The h Bar

Emilio Pisanty

10:01 PM

previous discussion of modems on this chatroom:

Nov 9 '16 at 18:11, by Emilio Pisanty

including the reminiscences of the actual greybeards from 'round here

Sir Cumference

@obe Mind if I take a stab at an advertisement using your logo?

0celo7

so...why does it make that sound

Emilio Pisanty

@0celo7 see bernardo's link above

0celo7

oops, didn't see

@heather Do you know what a power set is yet?

heather

@0celo7, I'm afraid I don't.

ACuriousMind

10:11 PM

→ 3 messages moved to Trash

Bernardo Meurer

@0celo7 SNL is funny even when I disagree with them. That's very commendable

@ACuriousMind What the fuck man

Tsc

ACuriousMind

Next one to post political material gets kicked.

Bernardo Meurer

It's a sketch

You're being stupid

AccidentalFourierTransform

Trump.

Bernardo Meurer

You can't just delete everything that could be political

ACuriousMind

10:12 PM

@BernardoMeurer It's political satire. Don't pretend you're too stupid to see the difference

0celo7

:)

Jesus

Bernardo Meurer

@ACuriousMind So what? I can't post a goddamn satire in this room now?

Emilio Pisanty

I'm out. g'night y'all.

Bernardo Meurer

What's up with that? Are we bowing to triggered crybabies?

0celo7

@ACuriousMind How come you didn't delete the things @BernardoMeurer said to you that were inappropriate?

ACuriousMind

10:13 PM

@BernardoMeurer Yes.

0celo7

yikes

heather

well, um, let's talk about rainbows! yay!

::not so subtle-y changes topic::

0celo7

Is @BernardoMeurer banned

heather

he better not be

0celo7

1 hour

heather

10:17 PM

what the heck

0celo7

> Your password must be at least 14 characters long

OH COME ON

heather

this is getting a tad extreme @ACuriousMind

deleting every single word about politics, and then banning a member, even if only for an hour, over it, is over the line.

0celo7

@ACuriousMind are you ok?

@heather He got banned for saying things to ACM he shouldn't have.

ACuriousMind

So, let me be completely clear here: Do not post politically charged material here. No matter whether it is funny, enraging, cute, or whatever. For justification, just consider that the first reaction to BM's satire post was a message that called a political faction "politcally insane".

6

heather

@ACuriousMind, for the record, will users get banned for posting political messages?

ACuriousMind

10:20 PM

@heather If they persist after they have been told not to, that is certainly an option.

heather

@ACuriousMind, okay, and one more question, was BM banned for the, uh, unfortunate comment about you, or the political comment? (Just trying to clarify.)

ACuriousMind

@heather If this were a main site suspension you'd see a "to cool down" as the reason.

0celo7

What does that mean?

heather

@ACuriousMind I'm confused as to how that answers the question. I assume it's a chat room only suspension.

0celo7

@heather Bernardo says you're cool, can ride dirty with him any time you're in Rio

trap on the street corner with a draco

slurpin lean

all that good stuff, y' feel me

AccidentalFourierTransform

10:25 PM

Bernardo right now

heather

@0celo7 tell him thank you, but I don't know what half of that means =)

Balarka Sen

you probably don't want to

0celo7

@heather It means: drive around with illegals guns in the car, sell drugs on the street corner with an AK-47, drink codeine cough syrup

heather

@0celo7 uh, well then.

0celo7

Bernardo to me: "Thanks for transmitting the message precisely"

Wait a moment. Is a reference to drugs against policy @ACuriousMind @rob

@heather So you don't know what a power set is?

How far away are you in Halmos

heather

10:30 PM

@0celo7, nope. Here, let me grab the book.

ACuriousMind

@0celo7 Not as such, no. However I urge you to reconsider the appropriateness of those..."invitations".

heather

@0celo7 Section 5, Complements and Powers.

