Right now I have no idea what context would lead to this, it's bizarre

@Daminark but I don't know what $F$ is...

@Daminark want the link to the paper?

Well that's not a problem any of us can help with

Oh sure, I'll check it out

arxiv.org/pdf/1508.04125.pdf - algorithm 1 on pg 8

(Note though that I haven't taken any algorithms or anything so I'm kinda gonna need to follow my nose)

i have taken no algorithms class either =P

and i have a cold, so my nose is stuffy.

Step 3 is what seems to be defining $F$

They aren't giving you something specific

yeah, but that's $F_\rho$

this is $F_i$

This seems like abuse of notation

See, they're indexing these vectors by elements in your set

right, that's the first one

The other way to go about it is to order the elements $\rho_1,\ldots,\rho_n$

Then call $F_{\rho_i} = F_i$

oh, $i$ references the $i=1$ under the summation

why did i not realize that?

so...at the risk of sounding stupid...is it basically summing all of the elements in the list $R$?

Not quite

So I don't know what these reactions are

each element is a vector

But these vectors can apparently take in a reaction and spit out certain objects that can be added

(r,p), where r is the stoichometry of the reactants and p the stoichiometry of the products

basically, it's kind of like if you have a list of chemicals {A, B, C}

and your reaction is A+B -> C

you would have r = (1, 1, 0) and p = (0, 0, 1)

so $\rho$ = ((1, 1, 0), (0, 0, 1))

it's confusing.

yeah, I would've written $F_{\rho,i}(\rho)$

i've been treating $\rho$ as the element's number - like element in list #1 and so on, which is probably wrong, but it's the only interpretation I can come up with that makes sense - along with the vector.

I don't have the domain knowledge to talk about chemistry or algorithms, but whatever these $\rho$ elements are, you have that $F_i$ is some function associated to $\rho_i$ which can act on some $\rho_j$ and give you an element in some set where addition makes sense

But this sum is saying $S(\rho) = F_1(\rho) + \ldots + F_{|R|}(\rho)$

oh, wait...is this really the thing in line 3?

Yes

so basically, sum all of the elements of $F$ and divide that by the length of $R$ (considering the thing outside of the summation)

?

Or at least I can see no other interpretation that makes any sense

Not elements of $F$, they're not sets

i'm abusing the term elements, sorry - here i mean if F = (0, 1, 2, 3) element refers to 0 or 1 or 2 or 3 - i don't know the proper term.

F is a vector.

You're not even doing that I think

Or hmm

These guys have nonsense notation

I don't understand the difference between S(p) and $F_p(p)$, they both seem to involve all |R| of F

line 3 doesn't make much sense either.

It's ambiguous, I had previously interpreted this as you assign a different vector $F$ to each $\rho$, and then you add up all those vectors when they're acting on a specific element

But this could also mean that you're just adding entries up in the weird way

Basically their use of "$F_i$" is really bad

Because this could mean $F_{\rho_i}$ where we've order the elements of $R$

Or this could mean $F_{\rho}^i$, like the $i^{th}$ component of $F_{\rho}$

oh, I see. first build an array of vectors F, each vector specific to an element, then apply all the F to each element. ??

no, my understanding can't be right, because the full line (line 8) is "for each $\rho \in R $ set $S(\rho) = ....$

Their statement earlier that $F_{\rho}(\rho) > 0$ suggests the former

What are you doing ?

so maybe, it is the element of F corresponding to the position of $\rho$ in R, divided by the length of R, iterating through all $\rho$ - does that make any sense @Daminark?

@Astyx trying to figure out this paper's cursed algorithm.

arxiv.org/pdf/1508.04125.pdf

pg 8, algorithm 1.

I'm really not sure anymore, the notation of this paper is invalid

They switch from $F_{\rho}$ to $F_i$ but this jump could mean two different things and there's no indication of which is right

but if that was the case, why do they need the summation...

i guess I'll just have to email the author.

But as of right now, my guess is this

well, since you apply the sum to all of F, order shouldn't matter

So you have a set and I'm going to call it $\{\rho_1,\ldots,\rho_n\}$

What's F ?

a vector being created

@Astyx, it's defined in line 3 (if looking at the paper)

Now, you take a bunch of vectors $\{F_1,\ldots,F_n\}$

So that $F_i(\rho_i) > 0$

I don't know what $F_i(\rho_i)$ means, maybe it's an inner product, maybe these vectors have some other functional meaning

Point is, now we define $S(\rho_k) = \frac{1}{n}(F_1(\rho_k) + F_2(\rho_k) + \ldots + F_n(\rho_k))$

They probably mean $\sum_{\rho' \in R}F_{\rho'}(\rho)$

Hi for a sequence of real numbers $a_n$, is the following true "$a_n\to a \iff a_n$ is Cauchy$?

