Mathematics - 2015-07-18 (page 3 of 3)

Alec Teal

19:02

I love the internet

pjs36

It is an amazing place, @Alec

Alec Teal

I'll miss him.

Semiclassical

@AntonioVargas which of his books? i've got his orthogonal polynomials / RHP / random matrices book on my desk on campus

skill patrol

I followed him into their room.

Cool room colours.

An all moderator room ownership is kinda scary though :P

Alec Teal

OMG a mod from Christianity has joined a maths chatroom.

El'endia Starman

19:15

@AlecTeal 'cause I'm a mathematician too!

Karim Mansour

HOW

2

El'endia Starman

I came here to link to my new blog post: Exploring and Understanding Hyperbolic Geometry Part 2: Movement.

3

Karim Mansour

lol

Alec Teal

I have so many questions...

Karim Mansour

one of the questions in christians page

"What is the evidence that the Angel of the Lord in the old Testament is probably Jesus?"

haha

people asking questions about fairy tails

is kinda of funny

El'endia Starman

19:18

If an expert could check the math on Wikipedia's page on the Poincaré disc model that would be great. I'm pretty sure the math regarding how to draw lines through two points in the hyperbolic plane is wrong, and I suspect the formula for translation might be wrong too.

Alec Teal

@KarimMansour I had a Christian friend (not a bit of faith like "there's a heaven" - because lets face it the Agnostic afterlife if bleak as fuck, but proper nutjob who thinks dinosaur fossils were planted by jews to take us off the path to heaven) - can model decay, understands radioactive decay, doesn't "believe" in Carbon Dating (because there can be errors!) yet can prove the central tendency theorem.

@El'endiaStarman you should probably ask a question, not link to blog.

Karim Mansour

I find such incidents very weird if a person can think logically then there is so many contadictions of the whole idea of religion very weird @AlecTeal

El'endia Starman

@AlecTeal Hmm, I suppose I could. Do you think a question like "Is the math on this Wikipedia page wrong?" would fly on the main site? It's too localized, especially in time because once it gets fixed, the question is no longer relevant.

Alec Teal

@El'endiaStarman that's why we have permalinks....

El'endia Starman

@AlecTeal How would that help?

Alec Teal

19:22

@KarimMansour I know, it makes no sense. I even tricked him into proving it worked and he shunned me for a week.

@KarimMansour then I bought him this kids encyclopedia that I had when I was like 5 that explains how pumps work, the ear works, all kinds of stuff (called "The big book of knowledge")

@KarimMansour he refused to touch the heathen book once I showed him the bit about tectonic plates

I was like "DID YOU EVER NOTICE THAT THE LAND MASSES FIT TOGETHER, look at that Africa shaped edge...."

And the scientists that did the rock surveys are liars.

Karim Mansour

@AlecTeal Yeah religious people are so ignorant of reality

Alec Teal

His world makes no sense! I don't understand how he DOES MATHS

Karim Mansour

like if you look at the whole idea of mosses arc itself you it doesn't make sense scientifically

yet people still believe such thing happened

exactly

skill patrol

That's their choice.

Antonio Vargas

@Semiclassical The OPs and random matrices book. I also got his one on Universality but haven't looked at it yet.

Alec Teal

19:26

@El'endiaStarman you've gone quiet. You can play Devil's advocate (if you dare) if you like!

@skillpatrol I don't get it. If someone says "2+2=5" you can correct them, but if someone's like "Nah, no fossils, it was the jews mate" you cannot bitchslap them.

Karim Mansour

yeah

Dave

I have a question about box plots and their left and right skewed. When you determine the skew - is it based on the whether the median line is closer to left or right whisker? or the length of the whiskers

El'endia Starman

@KarimMansour That's the over generalization fallacy if I ever saw one.

Karim Mansour

and problem with saying its their choice leads to making human mankind stands behind because of people believing absolute truth

Alec Teal

CENTRAL TENDENCY THEOREM @El'endiaStarman and differential equations

I made him prove it (as I said) and the nutter shunned me for a week. Genuinely.