0celo7

@ACuriousMind If heather was in Chiraq she'd be doing all of that. She's hecking 15

or maybe 16 by now, idk

rob

I have a proposal here. Let's separate actual on-topic discussions in this chat room from meta-discussions about what is or isn't on topic, the same way we separate physics questions from meta questions on the main site. There's already another perfectly good chat room which we can adapt for this purpose.

6

0celo7

It's a hard world in these streets

heather

10:31 PM

@0celo7 14

Balarka Sen

@ACuriousMind Drugs are kewl. All the beat stuff, y'know. 70's culture

0celo7

Bernardo: "The current moderation policy here is to prohibit anything that could possibly give the mods a bit of work, with no regards to how much it impairs average conversations"

rob

I find all these discussions about "who's banned" and "mod abuse" and "censorship" to be both boring and distracting.

0celo7

@rob It's not like you're participating in any discussions here right now.

heather

hmm, actually, i don't think that makes much sense @rob

DanielSank

10:32 PM

Hi, everybody.

0celo7

hello octopus

rob

@0celo7 I've been kibbitzing.

heather

no one's ever in the other room. that means those discussions will be most likely to die when they need the most attention.

@DanielSank, hello =)

0celo7

@rob I need a dictionary for that one.

DanielSank

@0celo7 ::waves tentacles::

rob

10:33 PM

@0celo7 Lurking. I think it comes from spectating chess matches.

Loong

Kibitzer

Kibitzer is a Yiddish term for a person who offers (often unwanted) advice or commentary. This term is used for a non-participant spectator in contract bridge, chess, go, and many other games. The verb kibitz can also refer to idle chatting or side conversations. In computer science the term is the title of a programming language released by NIST, as a sub-project of the Expect programming language, that allows two users to share one shell session, taking turns typing one after another. There is a 1930 film called The Kibitzer which is based on the 1929 three-act comedy play by the same name. Jane...

rob

@heather Self-fulfilling prophecy.

DanielSank

Lurking and kibitzing are not the same thing.

rob

@DanielSank Apparently not. Today I learned.

0celo7

@heather I will use the following convention: a set is a set of points and a class is a set of sets.

heather

10:35 PM

@0celo7, makes sense.

0celo7

Thus, the power set (the collection of all subsets of a set) is in fact a class.

heather

okay...

0celo7

This makes things nice in measure theory where you have points and sets and classes and sets of classes

sets of classes are collections

@heather If $X$ is a set, does $\mathcal P(X)=$ "class of all subsets of $X$" make sense?

heather

i think i follow, yes.

Balarka Sen

Exercise. if X is a set of n elements, count the number of elements of P(X).

0celo7

10:40 PM

@BalarkaSen $\sin(n\pi)$

Balarka Sen

Dude.

heather

x is a set of n elements. P(x). well, wouldn't it be...all of the possible combinations of n?

plus the void set

or null set

or whatever its called.

empty set, there we go.

Balarka Sen

"All possible combinations of n"? What do you mean by that?

Fix some set X of n element rather than working abstractly. My favorite is X = {1, 2, ..., n}.

heather

like, X = {x, y} the subsets would be {x}, {y}, {x,y}, and {}.

Balarka Sen

Right.

So for the X I said above, how many subsets (with the empty set and the set itself) are there?

Can you explicitly write down the number?

heather

10:42 PM

n+2? that doesn't seem right.

Balarka Sen

Check examples for higher cardinalities and you'll easily convince yourself that that's not it.

rob

→ 1 message moved to Physics Meta

heather

because if you had 3 elements, like X={x,y,z} you could do {x}{y}{z}{x,y}{y,z},{x,z},{x,y,z},{}

Balarka Sen

Exactly right. Certainly not 5 elements!

heather

n!+2?

no, ignore that while i check it =P

Balarka Sen

10:43 PM

Closer, but false. Don't guess, prove!

0celo7

How are you supposed to guess this

heather

well, okay. so we know there's going to be a minimum of 1: if n=0, {} is the only subset.

0celo7

I guess if you write them down for $n=0,1,2,3$ it will be easy

that should be enough for the pattern

heather

that's where n!+2 goes wrong...it doesn't work for n=0.

