Mathematics - 2022-05-23 (page 1 of 2)

Akiva Weinberger

00:49

Roman numerals 8-segment display concept

leslie townes

mdccclxxxviii seems like a good year for that concept.

i do remember clock radios and such having various variations on the usual 8888888 lcd display thing.

Akiva Weinberger

You could reasonably do Chinese numerals (一二三四五六七八九　十百千万亿) on a 5x5 dot matrix

leslie townes

one of my earliest pcs had a lcd display showing the clock rate of the cpu. it wasn't any kind of measurement, but set by jumpers. i redid it to display my initials, which helpfully worked at the resolution of the display.

i don't know how i'd do a W.

Akiva Weinberger

01:08

leslie townes

looks like they ran out of ideas around ? !

Akiva Weinberger

I think that's ? ! @ _ * # $ % & ( ) + - / : ; < = > [ \ ] ^ ` { | } ~

leslie townes

really? that is $?

i sorta see it

i like how with this extremely limited space they still worked in the division sign

nobody has ever used that outside of calculator manufacturing and grades 2-6

Akiva Weinberger

I'm not quite sure what that thing before the pound is, or the things after the Euro

Wait, is pound on there twice?

Oh, wait, degrees Celsius and degrees Fahrenheit

leslie townes

01:23

i assume some of those are in there just so doom will render better on whatever display

Akiva Weinberger

The last row and the end of the previous one is box-building stuff I guess

Unicode has a symbol, ℇ, for "Euler's constant". Wikipedia adds "It's unknown which constant this is supposed to be."

leslie townes

haha

euler's identity

bernoulli's function

the gauss theorem

Calvin Khor

just unleashed a cat on a cockroach

worth every bit of cat food

leslie townes

01:39

oh, we try to keep our cat away from them. worried about maybe the cockroach has eaten poison from somewhere outside.

she hates when we take them away.

Calvin Khor

hmmm....legit concern

leslie townes

she'll stalk the part of the house where she found it, like "i wish a cockroach would show up right now. let's go"

Calvin Khor

he didnt eat it tho

.......not this time anyway

leslie townes

we usually arrive between the killing and the eating.

cats are good.

Calvin Khor

lol

Akiva Weinberger

01:41

If the cockroach ate enough poison to kill a cat, it ate enough poison to kill a cockroach, I would've thought

I had a dream last night in which I was bitten by a dish-sized spider

copper.hat

i found mosquito coils seem to keep roaches away (not exactly a scientific experiment).

Calvin Khor

sounds right but cockroaches are hardy

yeah i think you could probably smoke them out

leslie townes

world war 4 will be fought between cockroaches and other cockroaches.

Calvin Khor

ai powered ones

copper.hat

didn't we just have a president....

leslie townes

01:45

copper: not to my memory, no.

copper.hat

i meant a cockroach

he has become something of a meme

Calvin Khor

02:01

HAKEN - Cockroach King - (Single Version)

►

Calvin Khor

02:24

thank god for air conditioning

one potato two potato

This is a proof that shows $SL_n(\Bbb R)$ is connected. During the proof, it says $\begin{pmatrix}
Q & 0\\ w& 1\\
\end{pmatrix} SL_{n-1}(\Bbb R)\to (wQ^{-1})^T$ is a homeomorphism. Why this is true?

leslie townes

03:10

it's a rational function in the matrix entries. one of those 'because we have a formula for it, it is continuous' kind of things, maybe.

copper.hat

03:40

are you asking about the continuity or the invertibility?

one potato two potato

03:59

@copper.hat Invertibility. Continuity is easy I think

copper.hat

I am probably missing the point, but isn't $\begin{bmatrix} I & 0 \\ y^T & 1 \end{bmatrix}$ not an inverse of $y$? (Or rather, the equivalence class thereof.)

one potato two potato

04:28

@copper.hat Yea I think it's true. Inverse of $\begin{pmatrix} I & 0 \\ wQ^{-1} & 1\end{pmatrix}$ is $\begin{pmatrix} I & 0\\ -wQ^{-1} & 1\end{pmatrix}$ and $\begin{pmatrix} I & 0\\ -wQ^{-1} & 1\end{pmatrix}\begin{pmatrix} Q & 0 \\ w & 1\end{pmatrix} = \begin{pmatrix}Q & 0\\ 0 & 1\end{pmatrix}$.

copper.hat

04:40

I was thinking more $\begin{bmatrix} I & 0 \\ wQ^{-1} & 1 \end{bmatrix} \begin{bmatrix} Q & 0 \\ 0 & 1 \end{bmatrix} = \begin{bmatrix} Q & 0 \\ w & 1 \end{bmatrix}$.