El'endia Starman

19:28

@AlecTeal Well, y'know, you can't do much to reason with someone who thinks that religious people are stupid and implies as such repeatedly.

@AlecTeal Looks to me like you're doing it too. Assuming that Christians in general behave and believe like that one friend of yours.

Alec Teal

I didn't say all of them. My first message on the subject I said I'd not take faith away from someone with a bit of faith. It's the nutjobs I mind.

That's why I gave you the chance to defend!

nigelvr

I am struggling to see what "ignorant of reality" actually means. We're supposed to be mathematicians here. Let's not use silly language.

5

El'endia Starman

@AlecTeal Ah, my apologies. I'm in agreement with you then.

Alec Teal

@El'endiaStarman I'm jealous of people with a "bit of faith" as I put it. This twat I mentioned leaves his oven on so when he comes home it is pre-heated. Why? "Because it says in the bible that the earth will provide for as long as man is upon it" and I'm like "FFS, you've just undermined all my light switch-turning-off ever!"

El'endia Starman

Still, it would've been nice for you (or especially @Karim) to ask me what I believe before attacking (explicitly or implicitly) Christianity or religion in general.

nigelvr

19:32

Anyway .. this is almost certainly a stupid question but I want some help. Let S = {(b^4, 4ab^3, 6a^2b^2, 4a^3b, a^4) : a,b \in R}. How can I compute the convex hull of this thing in R^5?

Alec Teal

@El'endiaStarman you've agreed with me already. My motive here is knowing this guy I met makes others go "WUT?" too, because I want to know that that isn't normal!

El'endia Starman

@AlecTeal Let me assure you that's definitely not.

At least, not among those I know.

pjs36

@El'endiaStarman Sorry about (some of) your reception here, not sure what all that's about!

Alec Teal

(Spanish Inquisition joke here)

skill patrol

Define: "normal"?

9 mins ago, by skill patrol

That's their choice.

El'endia Starman

19:35

@pjs36 Heh, it's alright. I wouldn't be a good Christian if I couldn't handle some harsh criticism.

skill patrol

Enough said.

Alec Teal

@skillpatrol vaccinating the population ought not be.

nigelvr

I know no one cares .. but should I try to (somehow) compute the extreme points of the convex hull (by magic) and then use the krein milman theorem or something (along with some fancy computer algorithm)?

RE: the set S above

Alec Teal

@nigelvr you should post a question really.

nigelvr

eh I guess I could...

skill patrol

19:37

We ALL have the right to have an opinion @AlecTeal

Alec Teal

@skillpatrol when I come to power that kind of thinking will be punished.

El'endia Starman

@AlecTeal Yeah, I don't like that kind of reasoning. Well, he's not wrong - if we keep going like we are, we might not be around for much longer. Then again, he doesn't know how long we'll be around, and that later generations will be harmed in ways that doesn't mean the Earth stops providing for us. That said, he could also save on his electricity bill.

skill patrol

Once bitten by power...

El'endia Starman

Also, there is at least one well-known Christian environmental scientist that I know of that goes around and speaks at churches, using the Bible to support her position.

Alec Teal

I admire her patience.

pjs36

19:42

And by the way, @El'endiaStarman, one of the graphics in your hyperbolic post reminds me of this post

Antonio Vargas

@Semiclassical next time you're in your office, if you feel inclined to take a gander at it I would be grateful for any insight you could offer. I have a feeling you're more familiar with that stuff than I am.

dREaM

I hate it when you write two paragraphs and a half and get no upvotes

and someone writes a small portion of the two paragraphs and gets upvoted

Alec Teal

Gonna link it now @dREaM and hope we upvote?

dREaM

No.

I'm already capped.

Alec Teal

Cool, totally with you BTW

El'endia Starman

19:55

@pjs36 COOL!