Balarka Sen

A good programmer can easily guess it. But I want a proof.

0celo7

10:45 PM

@heather I gave you a hint

heather

$\sin(n\pi)$?

but that makes no sense!

0celo7

@BalarkaSen Do you want a bijection between the power set and you know what, or can one do induction?

@heather then it's likely false

heather

okay, let me see.

0celo7

@heather No, write down the cardinalities for $n=0,1,2,3$

heather

i'm afraid I don't know what a cardinality is...*::googles::*

0celo7

10:46 PM

You already have $1$ for $n=0$

Balarka Sen

@heather Number of elements.

0celo7

@heather number of elements in the set

heather

oh. okay.

for n=1, you have $2$.

{} and $\{n_1\}$

Balarka Sen

@0celo7 Sure, one can prove this is many ways.

But the most illuminating one ain't induction.

heather

for n=2 you have 4

n=3 you have 8

Balarka Sen

10:48 PM

Wrong. Count again.

heather

must have missed a case previously

0celo7

@BalarkaSen Hmm?

Balarka Sen

Sorry, you've got it right.

I misread.

heather

oh, okay.

0celo7

now guess $n=4$

heather

10:50 PM

um...

0celo7

1, 2, 4, 8

what's the next number

heather

12?

Balarka Sen

count and check if that's right

0celo7

what?

heather

i have no idea @0celo7, it's probably wrong.

0celo7

10:53 PM

write out the power set for 4 elements

heather

well, okay, there are several different things your counting in P...you're counting

David Z

@heather after counting the elements in the power set of {0,1,2,3}, you might think about this: what operation takes you from each number to the next one in 1, 2, 4, 8, P({0,1,2,3})?

heather

the individual elements

the two element combinations, the three element combinations

Balarka Sen

Right!

heather

and then in this case the whole set

Balarka Sen

10:54 PM

That's good thinking. What does that tell you?

heather

the number of elements in P is exponentially larger as n increases?

AccidentalFourierTransform

yes

Balarka Sen

We're not looking for asymptotics, but some exact number. It gives you a systematic way to write down the number of elements if you know combination/permutation

But that is true.

heather

the power set for four elements is P = {{},{x},{y},{z},{w},{x,y},{y,z},{z,w},{x,w},{y,w},{z,x},{x,y,z},{y,z,w},{x,y,w},‌{z,x,w},{x,y,z,w}} I think

16 elements

1,2,4,8,16,...

32?

Balarka Sen

Mhm

heather

10:58 PM

this is a list of powers of 2

$2^n$

Balarka Sen

Correct. Now prove.

0celo7

Proof?

heather

okay...

::gulps::

let's see.

Balarka Sen

Your initial idea of counting the subsets of {1, 2, ..., n} by counting 0-elements (nullset), 1-elements, 2-elements, etc is useful

I don't know if you know permutation/combination though.

heather

I don't really, but I can always google.

0-elements -> 1 element, always.

1-elements -> n elements, always.

David Z

11:00 PM

@BalarkaSen Well there is a simpler way to do it

Balarka Sen

That takes more time to learn than googling. What is "->"?

@DavidZ Sure, I just mean, that's one way

heather

so then what's the "equation" for the number of 2-elements...

@BalarkaSen an arrow

Balarka Sen

I have no idea what you're trying to do

What does that arrow signify?

heather

n=0 -> 0
n=1 -> 0
n=2 -> 1
n=3 -> 3
n=4 -> 6

Balarka Sen

Oh, you're counting n-elements subsets.

heather

11:02 PM

@BalarkaSen i'm trying to break out how many of each "type" of element there is, and then sum it all up.

ACuriousMind

@BalarkaSen She's counting how many elements the powerset has. "x-elements -> f(n) elements" means the powerset of {1,...,n} has f(n) elements with size x

Balarka Sen

Nah, don't do that if you don't know the theory.

