serious-discussion

[deep mango]

A user here, Deep, put in "pigeon swimming in the deep sea with sea creatures"

Look at the fish. They're monstrous

[open aspen]

i wish there were a nonannoying way to zoom in on pfps

[bright hill]

the not very people role was supposed to go away after 24h but it hasn't yet

[open aspen]

what is that role anyway

[deep mango]

It's not timed

Do you want it off?

[bright hill]

yes please

[open aspen]

did you do a bad thing to be designated not cool?

[storm sage]

why did you request it?

[bright hill]

you guys can time roles tho, right?

[deep mango]

Here is the full image

[bright hill]

it was a joke lol

[deep mango]

Roles are either timed or not timed, we dont choose each time we grant a role

[open aspen]

so like... is there a different water on the top than on the bottom?

[deep mango]

If only you knew gmod

[open aspen]

fr

[ancient flame]

lol

[storm sage]

knew what..

[deep mango]

Ok not THAT ffs

[storm sage]

wait but knew what

[neat lintel]

this goes so hard

[deep mango]

TTERRA

Ok

crisis averted

[neat lintel]

[storm sage]

tterra!

[open aspen]

its a good image, just gotta know

is it the sky on top or is it a different water

[deep mango]

That is different water

[neat lintel]

to clarify, ryc, this does not

[deep mango]

Presumably its sunlight

[open aspen]

my headcannon is that the waters have different density and separated out

the top water is bottomwaterdrophobic

[deep mango]

yes that is how the ocean works

[open aspen]

im not a water scientist idk how this shit works

[storm sage]

that's actually true to some extent

[ancient flame]

oop

[storm sage]

in terms of salinity

there is a layer of separation

and temperature

[deep mango]

There is a pycnocline

[zealous garden]

the bottom is underwater

[deep mango]

Which is a sharp change in density

[zealous garden]

the top is surface water

[deep mango]

Cause of sharp changes in temperature and salinity

[storm sage]

the ocean is cool af

[deep mango]

Yes eric is describing it

[open aspen]

it really is

[storm sage]

oceanography 😍

one of the sciences that tells us how fast we're screwing up the world

[bright hill]

we're not screwing up the planet at all tbh

we're screwing it up for ourselves

[storm sage]

hmmmm

well

[bright hill]

the planet is gonna be fine in a few thousand years

[storm sage]

and causing a mass extinction

[open aspen]

i think the species we are dirving to extinction would take issue with that lmao

[bright hill]

those happen semi-regularly

[storm sage]

but on the plus side

[bright hill]

[storm sage]

biologists have a new urgency to get grant funding to study rare species!

[storm sage]

uhhh

:|

[bright hill]

lmfao

[storm sage]

questionable arguments

[open aspen]

the classic "climate change isnt real because the climate has changed in the past" argument

[deep mango]

u can screw something up for a few thousand years

thatd still screwing up

[chilly hull]

that only tells us that climate changes once in a while

[chilly hull]

not why the change is happening

[deep mango]

also all those other extinction events were ridiculous disasters!

[storm sage]

oceanography graphs >>

[storm sage]

hey they weren't a disaster for the cyanobacteria!

[deep mango]

we are under no obligation to cause another

[storm sage]

(obligatory /s)

[chilly hull]

why dont we convert CO2 to uhh

[storm sage]

we are

[chilly hull]

hang on i have an idea

[deep mango]

Baguettes

[storm sage]

it's only a short term solution though

that's not sustainable long-term

[chilly hull]

yes

baugettes

[deep mango]

This is literally what happens too

Cause baguettes are made of wheat

[storm sage]

personally, I don't believe in climate change denial

[deep mango]

[storm sage]

https://www.youtube.com/watch?v=WRKHYefEKcA

[bright hill]

[chilly hull]

also lets go nuclear

[storm sage]

nuclear is good, but it has its downsides

esp with the war right now

[zealous garden]

celestially they were all pretty normal events

[chilly hull]

i guess

[storm sage]

but that also gives more incentive for germany to switch from oil!

[chilly hull]

i mean come on

people dont like nuclear because of chernobyl

but im pretty sure chernobyl was hastily built

[storm sage]

yeah I mean, there are good reasons and dumb reasons to not want nuclear

[zealous garden]

nope, only dumb reasons

[storm sage]

:|

[deep mango]

sure, but ideally we would allow them to remain on the celestial timescale

[chilly hull]

i have a better idea overall

dyson spheres

[ancient flame]

wikipedia, "mathematical joke"

[zealous garden]

and where do we get the power we need to construct a dyson sphere to provide our power?

[storm sage]

,w tell me a joke

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Eric Tao#5735

[storm sage]

LOL

[chilly hull]

exponential growth

[neat lintel]

BanAnaMan time

[ancient flame]

LOL

[deep mango]

WEW

[zealous garden]

exponential growth of base amount zero is still zero

[ancient flame]

LOLLL

,w tell me a joke

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by gmod#1227

[neat lintel]

Engineers seem to get pretty far ignoring lots of stuff that’s deemed impossible

[bright hill]

that's where bananach got the joke from??

[storm sage]

LOL

[chilly hull]

i do not understand these jokes

[zealous garden]

LMFAO

[chilly hull]

please hlep me

[storm sage]

okay #bots

[chilly hull]

,w joke

[deep mango]

yes hes a wolfram thief

[storm sage]

#bots pls

[bright hill]

@neat lintel I'm disappointed

[ancient flame]

fuck u eric

[deep mango]

Yes, take this silly stuff to #bots or #chill

[ancient flame]

#❓how-to-get-help

[deep mango]

We were having a relevant discussion bere

[ancient flame]

fine

[deep mango]

Ty

Remember I added that dumb happycat sticker for you people. You owe me

[chilly hull]

thank you

[zealous garden]

Engineers are all approximately the same

[bright hill]

ok, so all jokes aside

why do you see them as disasters?

[storm sage]

giant asteroid strike isn't a disaster?

