumb-with-people, *and* rather slow, if they're the aspie type who's obsessively learned EVERYTHING in all their lonely time, and thus can answer lots of questions
<ec>
about 90% of this channel falls under that heading for me, brah
<whitequark>
ec: inb4 "this is ironic": yeah it may be, and that's a really good reason for me to be less of an asshole
<incomprehensibly>
well you see
<incomprehensibly>
i excel in all 3 areas
<incomprehensibly>
so i am the perfect human being
<ec>
incomprehensibly, joelteon, and jeannicolas are the only people out of the forty-some I see in and out of, that I'd consider “people-capable.”
<ec>
Oh, I'd only give you two of three.
<alexgordon>
ec: you see "in and out of"?
<ec>
You're not super widely versed. Your knowledge, such as it is, stems from the genius: I don't see that you've had the time to really be bored and obsessive, gaining that ridiculous breadth of knowledge.
<ec>
alexgordon: (this room)
<incomprehensibly>
ec: haha aight
<joelteon>
People capabale!
<joelteon>
cabprale
<alexgordon>
ec: am I not people capable?
<incomprehensibly>
ec: I get the knowledge one in real life with high school students
<incomprehensibly>
lol
<ec>
alexgordon: I don't fucking know. You're too mysterious; I've long since ascribed that to “is a basement nerd, but instead of wallowing in it and identifying with it à la Nuck or Navarr, he hides it and acts mysterious, à la sephr.”
<alexgordon>
ec: but I explain it, we don't have basements in the UK!
<incomprehensibly>
ec: YOU ACCENTED A LA RIGRHT
<incomprehensibly>
ec: SO PROUD
<ec>
/kick incomprehensibly à suck my dick
<ec>
grr
<alexgordon>
ec: wait, navarr is a basement nerd? I thought he had dozens of girlfriends
<whitequark>
who is navarr
<ec>
it's not like the two are mutually exclusive
<alexgordon>
ec: pretty sure they are
<ec>
I like to think I've escaped basement-nerdism (… although recent Minecraft period calls into question)
<incomprehensibly>
ec: let's do garage biopunk
<alexgordon>
yeah you're definitely a basement nerd right now
<incomprehensibly>
experiements
<incomprehensibly>
biohacker
<incomprehensibly>
make organisms
<ec>
and yet I'd definitely had ‘dozens’ of girlfriends in my period as a self-declared, proud basement-nerd.
<ec>
incomprehensibly: deal.
<alexgordon>
incomprehensibly: make orgasms?
<ec>
incomprehensibly: I'll get the equipment together if you'll help me learn.
<ec>
seems scarily over-my-head.
<alexgordon>
he's getting the equipment together!
<incomprehensibly>
i'm repeatedly having the sensation of text being claustrophobic and bottleneckey
<incomprehensibly>
reading askreddit threads
<incomprehensibly>
ec: sweet let's do it
<alexgordon>
and having sensations
<incomprehensibly>
ec: and also chemistry
<incomprehensibly>
ec: making meth
<ec>
ugh I hate chem
<ec>
no chem
<ec>
biochem is worse, though
<ec>
so idk
<incomprehensibly>
chem is sweet
<joelteon>
i'm so good at humans
<incomprehensibly>
biochem is sweete
<alexgordon>
THERE'S *NO* CHEMISTRY!!!
<joelteon>
everything else sucks though
<ec>
how much biohack can we do without learning icky biochem?
<incomprehensibly>
having taken only an honors chem class though
<ec>
chem is okay, biochem is bullshit
<incomprehensibly>
why
<incomprehensibly>
:(
<incomprehensibly>
seems really cool
<ec>
because I trust everything my dad says and that's what he says
<ec>
worst part of the medical degree was wishy-washy biochem classes
<ec>
whereas he loved chemistry
<ec>
whereas chem, to me, is mostly scary
<whitequark>
ec: ha
<ec>
I feel about chemistry what most people seem to feel about math.
<whitequark>
biochem is *hard*
<ec>
That it's terrifying and impenetrable and icky.
<incomprehensibly>
chemistry is lots of memorizing
<incomprehensibly>
but also
<whitequark>
it's astoundingly huge and complex and shit
<incomprehensibly>
shapes
<incomprehensibly>
legos
<whitequark>
and is also rather poorly understood
<ec>
huge, complex, and badly-understood from everything I've heard
<ec>
… yeah, that. brainsync.
<whitequark>
hivemind!
<incomprehensibly>
chemistry is shapes
<incomprehensibly>
i like it
<ec>
I hate badly-understood sciences, or at least, the formal study of them. Seems a lot like masturbation.
<incomprehensibly>
but yeah how the fuck protein folds
<incomprehensibly>
you know
<ec>
“how the fuck-protein folds”
<incomprehensibly>
ec: yeah psychology is fucking bullshit
<ec>
is probably *not* how you meant that, but definitely how I read that.
<incomprehensibly>
lol
<purr>
lol
<whitequark>
incomprehensibly: well you can xray it
<whitequark>
IF
<whitequark>
it crystallizes
<whitequark>
if it doesn't you're fucked
<ec>
bbl shower, and date
<ec>
but srsly incomprehensibly, hit me up, let's make plans. need to know your college schedule.
<ec>
and i'll need to price out the hardware/proprietary-software.
<ec>
get audy up in this bitch, he does this for a job.
<ec>
well, bioinformatics, so not really the same thing at all, but I'm still sure he knows more than either of us.
<incomprehensibly>
ec: have fun
<incomprehensibly>
ec: yeah plans scheule biohack
<whitequark>
ec: i wonder if it's within your league actually
<incomprehensibly>
audy: let's biohack
<whitequark>
well
<whitequark>
simple things you can do cheaply
<whitequark>
"ec cheaply"
<whitequark>
but that's just really simple
* ec
nods
<whitequark>
you won't advance to complex without extensive knowledge anyway
<ec>
but I also just declined to order a Tesla
<whitequark>
so i guess it's ok
<whitequark>
what's that, 50k?
<ec>
so in a certain mode of thinking, I've got a hundred grand “more-available” to be spent than I otherwise would have.
<incomprehensibly>
holy fuck ec how did you get money
<jeannicolas>
yay! I'm people-capable!
<incomprehensibly>
is this all from your dad's real estate investment when you were a baby
<whitequark>
oh 100, ok, not that much :)
<ec>
most likely, I'd be completely willing to dump ten grand into an interesting new hobby, if I'd had the time and energy to do a little research with somebody I trust, like alexgordon or inimino or micahjohnston
<alexgordon>
jeannicolas: I laughed
<ec>
if that yielded any further interest and innovation/excitement, then I'd happily dump much more
<alexgordon>
ec: hm, help me make fast food robots?
<ec>
alexgordon: … unexpected reply was unexpected.
<ec>
bbl shower-date-happyfeels.
<ec>
<3 everybody
<purr>
Let it be known that ec hearts everybody.
<alexgordon>
ec: oh me and sammcd were discussing it last week
<incomprehensibly>
ec: <3
<incomprehensibly>
have fun
<sammcd>
hah
<ec>
you have noticed that I don't pay attention to this channel anymore, right?
<ec>
and who the fuck is sammcd
<sammcd>
I AM
<alexgordon>
ec: not in here...
sammcd was kicked from #elliottcable by ec [NO YOU'RE NOT]
<purr>
whitequark: whitequark hates semicolonless javascript, javascript, any kind of javascript, having to maintain his own LLVM tree, did I say I fucking hate javascript, and JITs.
* whitequark
sighs
* ec
laughs
<ec>
adorable.