Akiva Weinberger

05:02

Finished The Pedestrian, a fantastic puzzle platformer with stunning art and great puzzles

You control a stick figure - like the figures on bathroom signs - running across traffic signs and the like

Took me about 4 hours, spread over two days, so it's relatively short

Violet Flame

08:02

Is it possible for a polynomial to divide two polynomials and be a divisor with highest degree and yet not be greatest common divisor?

robjohn

No. Every common divisor divides the GCD.

Write the GCD as a combination of the two polynomials (Bezout). The common divisor will divide both polys, so it divides the combination.

Violet Flame

08:20

@robjohn why would it divide both polys of the combination?

I mean I understood that the polynomial factor with the highest degree divides GCD by definition of GCD but what shows that itself must be Gcd @robjohn

robjohn

How can a polynomial divide another of the same degree and not be the same polynomial? At most it can be a scalar multiple of other one.

You know that the product of two polynomials has the sum of the degrees?

Thus, if a polynomial of degree $n$ divides another polynomial of degree $n$, the quotient has to be degree $0$ (a constant).

@VioletFlame You said it was a common divisor.

Violet Flame

08:35

So you mean that it must be the GCD because GCD also has highest degree and so they have to be constant multiple of each other.

Am I correct @robjohn? , I thank you for your kind help.

robjohn

That is sort of it, but it is more that all common divisors divide the GCD

Since the GCD is a linear combination of the two polynomials.

Violet Flame

Isn’t that the def of GCD that all common divisors divide it >

@robjohn

robjohn

@VioletFlame No, the GCD is the greatest common divisor. It requires some work to show that all other common divisors divide it.

Violet Flame

08:52

Right so call the (unique up to constant mult.) divisor polynomial which all common divisors divide MCD, clearly it is a divisor with highest possible degree, since GCD is also that, they are equal upto constant multiplication. Hence all common divisors divide GCD @robjohn I didn’t appeal to bezout

robjohn

How do you show that there is a polynomial that all common divisors divide?

Violet Flame

Yes that was my question?

I think appeal to bezout but not sure how

robjohn

You need to use the Euclidean Algorithm and thus Bezout

It is the non-zero polynomial with the smallest degree that can be written as a combination of the two polynomials.

Violet Flame

@robjohn I didn’t understand the details of how to prove existence, can you please give a short sketch?

robjohn

Do you know how to use the Euclidean Algorithm to write the GCD as a linear combination of the two polynomials?

it is the smallest polynomial that can be written as a linear combination of the polynomials

Violet Flame

09:08

I know EA, but not that.

robjohn

this answer uses the Extended Euclidean Algorithm to find the GCD of two polynomials.

in that case it is $1$

robjohn

09:29

this message shows polynomial division, but I assume you know how that works.

Violet Flame

11:39

@robjohn I got it, thanks for your help.

barista

13:07

I'm trying to solve the following boundary value problem:
$$\begin{cases}
\Delta u =1 & \{(x,y,z)\in\Bbb R^3:1<x^2+y^2+z^2<9\}\\
u = 0 & \{(x,y,z)\in\Bbb R^3: x^2+y^2+z^2 = 1\}\\
\nabla u\cdot n = 0 & \{(x,y,z)\in\Bbb R^3:x^2+y^2+z^2 = 9\}\\
\end{cases}$$
Here, $n$ is the outward unit normal vector field on $\{(x,y,z)\in\Bbb R^3:x^2+y^2+z^2 = 9\}$.
First change into spherical coordinate $u(x,y,z) = v(\rho,\phi,\theta)$. Since boundary conditions are independent of $\phi,\theta$, $v(\rho,\phi,\theta) = v(\rho)$. $\Delta v=1\iff {\partial^2 v\over \partial \rho^2}+{2\over\rho}{\partial u\over…

Did I solve correctly?