Alec Teal

20:12

This is gonna sound so dumb I am asking it here to avoid the shame of a question. Is it true that the complement of a closed set is open?

Balarka Sen

Yes.

dREaM

yup

El'endia Starman

Sounds right.

dREaM

that's one of the definitions

El'endia Starman

@dREaM I was about to start trying to think of a counter example and you saved me from doing that work. :P

Alec Teal

20:14

I can't find that. I was taught (and read in my books) "closed if complement is open" not iff

Balarka Sen

What defn of a closed set are you using? Are you working with a metric space or a topological space in general?

Alec Teal

Which is the same as "complement not open if not closed" but I dare not say "a set that isn't open must be closed"

Topological spaces @BalarkaSen

Balarka Sen

@AlecTeal A set can be both open and closed, so the latter is false.

A set can also be neither open nor closed.

Alec Teal

And "Closed if complement is open" (so $A^c\in\mathcal{J}\implies A$ is closed)

Is there a short proof? (Sorry to ask this, I feel really daft)

dREaM

So what is it that you know?

Balarka Sen

20:16

Short proof of "complement of closed set is open"?

It depends on what defn of closed you have.

dREaM

So your book tells you "a set is closed if complement is open"

So it's telling you all the complements of open sets are closed

oh ok

So the problem is that initially there may be more closed sets than those right?

yeah. It should have been stated as an if and only if.

Balarka Sen

I'm failing to understand the question. Anyways, I have to leave.

dREaM

ok

good luck in your future endeavors

pjs36

Indeed, there have been a few posts about how if in a mathematical definition almost unequivocally means "if and only if". It's a source for great confusion, occasionally :)

Alec Teal

I don't think he meant for ever.

While I can see that "if X has P" for a definition means that everything with P is X (the iff camp) I am not convinced that it applies ....

I require "either a set or its complement is open" to finish my proof. This actually sounds false. Because if you take the trivial topology (just $X$ and $\emptyset$) if you take ANY set that isn't one of those two, neither is open nor closed

@BalarkaSen which contradicts you

pjs36

20:29

Why do you require that, @Alec? It is definitely false, like intervals such as $[0, 1)$, for example.

Mike Miller

@AlecTeal: Yes, that's false. You still need to clarify what your definition of closed is before someone can prove to you that closed sets are precisely those that have open complements.

Alec Teal

math.stackexchange.com/users/9003/amwhy that's like a year ban - this guy's helped me. @DanielFischer can you shed light.

@MikeMiller "A set is closed if its complement is open"

Mike Miller

Okay, then what's meant is "A set is closed iff its complement is open". There is no other definition of closed.

That ban happened a while ago. I think there were like four users that upvoted everything the others posted.

Alec Teal

Yeah but a year ban for something as arbitrary as rep?

skill patrol

She used to be regular in here too :(

Daniel Fischer

20:32

@AlecTeal Not allowed to.

Alec Teal

That's a long time to be banned for something so small.

@MikeMiller I'm not convinced, all that statement tells us is that $A\in\mathcal{C}\implies A^c\in\mathcal{J}$ surely?

Mike Miller

If it did, then that wouldn't be a definition, would it?

A definition needs to precisely specify what a closed set is. If it really does just mean if, and not iff, then it has not actually specified what a closed set is.

Alec Teal

It's just a name we give to sets whose complement is open.

Mike Miller

Yes. What's your question, then?

Alec Teal

I need to show that $\mathcal{C}^c:=\{A^c|A\in\mathcal{C}\}=\mathcal{J}$ where $\mathcal{C}$ is the set of closed sets and $\mathcal{J}$ the open ones of a topology.

So then I can show that $\sigma(\mathcal{J})=\sigma(\mathcal{C})$ and finally be happy about the Borel sigma algebra!

I'm happy that $\mathcal{J}^c\subseteq\mathcal{C}$ I'd like the converse @MikeMiller

Ted Shifrin

20:39

Goodnight @MikeM. You make out like a bandit last night?

