Mathematics - 2022-04-13

copper.hat

00:48

@OliverDiaz the payment problem resolves itself after one iteration :-).

Ted Shifrin

01:09

Howdy @Copper

copper.hat

Hi @TedShifrin! Hope all is well.

Ted Shifrin

01:28

The room is on life support.

leslie townes

bhptphbtpht

Ted Shifrin

01:41

Yup. Incoherent life support.

leslie townes

phbpbht

Ted Shifrin

Talking to Munchkin is more edifying.

leslie townes

01:56

i took a 30 second video of her holding the cat aloft today. the cat was cool about it, jumped down on her own, and did not attack.

Ted Shifrin

Olivia is sweeter than Screech.

Also much older. Screech is mellowing, slowly.

leslie townes

olivia kept crashing a meeting i had. walking right in front of the camera. she even swatted at people on the screen.

mellowing does happen. olivia attacks us less than she used to, but it's still one or two a day.

Ted Shifrin

Of course. Cats want to sit right in front of the monitor. Duh.

leslie townes

people liked my cat on the meeting more than they liked me.

Ted Shifrin

Color me shocked.

And you still haven’t made the agridolce leeks. My patience is running short.

leslie townes

02:00

how's the recovery from the dental surgery? do you need to up the dose of pain meds?

:)

Ted Shifrin

Nope. Took nary a one!

leslie townes

wow. i was pretty doped up for almost a week after my last one.

Ted Shifrin

Wimp.

leslie townes

02:23

my daughter just referred to my wife by the name of the person who runs late-afternoon day care. this is what happens when you leave for a week.

it was an accident. she tried to turn it into a joke.

copper.hat

02:42

ever since work sent me a new 'laptop' i spend less time on mse, unfortunately

more of a portable desktop than a laptop, unless there are folks out there with gigantic laps.

ooooh, that hurts

i mean calling mom by someone else's name

leslie townes

yeah, haha

copper.hat

the closest i had was my father in law called me by his son's dog's name. i am/was the only son in law.

i suspect being called by another human's name is better than being called a dog's name.

user 726941

Perhaps, it was a Freudian slip for a man's best friend. 🤔

🐶

🥰

leslie townes

03:29

🐱‍👤🐱‍👤🐱‍👤

Ted Shifrin

Munchkin knows how to joke?

user 726941

Trying to hide an accidental slip of the tongue with humour is a life long skill.

Ted Shifrin

@user726941 which I do not expect a 3-yr old to have!

user 726941

Indeed.

💯

BAYMAX

03:47

I was thinking about the two simultaneous non-linear equations

$b-x-\frac{xy}{1+qx^2} = 0$ and $a - \frac{xy}{1 + qx^2}=0$

I could find may be one of the solution analytically like $x = a-b$ and $y= \frac{a(1+q(b-a)^2)}{b-a}$

but after graphing them I see that there more than one solution to it

Ted Shifrin

Sign error?

BAYMAX

$x = b-a$

yes right

Ted Shifrin

Is $q>0$?

leslie townes

ted: in this case, after realizing the mistake, she doubled down on it by calling her mother the name of another person at school in an exaggerated sing song voice. then she said "i'm just joking," paused, and asked for the thing she wanted (now for the third time) in her normal tone.

so, she'll have to work on subtlety. but it's there.

BAYMAX

@TedShifrin yes $a, b, q > 0$

Looking att his seems like when the $a,b,q >0$, we will get only one solution

but I wonder when $a,b,q$ turn to negative then they give more than one solution

desmos.com/calculator/zw9ddny2xq

Ted Shifrin

04:01

I think you should think critically about it.

BAYMAX

04:21

yes will try

user 726941

That's all you can do.

🤔

Dr. @leslietownes have you considered putting munchkin in a school for like minded "gifted" munchkins?

