Mathematics - 2016-11-28 (page 2 of 6)

Adeek

2:00 AM

is this a good definition what do you think ?

Ted Shifrin

Karim: Be consistent with your typesetting of $K$.

Akiva Weinberger

Yeah, don't have both $\rm K$ and $K$

Ted Shifrin

And you don't want set symbols around $\infty$ if you're defining the point.

Semiclassical

"Assume there is an $n$ such that $S_n$ is true. Then $S_{n + 1}$ is not true, so there is some $k > n + 1$ such that $S_k$ is true. But $S_k$ is not true because Sn is true and $k > n$. Assuming $S_n$ is true implies a contradiction, $S_k$ is true and not true, so our assumption is absurd. We must conclude for each $i$, the sentence $S_i$ is not true. But if $S_i$ is not true, it is also true, so we have the paradox that each sentence in Yablo's list is true and not true."

Akiva Weinberger

(Or K and K for those who don't have LaTeX on)

Ted Shifrin

2:00 AM

you left out $\mathbb K$, DogAteMy :)

Akiva Weinberger

k

Ted Shifrin

LOL

Adeek

what do you mean set symbols around $\infty$ ?

Semiclassical

What people have found interesting about Yablo's paradox (as that's called) is that it's referential but not self-referential

Ted Shifrin

you wrote "the point $\{\infty\}$." That's a set, not a point.

Akiva Weinberger

2:01 AM

Yeah, I see ^^

Semiclassical

And therefore doesn't seem to be circular in the way that the liar paradox is.

Secret

Given the outcome of the Yablo paradox analysis being $P \textrm{ and }-P$ I wonder if such statement has a consistent solution in the domain of inconsistent/paraconsistent logic...?

Akiva Weinberger

That makes it mildly horrifying

Ted Shifrin

AGGGH @Semiclassic resigns to checkmate

Semiclassical

What I always found interesting is that it ceases to be a paradox if one only has finitely many statements in the list.

Akiva Weinberger

2:02 AM

Right.

Adeek

good ?

Ted Shifrin

no, say point and leave off the set brackets.

Semiclassical

So it's paradoxical only in the $n\to\infty$ limit :)

Adeek

alright

Akiva Weinberger

@Semiclassical Not even in the limit, just at actual $\infty$

Ted Shifrin

2:03 AM

But what does the point $\infty$ mean, actually? Are you in $\Bbb P^2$ or $\Bbb P^1\times\Bbb P^1$?

Semiclassical

True.

Either that, or take there to be a statement at infinity :)

Akiva Weinberger

$\lim_{k\to\infty}\text{(1 if it's a paradox and 0 otherwise)}=0$

Ted Shifrin

I'm not sure I'd display the final inequality. In-line is fine.

Semiclassical

Heh.

Ted Shifrin

I guess you're stipulating one-point compactification. I withdraw my first complaint.

Adeek

2:04 AM

$\mathbb{P}^2$ But I don't need to be that rigorous prof mentioned that I shouldn't define it in terms of projective plane.

Mike Miller

@TedShifrin Is that a Socratic question, or should I answer?

Ted Shifrin

I was asking Karim, not you, @MikeM.

Mike Miller

So the former.

Ted Shifrin

If you must :D

Semiclassical

I like how Ted's talking about projective space when just jokingly suggested that it ceases to be a paradox if you suppose that Yablo's list contains a true statement at infinity :>

Ted Shifrin

2:05 AM

I did it on porpoise, @Semiclassic.

Semiclassical

oh deer

Ted Shifrin

Don't have a cow about it.

Semiclassical

We're being pretty dogged with these puns.

Ted Shifrin

And some are more catty than others.

Akiva Weinberger

Hm. For what ordinals does the set $\{S_k:k\in\alpha\}$ become paradoxical?

The limit ones probably

Mike Miller

2:06 AM

what is $S_k$?

Adeek

No if I do the projective plane etc I have to define how we define the projective plane and stuff.

Ted Shifrin

Karim, for whom is this paper written?

Secret

Let S_1 be true
Let S_2 be true. Then S_1 is false
Let S_3 be true. Then S_2 is false, then S_1 is true
Let S_4 be true. Then S_3 is false, then S_2 is true, then S_1 is true

Extrapolating to infinity, we found that the truth value of S_n depends on the truth value of S_n+1. Since there is no single n+1=infinity, the sequence $\{S_a\}_{a\in \mathbb{N}}$ have no well defined truth value unless it is paraconsistent

Semiclassical

$S_k:$"$S_j$ is false for every $j>k$."