[zealous garden]

nope, it is n o r m a l

[chilly hull]

i mean those extinction events are all like

natural disasters

[bright hill]

it allowed us to exist

[deep mango]

Because they greatly disrupted the evolutionary process, and made things a lot less interesting for a long time

[bright hill]

I think that's a W

[storm sage]

:|

[deep mango]

Yes I think so too but like

[storm sage]

that's an L if anything

[zealous garden]

they applied great evolutionary pressures and made evolution much more interesting over time

[deep mango]

Now u get a :|

[storm sage]

:|

[chilly hull]

honestly

[neat lintel]

U get a :|||

[chilly hull]

all of the past extinction events were justified

we ended up with cats

[deep mango]

Justice!

[neat lintel]

[chilly hull]

and i think that's a win

[zealous garden]

Remember, extinction is a good thing

[deep mango]

U mean we ended up with birds

[neat lintel]

this is a good emoji

[zealous garden]

it means you've made way for the new model

[neat lintel]

Every past extinction event was for the sole purpose of the development of corner taco trucks

[chilly hull]

birds too

[neat lintel]

Anything else is just a consequence

[zealous garden]

I'll drink to that

[storm sage]

I dunno, if I had a choice I wouldn't ask for all those species to get destroyed just for the purpose of being born

[deep mango]

I wouldnt ask for it

[neat lintel]

It’s not about you or me. It’s about the taco truck

[deep mango]

But i wouldnt reverse it

[zealous garden]

they were doomed anyways

there was no purpose to their destruction

[deep mango]

And I cant ask for it until it needs to be reversed

[zealous garden]

it was certain from the moment of their creation

we simply make a good thing from it

[bright hill]

eh

either way is fine with me

I wouldn't give two shit if I didn't exist

I mean

I don't exist to give two shits

[deep mango]

This is weird and usually I consider thinking too hard about things which are outside of my control completely to be a waste of my energy

[bright hill]

stoicism in a nutshell

[neat lintel]

Sometimes it’s nice to waste our energy for a bit :).

[storm sage]

eh I dunno about that, that's more or less the basis for some philosophical fields

[deep mango]

Instead I will try to do things Now that make people in the next like hundred years hurt less

And not think about random disasters from a million years ago

[storm sage]

dostoyevsky makes a similar point in the brothers karamazov

in the scene where ivan rejects the ticket to heaven

[bright hill]

am I being spoiled?

[sacred galleon]

Hi

[deep mango]

Others are welcome to do it, I do it on other stuff

[storm sage]

no not really

[bright hill]

ello

[storm sage]

it happens in the first few chapters

it's one of the best parts of the book

yeah

[bright hill]

would you say that's your goal in life?

[deep mango]

No it just happens on occasion as a consequence of smaller stuff that i do

In very very small amounts

I do not have a set goal

There are mostly just things I want to not do

I'm pretty happy as long as I don't do them and remain semi comfortable

[bright hill]

it's good to know that not everyone is driven as if by divine calling lmao

although I do wish I was like that tbh

but ig just wandering around mindless is also not that bad

[chilly hull]

got damn

i hate mosquitoes

[bright hill]

we all hate mosquitoes

who tf doesn't hate mosquitoes?

[jade crane]

I love them currently collecting more bites until school starts

[open aspen]

im gonna tell my qual graders that its my birthday this weekend and so they cannot fail me

i think its a winning strategy

[icy crag]

#help-16

[heavy plover]

Can anyone help with a simple proof

[bronze wedge]

#❓how-to-get-help

[left bridge]

I study physics

lecturer says something about work and that it's the line integral

well then I guess I need to learn about line integrals and what does a line integral mean

the mathematics lecturer says that we can think of a line integral being the work done on a force field

nice

[zealous garden]

Sounds about right

I'm expecting some peak latex doot

[wild lantern]

No latex. Too lazy. Isn't F.d the magnitude of the projection of F onto d or something? I've always understood a work line integral as summing these magnitudes?

I haven't done basic physics junk in ages so I don't even remember if that's accurate.

[left bridge]

yeah took some time to look it up but I understand it now

[wild lantern]

I.e. you're adding the amount of force applied in the direction of the path you take your line integral along.

[zealous garden]

A line integral can be thought of as a special case of a directed integral, between some oriented parameterization of a Path and a Vector field it gives you the sum of their dot products, a measure of how much the vector field flows along the path with the chosen orientation

[wild lantern]

Okay, that sounds pretty close to how I was thinking of it from an intuitive pov.

[left bridge]

yup the idea of it being a special case got me the "aha" moment

[zealous garden]

technically the full directed integral also collects a term that communicates the flux of the field through that path as well, and can be generalized to higher dimensional objects than vector fields and curves

GC

[wild lantern]

I only remember flux as a thing from surface integrals lol

I thought it just measured flow outward thru a surface in a vector field or something?

[left bridge]

but it's just frustrating, why can't the lecturer just explain the math in theory from the pure math perspective and not just give how we use the thing instead of explaining WHAT IS the thing

[wild lantern]

I'm probably mixing it up lol

[zealous garden]

that is an example of a flux integral yes

[wild lantern]

Different goals maybe?

[left bridge]

probably

[zealous garden]

though you're probably thinking of the one that uses the dot product with the surface normal

[wild lantern]

Yeah that's exactly what I thought of lol

[zealous garden]

in GC we take the exterior product with a bivector representing the surface

the value is the same up to a pseudoscalar coefficient

[wild lantern]

Idk what gc is not gonna lie

[zealous garden]

like if your answer was X, I would get X*e_{123}

so think about it this way

[fervent pebble]

imagine having a goal in life

couldn't be me 😎

[zealous garden]

you take a plane segment representing a piece of the surface

[fervent pebble]

wait thats a lie i do have a goal

[zealous garden]

in GC you use that, in Vector Calc you find the vector normal to that plane

[fervent pebble]

its kinda general tho ns if it counts

[zealous garden]

then take your vector field

in GC you take the vector, wedge it with the plane, and the answer is an oriented volume element, the volume tells you how much the field passes through the surface, the flux

in Vector Calculus you take the normal vector (which is the direction of maximal flux), and you take the dot product of the vector field with the normal vector, this tells you how much the field aligns with the vector passing directly through the surface, the flux

the catch is Vector Calc can't repeat its procedures regardless of dimension (i.e. unique normal vectors only exist in 3D and arguably 2D and 7D)

the GC approach (like the differential forms approach) generalizes without care to higher dimensional spaces and objects

so back to the statement from GC (with an analog in Complex Analysis)

I'm not aware of a vector calculus procedure for finding the flux of a vector field through a path in 3D (I assume the cross product could suffice)

in GC this is just done by wedging the vector field and path tangent vectors in your integrand

the output is a bivector with multiple components (3 in 3D), telling you the amounts of flux though the path in each direction (physically this is like the torque exerted upon something moving through the path by the vector field)

in the special case of 2D, combining this with the flow integral yields the complex integral

[left bridge]

I would say interesting

do you suggest some resources to study GC?