💝🎁💝

👨‍🏫👩‍🏫

copper.hat

04:37

@leslietownes that is pretty intuitive of her to realize the faux pas...

leslie townes

user, she's weird enough as it is :)

user 726941

👼

leslie townes

at bedtime she flipped a shirt over her head and wore it like a hat, with the neck of the shirt as a kind of headband. she kept shouting "I'M THE PIZZA MAN" because she associates wearing a shirt this way with a chef's hat, which she has seen depicted on a man on a pizza box

there's a lot going on, is all i'm saying

user 726941

They say during these developmental years there is the most going on cognitively.

leslie townes

sometimes when she goes to bed i can sense that. her head is just buzzing with questions. we have weird conversations.

user 726941

04:49

Do you read to her a lot?

:^)

leslie townes

not a huge amount, but a little every day.

her mom reads to her a lot. i spend more of my time on drawing and making up games to play

copper.hat

i used to give my daughter little puzzles like mazes, and graph paper featured a lot. anything that involved precise colouring appealed to her (not her brother, though)

reading is pretty high order

user 726941

True; deleted.

copper.hat

she used to like trains and similar more until she discovered pink & frilly

sad day when ho scale meant earring size and not model train gauge.

leslie townes

she can recognize her name when it's written out, and write letters on command if you tell her which ones to write, but it's too much like work for her. she tires of it.

she knows the six-digit code we use to unlock the device that we sometimes let her watch videos on.

thankfully she can't navigate menus yet, so if she gets in, she can't do anything. although if the thing she wanted is already open she can start it up.

copper.hat

05:04

i am sure i mentioned the time my daughter 'helped' me by dragging every icon into the trash.

we were in the middle of series b and i had many versions on the desktop

leslie townes

haha yes.

copper.hat

that was back when i had a life

user 726941

😳 ouch

copper.hat

quite by accident i had a video call with both offspring today, rather unexpected and nice

user 726941

Coolio.

Video conferencing is taking over.

copper.hat

05:08

i prefer the phone if i must communicate remotely

but their mom prefers video.

user 726941

I still prefer old fashioned email.

copper.hat

when i grew up phone calls were expensive (relatively) and everyone could listen so there was a 'get off the phone quickly' imperative

when i say expensive, i mean expensive relative to when my parents were growing up since that seems to be the measure of cost that parents apply

i@leslietownes i presume she is inundated with lego and the like?

user 726941

Speaking of emails, did you all know that the newest version of Yahoo mail requires iOS 13?

copper.hat

i just use telnet

user 726941

Not to mention the grand opening of Apple Park.

copper.hat

05:16

the space ship?

leslie townes

copper: yes. and a lot of toy trucks and tools. her fine motor control is pretty good.

user 726941

Head office:

$5, 000, 000, 000

copper.hat

corporate excess

user 726941

On a royal scale, considering Buckingham palace has been assessed at the same price.

copper.hat

i wrote lots of notes & problems for my kids on microcrap onenote and now i cannot access them.

user 726941

05:34

If we did these kind of things the old fashioned way, on paper, we wouldn't have these problems.

copper.hat

a few decades ago i decided to try going paperless. did not work out.

the onenote was handy at the time.

leslie townes

we worked with a consultant who had a ton of stuff in some kind of proprietary program. an absolute ton of stuff. he stopped consulting unexpectedly due to family issues and left us with this gargantuan database that nobody could open. all of his notes were in there as well as the materials he was citing.

we did get it open but it wasn't funny for a few days in there.

user 726941

05:52

I wonder if they've considered digitalizing the Library of Congress.

copper.hat

one of my projects was to write them up in latex, but i guess that will take second place to actually opening the stupid files

this is why steve balmer-monkey called linux a cancer. it doesn't leave you in the lurch like the good microsoft does

leslie townes

the copyright office was still requiring paper copies for a lot of deposits for registrations at the beginning of the pandemic. they wanted the authority to allow all-electronic, and couldn't get it. so literal warehouses were filling up with printed material and nobody was there to go through it. i think they still have a huge backlog.

i'm sure the librarians at the library of congress are all for digitization and it is more a question of getting the money and authority to do it.

copper.hat

its so annoying that i can't access the stupid files!

leslie townes

what's the deal? is onenote not supported anymore? do you need a cdrom from 1997 to unlock the right version?

i remember compatibility between different versions of MS office being a surprisingly huge thing for a really long time. it seems to be better now although maybe that is because docx is less crazy of a frankenstein format than legacy doc files were.

copper.hat

the files are from onenote 2003 and they have gone through a few incompatible versions.

leslie townes

06:03

oh i believe it

user 726941

I think the pandemic has, in a lot of ways, prematurely awakened the techlogical Frankenstein.