Calvin Khor

i didnt read super carefully but the idea is right @barista

why are you unsure about that step?

barista

I found some error. Let me fix my solution

Calvin Khor

ok

barista

$n(x,y,z) = {1\over 3}(x,y,z)$ and $\nabla u = \left({\partial u\over\partial x},{\partial u\over\partial y},{\partial u\over\partial z}\right)$. Since ${\partial u\over\partial x} = {\partial u\over\partial \rho}{\partial\rho\over\partial x} = u_\rho {x\over \rho}$, $\nabla u = \left(u_\rho{x\over\rho},u_\rho{y\over\rho},u_\rho{z\over\rho}\right)$. Hence, $\nabla u\cdot n = 0\iff {\rho u_\rho} =0\iff \left(-{c_1\over\rho^2}+{1\over 3}\rho\right){\rho} =0$. Since $\rho = 3$, $c_1 = 9$.

This is where I used second boundary condition.

I wonder if I did it correctly.

because changed cartesian coordinate to spherical coordinate to use it

Calvin Khor

$u_\rho x/\rho$ <--- here $x$ is the vector $(x,y,z)$ right?

ah i should have read the next line

looks right to me

gradient of a radial function points in the $e_r \propto (x,y,z)$ direction

barista

13:23

Thanks!

Calvin Khor

np!

user193319

13:59

If $X$ is an infinite set, then the finitary alternating group on $X$ can be defined in the following equivalent ways: 1. the group of all even permutations on $X$ under composition; 2. the kernel of the sign homomorphism on the finatary symmetric group on $X$.

First, what does even permutation mean if $X$ is infinite? Second, how does one construct the homomorphism mentioned in statement 2.

?

S.M.T

Hello everyone , I have a v important question. I am sure all of you + me love mathematics a lot. I am studying for engineering. So , count physics , computer science into it too. Now , I really do love my subjects. They give me the ability to create sth , I just like it at times to do it. I have my goals as to what goals I want to achieve through studying them. One being creating a rocket ship.

My Q is that there are times while studying that u don’t feel like working , learning that subject at the moment. U feel like doing sth else. I don’t understand this part here. If was work , study is like my passion. Why do I get tired , bored of it ?

It happens sometimes that u just don’t want to study that day but rather play sport or watch a movie or talk with friends.

The problem is that it doesn’t happen when I want it happen. I don’t feel like going to play sport when time comes. I feel like going to sport just after 2-3 hours of study and have entire day left.

There are times when u study for like 8-10 hours , 5-7 hours or sometimes even nothing at all. U just don’t want to do it.

Calvin Khor

because ur a monkey designed by Higher Management to eat fruit and swing on tree, but some snake told you how to play with fire and now we big brain

S.M.T

But u like it as well right. U think that this is ur passion.

But it just doesn’t work that way,,

Even if u try to sit , u won’t be able to grasp anything & end up with headache

@CalvinKhor What I have noticed is that whenever u r doing sth continuously for a long time. Same thing. U get bored.

let’s say I decide to play football everyday. After a week , I’m like I want to change the sport.

Let’s take into account - Pizza. Though it tastes good but if I try to eat it for like a whole week and nothing else. I get bored of it.

Calvin Khor

14:19

why do people get bored, why are we never happy with what we have

idk m8 is that not to be human

@S.M.T goodreads.com/quotes/…

S.M.T

Thnx for sharing

Calvin Khor

yw :)

S.M.T

@CalvinKhor I also notice is that we like the end goal but not the process(just everyday but ok sometimes). Let’s say: do u want a body like Chris hemsworth every day. Yes. But r u ready to work for it everyday. It’s a no

do I want to be an astronaut , have a space company. Yes. But r u ready to study about how physics work around it. Not daily

Calvin Khor

lol. if only every time you saw something, you could immediately ascertain the opportunity cost you would have to pay to get it!