<ec>
and well-played.
<ec>
I'M TALKING TO THE AUTOMATIC PEOPLE
<ec>
FINDING OUT WHY MY ORDER HASN'T SHIPPED
<ec>
I'M SO EXCITED
* ec
channels his inner micahjohnston
<whitequark>
-loves whitequark
<purr>
whitequark: whitequark loves git, console, purr, foo, Adrian Thurston, LLVM, alsa, Tomorrow Bright, llvm, #llvm, rotting rat fetuses with birth defects, chicken, anime, notebooks with full-HD screens, ec, Atomic Object, ocaml and good llvm bindings, llvm 3.3, ocaml, Biting Elbows, and Metallica.
<whitequark>
SO MUCH LLVM IN THERE
* whitequark
slaps whitequark around a bit with a large trout
<whitequark>
5AM. i should have been sleeping for five hours already. but... things.
<whitequark>
this sucks :/
<sammcd>
-hates sammcd
<purr>
sammcd: sammcd doesn't hate anything :)
<sammcd>
wooo
<sammcd>
-loves sammcd
<purr>
sammcd: sammcd doesn't love anything :(
<sammcd>
:(
<ec>
… lol
<purr>
lol
<alexgordon>
-hates alexgordon
<purr>
alexgordon: alexgordon hates ?, ಠ_ಠ, rock, faith_in_humanity, Eclipse, foo, is comment, c--, https://en.wikipedia.org/wiki/C, and applescript.
<whitequark>
-loves ec
<purr>
whitequark: ec loves Usenet, when devyn takes his pants off, alexgordon, purr, Safari, Safari 7, records., alexgordon's butt, alexgordon's face, alexgordon's words, devyn, whitequark, Vernor Vinge, Alistair Reynolds, Charles Stross, Isaac Asimov, Terry Pratchett, Neal Stephenson, George R. R. Martin, Frank Herbert, Totoro, half-arsed, and everybody.
<whitequark>
LOLWAT
<purr>
LOLWAT
<alexgordon>
"when devyn takes his pants off"
<alexgordon>
LOL
<alexgordon>
alexgordon's butt, alexgordon's face, alexgordon's words
<whitequark>
I'm somewhat ashamed to be in that list
<whitequark>
lol
<alexgordon>
I assure you, my butt is nothing to get excited about
<whitequark>
(not actually, no)
<whitequark>
-hates ec
<purr>
whitequark: ec hates eboyjr.
<whitequark>
...
<alexgordon>
and my face is a calculator
<alexgordon>
right jeannicolas ?
<whitequark>
oddly specific, I would say
<alexgordon>
whitequark: not if you knew eboyjr ;)
<dsamarin>
alexgordon: oh fuck you ;)
<dsamarin>
-hates dsamarin
<purr>
dsamarin: dsamarin doesn't hate anything :)
<dsamarin>
-loves dsamarin
<purr>
dsamarin: dsamarin doesn't love anything :(
<dsamarin>
-whohates dsamarin
<purr>
dsamarin: dsamarin is hated by no one :)
<dsamarin>
-wholoves dsamarin
<purr>
dsamarin: dsamarin is loved by no one :(
<incomprehensibly>
6:53 PM <•purr> whitequark: whitequark hates semicolonless javascript, javascript, any kind of javascript, having to maintain his own LLVM tree, did I say I fucking hate javascript, and JITs.
<dsamarin>
-hates incomprehensibly
<purr>
dsamarin: incomprehensibly doesn't hate anything :)
<dsamarin>
-hates micahjohnston
<purr>
dsamarin: micahjohnston hates unlambda, textual programming, and .
<incomprehensibly>
lol why do i hate unlambda
<purr>
lol
<incomprehensibly>
i don't have any particular feelings on it
<dsamarin>
-loves micahjohnston
<purr>
dsamarin: micahjohnston loves vim, the album leaf, gqbrielle, jason mraz, ellie goulding, on the wing, umbrella, freezepop, Game Maker, modular synths, tangled, applicatives, music, Burial, love2d and lua, ableton live, soundcloud, my monitors, npr, rinse.mf, rinse.fm, Imogen Heap, white stripes so much, peter gabriel, Iron & Wine, the submarines, the shins, SQL, the white stripes, the xx, mewithoutyou, ben folds, merge sort, four tet, jazz, alt-j, ∆, physics, p
<sammcd>
-whohates sammcd
<purr>
sammcd: sammcd is hated by no one :)
<incomprehensibly>
wait yeah it's impurely functional because they couldn't be cool like lazy k
<purr>
incomprehensibly: micahjohnston is loved by devyn, alexgordon, locks, elliottcable, gqbrielle, darkf, incomprehensibly, micomprehensibly, mix, remy, vil, hansolo, and gqbe_fabu.
<incomprehensibly>
-whohates micahjohnston
<purr>
incomprehensibly: micahjohnston is hated by no one :)
<alexgordon>
!
<dsamarin>
-whohates ec
<purr>
dsamarin: ec is hated by no one :)
<dsamarin>
-whohates elliottcable
<purr>
dsamarin: elliottcable is hated by Nuck, gqbrielle, darkf, and everybody.
<incomprehensibly>
I swear approximately half of those are cheecuebrieyah though
<alexgordon>
yeah
<dsamarin>
tf is cheecuebrieyah
<incomprehensibly>
lazy k is fucking cool
<incomprehensibly>
dsamarin: qbrielle
<incomprehensibly>
haha forgot the g
<incomprehensibly>
gqbrielle
<dsamarin>
ok
devyn has joined #elliottcable
<incomprehensibly>
ec: did you know that I live very close to _why, and most of my friends live even closer, and I have driven past a building he has mentioned in his book he wrote after disapperaing
<alexgordon>
incomprehensibly: why lives in utah? LOL
<purr>
LOL
<incomprehensibly>
alexgordon: yep
<incomprehensibly>
my friend's dad actually worked with him at a company where they used ruby
<incomprehensibly>
at one point
<devyn>
alexgordon: hahahaha before incomprehensibly responded I thought you were asking why incomprehensibly lives in Utah in bad grammar
<alexgordon>
devyn: LOL
<purr>
LOL
<incomprehensibly>
devyn: haha
<incomprehensibly>
devyn: you remember tim
<incomprehensibly>
devyn: his dad
<alexgordon>
devyn: meesa jar jar binks
<devyn>
incomprehensibly: of course I know Tim
<incomprehensibly>
of course
<devyn>
I knew Tim before I knew you
<devyn>
:p
<sammcd>
whats that dude up to these days?
<sammcd>
_why
<devyn>
he released a bunch of odd notes on the internet and nothing further happened, really
<alexgordon>
now THERE's a guy who isn't "people capable"
<alexgordon>
man I love that expression
<alexgordon>
++ people capable
<purr>
Let it be known that alexgordon loves people capable.
<devyn>
the person behind _why is, _why itself is not
<alexgordon>
devyn: ...
<alexgordon>
that makes no damn sense
alexgordon has quit [Remote host closed the connection]
<ec>
devyn: why lives in vancouver ?? LOL?
<purr>
LOL
<ec>
devyn: who the fuck is tim
<devyn>
lol
<ec>
alexgordon: it made absolute sense.
<ec>
_why is intentionally constructed to appeal to the lonely, the introvert, the child, the inexperienced, the impotent.
<devyn>
I'd tell you, but you have a habit of keeping kids captive in #elliottcable
<ec>
_why is built for those who can't. not those who can.