But you can always try. Look for a simpler way.

heather

@BalarkaSen, no? But it seems like it's working.

simpler way...um.

because I said so?

=P

David Z

lol

I think that's called "proof by Chuck Norris" but it only works if you're Chuck Norris

@heather are you Chuck Norris?

heather

0, 0, 1, 3, 6...$3^n-1$

@DavidZ lol no

Balarka Sen

11:04 PM

Once you tell me a quick, simpler way we (or someone else in the room) can talk about the harder way you were trying to come up with.

heather

so, we've got, $1 + n + 3^n-1$

Balarka Sen

Bad guess

David Z

@heather $3^n-1$ isn't the formula you need there. If you haven't studied combinatorics (permutations and combinations), you're probably not going to figure it out that way.

Balarka Sen

@DavidZ It's my favorite way to prove the binomial theorem by combinatorics.

heather

and then, let me guess, would the number of 3-elements in each thing be 4^n - 2?

or something like that?

Balarka Sen

11:05 PM

Nah

heather

@DavidZ oh. =/

::looks for different way::

David Z

@BalarkaSen Eh, whatever floats your boat ;-)

@heather at least for the way I had in mind, a hint would be not to group the subsets by their length. Group them by whether or not they contain a specific element.

heather

whether or not they contain a specific element...

maybe whether or not they contain a 1-element, 2-element, etc?

David Z

What do you mean by 1-element?

heather

oh, no wait, you were talking about the subsets, not the sets.

sorry.

so, whether they contain $n_1$, $n_2$, $n_3$,..., $n_n$

hmm, well in n=0, there will be no subsets containing any of those, but there will be one containing nothing...the empty set

in n=1, there will be one subset containing $n_1$ and one containing nothing

Balarka Sen

11:10 PM

The fact that there are 2^n many n-bit binary numbers is relevant (which I suppose a programmer like you would know).

heather

in n=2, there will be one subset containing nothing, two subsets containing $n_1$ and two subsets containing $n_2$

David Z

@heather well, one subset containing $1$. Maybe best not to use $n$ for both the number of elements in the set and the elements themselves ;-)

But generally speaking, you're right

heather

i don't know how that leads to $2^n$ though, because there's overlap between the $n_1$ and $n_2$ sets

Balarka Sen

Did you see my comment? :)

It relates to DavidZ's way of thinking, in a way

David Z

Let me suggest breaking it down like this: in $P(\{n_1,n_2\})$, there are two subsets that contain $n_1$. Out of those, how many contain $n_2$?

Sir Cumference

11:16 PM

Any stellar astrophysicists here?

heather

@DavidZ, one.

0celo7

There never are

Sir Cumference

;-;

David Z

@heather Yeah, and out of the two subsets that don't contain $n_1$, how many contain $n_2$?

heather

1

hmm...

a guess:

for n=3, there are 3 subsets that contain n_1, three that contain n_2 and three that contain n_3

and of these, two n_1's contain n_2, two n_2's contain n_3, and two n_3's contain n_1/n_2, and 1 of each contain both of the others

Balarka Sen

11:19 PM

Nope. {n1}, {n1, n2}, {n1, n3}, {n1, n2, n3}

All contain n1

heather

4 contain n1...oh.

=/

Balarka Sen

Also, you really should be counting (1) how many contain n1 (2) out of the rest, how many contain n2 (3) out of the rest how many contain n3 etc etc etc

Otherwise you'd overcount

David Z

@BalarkaSen yeah, exactly

0celo7

So do we know that it's $2^n$ yet?

heather

0celo7, nope, because I'm slow =)

@BalarkaSen, oh, okay.

David Z

11:32 PM

Maybe this will help @heather: make a list of the subsets of $\{n_1,n_2\}$ which don't contain $n_2$.

heather

{}, {$n_1$}

David Z

Does that look familiar?

heather

n=1?

David Z

@heather meaning what? (I think you're right, but can you be more clear?)

heather

the subsets of {n1, n2} that don't contain n2 are the subsets of {n1}.