[zealous garden]

There aren't a lot of good overly rigorous resources that I've had the pleasure of reading myself. like Alan Macdonald's Vector and Geometric Calculus was informative but he also waves his hands through a few things I would have preferred proofs of, and he stops at developing integration on open sets rather than arbitrary manifolds; and the chapter on differential geometry neglects to use many of the tools of GC that we've spent time developing (i.e. not using the GC form of the shape operator, quite perplexingly)

I would still recommend VAGC, also the vidoes linked on https://bivector.net/doc.html , especially sudgylacmoe's content (he has more than what is embedded)

and because of the techniques you can also benefit from studying content from differential forms, exterior algebra, and tensor calculus

not all of it

I've heard good things about Clifford Algebra to Geometric Calculus by Hestenes and Sobczyk, but I haven't had the pleasure of reviewing it myself

[left bridge]

very informative, thanks

[zealous garden]

Alan McDonald and David Hestenes also have some videos on the topic on youtube (easily found by searching Geometric Calculus or either of their names), Alan's aren't the most informative by themselves and function best alongside the content of his book, and Hestenes' opinions can be pretty radical

[unborn trench]

15x+41y = 1.
(b) 1234x + 4321y = 5.

[brittle socket]

??

Mfw doesn't read where to post help qns
Doesn't bother to elaborate on his qns
Only puts two equations there

[unborn trench]

im new

pls help

me navigage

[brittle socket]

#❓how-to-get-help

At least put some elaboration on what your question is, what you have attempted and what you are stuck on

Also these were in #rules, just an fyi if you missed it there you can check it out

[errant ridge]

geometric calculus

it's the calculus of functions on a clifford algebra

or "geometric algebra"

[errant ridge]

#info

[errant ridge]

since you know GC, what advantages does it offer over doing vector calc but with differential forms and the wedge product

like multivectors and stuff?

like it generalizes complex analysis and quaternionic analysis?

[zealous garden]

well one is that I've still yet to see a counterpart in differential forms for the general flux integral, the multivector formalism is easier to introduce than differential forms or tensors imo, and I think the theorems are a bit more general thanks to the multivectors (like The generalized stokes' theorem from Differential Forms only accepts k-form valued functions, but the GC version accepts general multivectors

[errant ridge]

fascinating

[zealous garden]

there's also no counterpart in forms for the geometric product, which forms the basis for the new representations of linear transformations via versors and the generalizations of complex numbers and quaternions

[errant ridge]

what are versors?

[zealous garden]

I might be getting a bit confused because there's two parts to it but like
$\overline{U}(\vec{v}) = U\vec{v}U^\dagger$

[fathom swallow]

wraithlord_koto

[zealous garden]

We often represent a linear transformation in GA as that overline, meaning a sandwich product between a multivector U and it's reversion U^\dagger

a versor either refers to the transformation, or the multivectors on either side of the sandwich product

i.e. a factorable multivector

I forget which exactly, but they're related in this usage

[errant ridge]

v is a vector and U is a multivector?

[zealous garden]

yes in this example

hold on

I've got a paper downloaded I'll check

[errant ridge]

I've seen representing rotations in GA like that, sandwiching a vector between two (something) but I've forgotten

also can vector manifolds be represented as a fiber bundle? where the base space and the fibers are also vector manifolds

[zealous garden]

Alright so versors do follow this form, except it's underline{U} not overline, and v can be any multivector

the versor itself is the U multiplied on either side, being a versor means that it is formed by multiplying together a number of vectors

[zealous garden]

so yes rotations are formed in the same way, we call the specific versors used in rotations "Rotors", a rotor is a unitary multivector with scalar and bivector parts

[errant ridge]

I see okay

[errant ridge]

so it's a term only really used in a 3 dimensional clifford algebra?

[zealous garden]

no

this procedure extends to arbitrary dimension

and it allows us to use the same equation to perform a linear transformation on any dimensional object in our space

[errant ridge]

oh I see okay it has scalar and bivector parts in any arbitrary dimensions

[zealous garden]

yes

basically the bivector marks the angle, and you need a scalar to keep things the right size after the angle is applied

[errant ridge]

ah I see

[errant ridge]

wow that's really cool

which book did you start with when you learned GA?

[zealous garden]

I think vector manifolds are more akin to tangent bundles specifically, but I'm not confident in my knowledge about manifolds

[errant ridge]

me neither

I wonder if people have rewritten GR in the langauge of vector manifold theory (or UGA I guess?)

[zealous garden]

yes

there was uh

[errant ridge]

wow nice

[zealous garden]

I forget the name

but one of the modern quantum gravity hypotheses is written using GC

[errant ridge]

wow that's pretty cool

[zealous garden]

Gauge Theory Gravity is the one

I started with LAGA by Alan MacDonald for reading material since it was like 20 bucks, he goes through linear algebra (without the geometric part) and then extends to geometric algebra, he only develops G^n though

which is perfect for starting

but not all of the ideas are as simple or transfer to different signatures

like in G^n it's true that any unit bivector will square to -1

whereas in G^p,q,r it could square to -1, 1, or 0 depending on which vectors created it (which plane it lies in)

[errant ridge]

that's intriguing

[zealous garden]

generally, in G^n the interpretation is pretty straightforward, but like you saw in PGA (G^3,0,1), whenever you choose a different signature interpreting your different vectors can become more challenging

[errant ridge]

can you have an inner product on a GA?