<ec>
purr: add a countdown timer for “ETA until Tim is an #ELLIOTTCABLE minion”
<ec>
bbl
<ec>
also, whitequark / alexgordon,
<ec>
you wanted -hates elliottcable and -loves elliottcable
<ec>
whitequark: start there, then drill down if I don't start drooling.
<whitequark>
actually, no, I think I suck at math and can misinform you
<whitequark>
which may or may not be true but don't wanna :/
<micahjohnston>
I only know it music-production-wise
<ec>
I'm currently A) running on *no* sleep, B) watching a TV drama about the fashion industry, and C) listening to Lil' Wayne at the same time, because I can't figure out how to make it stop
<micahjohnston>
haha
<ec>
so, you've gotta layer fourier transforms on top of all that
<ec>
and ec's already a bit dim
<micahjohnston>
ok cool so
<ec>
soooooo …
<micahjohnston>
this is a sentence:
<ec>
“This is a sentence.”
<micahjohnston>
a waveform is composed of an infinite sum of sin waves of every frequency, of varying amplitudes
<ec>
hm
<micahjohnston>
so a normal waveform is in the "time domain", meaning you can look at the amplitude at a particular time
<ec>
wait
<ec>
how so
<ec>
wouldnt,
<micahjohnston>
a fourier transform transforms it to be in the "frequency domain", decomposing it into these sin waves
<ec>
____-^-___-^-_______ already not be representable as a sine-wave?
<micahjohnston>
so you can ask for the amplitude as a particular frequency
<ec>
not even to get into more complex stufff?
<micahjohnston>
yeah if you have a plain old sin wave
<micahjohnston>
its fourier transform is 0 everywhere except the single point that is that sin wave's frequency
<ec>
… where it's instead the amplitude?
<micahjohnston>
yeah
<ec>
re-reading.
<ec>
still having trouble with the first sentence.
<micahjohnston>
ok
<micahjohnston>
so you have any waveform, like a sawtooth wave
<ec>
and it's obviously the same concept as your first sentence.
<ec>
so I think my question has gone from “how do fourier transforms work”
<ec>
to “how does wave work loll”
<purr>
loll
<micahjohnston>
hahah
cloudhea1 has quit [Ping timeout: 240 seconds]
<micahjohnston>
so you don't get what the wobbly square wave is?
<dsamarin>
a wave = k sin(f x) + c
<dsamarin>
sigma*
<micahjohnston>
I'll probably learn this in math this year or something
<micahjohnston>
right now I only know shit from using filters and eqs and shit
* ec
nods
<ec>
that's the understanding I'd rather have.
<ec>
What I'm trying to understand,
<micahjohnston>
aight
<ec>
is how that complex-wobbly gif, somehow decomposes into a set of sin waves.
<ec>
That, I don't see the mathematics behind. I can't *visually* see any relationship between the red line, and the blue lines that it's obviously implied are somehow “adding up to” it.
<ec>
maybe I need to go play with Grapher.
<ec>
got formulae for me to enter?
<micahjohnston>
ok think about this
<micahjohnston>
at each point
<micahjohnston>
take each blue sin wave
<micahjohnston>
and take its height from the x axis at that point
<micahjohnston>
take all those heights and add them up
<micahjohnston>
and that's your new height
<micahjohnston>
just adding them all together
<micahjohnston>
which coincidentally is what happens when you *play two sounds at once*
<ec>
hm
<ec>
hmmmm
<ec>
find me another gif for this!
<ec>
g'damn you're useful
<ec>
this is the least *visually* intuitive thing ever
<ec>
it simply doesn't look like they add up like that. but now that you've made it point-blank simple, it's obvious that they do.
<micahjohnston>
there is a perfect one that I can't remember
<ec>
okay. So, I get how *those* sines can add up to *that* wave … but I'm still lost as to how *any* wave can be constructed by adding up simple sine-waves. Perhaps that's just a proof that's over my head until I learn more geometrics.
<micahjohnston>
uhuh
<micahjohnston>
yeah same here
<micahjohnston>
I don't have a mathematical proof that it works every time
<micahjohnston>
but like
<micahjohnston>
I've started thinking about sound, always, as just a combination of frequencies being sounded at once at different volumes
<micahjohnston>
that's how you think in production
<ec>
which makes sense
<ec>
in terms of *sound*
<micahjohnston>
and you use filters and eqs and shit to sculpt it using that frame of mind
<ec>
just not visually / in terms of *graphs*
<ec>
it makes complete sense that it's a set of frequencies, with the amplitude of each member of the set varied over time
<micahjohnston>
yeah but when you realize that your eardrum is vibrating over time in the shape of a particular graph
<ec>
man.
<ec>
mind-blowing night.
<ec>
okay. next step.
<ec>
somebody explain to me how/why quantum processors are better at that than conventional processors.
<ec>
or, errrrrr, maybe, how a “quantum” fourier transform is different from a normal, discrete one.
<micahjohnston>
idk if that's anywhere near the specificity you're asking for
<ec>
dsamarin: what were you saying?
<ec>
micahjohnston: oh, that much I knew
<ec>
I was sort of looking to *understand* why, though, a little bit better
<micahjohnston>
aight yeah I don't think I'm a whole lot of help there
<ec>
that is, to some level of specificity, I can *understand* why soap-bubbles are good at solving that particular problem, but useless for general applications of that field
<ec>
whereas I don't understand what zone of these mapping-transformations that I've just had explained to me, are restricted to “quantum” processors.
<ec>
hey, micahjohnston, what's your schedule like
<ec>
alexgordon: and are you here?
<ec>
I'm on espresso, and can probably actually Paws for a short while before my gravity kicks in
<micahjohnston>
I can screenshot you
<ec>
hm?
<ec>
wait
<ec>
so what are you doing the day *before* you move!?
<ec>
fuck Paws, talk to me about Life
<micahjohnston>
I am probably packing
<micahjohnston>
:p
<micahjohnston>
today I'm gonna buy a bunch of shit like shampoo
<micahjohnston>
tomorrow I'll finish up all my laundry and pack all my stuff
<micahjohnston>
and thursday I'll move it all up
<micahjohnston>
yesterday smoked a cigarette and decided I like nicotine but don't like cigarettes ;p
* ec
grins
<micahjohnston>
hookah is good
<ec>
Cigars are excellent, if you haven't been there yet
<ec>
I think hookah is fairly retarded.
<micahjohnston>
cool, I'll have to try
<micahjohnston>
lol why
<purr>
lol
<ec>
It's quite a bit like alcohol, without the class.
<ec>
in that the only people who do it and/or enjoy it, are kids trying to impress other kids.
<micahjohnston>
haha aight
<ec>
At least with alcohol, you can ‘graduate’ from jägerbombs to martinis, or single-malt, or what-the-fuck-ever
<ec>
but with hookah, you graduate to not smooking hookah.
<ec>
when we meet up, I'll definitely explore some fine cigars with you. It's a interesting pastime. Calming, as much in the ritual of the thing as in the drug itself.
<ec>
Only done it a couple times.
<micahjohnston>
sweet
<ec>
oh, I meant, like, for the next two hours, re: schedule, lol
<ec>
although this is interesting to know. mmmmmheheheh
<ec>
so if I were to kidnap devyn and gqbrielle and appear in Utah so we can recreate the general ##Hat atmosphere, now I know *when* to do so.
<ec>
“CS2100” being … Learn Java, level 1?
<ec>
or did you place out into something slightly less mind-numbing?