David Z

11:34 PM

Yeah, exactly.

Now make a list of the subsets of $\{n_1, n_2\}$ that do contain $n_2$

heather

{}, {n1},{n2},{n1,n2}

the number of subsets of {n1} times two

David Z

@heather I think you misread or something. I asked for the subsets that do contain $n_2$.

heather

oh, only the subsets that contain n2.

{n2}, {n1,n2}

David Z

Yeah, now how do those relate to the subsets of $\{n_1\}$?

heather

they're the complement of {n1}?

the two sets of subsets together add up to P(X)

wait, ignore that...

David Z

11:39 PM

@heather no... well, not unless you mean something different by "complement". But that's not what I'm getting at.

@heather That is true, though also not what I was getting at.

0celo7

@heather Are you dead-set on this line of reasoning or are you open so something new

David Z

@0celo7 Well, we're getting really close

0celo7

ok

heather

@DavidZ, I don't know what you're looking for. the subsets that do contain n2 don't have any of the subsets of {n1}.

David Z

@heather True, well, think about this: starting from the subsets which don't contain $n_2$, what can you do to them to obtain the subsets which do contain $n_2$?

0celo7

11:41 PM

I really dislike "counting" proofs like these

David Z

@0celo7 If I were trying to explain this to you I'm sure I'd be doing it differently ;-)

heather

combine {n1} and {n2} and {} and {n2}?

David Z

@heather yeah

Note that in both cases, you're combining with $\{n_2\}$

heather

right...

0celo7

@DavidZ My proof uses induction and cartesian products, which she might not know...

David Z

11:46 PM

@heather OK, so consider this: you start with the subsets of $\{n_1\}$. Then from there, you can get the subsets of $\{n_1,n_2\}$ which don't contain $n_2$ by doing X, and you can get the subsets of $\{n_1, n_2\}$ which do contain $n_2$ by doing Y. Self-check: do you remember what X and Y are?

heather

@0celo7 you taught me what a cartesian product is, i think.

David Z

@heather It's kind of the same thing I'm trying to explain

0celo7

@heather then you should come to the dark side and learn my proof

heather

X: is taking the empty set and n1 itself. Y: is taking the subsets of {n1} and adding n2 to each subset.

@0celo7 sure, after I go through this way with DavidZ.

David Z

@heather You're right on Y

heather

11:49 PM

taking the empty set and the empty set and adding n1 to the second?

David Z

But for X, remember that you start with the subsets of $\{n_1\}$, which are $\{\}$ and $\{n_1\}$. What do you have to do to that collection of subsets to get the subsets of $\{n_1,n_2\}$ which don't contain $n_2$?

heather

nothing?

David Z

Yeah, exactly. X is "do nothing".

So, to recap: you start with the subsets of $\{n_1\}$. Then from there, you can get the subsets of $\{n_1,n_2\}$ which don't contain $n_2$ by doing nothing, and you can get the subsets of $\{n_1, n_2\}$ which do contain $n_2$ by adding $n_2$.

heather

right.

David Z

And together, those two collections of subsets make up all the subsets of $\{n_1, n_2\}$. Does that make sense?

heather

11:52 PM

right.

yes, it does.

David Z

So now you have a procedure for starting with the subsets of $\{n_1\}$ and turning them into all the subsets of $\{n_1, n_2\}$. Clear?

heather

right.

David Z

Then, what does that procedure do to the number of subsets?

heather

it...multiplies the number of subsets of {n1} by two?

because you add n2 to each one?

David Z

@heather Well, you add $n_2$ to each one, and also keep the original.

heather

11:57 PM

right, yeah.

David Z

But yes, it multiplies the number of subsets by two.

Now, can you try using this procedure, starting with the subsets of $\{n_1,n_2\}$, to obtain the subsets of $\{n_1,n_2,n_3\}$?

heather

well, that would give the subsets that don't contain n3, I think.

David Z

@heather Can you elaborate on your reasoning?

heather

it's like before, just "scaled up".

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