Mike Miller

@AlecTeal: If $J$ is open, then $(J^c)^c = J$ is open, so $J^c$ is closed. Is that what you were looking for?

@TedShifrin No, I lost first.

Ted Shifrin

And what second?

Mike Miller

Game lasted another few hours without me.

Ted Shifrin

Without you? In your own place?

dREaM

What does make out mean?

Alec Teal

20:41

@MikeMiller I need $\mathcal{C}\subseteq\mathcal{J}^c$ which is .... closed implies complement is open. Which is what I already had? WTF

Mike Miller

@TedShifrin: Games don't end the moment the host loses...

Ted Shifrin

Thinking of the Felix Unger/Oscar Madison poker games with the blue sandwiches ... :)

dREaM

I think I'm getting a wrong impression of what went on in Mike's place last night

skill patrol

in Mos Eisley, 4 hours ago, by Richard

→ → → → → This way to the Special Secret Chatroom

Alec Teal

My ... how stupid am I being. "A complement of an open set is closed" - I should be okay with this. Never speak of this again.

pjs36

20:49

I'm enjoying the Multivariable book, @TedShifrin. It'll take some time before I get to stuff that's new to me, but I've had some fun with exercises already

Chris's sis the artist

0

Q: A nicer closed form? $\int_0^1 \frac{\log (x) \log \left(x^2-x+1\right)}{x^2-x+2} \, dx$

Mathematica doesn't return a nice result for integral below, maybe because such one doesn't exist, or it exists but it depends much on a certain way of tackling things. What do you think? $$\int_0^1 \frac{\log (x) \log \left(x^2-x+1\right)}{x^2-x+2} \, dx$$ $$=\frac{2 i \log ^3(2)}{3 \sqrt{7}}+\...

Ted Shifrin

21:06

@pjs36: There are indeed a few excellent exercises. I'm proud of them. Enjoy!

Alec Teal

I did it!

I am finally happy that $\mathcal{B}((X,d))=\sigma(\mathcal{J})=\sigma(\mathcal{K})=\sigma(\mathcal{C})$ for any metric space.

For any topological space, $\mathcal{B}((X,\mathcal{J}))=\sigma(\mathcal{J})=\sigma(\mathcal{C})$ - but no comment about the compact one

But anyway, this means $\mathcal{J}\subseteq\mathcal{B}(\mathbb{R}^n)$ and $\mathcal{C}\subseteq\mathcal{B}(\mathbb{R}^n)$ AND $\mathcal{K}\subseteq\mathcal{B}(\mathbb{R}^n)$

Okay, one quick question, is $\mathcal{J}$ a distinct symbol from a J where the loop goes further around and back across the J? (By this I mean it carries on going around then through the middle of the vertical part of the symbol)

robjohn

21:26

Been busy all day. Now people want to get food. Guess I won't get a chance to do math until tomorrow (MSE time)

pjs36

I would assume so, @AlecTeal. These are all the fancy J's I can think of, at the moment (at least that are Mathjax-able)

$\mathcal{J} \mathscr{J}\ \mathfrak{J} \leftarrow$ mathcal, mathscr, and mathfrak

Alec Teal

Oh....

Thanks @pjs36

robjohn

@Chris'ssistheartist: I am working on an integral/sum. I hope to finish it tonight.

Chris's sis the artist

@robjohn Which one?

robjohn

I am on mobile. I'll show you later. Hopefully, I'll actually have finished it.

Chris's sis the artist

21:31

@robjohn It's related to my integrals and series? OK

Semiclassical

21:44

afternoon chat

pjs36

Hello, @Semiclassical

Karim Mansour

What is the definition of jointly continous ?