<micahjohnston>
no
<micahjohnston>
I tested out of the silly pre-java
<micahjohnston>
and then
<micahjohnston>
I got a 5 on AP CS
<micahjohnston>
so I tested out of the silly java
<micahjohnston>
this is "discrete structures"
<micahjohnston>
which I probably know already
<ec>
not even faaaaaaair
<micahjohnston>
shit like sets and logic
<micahjohnston>
but
<micahjohnston>
yeah
<ec>
How the FUCK is Grover's algorithm a real thing
<ec>
I'm reading the introductory sentence and going,
<ec>
“No, wait, I know all these words, and even *I* know this makes no sense.”
<micahjohnston>
haha yeah
<ec>
searching an unsorted database in less than linear time.
<ec>
“Unsorted search speeds of up to constant time are achievable in the nonlinear quantum model.”
<ec>
See, now that makes a little more sense to me.
<ec>
At least, that, I can sign off to “some dataset-superimposition physics magic™.”
<ec>
but less than linear time, in a linear computation model, I just can't wrap my head around.
<ec>
I feel like a “quantum” toy programming language, something with an interprative REPL that nonetheless emulated (with, obviously, only the purpose of teaching) some of the properties of a quantum processor, could be useful
<ec>
wrapping one's head around qubits and N-dismensional state spaces, is a bitch.
<ec>
“We are provided with (quantum black box) access to a subroutine …” WHAT DOES THAT EVEN MEAN
<micahjohnston>
that's the quantum hardware you get to use
<micahjohnston>
in the algorithm
<ec>
ah, so, “subroutine” meaning “quantum instruction”
<micahjohnston>
ec: hahaha you were looking up phonology terms
<micahjohnston>
I love those
<ec>
RIGHT
<ec>
LOVELOVELOVELOVE
<ec>
I do that all the time
<ec>
they help me understand concepts, as backwards as that might sound
<ec>
sometimes the easiest way for me to truly grok something, is to grok where the word *came* from; and sometimes the easiest way for me to grok *that*, is by figuring out exactly how it sounds to different peopl
<micahjohnston>
haha
<ec>
origin of words, and the *vocal* origin of words, is hugely linked to concept and meaning in my internal model of the world
<ec>
if I can't find the right set of words for it, it very much doesn't exist.
<ec>
if I can't find the right set of *sounds* for the right set of words for it, it also doesn't exist.
<ec>
so lemme review this one more time:
<ec>
waves are functions;
<ec>
functions are compositions of other, simpler functions;
<ec>
wave-functions in particular are guaranteed (somewhow™ that I don't understand) to be compositions of sin()-form functions;
<micahjohnston>
this might make the somehow™ more believable:
<micahjohnston>
often it takes an infinite sum of sins to get a particular waveform
<micahjohnston>
and so you can only approximate when you're adding up your own sins
<ec>
Fourier transformations are a class of higher-class functions that change the *domain* of aforementioned simpler functions, mapping the composed-over sin-functions to their amplitude;
<micahjohnston>
as you can see in the wobbly approximation of a square wave
<ec>
is there a generalization of this topic?
<ec>
what do you call these domain-changing upperclassmen functions?
<micahjohnston>
is a name I hear a lot but I don't know what it is
<ec>
thought I saw something somewhere about Fourier transform-decomposition being limited to waveforms that are composed of a finite number of forms …
<micahjohnston>
that's probably dft or fft
<micahjohnston>
or something
<micahjohnston>
like, actual algorithms
<micahjohnston>
and data
<ec>
dft
<ec>
is what I was reading on
<ec>
no idea what fft is
<micahjohnston>
discrete fourier transform
<micahjohnston>
yeah
yorick has quit [Remote host closed the connection]
<ec>
hm.
<micahjohnston>
fast fourier transform
<micahjohnston>
an algorithm
<ec>
now I need to learn enough to *implement* a naïve fourier transform in terms of code.
<micahjohnston>
laplace transform also decomposes but not into frequencies
<micahjohnston>
yeah
<ec>
my dad said it was his second project with programming, ever. obviously he had more mathematics background than me
<ec>
but still.
<micahjohnston>
I'm not there yet
<micahjohnston>
haha yeah
<micahjohnston>
my second project with programming was
<ec>
he did it in fortran, I've *gotta* be able to come around to it from the other side, with my knowledge of the toolsets.
<micahjohnston>
print HELLO WORLD a billion times with no space so it wraps around
<micahjohnston>
on a color computer
<ec>
LOL
<ec>
dude
<ec>
ComputerCraft
<ec>
is so very much something you wouldn't care about AT ALL
<ec>
but is SO COOL nonetheless
<micahjohnston>
haha sweet
<micahjohnston>
do you know wiremod for garry's mod
<ec>
never done garry's mod at all
<micahjohnston>
me neither
<micahjohnston>
but wiremod looks cool
<micahjohnston>
<3 chance the rapper
<purr>
Let it be known that micahjohnston hearts chance the rapper.
<ec>
so
<micahjohnston>
hip hop is literally the best thing
<ec>
I need to learn to use OpenSCAD for 3D printing
<ec>
you played with this crap at all?
<ec>
<3 Atmosphere
<purr>
Let it be known that ec hearts Atmosphere.
<ec>
<3 Macklemore
<purr>
Let it be known that ec hearts Macklemore.
<ec>
but that's about it
<micahjohnston>
you only like white rappers
<ec>
I like some other stuff, but I don't OMGLOVE any of it
<ec>
RELEVANT:
<ec>
I JUST STARTED TO LOVE BURIAL PROPERLY
<ec>
it's only sooooomeeeetimes
<micahjohnston>
:DDDDDD
<ec>
it's super-rare where I'm in the proper mood
<ec>
it's a lot like alva noto like that
<micahjohnston>
uhuh yeah definitely
<ec>
but COMPLETELY different mood.
<micahjohnston>
yeah
<alexgordon>
ec: here
<alexgordon>
PRESENT
<ec>
cool
<alexgordon>
ec: ready for paws?
<alexgordon>
-spec
<purr>
alexgordon: Paws' half-arsed Version 10 specification <http://ell.io/ihQzs>
<ec>
I'm 9/10ths dead
<ec>
but FUCK IT SURE
<micahjohnston>
<3 burial
<purr>
Let it be known that micahjohnston hearts burial.
<micahjohnston>
but yeah can't listen a lot of the time
<ec>
at least, assuming I can even understand my own spec in my current state-of-mind
<micahjohnston>
but it's fucking genius
<ec>
alexgordon: I kiiiiinda understand what a fourier transform is right now.
<micahjohnston>
anyway ec i gotta send you some real hip hop
<micahjohnston>
like nas and shit
<ec>
alexgordon: which completely unrelatedly makes me want to tackle monads and write Haskell.
<micahjohnston>
haha
<micahjohnston>
ec: monads suck
<ec>
because I suddenly feel capable and not-retarded-by-comparison-to-everybody-else.
<ec>
micahjohnston: spotify-social-share. GO.
<alexgordon>
ec: capable, but not people capable?
<ec>
micahjohnston: can't guarnatee I'll listen to it soon.
<micahjohnston>
so just learn them so you can realize how trivial and not fundamental they are
<micahjohnston>
:p
<micahjohnston>
ec: aight will
<ec>
heads-up, all: My schedule apparently calls for me to be stuck in Alaska for a couple *more* extra weeks. Expect some Paws, expect some more lively discussion, and expect some good 'ol flamewars of the Elliott flavour. LOVE YOUUUUUU ❌ ⭕ ❌ ⭕ ❌ ⭕ ❌ ⭕
<alexgordon>
LOL
<purr>
LOL
<ec>
micahjohnston: when I say “monads,” it's a code-name for “category shit that I can't understand, and thus makes Haskell a useless toy to me until I understand it.”