Akiva Weinberger

@MikeMiller The statements of Yablo's paradox, $“\forall i>k,\lnot S_i”$

@Semiclassical If it's fine with successor ordinals, then the problem isn't that there's infinitely many, it's that there's no last one, which is a subtle difference

Adeek

2:08 AM

@TedShifrin this is first year grad algebra class. She told me know who is your audience. Most of the people in the class didn't take geometry course with me, so they don't know about projective plane.

Semiclassical

Yeah.

If the domain of S_k is finite, it's consistent since you can take every statement but the second-to-last as true.

Adeek

@TedShifrin I am doing it mainly on elliptic curves and elliptic curve cryptography.

Semiclassical

That's what Secret pointed out above.

Mike Miller

meh

Semiclassical

Interestingly, in the context of the talk he translated it into a claim about graphs.

I don't remember what that claim -was- but hey

Akiva Weinberger

2:09 AM

Interesting. (Possibly.)

Ted Shifrin

OK, so everyone in the class is supposed to read your paper. Fair enough.

Semiclassical

Something about kernels of digraphs.

Adeek

I also have it already and 13 pages and I am not nearly done she mentioned it needs to be 10 pages, but if it super interesting maximum it should be 20 pages.

Akiva Weinberger

What's a digraph @Semiclassical

Semiclassical

Directed graph

Akiva Weinberger

2:13 AM

Ah

Adeek

is this good English ?

There is a natural way to define a binary operation on E which makes E into a group.

Akiva Weinberger

I'd probably want a comma in there

"on E, which"

Wait no

Never mind

That changes the meaning

@Adeek Change "which" to "that"?

Adeek

yeah

"There is a natural way to define a binary operation on E that makes E into a group."

Akiva Weinberger

Yeah that sounds better

Ted Shifrin

DogAteMy: Native English speakers mostly screw up "which" and "that." :)

Secret

2:19 AM

[scifi context?] Actually, I suspect Yablo paradox can be used as a proof pathway to show that the liar paradox is inconsistent, because the liar paradox seemed to act like the yablo paradox except with all statement equal to itself as a requirement of self rerential.

Meanwhile, the grandfather paradox can be modelled with a logical structure that it reverses its truth value after a fixed period T, thus the Yablo paradox can be applied to that context by imposing a period T as the delay it takes before the S_n+1 th statement appear, hence reversing the truth value of all previous statements.

Ted Shifrin

DogAteMy: You'll be amused to know that with all the four books I've written, I've done a search on "which" and "that" to make sure I had them all correct.

Akiva Weinberger

@Secret I'm not quite sure I understand what you're getting at, but I think this is related to my statement on how $\lim_{k\to\infty}(\text{1 if the version with $k$ statements is a paradox and 0 if not})=0$

Semiclassical

A Yablo list of k statements is not paradoxical, but a Yablo list of countably infinite statements is paradoxical.

Adeek

The discriminant being non-zero implies there is no repeated roots ?

Akiva Weinberger

@TedShifrin But you can see why my first instinct was to put a comma in, right? Because "which" needs a comma (even though "that" doesn't).

@Semiclassical Not necessarily — make the indices the negative integers rather than the positive ones

Semiclassical

2:23 AM

Ah, yes.

Akiva Weinberger

Make $S_{-1}$ true and $S_{n},n<-1$ false

Ted Shifrin

I'm not complaining you were wrong, DogAteMy. You rarely are.

Semiclassical

Yeah.

Akiva Weinberger

or $S_{-2}$ true and the rest false

Ted Shifrin

Karim: Yes (not that I know the context).

Secret

2:25 AM

Well, the liar paradox does look like the yablo paradox except that all statements are the same statement

and the grandfather paradox is like a yablo paradox where going from statement n to statement n+1 has a fixed delay of time t.

So they are both similar , and possibly specific cases of yablo paradox as they all reverses the truth value of their previous statements, and is only consistent if the set is finite as semiclassial pointed out

Mike Miller

yablo is a funny word to ay

Akiva Weinberger

Is it "yab" or "yahb"

Semiclassical

I think it was Yah-blow

and yes, it is funny

Akiva Weinberger

(Extra credit: For those who don't speak with the cot–caught merger, is it pronounced with the vowel in cot or the vowel in caught)

Adeek

oh oke

Ted Shifrin

2:27 AM

spews GHOTI at DogAteMy

Akiva Weinberger

@TedShifrin I feel like you'd speak without the merger.