[zealous garden]

Yes, an easy basic construction of a Geometric Algebra starts with an inner product space

[errant ridge]

I see okay

[zealous garden]

I've talked about this before but there are 4 big (contradicting) definitions for an inner product between general multivectors

like between any two k-vectors of the same k, it's simple

the dot product you'd expect

commutes, scalar valued, associative and distributive, all the good stuff

[fathom swallow]

wraithlord_koto

[errant ridge]

[zealous garden]

it's really simple

scalar product says take the geometric product (distribute everything out), and then return the scalar part

"Fat" dot product says take the max(left contraction, right contraction)

left contraction says that the j-vector on the left "eats" vectors from the k-vector on the right (0 if they don't have any dimensions in common, or j > k)

the right contraction is the left contraction but with the directions reversed

[errant ridge]

hm I'm gonna have to pick up a GA book

thanks!

[zealous garden]

ywyw

[errant ridge]

good luck on diff geo!

or more analysis i guess, lol since you said you were learning that before diff geo

[zealous garden]

I will accept the luck on both thank you very much

Good luck to you too!

[errant ridge]

[arctic grove]

Don't u dare

[surreal sapphire]

what is this servers obsession with geometric algebra

[arctic grove]

Who knows lmao

But I'm not stopping him coz it's GA

[errant ridge]

because apparently geometric calculus is really powerful, and I wanna know exactly how powerful it is

[deep mango]

[ancient flame]

lol

[deep mango]

apparently (according to one dude who made a youtube video)

[ancient flame]

I did a talk on geometric calculus (just another kind)

[deep mango]

nevermind the fact that there is no active research field around this topic and no one uses it for anything

and that it's effectively a direct rephrasing of forms / tensor calculus

[surreal sapphire]

ryc GA hater!!

[deep mango]

indeed

[severe swallow]

are we referencing wildberger here?

[odd narwhal]

No

[zealous garden]

I appreciate the haters because they keep us honest

but please refrain from making libelous and false statements

[arctic grove]

i really wonder, if GA is as nice as people say, why isnt it more common

[zealous garden]

because most people only care to learn enough to get the job done, and they already have their tools

like it shouldn't need explaining that matrix math can do anything GA can do, it's not like we define something that isn't a linear transformation between vector spaces in order to get our groundwork running; so for the vast majority they likely just hear "my tool works" and move on. There are some exceptions to that, a form of geometric algebra (PGA) is increasingly popular in computer graphics and vision for example, and there are a few indie games out there using geometric algebra to play around in 4 dimensions

[arctic grove]

[zealous garden]

namely because to do the matrix representations of the things you want, you end up with a lot of wasted space and elements that don't mean anything

along with, depending on the exact representations you chose, some ambiguity in what is what

but Projective Geometric Algebra gives a very nice fit to the objects (points, lines, planes) and transformations (rotations, translations, reflections, etc) you want to represent

basically GA is seeing adoption where quaternions or dual quaternions are typically used

like I mentioned earlier, one of the modern quantum gravity candidates, Gauge Theory Gravity, is also formulated using Geometric calculus

[errant ridge]

https://en.wikipedia.org/wiki/Gauge_theory_gravity

[surreal sapphire]

do you have something i can read about this?

[next schooner]

looks like math invented by physicists and therefore cringe

[zealous garden]

you mean like calculus?

[next schooner]

yes

[errant ridge]

gottem

[next schooner]

great example

[zealous garden]

LMFAO

[arctic grove]

rattus physics hater?

[surreal sapphire]

ye, that isnt a good counterexample lol

[errant ridge]

newton

[next schooner]

more like pooton

[arctic grove]

jack i thought u were based

[next schooner]

imagine getting your math from an alchemist

[arctic grove]

[next schooner]

my research is similar to condensed matter physics but that doesn't suit the purposes of the meme I've embarked on

[errant ridge]

[next schooner]

also who tf is JACK

[errant ridge]

jack

aka

raiden

[arctic grove]

[arctic grove]

somebody that i used to know

[errant ridge]

do you use TQFTs?

[next schooner]

do i look like a nerd?

[errant ridge]

yes

[next schooner]

mm fair enough

[errant ridge]

[next schooner]

no I don't

[arctic grove]

u are a bit nerd

rats are cool nerds

smh

[errant ridge]

what do you use

[surreal sapphire]

your memes buried my actual question on where to learn Projective Geometric Algebra

[errant ridge]

[zealous garden]

nah but I got a video or two
https://www.youtube.com/watch?v=T7xVTBpHMjA
https://www.youtube.com/watch?v=ichOiuBoBoQ

[next schooner]

I don't actually use anything like QFT or whatnot. It only vaguely resembles condensed matter physics. but also not really

[errant ridge]

[surreal sapphire]

ok thank you, i will check it out

[arctic grove]

rattus is an applied maths guy

wait rattus, which maths do u apply?

[errant ridge]

shyshu look at chill right now

[next schooner]

PDEs

and markov jump processes

[errant ridge]

PDEs

personal dog energy

[surreal sapphire]

applying math to other math

[arctic grove]

Ooo

[errant ridge]

so you're ryc 2?

[next schooner]

I recently published a paper that developed a continuum (PDE) description of a particular age-structured Markov process model for the eukaryotic cell cycle. So really I'm a mathematical biologist

[errant ridge]

rattus doing original research out here

respect

[zealous garden]

I know a biologist

[errant ridge]

same

[next schooner]

hmm if you google that description of the paper its the first result so go wild doxing me folks

[errant ridge]

that's not the right way to get citations on your paper

[errant ridge]

markov process model?

[next schooner]

yeah

basically just a birth-death process but with no death

[errant ridge]

wait what exactly does it model?

[next schooner]

and where there are additional states that give, rather than the usual exponentially distributed waiting time between birth events, hypoexponential waiting times

[errant ridge]

[bright hill]

the king of rats is back!

[next schooner]

it models the cell cycle

[bright hill]

[errant ridge]

cell cycle?

[surreal sapphire]

how much biology do you actually have to know?

[next schooner]

yeah, the lifetime of a cell

[surreal sapphire]

are your papers (or papers in mathematical biology in general) read by biologists too?