S.M.T

the problem I am having is that: i am finding it difficult to do anything. Knowing that I would get bored of it after sometime. How to live life to fullest - I am finding it hard to manage and discipline myself

When u are studying. Why do u think get bored of your subject which is so significant to you that u want to do sth else

Calvin Khor

14:31

because im lazy, like top 1% of lazy people

S.M.T

But it needs to have is a definition

Calvin Khor

well, monkey brain tells me, why feel good in 5 years, when u can feel good now

S.M.T

Yes. It is mostly noticeable like for a student

but , think about this.

lets say u get onto watching a movie

ur monkey brain has said that watching a movie is a feel good now thing

but , u can’t watch movies ur entire life. Can u ?

u can’t search social media entire day , every second. Can u ?

Similarly , u can’t study all day

Calvin Khor

nah, but I can waste a whole day (or more...) on doing nothing useful

S.M.T

A day is ok. Understandable

Calvin Khor

14:37

entire summer? :)

S.M.T

@CalvinKhor When u do really want to study also. U Consider ur work to be even more important than other tasks(Social media,sports,movies) for some time :) but u do consider it.

@CalvinKhor Yes , hypothetically. I get bored of all these things at max - 3days

Worst I have ever been

Calvin Khor

unless interrupted by hunger, tiredness, or a certain sense of duty, i can spend the rest of my life playing video games

S.M.T

Hmm

Notice Sth here.

I have been an avid gamer. I have played for like 8 hours a day

Lets say you’re playing GTA 5. Amazing game. Now , u have finished all the levels

There are 2 things here

Asinomás

8 hours a day of gaming is considered a lot?

Calvin Khor

@Asinomás hahaha

S.M.T

14:41

1) U will want to switch to a new game since all ur levels are finished now. U wont play it. Agree?

@Asinomás How much is a lot for u ?

Asinomás

16 hours

is a decent number I think

S.M.T

2) Notice. Ur point @CalvinKhor is good that u can play video games entire life. But u want to switch to a new game

Just like any other thing monkey brain does.

@Asinomás Wow. When do u sleep or eat man :)

Asinomás

you eat while you play

and you sleep when you don't

S.M.T

It is the monkey brain that tells u to study now because of ur bored of every other thing

It happens at its best after a lot of procrastination or a nice vacation

@Asinomás LEGEND. Ur my god :)

Asinomás

glad to hear it

S.M.T

14:47

So , what do u think about this point

Also , study is more harder when it is mostly textbook type than visual type. Why? Instant gratification

Same concept u said at first

People are able to be disciplined at sports as a career since it is mostly an instant gratification job

leslie townes

this is a good point. people also accept a far greater level of rigor in sports instruction (they expect a coach to push them hard) that they might not accept in the math classroom.

a lot of bad math teaching amounts to boiling difficult concepts into something that gives the feeling of instant gratification, but loses something in translation.

S.M.T

Exactly. Being a professional cricketer myself , I know it

i have felt it

@leslietownes nice to meet u btw

leslie townes

good morning or, as i suspect, evening.

Asinomás

yes that sounds true @S.M.T

S.M.T

@leslietownes What do u think about the points I have made so far now

leslie townes

14:55

i've only read the most recent one.

scrolling back, it is difficult to maintain motivation at the same thing for a long period of time. and there's no one way to do it, people who are able to do it do so for different reasons.

people sometimes spend many years in therapy to discover that their reasons might not have been the best reasons.

S.M.T

@leslietownes Hmm K

leslie townes

for some people the motivation is external, they want to satisfy their relatives, or a spouse, or some imagined group of peers. wanting recognition or money isn't a bad thing if you know where the impulse is coming from and do not let it consume you.

when i worked in math, mostly i was motivated by curiosity about the subject. but there would definitely be days, sometimes weeks in the summer, where i took a vacation from caring about it.

S.M.T

@leslietownes I was talking about procrastination , discipline , laziness. I was trying to understand what they truly mean. So , if u want. U can scroll up and read. It will be great to continue the chat further with u

@leslietownes Exactly the point

Asinomás

what do you mean what they truly mean?

leslie townes

well yeah, for some people, what gets them over the procrastination is a desire for recognition. or a desire to be seen by others as hardworking. you have to have something that gets you over the line.

otherwise we'd all just sit around. if i didn't need to earn money i'd probably just play with my cat and my daughter all day. i might end up doing that anyway.