<micahjohnston>
ec: haha aight
<ec>
and I can't move on to the *useful* shit like Erlang, somehow, until I can crack the Haskell Wall™
<alexgordon>
ec: PAWWWWWS
<ec>
three years, I gave some very salient advice to somebody I cared a lot about:
<ec>
“Learn three new programming languages, every year.”
<ec>
It's been three years. I've learned zero.
<ec>
#dogfoodingfail
<ec>
<3 Burial
<purr>
Let it be known that ec hearts Burial.
<ec>
alexgordon: BUTTTTTTS
<ec>
alexgordon: WHAT'S AN INTEGRAL TRANSFORM
<alexgordon>
ec: I CAN'T REMEMBER
<ec>
MY THICK, BITTER, DARK-ROAST COFFEE WITH EXTRA SHOTS OF ESPRESSO IS NOW COLD
<alexgordon>
all that maths I did is finally useful or something!
<joelteon>
a linear function is just an endomorphism, ec
<joelteon>
c'mon dude
<ec>
dunno what that is
<joelteon>
me neither, but the guys in #haskell say it a lot
<joelteon>
it's a map from something to itself
<joelteon>
go look at the definition, though
<alexgordon>
ec: first rule of being a proper mathematican: ignore the category theorists
<ec>
“The expression "linear operator" is commonly used for a linear map from a vector space to itself (i.e., endomorphism).”
<joelteon>
that's helpful
<ec>
okay, I understood a little bit of that.
<joelteon>
ec: f(x+y) = f(x) + f(y)
<joelteon>
f(ax) = af(x)
<ec>
slow down.
<joelteon>
sounds like a normal function to me
<ec>
god, I hate mathematician's notation.
<alexgordon>
ec: do you know what a vector space is?
<joelteon>
just applied to things other than like, simple algebra
<alexgordon>
need to start there
<ec>
Trying to explain these concepts with the notations mathematicians have come up with for themselves,
<joelteon>
sucks
<whitequark>
ec: ohhhh, you'd like the last strangeloop (I think?) talk
<joelteon>
hey, whitequark is gone
<joelteon>
oh
<ec>
is like trying to explain computers using the notations UNIX programmers came up with for sh and the *NIX toolsets.
<ec>
alexgordon: no.
<ec>
alexgordon: rather, vaguely.
<alexgordon>
ec: well you know what a vector is right?
<alexgordon>
like (x, y)
<ec>
alexgordon: pretty sure I learned a *lot* about them, under a different name, at another point.
<whitequark>
it was about using scheme notation to represent mathematical concepts
<whitequark>
and perform symbolic manipulation, and so on
<ec>
whitequark: oooo that sounds delicious
<ec>
but really, really dangerous
<whitequark>
why?
<joelteon>
i know what a vector is!
<ec>
I'm exactly the person who would start learning this stuff from the ground up, translating everything I read into sexps
<ec>
and then do all my own learning and calculations in that esoteric (in the field) notation
<joelteon>
i actually kinda get linear map
<whitequark>
that's not a bad idea at all.
<ec>
and then go try and have salient discussions with other professionals, once I had the *knowledge*, using COMPLETELY foreign notation and priciples
<joelteon>
i don't see how it's useful
<joelteon>
but it makes sense
<ec>
(have you *seen* my JavaScript?)
<whitequark>
ask @silentbicycle on twitter, he probably remembers the talk.
<whitequark>
I don't have it bookmarked.
<ec>
alexgordon: okay. I learned vector-spaces, I believe, as whatever the fuck the dude calls them in Anathem
<ec>
but I think I know the concept.
<alexgordon>
ec: vectors != vector spaces btw
<alexgordon>
many programmers know "vectors"
<alexgordon>
but they don't know the mathy stuff behind vector spaces
<ec>
it's like mapping x,y,z,p,y,r,T to seven points in a seven-dismensional space
<ec>
I don't fucking know what a vector is
<ec>
and I gods-damned HATE it when programming languages use that term for what I know as an “array”
<alexgordon>
ec: it's just C++ really
<alexgordon>
:P
<ec>
I have a huge pet-peeve about programming languages inheriting terms from math, just to sound more fancy
<alexgordon>
yeah
<alexgordon>
vector, functor
<alexgordon>
fucking C++
<ec>
sure, if you're *differentiating* a vector from an array,
<ec>
great. sure.
<ec>
but if you've got only one goddamn list structure, either call it a goddamn “list” (forward-looking.) or an “array” (widely understood, and backwards compat.)
<ec>
… anyway. no elliott-ranting. only elliott-listening.
<ec>
what is a vector.
<ec>
not a C++ vector, the mathematical concept.
<alexgordon>
ec: there's a practical definition and a pure math definition...
<joelteon>
ok this is boring
<ec>
well either, as long as it has nothing to do with programming.
<joelteon>
let me know when whitequark stops ignoring me
<alexgordon>
joelteon: yeah linear algebra is boring
<whitequark>
there are also actual vectors in programming, like those on GPUs
<joelteon>
well no, wait, he can probably read what i'm saying anyway
<whitequark>
and in "vector instructions".
<ec>
whitequark: *nods*
<whitequark>
those are the same as mathy ones.
<joelteon>
doesn't he have a log bot or something
<ec>
whitequark: understood.
<ec>
whitequark: hence my pet-peeve of languages *calling* their list-structures that.
<alexgordon>
ec: the practical definition is used in programming a LOT
<alexgordon>
ec: the pure math definition, not so much
<alexgordon>
not sure if you'll be able to understand it without knowing the practical one, but fuck it
<ec>
alexgordon: why don't we just made the difference clear, right here and now
<ec>
so do *both* and tell me what's different
<alexgordon>
ec: ok well in practical usage, a "vector" is a tuple of numbers
<ec>
numbers?
<alexgordon>
yeah
<alexgordon>
could be integers, real numbers, complex numbers
<ec>
since we're saying practical usage,
<ec>
ah
<ec>
that's what I was asking
<ec>
two of the same type of numbers
<whitequark>
complex vectors are used in e.g. DSP.
<alexgordon>
ec: two or more
<whitequark>
so it's really practical
<ec>
since we're saying “tuple,” and for me, that word has a lot of type-system baggage for it
<alexgordon>
ec: like a point in 3d could be (x, y, z)
<ec>
whitequark: ‘complex’ vectors?
<ec>
alexgordon: so:
<alexgordon>
ec: a tuple is just a struct
<whitequark>
vectors of complex numbers.
<ec>
alexgordon: “vector == point-designator in a manifold-space”
<alexgordon>
ec: doesn't have to be point
<ec>
(iiiiiiiiirc, manifold being the appropriate word here)
<ec>
(beeeeeeen a while)
<ec>
alexgordon: how so?
<alexgordon>
like whitequark was saying, it's used for stuff like audio too
<ec>
what possible tuple of numbers is *not* a point?
<ec>
oh
<alexgordon>
everything
<ec>
but for me, I long ago started to think in terms of multidismensional spaces
<ec>
so maybe it's best to turn what I said on my head:
<whitequark>
that actually used to be a problem in math: it was all too tied to euclidean geometry
<ec>
“for any given vector, there's a possible space of vectors in the same number of dimensions and measurements?”
<ec>
how's that sound?
<whitequark>
so people didn't really understood what it meant to have a space of complex numbers representing waveforms
<alexgordon>
ec: well this is just the practical definition
<ec>
i.e. a vector is something that we can elongate along one of the members', thus turning that member into a new dimension
<whitequark>
ec: that sounds like something I'd get an F in uni :D
<ec>
trying to recall what I previously knew on this topic D:
<alexgordon>
ec: so mathematicans decided that was all too... useful
<ec>
hol' on, lemme make sure i've got this right.