By that^ I mean the medium is the monster.

*technological

copper.hat

unbelieveable, they discontinued windows journal too. pos

user 726941

06:23

Is there not a relevant stackexchange that you could ask on?

copper.hat

I will try.

I found a legacy windows journal version, but I am annoyed at losing the 2003 onenote stuff. Seems like it violates something, especially when one pays through the nose for it

good night!

user 726941

cya

Good luck!🤞

☘️

🍀

love_sodam

07:27

Is there anyone who knows Clifford algebra?

0

Q: Degree of the splitting field of $x^6+5x^3 - 2$ over $\Bbb Q$.

Compute the degree of the splitting field of $x^6+5x^3-2$ over $\Bbb Q$. From this answer, I first let $y := x^3$ then the given polynomial transformed to $y^2+5y-2$ so roots of $y$ is ${-5\pm\sqrt{33}\over 2}$. letting $\alpha := \sqrt[3]{-5+\sqrt{33}\over 2}$, I can conclude that $[\Bbb Q(\al...

Matheus Sousa

11:04

Hi guys, can someone explain to me how can I find a closed formula for this series?:

$\sum_{n=1}^{\infty} \frac{1}{n*2^n}$

My solution:

I tried to split this sum of product in a product of sums. It was like this:

$\sum_{n=1}^{\infty} \frac{1}{n} \cdot \sum_{n=1}^{\infty} \frac{1}{2^n}$

But if I do this, I know I'm wrong because this is equal to $2 \cdot \sum_{n=1}^{\infty} \frac{1}{n} = \infty$ I know I'm wrong but I don't know what mistake I'm doing. Please help.

Jakobian

12:04

About Warsaw circle not being the image of unit interval again

I found an elementary proof

If $X$ is the Warsaw circle and $Y$ is the partof it homeomorphic to the unit interval which corresponds to the interval obtained from closure of graph of $sin(1/x) $ plus a little more, then we can find a neighbourhood $U$ of $f^{-1}(Y)$ such that $f(U)$ is entirely contained in $Y\cup V$ where $V$ is open (path-connectedness is used here)

V means a small interval addition to Y so that their union is a space homeomorphic to [0, 1)

Leaky Nun

@MatheusSousa replace the numerator with x^n and differentiate

@MatheusSousa the mistake is that ab+cd is not equal to (a+c)(b+d)

Jakobian

Then $f^{-1}(Z^)$ is open, so we obtain a map from compact $f^{-1}(Z^c)$ onto an interval homeomorphic to $[0, 1)$, but this is impossible

Alessandro Codenotti

12:33

Quotient of locally connected spaces are locally connected, and if $\colon [0,1]\to X$ is a continuous surjection, then it is in fact a quotient map, since it is closed

In other words continuous images of $[0,1]$ are locally connected

This is (part of) the easy direction of the Hahn-Mazurkiewicz theorem

Jakobian

12:52

Oh, I didn't know quotients of loc connected spaces are loc connected

It's nice that it can be shown in a less direct way

love_sodam

@Jakobian you know what? It's actually one of the exercise problem in Munkres

Jakobian

I haven't read Munkres

Alessandro Codenotti

13:10

@Jakobian yes it's a nice result

Very false for general continuous images of locally connected spaces though

Jakobian

15:18

@AlessandroCodenotti does the concept of one-dimensional continua agree across all definitions of dimension?

Samyak Marathe

Hi

I need help in probability

If someone can help me in this regard

0

Q: What is the probability of the given event?

Consider 2 Boxes. One has 99 white balls and 1 red ball. Another box has 99 red balls and 1 white ball. Now one has to chose a box at random and take out a red ball. It is given that the person has taken out the red ball. Now what is the probability that the ball has been chosen from box 1 which ...

probability

Alessandro Codenotti