S.M.T

15:02

@Asinomás What I meant from it was that why do we really procrastinate ? Maybe we are not or r just tired. Maybe we are down and that’s why. Maybe ur not lazy but just don’t know how to maintain a healthy discipline and why u really get bored. What is boredom exactly ? These kind of points

Asinomás

greatness should not be expected

50 years ago you could be an alcoholic baker and have a family

S.M.T

For me , it is like if I achieve this goal. How great would be its outcome ?

That's what I like

Example: If I am playing football , my goal is to win or score goals.

Calvin Khor

@S.M.T at the moment, this is lighting the fire under me: everyone has regrets when they die. Try to make decisions so that you can choose what you regret

S.M.T

@CalvinKhor Lightning fire under me - I really don’t know what u mean exactly. I hope I have not upset you or made u feel sad. 2nd point of yours , We r not machines. So , there wil be some regrets but I don’t want them to big regrets. It can be like a small thing where ur business failed but I dont want to regret that I didn’t try

Calvin Khor

@S.M.T no, you misunderstood, and didnt do anything wrong

if you have a fire under you, you can't sit down :)

S.M.T

15:08

A regret to fail after trying is ok but its not if u have not tried at all for it

U feel like to work I think is what u mean

Calvin Khor

better about what?

S.M.T

@CalvinKhor Sorry , not right word

Calvin Khor

yes

no problem

leslie townes

calvin: "why did i do all of those killings? most of them didn't even ask for it, it wasn't fair."

S.M.T

Thank you for your beautiful comment @CalvinKhor

Calvin Khor

15:10

@leslietownes dont bring your work home

@S.M.T yw

S.M.T

@leslietownes If u notice , I would be happy to make a space shuttle but not work on it like every second

Calvin Khor

@leslietownes actually im feeling rather dense i think im missing a joke

S.M.T

I would be happy to have written the calculus (When mathematicians were trying and failing) but maybe , I would not working on it everyday

So , we understand that we need a break from anything were doing after some time

leslie townes

calvin: just the idea of choosing regrets about serial killing. you know, the good kind of regrets. not "why didn't i spend more time with my kids?" but "why did i kill all of those people."

Calvin Khor

unless ur elon musk

S.M.T

15:13

Since we like to live our life in creativity , do different things , experience different things

Calvin Khor

yikes lol @leslietownes

Asinomás

I don't like to experience different things or do different things

S.M.T

@CalvinKhor It is interesting to see how that guy works. He does take breaks. He goes to party , met gala(He was there) , SNL(TV SHOW).

He finds his work like instant gratification

He is on twitter every 3 hours

He has even gone to NBA seasons

Understand Seth really important. He does not create everything going on in his companies

Calvin Khor

p sicc

S.M.T

He mostly works on is designing part - the cool part. Why? HE is the boss. It is his team because of which he is Elon musk , not him alone

@CalvinKhor Just like Steve Jobs doesn’t know each and every thing about how an apple device is made. He is mostly there for ideas , motivation and some coding

leslie townes

15:17

he's mostly deceased, at present

Calvin Khor

lol

S.M.T

It’s an example

leslie townes

i deliberately misunderstood :)

S.M.T

Do u guys agree with me on that ?

Calvin Khor

i think you are right in the techinical detail but i don't see your point

leslie townes

15:19

if i were advising any famous celebrity CEO i would tell them to delete their twitter account and work on not being a celebrity anymore. it has so many potential downsides. satya nadella at microsoft is doing a perfect job.

mark zuckerberg sort of gets it, except he wants to star in promotional videos. i would tell him to stop doing that.

jobs and musk and some of the others, i dunno. some upsides, many downsides.

S.M.T

What is our goal of this entire conversation ? To always have control over our motivation in a way that u can work whenever u like

U can enjoy the process so do u fantasize about the goal

Calvin Khor

hey man if we could solve that we'd be bigger than elon musk

S.M.T

We can be. Always believe in yourself

Calvin Khor

trying :)

S.M.T

I got a scholarship of 1000 dollars from my institute

So , it is small steps. We can do it

Calvin Khor

15:22

congrats

S.M.T

1) What is ur goal in life ? What do u want ?