<ec>
vector == tuple.
<ec>
without complex types.
<alexgordon>
of numbers
<ec>
or, turning it on its head,
<alexgordon>
practically
<ec>
tuple === vector, with some category theory thrown in.
<whitequark>
what
<ec>
to have types other than numbers.
<ec>
too atrocious? :x
<alexgordon>
actually I just remembered that there's some usage of non-number vectors, but 99% of them are of numbers :P
<whitequark>
I'd say that a vector is a tuple of something that has a total ordering relation defined on it
<ec>
whitequark: there we go, that sounds *robust*
<ec>
whitequark: now teach me all the words in it I didn't know.
<ec>
“total ordering” relation?
<ec>
“defined” on it?
<alexgordon>
no lo
<alexgordon>
l
<whitequark>
better trust alexgordon on math
<whitequark>
for reals
<alexgordon>
yep
<ec>
(assuming ‘defined’ has a specific meaning in this context, because it sure sounded like it did.)
<alexgordon>
I KNOW MATH
<ec>
OKAY BUT HOLD ON
<whitequark>
I can give you a lot of bullshit with a straight face, probably
<ec>
just because he's wrong doesn't mean he didn't use words I don't know D:
<ec>
teach me the words *first*, then teach me why that arrangement of them was bullshit.
<alexgordon>
ec: the main thing is that you understand how vectors are used in the real world
<alexgordon>
for like points and shit
<ec>
k.
<alexgordon>
so you'll be able to understand the formal definition
<ec>
I need more info on these non-number vectors.
<alexgordon>
not yet
<ec>
because I still can't see how it's Not A Tuple
<alexgordon>
ec: so in maths, a vector is defined over a field
<alexgordon>
well, a vector SPACE is defined over a field
<ec>
defined over a field … presumably, you're getting there …
<alexgordon>
right
<ec>
(note to self: alexgordon is the go-to for concrete mathematics.)
<ec>
(*never* would have called that.)
<alexgordon>
ec: a field is something you can add, subtract, multiply, and sort of divide in
<alexgordon>
it has a 0 and a 1
<ec>
wat
<ec>
something you can <...> *in*
<ec>
keyword ‘in,’ is confusing me.
<alexgordon>
sorry, math speak
<alexgordon>
ec: example, real numbers are a field
<ec>
how do you <preform operations> *in* anything?
<alexgordon>
you can do π + 2
<alexgordon>
you can do π * 2
<alexgordon>
you can do π - 2
<alexgordon>
you can do π * 1/2
<ec>
I need to poo.
<alexgordon>
xD
<ec>
keep going. I'll let you know when I'm leaving. To poo.
<ec>
but it'll be soon.
<alexgordon>
this is the strangest deadline I've ever been given
<ec>
no deadline, I'll be back.
<ec>
just sharing the wealth.
<prophile>
a field is a ring with division
<ec>
I'm always one to share the happy wonderful warm-feels of Information™ with my friends.
<whitequark>
oooo prophile
<ec>
just like you do for me.
<whitequark>
hi prophile
<alexgordon>
prophile: that's helpful
<ec>
You teach me about matsh,
<ec>
I tell you about my poo.
<ec>
… but in all seriousness.
<prophile>
a monad is just a monoid in the category of endofunctors
<ec>
go on.
<prophile>
:3
<ec>
I'm gonna add a goddamn auto-ban with any combination of the words “monad, monoid, endofunctor” in that order.
<ec>
I swear I see that psuedo-joke once a month.
<alexgordon>
ec: anyway in practical usage the only fields that people use in analysis are the real and complex numbers (but there ARE others)
<whitequark>
ec: better auto-ban everyone who uses "X is just Y"
<whitequark>
that can actually be helpful.
<ec>
whitequark: also, “It's like X, but for Y”
<whitequark>
god yes
<ec>
alexgordon: I'm thoroughly confused.
<whitequark>
alexgordon: what about crypto?
<alexgordon>
ec: shit.
<ec>
you were explaining something with pi, 2, and 1/2.
<alexgordon>
whitequark: that's not analysis!
<ec>
no, no shit.
<whitequark>
oh, sue
<whitequark>
*sure
<whitequark>
cannot read
<ec>
*what* is a field.
<alexgordon>
ec: exactly?
<ec>
and then, what's it got to do with a vector-space.
<alexgordon>
ec: there's a set of axioms
<ec>
not necessarily exactly.
<ec>
but you sounded like you had a good analogy or example up your sleeve before I shat on you.
<alexgordon>
ec: mmm well it has to obey some rules
<ec>
my traditional understanding of reals/complexes/whatever
<ec>
is that they're successively-enclosing number-lines
<alexgordon>
it has to have addition and multiplication
<ec>
or at least, something approaching lines
<alexgordon>
it has to have identities (things which you add, or multiply, to get the same as you had before)
<alexgordon>
and other stuff
<ec>
okay but, not what I was needing
<alexgordon>
ec: yeah it's more abstract than that
<ec>
what've they got to do with vector-spaces
<alexgordon>
ec: like whitequark was saying, there's a field called GF(2)
<alexgordon>
ec: which is just two numbers, 0 and 1
<ec>
you were defining vector-spaces *in terms of* this ‘fields’-thing.
<alexgordon>
they use it in crypto
<ec>
“GF(2)” being analogous to “the set of all reals”?
<whitequark>
you know what alexgordon
<whitequark>
i respect you a lot
<ec>
GF() being some sort of “field”-generating function?
<alexgordon>
lol
<purr>
lol
<alexgordon>
ec: no, it's just two numbers, 0 and 1
<ec>
yes
<ec>
but it's a field
<whitequark>
generally
<alexgordon>
ec: the + is xor, the - is and
<ec>
in the same way that “the reals” are a field
<alexgordon>
ec: but if you care about integration... none of this is relevant
<ec>
…
<alexgordon>
nobody integrates over GF(2)... I don't think
<ec>
I don't care about integration.
<ec>
Unless I care about integration, and don't know it.
<alexgordon>
you were talking about integral transforms earlier
<ec>
I want to understand every term I see, a little better than the first time I saw it.
<ec>
Particularly, *enough* to understand the *other* term, that it was originally introduced to explain.
<ec>
I want to understand “an integral transform” and “a linear map” enough to understand the first sentence of explanation as to what a Laplace transform is.
<ec>
and I want to understand vector-spaces enough to understand a linear-map/linear-transform.
<alexgordon>
erm correction ^ the + is xor, the * is and
<alexgordon>
ec: right well linear transforms are Mathematical Analysis, and in Mathematical Analysis, they only use two fields
* ec
nods
<alexgordon>
the real numbers, and the complex numbers
<alexgordon>
wait
<ec>
so, fields are a thing, that have more meaning to them, that we don't care about.
<alexgordon>
yeah I thought you meant whatever we were talking about before
<ec>
“The Laplace transform is a widely used [integral transform] … a [linear operator] of a function f(t) with …”
<ec>
we're up to the second wikilink in that sentence.
<alexgordon>
ec: yeah laplace transforms are analysis...
<ec>
currently,
<ec>
trying to understand the sentence, describing one form of linear transform,
<ec>
“The expression "linear operator" is commonly used for a linear map from a vector space to itself (i.e., endomorphism).”
<ec>
so. vector spaces.