[next schooner]

depends, there's quite a broad spectrum

I work much more on the mathematical end of things

but I have a collaborator who works with actual experimental data

the point of the models I try to develop is that they're sufficiently general so as to apply to really any biological process that exhibit certain mathematical structure

[errant ridge]

even humans?

[surreal sapphire]

mathematical biology seems like a cool field

[errant ridge]

it does

[gritty copper]

Just enough to reproduce

[next schooner]

well, the recent model I developed could apply to any growing population, under the assumption that birth times are hypoexponentially-distributed (which is, like, a hilariously week assumption for any biological process)

[hushed turret]

what does hypoexponential mean

[arctic grove]

literally the first
i googled what u wrote and still the first one

[errant ridge]

I don't understand what you're doing but it seems awesome

[gritty copper]

,w hypoexponential

[next schooner]

so yeah it works equally well for tumor cells as it would for a population of humans

age-structured population growth models are quite common in demography

[errant ridge]

so it models the population of the eukaryotic bacteria?

[next schooner]

a hypoexponential distribution is a generalisation of an Erlang distribution

[arctic grove]

hmmmm

[errant ridge]

"a tensor is an element of a tensor product space"

[next schooner]

Not nececssarily eukaryotic, actually. Though that was the original distribution

[errant ridge]

I see

[surreal sapphire]

we are getting closer to a word i know

[gritty copper]

[next schooner]

a hypoexponential distribution is just the sum of exponential distributions

[gritty copper]

"all bacteria are prokaryotic,"

[arctic grove]

Oo

so a linear combination of exponentials?

[errant ridge]

distribution as in generalized functions or....?

[next schooner]

not a linear combination, just a sum

[arctic grove]

[tight comet]

no

[arctic grove]

i was trying to be linear algebraic

[next schooner]

haha

it's fine

[errant ridge]

then?

[tight comet]

A sum is a conical combination

[zealous garden]

if order 3 polynomials aren't linear, how come they're vectors

[next schooner]

but yeah that'd be an even more general version

if you were to take linear combinations

[tight comet]

it's just a typical distribution in probability

[arctic grove]

[next schooner]

OH it's not the linear sum of exponential functions. Its probability density function is given by the convolution of exponential probability density functions

[errant ridge]

so a function f : A -> [0, 1] where A is any set?

[next schooner]

It has no neat form

[tight comet]

I recall it should have some matrix form?

[gritty copper]

https://en.wikipedia.org/wiki/Hypoexponential_distribution

[errant ridge]

i don't know probability theory

[zealous garden]

I have a book called probability theory on my shelf

it's a thicc boi

I haven't opened it yet

[tight comet]

By who?

Chung or bust

[errant ridge]

"probability theory on my shelf" what a strange name for a book

[zealous garden]

brb

[next schooner]

a probability distribution can be associated with a probability density function, which is just a measurable function that integrates to 1

[tight comet]

distributions are more probability applications than probability theory

[next schooner]

non-negative measurable function, I should clarify

[tight comet]

PDFs don't have to exist

[errant ridge]

exist as in?

[zealous garden]

Loeve

[tight comet]

nope, don't recognise

[next schooner]

but yeah that's a good point. not all probability distributions have an associated density function

[tight comet]

It's a GTM on probability theory >_>

[next schooner]

anyway the thing I'm talking about is exponential distributions

which are super simple and nice

[zealous garden]

que

[errant ridge]

the probability increases exponentially?

[tight comet]

no

exponential distribution is just e^-x

for x >=0

[next schooner]

$\lambda e^{-\lambda x}$, more generally

[fathom swallow]

rattus neanderthalensis

[errant ridge]

how does that relate to actual probabilities from 0 to 1?

[tight comet]

it's uniquely the continuous memoryless distribution

You integrate the le^{-lx} function to get probabilities

[errant ridge]

I see

[zealous garden]

I've decided, I'm going to use geometric algebra to give meaning to negative and complex probabilities 😎

[tight comet]

Anyway you will see exponential everywhere if you like markovian models

[next schooner]

In my case, I consider exponential waiting times. So, you integrate $\lambda e^{-\lambda t}$ over some interval $T$ to find the probability that the event happens within that interval

[fathom swallow]

rattus neanderthalensis

[arctic grove]

[errant ridge]

ahh okay makes sense

[neat lintel]

not a real field of math

[tight comet]

@next schooner Is there a reason for the Markovian model? Or 'fits data'?

[errant ridge]

the only probability density functions I know is $\psi \hat{x} {\psi}^*$

[fathom swallow]

Neamesis (Neamesis for honorabl)

[errant ridge]

[gritty copper]

i||imaginary field||

[errant ridge]

\mbb{C}

[zealous garden]

is that a versor

[next schooner]

It can be "partitioned" in a way that certain groups of states correspond exactly to phases of the cell cycle, so it's got good biological justification and fits the data well. Also its very amenable to computation, which is mostly what I'm interested in

[errant ridge]

[gritty copper]

Epic latex fail

[tight comet]

You mean the M phase that kind of thing?

[next schooner]

yeah

[errant ridge]

I didn't want the latex bot to render it

[tight comet]

I can't imagine how a biochemical phase results in memoryless phenomena

Maybe I'm not very creative

[tight comet]

I would think there's some correlation between how much time is spent in some phase

[errant ridge]

okay

[next schooner]

Oh it doesn't at all. But a sequence of memoryless processes provides an excellent model for said phase.

[tight comet]

yes but there must be a reason for memorrylessness

[zealous garden]

mitochondria is the powerhouse of the cell

[tight comet]

For nuclear processes, the physicists just say god rolls dice

[next schooner]

The markov model isn't perfect by any means, as it can't account for inter-generational correlations (or even inter-sibling correlations) in the cell cycle

But for certain processes it works very well

[gritty copper]

1453 fall of Constantinople

[errant ridge]

I think they use an effective field theory for that not sure though

[next schooner]

Not really. It's just mathematically convenient and fits the data well.

[tight comet]

maybe the exponential fit is because there's like a hidden/unknown Poisson process that advances the phases

so there's a geometric sequence of coin flips that decides if the cell will advance

[next schooner]

Yeah

Phase lengths are generally Erlang

The exact mechanism for this isn't entirely understood

[odd narwhal]

that's already a thing...