Yes but be careful about wording

Yes @mrnovice

::sighs:: I don't know why i thought i could understand this paper...it's way over my head.

You need to say "for some $a$"

but I thought it doesnt hold in Q?

Yeah, but what "not holding in $\mathbb{Q}$ means is that a Cauchy sequence may converge to an irrational number

Even a Cauchy sequence of rational numbers

Ahhhh thank you

Imagine 3, 3.1, 3.14...

That's because $\Bbb Q$ is not complete

So if you're looking only at $\mathbb{Q}$ and you throw away the irrational numbers

So a Cauchy sequence can converge to an irrational number, and therefore does not converge in Q correct?

Yup

necessarily converge*

You still have Cauchy sequences, but you just threw away the point it would've converged to, so it doesn't converge

okay thank you Astyx

That's one of the possible construction of $\Bbb R$ IIRC

"Making $\Bbb Q$ complete" in some sense

interesting fact @Dami, if $a$ is a square in $\Bbb F_p$ where $p$ is $3$ mod $4$ then there is an efficient algorithm to find a square root of $a$, if $p$ is $1$ mod $4$ then only probabilistic algorithms are known

The only efficient one is probabilistic? Or are there no algorithms period?

the only efficient known algorithms are probabilistic

OK the other option sounded odd

That's saddening

I mean just testing every element is an algorithm and it's guaranteed to give an answer

then just calculate the square root of (a + 2) - 2. :-/

Another interesting fact, if $n=pq$ with $p$ and $q$ primes then finding the four roots of a square in $\Bbb Z/n\Bbb Z$ is as hard as factoring $n$

Meh, work will wait, Undertale ftw

Huh

And @Astyx woo!

I am wondering how many of us are from the United States, I am

('-')/

Here we go Mettaton

What context?

('-')/

Final fight unless I'm mistaken

I would like to think the United States has the best math people

(.-.)\

Oh you're gonna fight him? Dayum

Which I've already lost thrice

@Bob Neh, France does

Or Russia maybe

Mathematicians are from everywhere, it's true

@jason I tend to agree with you

the best of the best seem to be well distributed

i can say the physicist question is much more decidable - clearly the u.s., because we had feynman.

America's got a lot of good ones because it's big in general, France has a culture which does proof based math from the start

Or maybe not from the start, but like, high school math is rigorous

@Bob Most people in this room disagree with most things I say, and many put me on ignore mode

In America high school math is nonsense

@heather I hope you are right but again I believe it is not true

if america's elementary/middle/high schools were better, there would be many more american mathematicians.

Right?

what is wrong with American high school math?

@Bob i know, i'm just joking, because feynman =P

Whether I can call it math is debatable, for one

@Bob i don't know about highschool math (not there yet), but middle school math is terrible.

Suppose that you're given $\pm b,\pm c$ such that $b^2=(-b)^2=c^2=(-c)^2=a$ in $\Bbb Z/n\Bbb Z$ so we know that $n|b^2-c^2=(b-c)(b+c)$. Now calculate $\gcd(n,b+c)$. This can be only $1,p,q,n$. It can't be $n$, otherwise $n|b+c$ so $b=-c$ but the roots were distinct. It can't be $1$ otherwise $n|(b-c)$ so $b=c$ and you're done @Dami

well, actually, wait, algebra I/geometry is highschool here, right @Daminark?

I think I will delete my account soon. I will talk here for a few more days.

@Bob I'm not

They teach you a bunch of algorithms for how to crank things out on paper. If you can see past it you're in good shape

Alegra I is high school

I had one awesome math teacher in HS. And was forced to take algebra and trig 3 years running because I moved each year ...

Otherwise you just see symbol pushing that just turns you off from the subject entirely

this past year, i've learned so much about math on my own - it's what made me start really enjoying math and science and doing it on my own. not that i didn't before, but it's much more of an exciting topic for me.

SE has helped that quite a bit.