Mike Miller

don't you mean for those who have decided to differentiate the two

Secret

typo: (forgot Alkiva's analysis) or when the "$\infty$th" term is specified, as what the negative numebr case is doing

Akiva Weinberger

I mean, there are videos of you speaking out there so I could check if I wanted to

Adeek

Ted Shifrin

2:28 AM

DogAteMy: Do you know the famous G.B. Shaw GHOTI?

Akiva Weinberger

Yeah

Adeek

for theorem 2.1 I would like to the reference for this result

Ted Shifrin

I withdraw.

Adeek

do I add it just beside it ?

as (see [8])

Akiva Weinberger

But that's more about making fun of English spelling than pronunciation

Adeek

2:29 AM

theorem 2.1 : .... (see [8])

Ted Shifrin

no, DogAteMy, it's precisely making fun of English pronunciation and its illogic.

Akiva Weinberger

But it's all about how, for example, the "gh" means so many different things in different contexts. That's spelling

Ted Shifrin

Ordinarily, you'd put Proof. and then see [8], but it's not a huge deal now, Karim. You will need to learn this all in the end.

Mike Miller

akiva's distinction is between dialects and pronunciation

Ted Shifrin

We're not doing dialects here.

Akiva Weinberger

2:30 AM

I am

Mike Miller

yes we are; he was just talking about the caught-cot distinction

Ted Shifrin

Regions perhaps, not dialects. But OK. My GHOTI had nothing to do with either.

Akiva Weinberger

Also, something you might not have thought about: In my accent, at least, the words "writer" and "rider" are pronounced with identical consonants and different vowels.

Ted Shifrin

HUH?

I speak California, New England, and Southern, and I can't parse that.

Mike Miller

there is a t/d distinction in ca

Akiva Weinberger

2:32 AM

The 't' and 'd' both become more of a 'd'-sound because of intervocalic flapping, a thing most Americans have

Adeek

@TedShifrin I just want to reference a proof found in a book ?

Ted Shifrin

How does the f***ing vowel change?

Adeek

I have my list of reference and 8 is the one that I need.

Akiva Weinberger

and the 'i's suffer the price–prize split, an instance of "Canadian raising" that a growing number of Americans have.

Ted Shifrin

I know, Karim. I would put it after Proof. But you can put it after Theorem 2.1.

I want my linguist friend from UGA back ...

Akiva Weinberger

2:33 AM

https://en.wikipedia.org/wiki/Canadian_raising

Ted Shifrin

crawls in a whole :D

Mike Miller

@TedShifrin for me, rider is more of an aye, and writer is more of an... uh,... hard to say, but it's shorter

Ted Shifrin

Identical for me, @MikeM.

Akiva Weinberger

uh-ih rather than ah-ih

Mike Miller

the eis the same for me tho

Akiva Weinberger

2:34 AM

Me too. (Did you mean to put a space between "e" and "is")

Ted Shifrin

DogAteMy needs to be a linguist, although I thought he'd make a damned good mathematician.

Akiva Weinberger

I can have other interests, can't I?

Also thank you

Mike Miller

or he could be a popular anarcho-syndicalist

Akiva Weinberger

i wut

Ted Shifrin

I have other interests, including food and languages. I'm just saying ...

Akiva Weinberger

2:36 AM

For what it's worth, the Wikipedia page I linked to actually has a recording of "rider writer" on it

Adeek

next summer I should enroll in some english class.

I want to improve my writting.

Ted Shifrin

LOL, Karim.

It's tough to do everything.

Mike Miller

interests: math; film; political engagement through the modern labor movement, esp in an academic context

Ted Shifrin

But I admire your attitude.

Mike Miller

i wanted to sign up for a film crit class but really do not have the time

Adeek

2:38 AM

yeah. My writing isn't really academic. I want to improve it.

Ted Shifrin

I would put "disgust with politics" on my list, @MikeM :D

Mike Miller

disgust won't fix the situ

Akiva Weinberger

Will writing political blog posts that no one reads fix it?

Semiclassical

Here's a lefty sort of question, then.

Mike Miller

nope

Akiva Weinberger

2:39 AM

'Cause that's already too much effort for me

Ted Shifrin

Even if people read them, does that fix anything? ... It's a tough question. My bridge partner asked me this afternoon what we should be doing.