[tight comet]

no, not about the theory, about the fact that it is not possible to predict if/when some electron can escape its coulomb barrier for example. This is a naturally probabilistic model

[next schooner]

But there is some evidence to suggest that what you're saying is the case

[zealous garden]

you can't say that and not drop a link and/or theorem

[tight comet]

but he just did

[gritty copper]

trustmebro.com

[odd narwhal]

https://en.wikipedia.org/wiki/Exotic_probability

you can also have random variables that take values in complex numbers, but that's different

[tight comet]

Kolmogorov right now:

Kolmogorov didn't die a polymath for you to ignore his axioms

[zealous garden]

oh my god that is beautiful, I hope it remains beautiful whenever I learn how to use it

[ancient flame]

lol

[split island]

Oh @next schooner sorry for the ping out of nowhere, but back in June I went to a conference on optimal transport, and there was a cool talk about it with respect to developmental biology you might find interesting

https://www.sciencedirect.com/science/article/pii/S009286741930039X

[tight comet]

Cell's a pretty good journo o,o

I only recognise Rigollet

it seems he's the only statistician

[split island]

Yeah the person who gave the talk was Schiebinger, he's over at UBC

The idea is that optimal transport can be used to determine the ancestry of cell lines and hence be used to more easily create things like ipscs. The thing is sampling probability distributions, and in short timescales, the true coupling (think what cell descends from what) is approximated by the optimal transport coupling given those sampled data

[storm sage]

YOOOO that's so cool

I want to do some mathematical biology in the future

prob more on the behavioral ecology side though

[next schooner]

Neat, thanks, I'll check it out. I've read several papers and done some modelling of gene regulatory networks in the past. I'm unfamiliar with optimal transport, though D:

[next schooner]

Good choice

It's a fun field. All sorts of math applied to all sorts of problems

[storm sage]

I'm excited!

Seems like there's so much stuff to be done

Relatively low-hanging fruits and more ambitious stuff

[split island]

It's not too difficult to pick up the basics, if you go into #talks, I have a ~60 minute introduction to it recorded

Actually

[storm sage]

where is #talks?

[split island]

https://youtu.be/oiBzH1c6qJ4

[next schooner]

Oh neat, cheers

[split island]

#events is what I meant

[storm sage]

oh gotcha

[bright hill]

lol

[chilly hull]

ok lets see if i remembered the quadratic formula from yesterday

(b+-sqrt(b^2-4ac))/2a

[bright hill]

yes.

[split island]

Lol

[chilly hull]

i dont know why i didnt have the quadratic formula down when im at calc 2

[ancient flame]

bruh

also it's -b

[split island]

[\frac{-b\pm\sqrt{b^2-4ac}}{2a}]

[fathom swallow]

kirby

[chilly hull]

reference sheets my beloved

[neat lintel]

this is a trivial special case of the formula for the roots of any polynomial

[ancient flame]

bruhhh

that's what sucks about formula sheets

you don't learn necessary formulas

[tight comet]

Complete the square should get you the formula?

[neat lintel]

gmod...

[ancient flame]

thanks tterra

hi

what

[neat lintel]

see "Abel-Ruffini"

there is no general (algebraic, involving roots and shit) formula for the roots of a quintic or higher

[ancient flame]

oh yeah ik that

that's what a lot of galois theory talks about

[bright hill]

doesn't mean there is no formula that uses stuff other than roots and shit

[neat lintel]

well

[bright hill]

lmao

[ancient flame]

do u guys like my nick

[bright hill]

it was funny for a sec

[next schooner]

no

[bright hill]

but you ruined it by mentioning it

[next schooner]

it doesn't include rattus neanderthalensis and is, therefore, a terrible meme

[ancient flame]

fuck u

[bright hill]

fuck me yourself

you coward

[ancient flame]

wtf

[chilly hull]

what

[bright hill]

don't stop

[ancient flame]

pp

[bright hill]

fuck

[chilly hull]

[bright hill]

couldn't get the secreen shot

my pc suxxxxx

[ancient flame]

lol

[bright hill]

ok got it

[deep mango]

no

[bright hill]

[ancient flame]

LOL

[deep mango]

why does only loch get the capitals

[ancient flame]

bc only his name is capitalized

[chilly hull]

he is simply cooler

[deep mango]

you think i buy that sorry excuse?

[ancient flame]

no

ur just tooooo cute

[deep mango]

which one of ryc, mniip, or loch is calling me cute

[ancient flame]

gmode

[deep mango]

wtf is going on in your about me?

yeah

[bright hill]

ryc, don't worry

I'll translate

I'm a nerd.

[zealous garden]

yo what the fucc

lmfao

[ancient flame]

pp

[bright hill]

what languages do you know btw?

[surreal sapphire]

wtf is happening

[next schooner]

mike wazowski feet pics

shit sorry wrong tab

[bright hill]

ye

[deep mango]

your interests include...

oh

[bright hill]

I honestly don't know either

[deep mango]

you expect me to know that?

[ancient flame]

roll my weed on my dash
you can call me rolls royce

[bright hill]

eh

[deep mango]

and if you don't know it

[bright hill]

fluent is relative

[deep mango]

i got filtered

i'm too normal and well adjusted

[storm sage]

oh it's the dies irae

that's haunting

do you have a favourite musical setting of it?

ah lol

tbf so was beethoven toward the end of his life

there's a really famous deaf percussionist

evelyn glennie

[zealous garden]

I like beethoven

[sacred forge]

what if we were to rid politicians of all privacy

[storm sage]

was profoundly deaf since 12 (and losing hearing since 8)

[bright hill]

wait, yeah that's true

[storm sage]

but she still feels the music

[bright hill]

why do you like doom's ost then?

[storm sage]

just not with her ears

[bright hill]

the lyrics???