Hi @Semiclassical

Semiclassical

@AntonioVargas not certain you're right about that, but sure

tbh i haven't read a lot of it. partly that's just a matter of prioritizing other things, but i also didn't feel like i was really following his presentation very well

on OPs i've tended to go more towards Barry Simon's books; for RHP, stuff by A. Its / Fokas / Kitaev

the latter of which, amusingly, includes a physics application very similar to one we've been researching (same concept, different system)

pjs36

I've wanted to look at Simon's Analysis books, @Semiclassical. But I suspect you're talking about something different?

Semiclassical

yeah

this and this

pjs36

21:55

Holy mackerel, that's about 12 math grades above my pay, but it looks engaging, at least

Semiclassical

it's tough going, yeah

i use them mostly as references rather than trying to grind through them

Eric Stucky

hello, world

Mike Miller

gravatar thief

Eric Stucky

:P but also ?

Math is Life

Is the answer to this problem 225 degrees? math.stackexchange.com/questions/650090/…

Eric Stucky

22:09

@MathisLife: to which problem?

Math is Life

@EricStucky "Find $\theta_1 + \theta_2 + \dots + \theta_7$. Give your answer in degrees." Original problem linked here: math.stackexchange.com/questions/650090/…

Alec Teal

In LaTeX how do you do the [ ] without the top part ("floor" function)?

Eric Stucky

\lfloor and \rfloor @Alec

dREaM

\lfloor

@EricStucky what is a senior project?

Eric Stucky

@MathisLife: What's the logic there, did you just compute all the $\theta_k$

Dream: context?

Alec Teal

22:15

I should have guessed, thanks @EricStucky

pjs36

@EricStucky Presumably your "About Me" section :)

dREaM

yeah

@pjs36 Is it true you like to prefer to keep an air of mystery about you?

Eric Stucky

Oh, some schools call it a "thesis" and some call it a "capstone project", just lots of language. It's just a mini-research project done in senior year of undergrad

dREaM

oh I see, I wanted to know if it was undergrad or highschool.

what did you do it on?

pjs36

@dREaM Can you interpret this evasive non-answer as an answer?

Eric Stucky

22:18

Kasteleyn's solution to dimer model: answers the question "How many ways to tile rectangles with dominos"

dREaM

no, I'm stupid

Eric Stucky

(haha I am at someone's house who has a block on tumblr.com :( otherwise I would link you)

pjs36

Woah - a person who has a block on tumblr, like you'd find at some schools, or workplaces? Weird!

dREaM

oh, I think that has been solved for aztec diamonds or something like that

Eric Stucky

It's solved for rectangles too but the answer is weird

dREaM

22:19

recursive and horrible?

Eric Stucky

Nope, explicit, just weird

Domino tiling

A domino tiling of a region in the Euclidean plane is a tessellation of the region by dominos, shapes formed by the union of two unit squares meeting edge-to-edge. Equivalently, it is a matching in the grid graph formed by placing a vertex at the center of each square of the region and connecting two vertices when they correspond to adjacent squares. == Height functions == For some classes of tilings on a regular grid in two dimensions, it is possible to define a height function associating an integer to the nodes of the grid. For instance, draw a chessboard, fix a node with height 0, then for...

dREaM

This is what I was tellng you about aztecdiamondequestrian.com

I did the $2\times n$ case as a problem in an olympiad a couple years back.

Eric Stucky

@pjs36: Yeah, they have a little kid and tumblr is kinda known for porn, so I figure it's about that.

dREaM

of course that won is really easy in comparison.

pjs36

@EricStucky Haha, thanks for that shot of reality! (I forgot tumblr was one of the image ones, makes sense!)

dREaM

22:22

so your project is on tumblr?

Eric Stucky

Not on tumblr explicitly, but it's a fairly detailed high-level explanation

erm, that was confusing

The project itself is not on my blog, but I did put up a fairly detailed high-level explanation.

dREaM

That formula looks really weird, it isn't even clear to me that would be an integer

Eric Stucky

Yeah XD

dREaM

anyways I have to sleep acoording to my parents, good night all.