<alexgordon>
right
<alexgordon>
so a vector space has members which are of some field
<ec>
(i.e. the reals)
<ec>
(or the complexes)
<alexgordon>
right
<ec>
(i.e.i.e.i.e the space itself is spread over the reals, or spread over the complexes)
<ec>
(right?)
<alexgordon>
if you want to imagine it like that
<ec>
are the ‘members’ (that are “of” some field) still vectors?
<alexgordon>
the members of the vector space are vectors
<ec>
so [vectors] are “of” a [field], and a [vector space] has [members] that are vectors
<ec>
still off as to what “of” means, exactly, but I have a vague inkling
<ec>
and given that, for now, we've restricted ourselves to reals and complexes, which I understand a bit from a different topic … I guess we can move on.
<alexgordon>
ec: so vector spaces have rules too...
<alexgordon>
axioms
<ec>
so it has members (vectors, of a given field) … what else do I need to know about it?
<alexgordon>
the most important one is that you can add vectors together
<ec>
“add” meaning, well, add. right?
<ec>
a + b
<alexgordon>
like if you do (3, 10) + (6, 2) you get (9, 12)
<ec>
does that *necessarily* mean adding the individual elements together?
<alexgordon>
ec: yes
<alexgordon>
I think?
<alexgordon>
maybe not actually
<ec>
or rather, for all possible vector-spaces, does the vector-space's “add” operation necessarily decompose into the field's “add” operation?
<ec>
or can it be a vector-space, if we define “adding” two vectors within that space to be something *other* than “adding” each field-member to eachother?
<ec>
hold on there's a duck trying to break in
<alexgordon>
ec: hold on let me get a book with the definition in it that isn't wikipedia :P
<alexgordon>
vector addition does not have to be element-wise addition
<alexgordon>
strictly speaking vector spaces don't have to have "elements" as such, it's just that usually it's pretty obvious that they do
audy has left #elliottcable ["something went wrong"]
<alexgordon>
ahhhhh
<alexgordon>
it's all coming back to me now
<alexgordon>
I'M MATH-COMING
<joelteon>
eww
<ec>
hi
<purr>
ec: hi!
<alexgordon>
ec: OK SO
<ec>
“pretty obvious that they do”
<ec>
does this mean:
<ec>
A) it derives from the requirements for a vector-space to be a vector-space, that vector-spaces' members must have “elements”, even though that's not in and of itself a requirement,
<ec>
or B) that all *useful* vector-spaces have elements, but there *do* exist vector-spaces without them
<alexgordon>
ec: there is no requirement to have "members" at all
<ec>
sorry, have to be pedantic to understand
<alexgordon>
the axioms don't mention having members
<whitequark>
I won't say _all_ useful
<ec>
hm l now I'm definitely confused
<alexgordon>
ec: it's very abstract :P
<whitequark>
just that most used vector spaces indeed do have elements
<ec>
completely mis-understood what a vector-space is, then
<ec>
what's an axiom?
<whitequark>
what
<alexgordon>
ec: an axiom is a rule used in the definition of something
<ec>
I was using vector-space as “take a member, and extrapolate along *that member's* elements.”
<alexgordon>
ec: that's normally how it works...
<ec>
then I was told that the members don't have to have elements, which was upsetting-of-my-proto-viewpoint *enough*,
<alexgordon>
but that's not the formal definition
<ec>
only to be followed up by “they don't even have to have members”
<ec>
which throws my definition right in the shitter :D
<ec>
so, I need a better definition.
<alexgordon>
ec: practical vs theoretical
<alexgordon>
ec: the formal definition is:
<alexgordon>
first you need to to be able to add vectors together
<ec>
hold on.
<ec>
you said it didn't have to have members.
<alexgordon>
ec: vectors in the abstract
<ec>
doesn't saying “you have to be able to add members together” imply “it must have members?”
<alexgordon>
like if you have a point P
<alexgordon>
that point P is a vector
<alexgordon>
without speaking of its elements
<ec>
I'm sorry, I was of the impression that vectors === members, in this discussion.
<alexgordon>
no no
<alexgordon>
vectors HAVE members
<alexgordon>
vector spaces HAVE vectors, and vectors HAVE elements
<ec>
AHHAH
<dsamarin>
ec: graph.tk
<ec>
okay, members === elements in this discussion, then
<dsamarin>
ec: add a bunch of sin waves together
<ec>
that makes more sense to me
<ec>
so vector-spaces *do* have to have vectors.
<ec>
but vectors, do not have to have elements.
<ec>
(/members/whatever.)
<ec>
correct?
<alexgordon>
ec: but formally, there's no mention of vectors having elements/members
<alexgordon>
it's not part of the axioms
<alexgordon>
ec: so the axioms are: 1. you need addition
<alexgordon>
(with some rules about that which you probably understand intuitively)
<alexgordon>
2. you need to be able to "scale" vectors
<alexgordon>
so if you have
<alexgordon>
10 * (1, 2) = (10, 20)
<alexgordon>
ec: get that?
<ec>
hol' on.
<alexgordon>
lolol
<purr>
lolol
<ec>
does “ability to scale vectors” ≠ “multiplication?”
<alexgordon>
sorta
<ec>
because you were pretty specific in your terminology there.
<alexgordon>
it's not really multiplication in the classical sense because you're "multiplying" different things
<ec>
mmm
<ec>
in that example, number times a vector
<ec>
and vector not necessarily haz memberz
<alexgordon>
the number in this case is called a "scalar"
<alexgordon>
because it scales
<ec>
so, if it's a space of <arbitrary vector that isn't numbers>
<ec>
then 10 * <avtin> still needs to have meaning?
<ec>
and that makes it a vector-space?
<alexgordon>
ec: the number has to be a member of the field that we defined the vector with
<ec>
believe me, it's unhelpful to my ability to understand
<alexgordon>
Vector<F> scale(F, Vector<F>)
<ec>
nonetheless, I understood that
<ec>
okay.
<ec>
I know some rules *about* vector-spaces, now.
<alexgordon>
ec: the "scaling" doesn't have to be element-wise multiplication either, it just usually ends up like that because of the other rules...
<ec>
yeah, gotcha
<ec>
saying scale() has to be defined
<ec>
not that it has to preform any particular manipulation to the elements of Vector<>
<ec>
even assuming it has elements
<ec>
GOD DAMNIT PROGRAMMING TERMINOLOGY
<ec>
WAS TRYING TO AVOID THAT
<ec>
Okay.
<ec>
which I think it makes safer to get a bit wishy-washy now.
<ec>
so, I still don't intuitively understand what a vector *is*.
<alexgordon>
there's some other boring rules like, you've got to have an identity vector and scalar...
<alexgordon>
e.g.
<ec>
I have formal rules, which'll help me *shape* my understanding, but I'll need an actual description to *get* that understanding.
<alexgordon>
(0, 0) + (1, 2) = (1, 2)
<alexgordon>
and 1 * (1, 2) = (1, 2)
<ec>
gotchagotcha
<ec>
so, to put it in other terms that are starting to form in my head,
<alexgordon>
the most important (or in some sense limiting) rules are the rules about distributivity
<alexgordon>
they tie the whole thing together
<alexgordon>
e.g.
<ec>
“You've gotta have a zero point, a relationship to *other* instances of the space (resizing by some scalar member-of-the-field), and the ability to preform Basic Operation X (“addition”) on the points”
<ec>
any of that sound *particularly* wrong?