[sacred forge]

i quite like bach

lately ive gotten into metal

ive been enjoying metallica

quite a bit

[zealous garden]

what about megadeth

[sacred forge]

idk what that is

[zealous garden]

what about Death

[sacred forge]

oh ive heard of death

the guy killed himself right

anyways i dont like death metal

[zealous garden]

OK so Megadeth is this bombass band that was founded by Dave Mustaine, original lead guitarist for Metallica who got kicked out on the way to record Kill 'Em All because he was an angry drunk

But they still use his solos for that album, and riffs for about 3

[sacred forge]

"sad but true" is my favorite metallica song

[zealous garden]

So he makes Megadeth and does his own thing starting in 84

They're similar at times but Megadeth has more of an edge to it

generally they're faster and more technical

but not far off on approachability, unless you just hate Dave's voice

a lot of people do, I love it

[bright hill]

oh, I didn't know that's a thing

that's really cool

hm?

why is that?

[storm sage]

.>

[bright hill]

that's awful

that's like the genie case

[sacred forge]

hmm

[bright hill]

the one whose parents didn't let them (her?) learn a language

[sacred forge]

i rarely think with a voice in my head, usually my thoughts dont involve words, i bet a lot of people are the same

[storm sage]

I think with a voice in my head

[bright hill]

how often does this happen?

like, when I heard the genie case, that alone was deeply disturbing

but I thought that was just a one time occurance

[errant ridge]

what about involving other stuff like idk derivatives and integrals or whatever other operation you might need?

[clear parcel]

Actually a lot of people don’t have the ability to do this at all

[errant ridge]

I'm a mix of both I think

[clear parcel]

Talking in my head when reading has become so automatic to me it’s hard for me to read really fast

[sacred forge]

yea, i do that too, usually if i know what the author sounds like, i imagine that voice

i find books more readable if you know how the author talks

cause then you can figure out what intonation is supposed to be used, for a given word

giving it more context

[storm sage]

yeah you gotta unlearn this at some point if you want to read fast

[bright hill]

reading fast is overrated

[storm sage]

eh it's a useful skill

[bright hill]

ah yes, love me some glorified skimming
- some speed reader, probably

[storm sage]

lol I mean the key is keeping up the speed and the comprehension

it's not just reading every other word

it's reading all of it

[errant ridge]

https://tenor.com/view/cope-cope-harder-saul-goodman3d-better-call-saul-saul-goodman-gif-24033192

[storm sage]

but if you speak it in your head while you read, that limits how fast you can read and comprehend

[errant ridge]

[storm sage]

whereas if you internalize the process of reading, you can go a lot faster

and still keep up comprehension with some practice

[errant ridge]

yea like when you're looking at a sign outside a shop you don't read it out loud do you? you just look at it and you know what it says

it's exactly like that but on a larger scale

[zealous garden]

I think doing it the slower way is just better for actually understanding what you're reading

[errant ridge]

not really

I mean

[zealous garden]

because going slower is better

[errant ridge]

if you actually practice it, you can "understand at a faster rate"

[gritty copper]

Hi mean

I variance

[zealous garden]

if you mean comprehend the words on the page, sure

[errant ridge]

yes

and understand what the sentence is saying

honestly I'm not gonna argue about it without looking up some actual research behind it

[zealous garden]

I am specifically thinking of mathematical (even technical non-fiction in general) reading rn so that's also hugely different

[clear parcel]

atm I usually just skim read for the important information but yeah I should work on it

[errant ridge]

imma go learn math

[errant ridge]

oh yeah definitely, if it's like math or physics or anything you're learning, then you cant read it like a novel

I was talking about the complement of the set of textbooks

[arctic grove]

what did u say

dont u dare

[zealous garden]

what about me

can I learn math

[errant ridge]

takes months to go through a math book, but you can finish other books that's the same size in like a week

[errant ridge]

no

[zealous garden]

well I'm gonna read my book anyways

[errant ridge]

you're banished to the realm of set theory

[zealous garden]

not yet

[errant ridge]

axiomatic set theory

[arctic grove]

do as u wish

neam however

will not

[errant ridge]

go to #foundations and collect -200 dollars

[errant ridge]

[bright hill]

lol

I'm stealing this

[zealous garden]

I return with a new name for the exterior derivative

The Total Differential

[hollow sundial]

Great summer day /s

Sweltering 15C/60F

[bright hill]

why is the sand so high?

and why does the beach look so sad?

:(

[hollow sundial]

Lazy excavating

Or the city is too broke to do it properly

[deep mango]

Wtf

[hollow sundial]

Also the wind is an average 14mph/22kph and the sand is very fine so it's constantly being blown

[deep mango]

Well at least its a beach

Theres no such thing as a sad beach

[cyan goblet]

im a sad beach

haha get it

im actually not i just thought the joke was funny

[deep mango]

If it were clear skies then it would look great

[hollow sundial]

I love the waves

[deep mango]

Yeah great looking waves

[hollow sundial]

I can hear it outside my bedroom window, but sand blows in at night even though I'm a couple blocks away so I can't leave it open at night, plus it gets too cold

[neat frost]

Sandstorms……

[hollow sundial]

Darude

[sick kite]

du du du du du

[deep mango]

WTF

You live on the ocean???

So jealous

[hollow sundial]

🤽‍♂️ yes me right now

[deep mango]

[sacred galleon]

Hi

[hollow sundial]

It's pretty nice

[cyan goblet]

professor types syllabi in latex

so fucking based

[sick kite]

swimming in open water is so fun but so scary god damn it

[sacred galleon]

Is latex pronounced with a k?

[hollow sundial]

Lay-tech

[sacred galleon]

Is latex used for math equations and then copy pasted onto word/doc or do u write everything on latex

[deep mango]

Rhymes with fetch

[deep mango]

You can write everything in latex and then get pdfs out of it

[sacred galleon]

Oh okay

[odd narwhal]

Where the ch is as in loch or blech

Lah-tech is also acceptable

[sacred galleon]

Do you do homework on latex

[hollow sundial]

Only if your handwriting is that bad

[sacred galleon]

Then print it and turn it in

[hollow sundial]

[sacred galleon]

For my next assignment I'll use latex

[hollow sundial]

It's a good skill to learn. But budget time to writing it

[sick kite]

it'll take you an age a_fire

[hollow sundial]

You could do just one problem

[odd narwhal]

I've texed all my homeworks since the end of my first semester. It starts out slow but you can quickly get very quick

[hollow sundial]

And handwrite the rest. That'll get you pretty far.