If you are a smart 13 year old maybe you can learn all of high school math in 1 day. =)

Basically, it's a badly executed "Math with the singular goal of building tools that engineers need"

and the proofs are those two-column proof pieces of nonsense.

and they're only in geometry!

@Daminark That's the only true goal.

The downgrading of math at school levels is a universal phenomenon.

science in middle school is just as bad.

(the other direction, getting the roots from a factorization of $n$ is basically an application of the chinese remainder theorem to turn the equation $x^2=a \text{ mod } n$ into a system of equations $\text{mod } q$ and $\text{mod } p$ which can be solved efficiently)

I did those two-column proofs and I thought they were good

@Daminark well america isn't trying to create mathematicians en masse. We need engineers in the world first to get things fone.

The two column proofs are nonsense. Proofs should be written in sentences, lol.

^

my fear about high school math is that the proofs are going away

also, we were only proving things like given 2x =4 , prove x = 2 - no wonder everyone hated it.

we need moar bombs

And when people solve equations it should be checked that the steps are bidirectional.

and it didn't get much more complex from there.

So I'd say there's some sense of sustainability

proving things in math requires a level of maturity in mathematics that can only arrive at a college level

Why? Because as it stands, teaching at a high school level just isn't often worthwhile for most math types

pffff, proof should be fully formalized and be written in coq or another proof assistant/checker.

It's wrong to solve equations in one direction and simply reject those that don't work, because the unrejected ones may not work either unless tested manually

i mean, for the most part.

@AlessandroCodenotti correct. homotopy type theory or bust

i kid you not - there are multiple times where i've raised my hand, asked for the why behind a formula, and the teacher has stumbled around and ended up with "because."

I had bad math teachers at all levels.

when I reached differential equations, all the examples and problems were contrived so I couldn't grasp the actual usefulness of it

I strongly disagree with @TheGreatDuck but many high school math teachers agree with @TheGreatDuck

@BalarkaSen lol I must admit that type theory does sound rather interesting to me

In middle school, no proofs, in high school, wrong proofs, in college, not enough proofs.

@TheGreatDuck, with that kind of attitude, I could never do proofs right now.

@Alessandro i really liked the idea

proofs are hard and everybody needs to understand it

i think i read 2 pages in the HoTT book

but then i ducked out

A proof is just an explanation of why something is true. It's not magic.

No idea why teachers keep not doing proofs in class.

I was tutoring somebody a while back in math

I don't know anything about HoTT, but I read a bit of "standard" type theory

his idea of a proof was to show a bunch of examples

no rigor

A proof is an argument, nothing more. The only issue is what rigor of proof.

a proof is a lie

my proofs aren't good, but they're so fun.

@heather that's cause math teachers are not mathematics majors. They are math teaching majors. In fact do you know the highest math they take in college: calculus 2. After that they take classes to learn how to teach lower level math. They never take any classes on learning to prove things, which is a course required by regular mathematics majors.

Showing examples don't prove anything at all.

Examples are useful as sanity checks. They're a way to confirm whether you've done something wrong.

@BalarkaSen a proof is a cake

cake is a lie

Now, if it were a good profession for mathematicians, you'd have more going in that direction, but then you'd also create more mathematicians as people who were irreversibly turned off from the subject now start to enjoy that side. Right now, there are fewer people who want to go into math, but also fewer viable careers for mathematicians

Balarka "Glados" Sen

@JasonBourne a mathematical proof is, imo, the most formal kind of english writing you can write. They are not just an explanation. They must be of an exact precise form and must be perfect in writing.

@Semi they are useful, it's more like, when teachers do it to 3 numbers and say "See? So it works in general!"

I think after I delete my account this time I will never return

@Daminark Right.

@JasonBourne why leave? You seem like a pretty cool person.

Have a nice day

@Duck re maturity: The way things are currently set up, sure

@TheGreatDuck Here math teachers have to complete a math bachelor just like any other student and they study pedagogy and similar stuff at the master level

@Bob if it were false on a large level, they'd be teaching real analysis and advanced number theory in high school.

a math explanation is laying ideas out in a row. A math proof is stacking them up. It has to stand.

But presumably, you could have a sort of "Are you interested in mathematical ideas with an eye toward math math?" thing going on, where you give an age appropriate introduction to proof based math without any eye toward engineering

@TheGreatDuck well maybe they should be.

