Mathematics - 2021-08-16

mme

00:00

Feels a bit Pascal's Wagery except you remove the conscious cynicism

leslie townes

my immediate family is roman catholic, which in these days puts the same amount of stress about what people actually believe in. my wife is basically atheist. my mom goes to mass multiple times a week but probably doesn't buy into the full doctrine.

shintuku

i guess it's a bit like catholicism and the different saints

leslie townes

when her uncle died we lit a candle. it doesn't need to be too complicated.

mme

catholics famously don't read the bible as much as protestants, which in an era with decreased churchgoing probably doesn't breed religious fervor

shintuku

mass was in latin up until 1965

leslie townes

00:03

that's a weird thing. i used to know a priest who was really into trying to get catholics into reading the bible, with no luck.

Thorgott

@leslietownes very nice, I've hard sword of doom recommended by a friend just a while ago; guess I should watch it

leslie townes

thorgott you should watch it tonight. i can recommend other samurai movies.

kaneto shindo's "kuroneko" is another good one.

and more recently takashi miike's 13 assassins.

mme

13 assassins is one of the better samurai movies since kurosawa

leslie townes

it's the best i've seen in ages.

mme

which isn't to say it feels like you're watching yojimbo

it does really well perhaps because it's not just a kurosawa script with updated visuals

leslie townes

00:08

toshiro mifune is in sword of doom. he's the swordsman who drives the guy crazy because he realizes he isn't the best.

mme

i haven't seen it but i'll add it to my list. my wife doesn't usually go for things which feel actiony so it'll be a hard sell

it's a fine line. it can't be an action flick but it can't be boring. but so many good movies are very boring

leslie townes

my wife hated it until about halfway through.

mme

eg stalker is beautiful but you do have to be willing to sit there and watch the grass grow for 5m at a time

leslie townes

i love samurai movies because they tend to emphasize artistry over violence, and also emphasize nonviolence while sometimes being very violent. the post-WW2 generation of japanese directors was understandably very cynical about state authority.

mme

that reminds me that there's a great miyakazi interview somewhere in which he poo-poos abe for wanting to remove the pacifist bit from the constitution (as you might expect, this was a really quite unpopular comment in Japan). they asked him why and he says, more or less, "we are very bad at war. no further comment."

too bad Ted left as I popped in. Hi, @Ted. I'm off aagain soon.

leslie townes

00:13

there are so many really good violent japanese films that are, in substance, about the insanity of violence.

shohei imamura is one of my favorite directors. his film 'vengeance is mine' is unbelievably violent and explains nothing about the main character's motivation. they asked him in an interview, 'vengeance for what?' and he just didn't answer the question.

he did a weird post 9/11 short film about a man who was so traumatized by war that he thought he was a snake.

it's on vimeo. vimeo.com/111652156

mme

that's nice

i've had my fun for the night. enjoy

Thorgott

I'll have to pass on tonight, it's already past 2am and I'm stuck on a stupid computation

@leslietownes I should try that, too, maybe that'll warm me up to Miike as I sadly wasn't a fan of Ichi the Killer

leslie townes

ichi the killler is extreme. i think it is his worst film.

just too much going for shock value.

he's also made a ton of good movies.

Thorgott

@leslietownes I watched Kitano's Violent Cop recently, that very much falls in line with this

leslie townes

oh, i love that one. and kitano in general.

my wife loves violent cop, weirdly.

Thorgott

00:35

yeah, the juxtaposition between the extreme bouts of violence and how serenely shot it is works really well

emotionally empty in the best way possible

I've decided to watch Kitano's filmography in chronological order, looking forward to Boiling Point soon

with Ichi the Killer, I didn't really mind the extremity. it just felt like a tonally disjointed experience to me. so many characters with bizarre quirks, but nothing to really latch onto. some of the individual scenes are pretty cool, but the whole experience didn't get me invested

leslie townes

with kitano i like hana-bi and his zatoichi remake the best. with miike i like 13 assassins and audition. although i would not recommend the latter to people who are not horror fans.

shintuku

what are your favourite movies? japanese or otherwise

leslie townes

my wife for example loves 13 assassins but i would never dream of showing her audition.

shintuku, some of the samurai movies mentioned above. in french film i like le corbeau and army of shadows. in US/UK films, the third man, make way for tomorrow, and night of the hunter. and the original suspiria from the late 70s. it has been remade.

i watch a whole lot of horror movies that are terrible just because i like the genre.

stanley kubricks the shining is also really good. i've probably seen that movie 20 times.

shintuku

i know none of them, stuff to add to the list hehe

ah except the shining

woah, all of them are pre-1980

big statement

leslie townes

they stopped making good movies.

kuroneko is a really good movie.

i think the only more recent movie that i like is henry: portrait of a serial killer. which is just a remorseless film about serial killing. the guy who commissioned it wanted some exploitation flick and got something else. michael rooker has gone on to star in the walking dead and is a talented actor.

but the subject matter is very unpleasant.

shintuku

00:53

heheh

Thorgott

leslie, that's from 1986

shintuku

"recent"

leslie townes

i'm old, OK?

i just love the idea of commissioning what you think is going to be a teen slasher flick and what you get is someone remorselessly killing people for almost two hours. that must have been a fun conversation.

some of the pixar movies are OK. i really liked ratatouille.