I want to travel different planets

I want to create cars. I want to go into designing clothes

I want to write a song. I want to do sky diving

These are just few of mine

@CalvinKhor @leslietownes U can prepare yours

Calvin Khor

writing "a song" is easy. Writing a song you like, that's another thing

leslie townes

i wanted to be the greatest rapper of all time. having achieved that, i don't know what else to do.

S.M.T

No , its v hard to write a song depending on what u r creating

Calvin Khor

right, you can add interesting constraints, but the unconstrained problem is easy

S.M.T

15:25

I want to create on gun violence , drug abuse , racism. Many things. That song has to be sth like people can groove to and also understand its depth

It’s poetry , I find it hard

U have to go deep in thoughts

Calvin Khor

yup thats hard

S.M.T

@leslietownes K

2) Why do u want it ? Would u want to play video games instead ?

MY answer: I have only 1 life. I will not live it again

I want it to be special. Video games is fun but is it your highest potential ?

Is that the only highest amount of courage in you ?

I will say no

Then , I decode video games

Video games is a fake reality. Life doesn’t work on the clicks of your keyboard , controller

Calvin Khor

but what if i get a sick hiscore

S.M.T

Video games are just light flickering on a TV screen , that’s all. U can not lose in a video game. They are always made for u in that way u win

I find it incredibly depressing to work on sth like that

@CalvinKhor As of the moment , I only play is car racing game.

If I ask u , Would u like to Run on walls or fight like the guy in prince of Persia video game does OR would u rather learn his skill and use it in real life.

That’s why I don’t play video games anymore

Be the superhero in reality , not in virtuality

Which only uses is a keyboard and controller to work

I want to travel because I want to see how the world looks like. I would rather fall in love with a woman than in love with a video game

Accepting your mortality in a way that u make the best out of it is the goal here

3) What do u need to reach that level ?

Well , I need to study astrophysics. How a rocket is made. I need to exercise(To like amazing and healthy) etc

These are subjects through which the process is done

Now , what we find hard is to work on them , learn the basics

Here , u need to ask urself. Do u want to learn the process or u just like the goal but not process

If u ask me , I enjoy the process some days but I would also like to work on my other goals simultaneously

Not just one goal

Einstein didn’t have just 1 goal - studying physics. He liked communication , violin.

It was a goal too but his physics goal had was more priority

4) Why do I not enjoy the process all the time ?

@leslietownes I pray that u be more productive and achieve what u want - goals. Bye , take care

Calvin Khor

15:57

i'll have what he's having

leslie townes

my daughter stumped us this morning at breakfast. she kept asking "why do we own this house?"

we could not figure out what, exactly, she wanted to know, but she was very insistent

Calvin Khor

good question hahaha

leslie townes

i couldn't tell if she meant, why did we pick this house, or if she meant what does it mean to own a house, or if she wanted to see our purchase contract and other documents

she's probably too young for a full explanation of secured financing

Calvin Khor

so that you're dry when it rains and warm in the winter wasn't good enough?

leslie townes

it wasn't. she somehow realized that someone must have lived in our house before we did, and also asked why they were doing that.

i really don't have answers to these deep questions

AMDG

16:11

Long time no see, guys!

leslie townes

hi AMDG. why do i own this house?

AMDG

What?

Oh

leslie townes

yeah, that's my reaction too.

i was hoping somebody would know

AMDG

There are a number of answers. The issue is knowing the question.

leslie townes

yeah, we were trying to figure that out. what is it that she wanted to know? there must have been something

AMDG

16:15

A manual of moral theology would tell you that you own a house because you bought it and therefore have a qualified ownership of it. You are free to dispose of it within the limits of any civil laws imposed upon you.

leslie townes

why do we own this house? why do we own this house? why do we own this house? those are only three of many alternatives in the multiverse.

AMDG

lol

leslie townes

why do we own this house? because it was cheaper than renting.

AMDG

I assume you did the calculations and projected that it would be cheaper than renting

Anyways, could I get some recommendations as to how to improve the wording for my question here? There's some things that I could use some help to make perhaps clearer or more succinct: cs.stackexchange.com/questions/150790/…

leslie townes

our mortgage payment is maybe $1000 below market rent for equivalent housing.

this may be more a reflection of inflated rents than the deal we got, but i'll take it.

looking at the question now.

AMDG

16:17

Over the course of a worst case of 120 years of rent?