Eric Stucky

the proof splits cleanly into two parts, and I think that the second part is the easiest known way to prove it is an integer XD

dREaM

22:23

or day depending on stuff

oh. I'll have to ask you about that later. Sounds cool.

Eric Stucky

I'll link and tag you when I get privileges :/

Good night :)

Alec Teal

22:36

math.stackexchange.com/questions/1365990/… My first question which is "own research" (sort of) and "cross areas-of-maths" (set theory to prove measure theory) - quite proud right now.

Alec Teal

23:15

I still can't believe a year's suspension was dished out for an upvote ring of 4 people - that seems VERY heavy handed. AmWhy has nearly 5k answers, 3 questions and has helped A LOT of people. meta.math.stackexchange.com/questions/21037/amwhys-suspension Just asked on Meta about it.

@robjohn you're a mod, and also really helpful.

Eric Stucky

Alec, I don't know what the situation was but if it was not a first offense then this may just be standard policy.

Alec Teal

@EricStucky 1 year over something as arbitrary as rep is an awful excuse. AmWhy has helped me a lot, (I recognised the name when I came in from Google earlier and saw rep as "1") any amount of rep scammed above what they earned legitimately is insignificant

Upsetting it got 3 downvotes. Knowing if I ever get a ban you guys wont give a shit hardly makes me want to help you lot.

Eric Stucky

23:30

You still literally have no idea what the ban was about, Alec :/

Alec Teal

@EricStucky that doesn't rule out it being heavy handed.

I got a 30 day ban for telling a user on SO to RTFM (which counts as swearing) and when he claimed he did saying "don't be a tard, read it again" - the accepted answer was a quote from the manual.

Karl Kronenfeld

@AlecTeal there always is that possibility.. yes..

Alec Teal

So if it was as arbitrary AND REVERSIBLE as an upvote-ring... how does that justify a year?

Karl Kronenfeld

You admitted that you are not certain of the actual justification of the 1 year ban

Alec Teal

Do I need to to appeal it? If other mods go "No trust me, it was totes justified" fair enough. But it could be a tool for all we know.

Also @KarlKronenfeld an appeal can be denied.

Dave

23:36

can some one link me to a good website that does line equation graphs.. wolfram is too small to use

Alec Teal

desmos

Dave

i tried that - its buggy as hell

couldn't even draw to simple lines

Alec Teal

Then no

Dave

can you try see if you reproduce the bug i get on demos might help rule out if its my browser

Alec Teal

@Dave are you using IE?

Dave

23:40

Chrome

Alec Teal

Use Firefox see if it works.

Yeah I'm never answering a question on this site again

Dave

okay

Does the same on Firefox.

this doesn't make any sense

Karl Kronenfeld

What are you graphing?

Dave

can you try these two lines on desmos and print screen what you get

y = 2160x - 43200 and y=1845x

Alec Teal

Did you try zooming out?

Link me the website and I'll look

Dave

23:48

desmos.com/calculator

this is what i got

Karl Kronenfeld

You have to go into settings and adjust the x and y coordinate ranges to get anything useful

I started off with 0-0.5 by (-10000)-10000 and then zoomed out

Alec Teal

That doesn't look wrong @Dave

Dave

it looks hugely wrong

this is wolfram's and the lines are not completely vertical

Alec Teal

....

Is this guy serious @KarlKronenfeld

Dave

changing x is not changing the lines im convinced it bugged

Alec Teal

23:53

Are you on any drugs or medication @Dave ?

Dave

Helpful.

Alec Teal

But seriously ADJUST THE SCALES and it will look like that

READ the scales to see they're different

Dave

well unless what im adjusting on desmos is wrong...

Alec Teal

Try entering the scales you see on the alpha thing

You'll find the graphs look the same (click to edit them)

Dave

Where? =/

Ahh

ok i was adjusting the wrong thing :P

Alec Teal

23:58

Things like that are not normal @Dave but I have it on good authority that on meth it is.

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$Mathematics$ Mathematics