Thorgott

for the sake of balance, I'll recommend a recent film I like: One Cut of the Dead

leslie townes

is that streaming somewhere in the US, thorgott?

shintuku

00:56

japanese zombie comedy

difficult genre

leslie townes

i'm not familiar with the director but i will look into it.

shintuku

let's see how the crowd reacts

leslie townes

there's been more recent stuffed that i liked. 28 days later was really good.

and the david copperfield remake from a year ago.

i tend to lean toward very violent movies, and my wife tends to lean toward romantic whatever. we don't have a lot of common ground.

Thorgott

I think it's on Amazon Prime

leslie townes

it does look like it's streamable on amazon prime.

shintuku

01:00

looks like good reviews

Thorgott

@leslietownes the middle ground is Bonnie and Clyde?

leslie townes

yeah, my wife did like that one.

shintuku

a "recent" one I liked is short cuts

leslie townes

robert altman is a genius. have you seen 3 women?

3 women and McCabe and Mrs Miller are two of the best films of all time.

i saw the two of them at a double feature at the castro, pre-pandemic. i miss hanging out there.

shintuku

all added to the list

i should do that more often, choose movies based on director

oh he's the guy that did MASH

Ted Shifrin

01:21

@leslietownes There’s a Castro in Long Beach?

Bob

03:13

Hi

is anybody around?

shintuku

03:25

finally! the day when knowing how to count in binary is useful has come

you can make sure you're listing all elements of a power set counting by in binary

S.M.T

04:15

-1

Q: What is the usage of studying trigonometric equation?

I have solved many Q regarding trigonometry in which we have to equate LHS to RHS. For example , $\frac{1}{\csc A-\cot A} - \frac{1}{\sin A} = + \frac{1}{\sin A} - \frac{1}{\csc A+\cot A}$ and many more. As I see this equation and if I try to visualize this. Let us take a triangle with sides 3,4,...

Please share your answers regarding my Q.

shintuku

@S.M.T an example of the usage of sec, csc, and cot, is for integrals that are solved using trigonometric substitution

for example $\int \frac{1}{\sqrt{x^2+1}} \ dx$

you will very likely encounter an integral similar to this one, in any career that uses calculus

S.M.T

K

Euler 2

greetings fellow math-tickians

Koro

04:36

Given $f$ differentiable everywhere in $\mathbb R$ such that $f'(x)\le l\lt 1$ for all $x$, where $l$ us a fixed real number. I'm looking for an example of such $f$ which satisfies the aforementioned hypothesis and yet fails to have any fixed point.

I thought $f(x)=x-10e^x$ could work but almost immediately realized that we must bound $f'$ by $l$, which is $\lt 1$.

Had the hypothesis included $|f'(x)|\le l\lt 1$, then I would have had no problem in proving the iterative sequence $(x_n)$ defined as $x_n=f(x_{n-1})$ for all $n\ge 2$, given $x_1$, a Cauchy sequence.

Koro

04:55

I managed to come up with a counterexample: Let $l=\frac 12$, $f(x)=-10x^4+\frac 12 x -10$ then $f$ has no fixed point.

no this example is wrong :'(

I'm an alien Im an eagle alien

05:23

Topology masters?

0

Q: $f^{-1}(C)$ is not a finite set, whenever $C$ is a closed subset of a topological monoid, and $C$ is saturated as a set (but not necessarily a monoid)

Let $X, Y$ be topological spaces on the ring of integers such that $Y$ is a topological monoid (multiplicative, on $\Bbb{Z}$) and let $C \subset Y$ be a closed set that is multiplicatively saturated: $xy \in C \implies x,y \in C$, but not necessarily closed under multiplication. In other words $...

abstract-algebra general-topology elementary-number-theory topological-groups monoid

Euler 2

I'm an alien Im an eagle alien

@Euler2 can you look at my post? Someone downvoted...