@heather those are classes people take in grad school.

people underestimate the mental capacity of kids and teens.

I'm not talking about basic number theory

im talking about advanced number theory and group theory

let's just teach all math in high school. What could possibly go wrong? :p

let's teach enough math so people are interested in high school.

Today my book Algebraic Number Theory by Neukirch arrived in the mail. Very nicely printed. =)

the way it is, things aren't working.

fair enough

but math isn't interesting to everyone

@Jason nice.

(indeed, it should not be)

and I don't think it would be fair to say everyone needs to be interested

The problem is that high school makes it far worse than it needs to be

what if instead of spending all of elementary school on the same basic junk, you could actually start working on prealgebra, "highschool" math, and continue.

not everyone goes into something related to math

@user16839 Maybe you can consider giving yourself a username other than userxxx. =)

@TheGreatDuck no, but i think more would be interested than you'd expect.

a lot more people take art than enter an art related field.

@heather I would be cautious about that exactly

@heather honestly, I've wondered why complex numbers, real numbers, and the concept of rings aren't all taught in first grade.

along with set theory

and boolean algebra

heh, I first joined an odd SE to comment, so didn't pick a name

@TheGreatDuck, I assume you are being sarcastic

seems like arithmetic is a really simple process. It shouldn't take more than a day or two to explain

okay, yeah, you are.

What I think is more, there are going to be a number of people who would love math but have a disposition that is somewhat heavily opposed to science and engineering

I think schools should teach people more about life. Life is hard and school doesn't prepare you for that.

@heather No, not at all. It seems strange to me that people need so long to learn something that simple...

does it take 3+ years to explain arithmetic @TheGreatDuck?

i'd hope not

that's a large waste of time on something that should be much easier to explain

well, in 1st grade I was taught addition, and in 5th grade we were still doing addition.

O.O

geez

And schools should give kids more options to choose what they want to learn more of or less of.

I am still doing addition

by third grade I understood fractional addition and multiplication

sure, we were doing other stuff, yes, but we were still practicing addition and not moving on into advanced stuff.

and i am bad at it

So in NY I was in this AP1 program in elementary school which was faster

@TheGreatDuck could you please be serious?

and I had known the other arithmetic for a while

And we did stuff like order of operations in 2nd grade, I think

@heather I AM BEING SERIOUS. STOP THAT.

Or 3rd

I had a teacher explain negative number really early, and another explain imaginary numbers as an aside.

geez

@TheGreatDuck well geesh, it's hard to tell.

In Texas we never got to the stuff until way later

"Mettaton, there's a mettaton-shaped hole in my mettaton-shaped heart" @Dami

Hey two people have thought that Waiting and I are the same person. Strange right?

@Duck you have been sarcastic previously, and have not made any clear transition so it's rather unsurprising if you were being sarcastic now

So no right to yell

he's just writing all caps yo

that's not yelling

ALL CAPS LOOK GREAT

when talking in chat that is @Balarka, or it comes across as more emphatic than normal lower-case

ORLY

@Daminark I've never been sarcastic at all lately. So that's people making rude assumptions.

False

small caps might be not-yelling, but all caps is - to me.

when today have I been sarcastic?

Seems that the singer Chris Cornell just committed suicide. =(

honestly, I've wondered why complex numbers, real numbers, and the concept of rings aren't all taught in first grade.

@Daminark I was being dead serious and it is really making me angry that people don't believe that.

lol

i've said 5 times now that was a serious comment

When I take over the world I can change the math syllabus

whatever @TheGreatDuck, I've got better things to do then argue with waterfowl.

You said earlier that the stuff needs maturity, now you're saying we need to do it in first grade

At this point you're lying somehow

"yo squakin' like a pink monkey bird"

@Daminark I was referring to doing rigorous proofs such as proving the fundamental theorems of algebra. Teaching someone the concept of rings isn't a really complicated idea. I didn't say we needed the kinds to be proving prime number conjectures. I'm just saying to introduce the idea of sets and the different number sets we use.

@Jason You don't need to take over the world for that, only the US

Have you wondered why you learn so few things from grade 1 to grade 12? Because they make you do the same thing over and over again...

That is 12 years of life lost to learning almost nothing in school.

just wait 4 years, the syllabus will be blank and you can start fresh.

Most people are not interrested by maths unfortunately

Understanding basic ideas at a better level is far easier than learning to manipulate high level technical tools