[odd narwhal]

I suggest learning it over holiday so you don't have to stress yourself out with deadlines

[sacred galleon]

Nice

[hollow sundial]

You just end up doing less googling for symbols you need and end up memorizing them

[odd narwhal]

And yea, start with writing a few questions in it then go up gradually

[deep mango]

Look up detexify, it lets you draw symbols and tells you their commands

Super useful

[hollow sundial]

Oh yea forgot about that tool

I should bookmark it

[deep mango]

Also I gave a latex workshop in this server, if you search my posts in #events you'll find the recording.

It's for total beginners

[sick kite]

i find detexify to be pretty bad tbh

[deep mango]

I might give it again at the start of the semester

[hollow sundial]

Good for beginners probably

[deep mango]

In a week or two

[sacred galleon]

Okay

[sick kite]

also Dr. Trefor Bazett has a TeX tutorial series on yt

[sacred galleon]

I'll check it out

[hollow sundial]

And ask in #latex-help

[sick kite]

as part of your teaching duties or on the server?

[deep mango]

It would just be fun

[hollow sundial]

Teaching is fun

Teaching math at least

[neat frost]

Just read the TeXbook

[neat frost]

If you read the texbook you’ll learn all the secrets…………..

[storm sage]

iirc LaTeX has no official pronunciation

leslie lamport didn't want anyone to be locked into a specific pronunciation

[neat frost]

Yeah

But that’s a dumb take and just cuz you make something doesn’t mean you get to name it

I do

[hollow sundial]

gif is pronounced zif

[neat frost]

Pexactly

[wooden flax]

i say latex as laytecks

most people ik say lahteck

[neat frost]

And you’re both wrong

[hollow sundial]

slurp is pronounced burp

[neat frost]

Indeed

[deep mango]

Slurpie burpie

[neat frost]

Rycie bycie-shmoochikins-gigglehead-muffin

[deep mango]

I just had a muffin

[odd narwhal]

If you pronounce it differently I will judge you

[fair mural]

lay techs is the correct pronunciation

[wooden flax]

fr

[odd narwhal]

Lah tech

[wooden flax]

ew

[deep mango]

Lay tek

[odd narwhal]

There's no reason for it to be lay

[fair mural]

no

[deep mango]

It's an e

E makes a long

Late

[odd narwhal]

I will teach you the correct pronounciation when you come here

[deep mango]

If you're going to complain about lateral

[odd narwhal]

Except it's not an English word so english phonology doesn't apply

[deep mango]

Note that LATERAL has a different a

Its not ah

Its aaa

[neat frost]

That is the most incorrect pronunciation unironically

[fair mural]

shut up slurp

[deep mango]

What does that have to do with anything

What are you gonna do, enunciate words to me slowly?

[odd narwhal]

I will beat it into you

Metaphorically

[deep mango]

[odd narwhal]

And also physically

[neat frost]

Hebrew has the correct letters for this לאטך

[deep mango]

[odd narwhal]

לעטך

[neat frost]

Learn Hebrew, remove ambiguity

[neat frost]

Nah I checked Wikipedia before posting

[wooden flax]

Lmfao

[odd narwhal]

Imagine trusting Hebrew math wiki?

[neat frost]

Uh yeah

[deep mango]

Latex but the last letter is chet

[neat frost]

It’s not a chet

[deep mango]

Yeah but what if it was

[neat frost]

Oh

[deep mango]

That would be sick

[neat frost]

Then that would be

[odd narwhal]

Would sound bad

[deep mango]

Shit taste

[neat frost]

Would it

[odd narwhal]

Yea if you pronounce chet as it's supposed to be pronounced

[neat frost]

Would it sound differently shin?

Oh

[odd narwhal]

i.e. throaty

[neat frost]

You’re one of those

[deep mango]

Yessss

Throaty

[odd narwhal]

I don't pronounce it like that

But that's the intended sound

[deep mango]

Both of you are bad

[neat frost]

Intention doesn’t matter shin

[odd narwhal]

You don't get to have an opinion ryc

[deep mango]

Speak throaty chets

[neat frost]

Yeah ryc kindly shut the hell up

Let the grown ups talk

[open aspen]

that professor on twitter said L'tech and thats how i say it from now on

[odd narwhal]

I am not orthodox

[neat frost]

It’s more like a mizrachi thing no?

[odd narwhal]

It's both

[deep mango]

I learned like 5 hebrew words in 3rd grade

So im qualified

[odd narwhal]

I am evidently not mizrahi either

[neat frost]

One of them better have been pilpel

[odd narwhal]

Ryc when he gets to israel "ahhh, shalom"

[neat frost]

[odd narwhal]

"ma shlomcha"

[deep mango]

U think i remember any of that sbit now

[neat frost]

Yes?

[deep mango]

Time to download duolingo

[odd narwhal]

"ani ar wai see"

[deep mango]

I will roast your asses

Well slurp at least

[neat frost]

I think that’s too advanced for him

[deep mango]

I dont think i can beat shin

[deep mango]

It is but thats besides the point

[neat frost]

Okay at least you’re somewhat realistic

[deep mango]

I will have to settle for beating him at everything else

[neat frost]

I hate listening to all those birthright people speaking Hebrew even though that’s probably what I sound like

[deep mango]

Oof

I will be the model birthright tripgoer

[odd narwhal]

Name one thing you think you can beat me at except wordle and the daily mini

[neat frost]

I still can’t figure out how to correctly pronounce a reish

[deep mango]

(speak literally no hebrew and eat all the food)

[neat frost]

Makes me sad

[neat frost]

Good!

[deep mango]

you can't take those two things from me!

[odd narwhal]

I don't wanna argue about those rn

You said everything else didn't you

[neat frost]

If this were a fair competition you’d have to compare Hebrew wordles

As well as English ones

[odd narwhal]

True

Ryc start playing וורדעל

[neat frost]

[bright hill]

ha ha

[odd narwhal]

Lmao slurp

Haaretz bought/made Hebrew wordle

[deep mango]

i'm not playing hebrew wordle

no way

alright how abouuuut celeste

i'm better than shin at that

[bright hill]

at any rate, everyone knows both ShiN and Slurp are chronically online

so they're probably more fluent in english than their own native language