For realz. Makes no sense

it's a valid question I had

Euler 2

@I'manalienImaneaglealien um.. the new policies are a bit too strict

I'm an alien Im an eagle alien

@Euler2 I know right

Euler 2

they want motivation, context and/or work

I'm an alien Im an eagle alien

05:37

you being Euler, they must be so futuristic to you :)

Euler 2

otherwise your question can end up in CURED

I'm an alien Im an eagle alien

The motivation is twin primes, but no one wants to hear that so I left it out

The work? I'm asking for how to approach it essentially, it's such a high level question that of course I did a lot of work on it

Euler 2

they want it

I'm an alien Im an eagle alien

I'll try to put in an attempt. Thanks @Euler2 you're my math hero

Euler 2

nay

ok

a good math hero should be... a bit 'experienced'

I will be an expert when pigs fly

I'm an alien Im an eagle alien

05:48

You're speaking obtusely

What's your angle

Euler 2

hehe

I'm an alien Im an eagle alien

You're stoned, like me :)

Euler 2

yes and no

I'm an alien Im an eagle alien

The duality of the universe

^_^

Euler 2

duality is my primary characteristic

or... secondary

I'm an alien Im an eagle alien

06:06

@Euler 2

Say you have a topological monoid $Y$

and a continuous map $X \to Y$

call it $f$

and this certain closed subset $C \subset Y$ while infinite, we suppose that $f^{-1}(C)$ is finite!

Also, the set $C$ is such that $xy \in C \implies x,y \in C$ (opposite of multiplicative closure, called "saturated")

Is such a thing possible?

I'm assuming it's not, so I look for a proof by contradiction

But I need some additional conditions most likely.

If you can prove that there's a contradiction, then you've proven twin primes with my setup which I haven't posted yet, but the topologies are:

$X = (\Bbb{Z}, \tau_0), Y = (\Bbb{Z}, \tau_1)$ where $\tau_0 = $ arbitrary unions of submonoids (multiplicative) are open, and $\tau_1 = $ arbitrary unions of ideals are open.

The map $f: X \to Y$ is $f(n) = n^2 -1$ and I can easily prove that it is continuous

Another continuous map out of $Y$ is $\Omega : Y \to (\Bbb{Z}\cup \infty, \tau_2) = Z$ where $\tau_2 = \{ [a, \infty] : a \in \Bbb{Z}\}$ are all the infinite intervals. $\Omega(q_1 \cdots q_r) = r$ is from number theory, $q_i$ are all prime.

Euler 2

beware
this is what leslie says about me

15 hours ago, by leslie townes

you're the non-expert who offers the view of the common man on the proceedings.

I'm an alien Im an eagle alien

Since $\Omega$ is continuous as well, we get that $(\Omega \circ f)^{-1}((-\infty,2])$ is infinite is the same thing as the twin primes.

But $\Omega^{-1}((-\infty, 2]) = C$ is our closed set

and it is saturated

Euler 2

ask someone worthy or the version of me in 2 years

I'm an alien Im an eagle alien

I'm trying to do a topological proof of infinitude of twin primes

Euler 2

oh?

I'm an alien Im an eagle alien

06:15

That's all one needs to know (the above) to make it work

However, I don't know if it will work

Furstenberg's infinitude of primes is different since it uses cosets of ideals as open sets

in fact doing so gives you a topological ring

*a basis for open sets

So I've reduced the question down to the first few lines of the above paragraph regarding a saturated closed set

Euler 2

idk what has happened to me maybe i am ignorant but whenever I see something which can 'prove' a conjecture i disagree

I'm an alien Im an eagle alien

You're probably right

doesn't hurt to try though

Evil John Rennie

08:30

It hurts when you think about same proof for 3 hours straight and you start to doubt that you are not made for mathematics. You feel like you are worthless and start to be suicidal and after you give up then suddenly you know answer and you will start to realize that is so simple. This repeats all the time. All of the things a person goes through in life cause suffering and they cannot do anything about it. Instead, they have to accept that it is there.

Most suffering is caused by a tendency to crave or desire things.

People should not be too focused on wanting many different things as the enjoyment won’t last.

People must try to stop craving as much as they can in order to work to end suffering.

Before I am banned I will teach you how to end suffering :u:

Right action ,speech, livelihood, mindfulness, effort, concentration, understanding and intention.

OK I am ready to get banned for 30 min for being off topic :-)

Buraian

09:24

damn

redemption before one's death

almost feels biblical

geocalc33

good morning

geocalc33

09:52

$S=\bigg\{\begin{pmatrix}
e^a & e^b \\ e^c & e^d
\end{pmatrix}: a,b,c,d \in \Bbb Z : e^{ad-bc}=e\bigg\}$

$\begin{pmatrix} e^2 & e^1 \\ e^5 & e^3 \end{pmatrix} \begin{pmatrix} e^1 & e^1 \\ e^5 & e^6 \end{pmatrix}$

$=\begin{pmatrix} e^7 & e^8 \\ e^{20} & e^{23} \end{pmatrix}$

the first row times the first column is done as: $e^{2(1)+5(1)}$

so $S$ under this operation forms a group right?

Astyx