As you can see, I don't know how to put it more succinctly for describing that there can be no smaller value than another as the definition of "minimal".

(detailed in the part "we seek to find a common subset ...")

It works but I don't like how convoluted it feels

leslie townes

the nesting of quantifiers is making my head hurt, but it feels like it ought to be related to one of the 'big' problems, e.g. the exact cover problem. that's more of a vibe than a well-formed thought.

AMDG

What does quantifier mean in this context?

leslie townes

exists subset forall indices there does not exist ...

the goofy E and A

AMDG

oh that lol

leslie townes

as you can tell, i am a logician

AMDG

16:24

I'm more of a logician myself, but I'm now more comfortable describing things mathematically than with a bunch of paragraphs given that I lack the terminology necessary otherwise. I didn't even know what pairwise distinct meant before this question.

Huh, now that I read up on exact cover, I think that's exactly what this problem is.

leslie townes

knuth is a good reference for that stuff.

and for tons of other stuff.

AMDG

I've done some informal analysis through contemplation. What I have thus far is some unproven theorem(s): the frequency of each unique digit in any column $c_x$ from a given base $n$ is inversely proportional to the logarithmic order of the associated column.

Suppose for instance I have three elements. In base three, the column associated with the order $3^1$ will have digits 0, 1, and 2 occur equally with a frequency of $\frac{1}{3^1}$

So in other words, we'll get any permutation of $[0,0,0,1,1,1,2,2,2]$.

My hope was that I'd catch a break finally and let someone else do the heavy lifting to rest my mind, but I guess thinking upon such fundamental and important concepts as these does not come so quickly and freely.

At least I'll get bragging rights kek

I'll have one of the best and most robust standard libraries in the world for Project Aquinas.

This particular algorithm I'm looking into is for making a hash map that can map anything, but efficiently, specifically a minimal perfect hashing function that maps arbitrary strings to arbitrary strings.

When I say I solve problems once, I mean once

The benefits will then trickle down to everyone else as more people adopt my project (when it becomes available)

I'm monologuing again, so I'll quickly wrap this up.

Asinomás

I will never adopt your project

AMDG

16:40

Indeed, you can get any permutation of that set, but obviously, if we allow permuting columns, the amount of unique information varies as the columns themselves vary, so we have to look at both columns and rows to determine the number of unique values present.

@Asinomás Why's that? lol. Do you even know what my project is?

Asinomás

No

AMDG

It's a project to fix all the problems we have in information technology, mostly oriented towards us programmers and software engineers.

Asinomás

I am not a programmer

I am a mathematician

AMDG

Do you use python for making computations, or some other form of calculator perhaps, or mathematica?

Asinomás

No, I use programming languages for smart people

AMDG

16:44

Ah, so C and assembly?

Asinomás

no, wolframalpha

AMDG

big brain

Well, if it's software, my project is applicable. That's all you need to know, then :)

Asinomás

Given strings S and T find the shortest substring of S that is not a substring of T

oh nvm

I can't read your problem

$S := \left\{s_y | s_y = B_y \right\}$

AMDG

Yes, an $s_y$ is a set $B_y$

Asinomás

S is a set

AMDG

16:49

Yes

Asinomás

oh, it should be y | s_y = B_y

AMDG

Why?

How does that make sense?

Asinomás

I don't know

what is $s_y$ and $B_y$

AMDG

They're defined...

It's set builder notation, and $:=$ means "is defined as"

S:={s_y|s_y=B_y} in plain English reads (so I would hope): S is defined as the set of elements $s_y$ where each $s_y$ is some object [set of objects] $B_y$.

$B_y$'s definition immediately follows that

I've done things in such a way that I can refer to different rows and columns as indices, e.g. "row 3, cols 4-9": $s_{3,4...5}$".

Asinomás

in the example algorithm we have 4 strings of the same length

that is the only input?

AMDG

16:56

Yes, but they could be strings of arbitrary length since you can just make them to be the same length because of trailing or leading zeroes. The algorithm is not affected by implicit information.

Asinomás

you just want to find $l\leq r$ that minimizes $r-l$ such that no pair of input strings coincide on all of $l$ to $r$ ?

AMDG

What does coincide mean, please?

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$Mathematics$ Mathematics