<alexgordon>
ec: right, but it's abstract so "space" doesn't necessarily mean euclidian space
<ec>
mmmm
<ec>
so it, *is* kind of defined in terms of operations
<alexgordon>
like if your field is GF(2), then you have only two numbers that can be members, 0 and 1, and 4 vectors in the whole set
<ec>
perhaps the programming-y mode of the thought *is* the ideal one here … disgustingly …
<ec>
yeah
<alexgordon>
(0, 0), (0, 1), (1, 0) and (1, 1)
<ec>
but you've still got identity
<ec>
(0,0)
<alexgordon>
right
<ec>
and scalar-identity, 1
<alexgordon>
yep
<ec>
and addition and
<ec>
wait, what's scaling
<ec>
also, you haven't elucidated on “rules about distributivity” yet
<alexgordon>
well it works like normal
<alexgordon>
0 * anything = (0, 0)
<ec>
oooo duh
<alexgordon>
1 * v = v
<ec>
yep got it
<ec>
so that's *scaling*
<ec>
but it doesn't actually scale
<ec>
WAIT
<alexgordon>
actually GF(2) is quite a good thing to explore vector spaces in
<ec>
doesn't that imply the existence of a GF(1)?
<alexgordon>
ec: there's no GF(1)
<alexgordon>
I don't think so anyway, there might be some trick way, but I think the smallest finite field needs 2 elements
<alexgordon>
because you need both additive and multiplicitive identities
<ec>
(0,0) … identity is (0, 0), because (0, 0) added to any value in the field is still (0, 0), scalar-identity is 0, because 0 * <anything> is (0, 0); scaling by any value in the field (0) works
<alexgordon>
in other words, you need a 0 and a 1
<ec>
no that works
<ec>
because additive identity is (0, 0) + N
<alexgordon>
it has to fulfil all the field axioms as well as the vector ones
<ec>
for any N, because the only N is (0, 0) [(0, 0) + N(0, 0) = N(0, 0)]
<ec>
oh okay
<ec>
idk field shit
<ec>
ignore my noobism
<alexgordon>
yeah not sure, probably not interesting anyway
<ec>
go on, rules about distributivity?
<alexgordon>
so
<alexgordon>
(a + b) * v = a * v + b * v
<alexgordon>
e.g.
<ec>
v being a scalar as well?
<alexgordon>
no no
<alexgordon>
v is a vector
<ec>
oh
<alexgordon>
(a + b) is a scalar
<ec>
mis-read that entire thing
<ec>
hold on, side-question:
<ec>
didn't you say that, in the type-notation, “scalar” is <T>?
<ec>
i.e. it's the same type as the ‘elements’ (or whatever) of the vector?
<alexgordon>
yes
<alexgordon>
it has to be the same type
<ec>
but I thought scalar *was* a type
<ec>
integer, scalar, real, complex,
<alexgordon>
nah
<ec>
… etc … or am i mis-remembering some programming bullshit that has no application here.
<alexgordon>
scalar is just the type of the elements of the vector
<ec>
mkay.
<ec>
okay.
<ec>
ooo.
<ec>
so it's (scalar | vector)
<alexgordon>
also in mathematics we have sets instead of types, except when you get into logic and then you get types back :P
<ec>
i.e. differentiating the sub-type (elements, if it has elements, or wtfever), from the composite type (the vector itself)
<ec>
or, actually, that's another thing better viewed on its head …
<ec>
we *define* the set over which a given vector exists, by the scalar you can multiply it by?
<ec>
or is that complete BS?
<ec>
since vectors aren't necessarily defined in terms of members,
<ec>
the only thing left to define it by (the only place <T> is “used”), is the valid scalar. right?
<alexgordon>
ec: vectors are defined "over" a field
<alexgordon>
the word over means <T>
* ec
nods
<ec>
yeah, got that
<ec>
sorry, was saying set
<alexgordon>
s/vector/vector space (same difference)
<ec>
since you'd said sets-instead-of-types, whatevz
<ec>
so:
<ec>
a “vector space” is a ‘class’ of vectors, specialized to a particular field.
<alexgordon>
6*(1, 2) = 2*(1,2) + 3*(1,2)
<ec>
and a “vector” is an ‘instance’ of that class, with particular value(s) chosen from that field.
<alexgordon>
= (6, 12)
<ec>
scalars used in operations against that vector, are chosen from the same field.
<ec>
okay. I feel like I understand this.
<ec>
I'm probably wrong.
<alexgordon>
haha probably
<alexgordon>
this is just the start :P
<alexgordon>
...of the start
<ec>
but let's go build an entire scaffolding of mistaken understanding on top of this!
<alexgordon>
...of the start
<alexgordon>
yay!
<ec>
-pop
<alexgordon>
ec: ok there's one more distributivity
<ec>
wat
<ec>
what's a distributivity
<ec>
oh
<ec>
a+b = a + b
<ec>
go on
<alexgordon>
distributivity links addition and scaling
<alexgordon>
there's two rules of distributivity that you need to fulfil to have a vector space
<alexgordon>
first one is
<ec>
“distributes” addition *over* scaling
<alexgordon>
a * (u + v) = a*u + a*v
<alexgordon>
(where a is a scalar, and u and v are vectors)
<alexgordon>
second one is
<ec>
okay
<ec>
scaling *over* addition
<alexgordon>
(a + b) * v = a*v + b*v
<ec>
so it has to be distributed in both ways, then
<ec>
interesting.
<alexgordon>
right, vectors are sluts
<ec>
some day I'd like an example that *isn't* addition, multiplication, and reals
<ec>
alexgordon: wat.
<purr>
beep.
<alexgordon>
ec: coming up
<ec>
oh?
<alexgordon>
ec: ok so those are the rules
<alexgordon>
1. vector addition (mostly as you'd expect)
<alexgordon>
2. identity elements
<alexgordon>
3. distributivity
<alexgordon>
I'm simplifying because the details are longwinded and boring :P
<ec>
4. scaling
<alexgordon>
right
<ec>
yes, simplifying is fine
<ec>
as long as I don't say anything particularly dumb and you let it slide
<alexgordon>
haha maths is like law, there's lots of details but if you don't kill anybody you're probably alright
<ec>
… then I don't think you understand law
<alexgordon>
xD
<ec>
'cause it's the exact opposite
<alexgordon>
or I don't understand america :P
<ec>
probs
<ec>
anyway.
<ec>
I think you're getting to examples, now?
<alexgordon>
but NOWHERE in there is any mention of "elements"
<ec>
gotcha
<alexgordon>
in fact the concept of elements arises out of the concept of "dimension"
<alexgordon>
which itself arises out of other concepts
<alexgordon>
which arise from the axioms
<ec>
wat.
<ec>
lemme re-read that.
<alexgordon>
well you know the difference between 2 dimensions and 3
<ec>
can you put a name to the “other concepts” in that paragraph?
<ec>
okay.
<alexgordon>
no because then you'll want to know about them and it'll take all day :P
<ec>
of course it will that's the point
<ec>
and on that note, I'm reaching the point of dead
<ec>
plenty more time for this later.
<ec>
alexgordon: you've just signed *more* of your life over to serving-elliottcable, *on top* of the time I'm stealing for Paws.
<ec>
you poor thing. ;)
<alexgordon>
ec: they say you can't claim to know something unless you can explain it!
<ec>
but, for now, if not even remotely mentally exhausted, I'm too *physically* exhausted to continue. I've been awake for N hours, with N being Very Large™, and it's time to veg out into teevee instead of thinking math.
<ec>
well, perfect
<alexgordon>
ec: so you wanted to know about linear transformations
<ec>
you can go around telling people you're smarter after every thing you teach me, because each thing will be a thing you've verified that yo know well enough to explain,
<ec>
no. that later.
<ec>
how's that purr feature none of us use, work.