Semiclassical

To what extent, and in what manner, can mathematics be used in the service of political action? (not liking the wording of that)

Akiva Weinberger

@TedShifrin Actually, you're in CA, so you hear a lot of Spanish, right? The 't' and 'd' in "writer/rider" kind of turns into the 'r' sound of Spanish. (Not the 'rr', the 'r')

Semiclassical

By that I don't mean politicization of mathematics

But rather, to what extent does math 'matter' when it comes to politics?

Mike Miller

@Ted I can talk to activists I know about this and possibly try to put them in touch.

Akiva Weinberger

2:41 AM

Statistics and finances probably matter to politics

Mike Miller

That's the eternal question. I've been reaching out about it lately. For the moment, the answer is probably 'nothing'.

Ted Shifrin

DogAteMy: I'm wrestling with trying to learn some Spanish. Get back to me in a year :)

Akiva Weinberger

Politics, by the way, comes from poly- meaning "many" and tics meaning "bloodsucking creatures"

Ted Shifrin

Math matters when it comes to the politics of education ...

smacks DogAteMy

Mike Miller

@Semiclassical applied math produces some toxic research, eg predictive policing.

Secret

2:42 AM

ipam.ucla.edu/programs/workshops/mathematics-of-politics

Semiclassical

I'd count derivatives as another toxic output

Akiva Weinberger

@MikeMiller Applied math also literally produces some toxic research

Semiclassical

And financial products in general.

Mike Miller

yup

Akiva Weinberger

in the form of toxicology

Ted Shifrin

2:43 AM

And then there's the atomic bomb ...

Akiva Weinberger

which uses math probably

Secret

Most things are complex systems nowadays and since they are complex systems, they involve networks, and when it comes to networks graph theory is important

Mike Miller

whether or not I'll stay in academia, regardless of the job search, is a serious question on my mind

Semiclassical

More generally, algorithms and machine learning

Mike Miller

same with many people I know.

Ted Shifrin

2:43 AM

I understand, @MikeM, but in some sense I'm sad because you are a math talent.

Semiclassical

To what extent has the math become a machine that people in power use to exploit/extract from others?

Ted Shifrin

hides from @Kaj

Akiva Weinberger

Hi Kaj

Kaj Hansen

Wise choice @Ted :)

Hey there

Ted Shifrin

BTW, much nicer seeing your handsome face than a black box :P

Mike Miller

2:45 AM

appreciate the compliment, but it's still a matter of whether I'm doing good. at least working in math means I'm not doing any bad, unlike I'd argue many of the standard alternatives (none of which I'd do)

Kaj Hansen

haha, I made that in MSPaint a while back

Semiclassical

It sorta goes to the question of "what kind of math should people know?"

Mike Miller

i'm going to finish the PhD at least, since one of the possibilities on my mind is staying involved w the academic labor movement.

Semiclassical

I mean, there's the stuff I like, and there's more rarefied things (some of which I like, some of which I don't like)

Mike Miller

@Semiclassical see cathy o'neill's book

Semiclassical

2:45 AM

I've been meaning to read that.

Mike Miller

read it with me over xmas?

Semiclassical

And for precisely that reason.

I'll see what I can do.

I mean, on the one hand, I hate the whole "oh i'm just bad at math" notion

Mike Miller

thx for reminding me; just ordered

Ted Shifrin

Academia is becoming a mess unto itself, no question. I felt like I was contributing by teaching thousands ... but I never intended to be a research super-star.

Akiva Weinberger

imgur.com/QwQvDpL

Nice thing I found

Mike Miller

2:47 AM

certainly if I stay in research the contribution I make will be in teaching / advising

Semiclassical

On the other hand, the kind of math I find interesting is probably just plain useless

Kaj Hansen

What's your pic @Ted? It's reminiscent of a one-sheet hyperboloid topped off with cones?

Mike Miller

@Semiclassical Me too, but I think that's good

Semiclassical

I guess you could say a similar thing about art.

Mike Miller

@KajHansen exercise

Ted Shifrin

2:47 AM

Right, @Kaj. It's the shape you get by spinning a cube about a long diagonal. :)

Semiclassical

Of course, that's what Hardy thought. And now we have the NSA :P

Mike Miller

they'll take Floer homology from my cold f-ing hands

Semiclassical

lol

Adeek

Kaj Hansen

Oh neat. And I do to some extent @Mike. Lots of calisthenics.

Akiva Weinberger

2:48 AM

@TedShifrin Oh my god

Mike Miller

-_-

Adeek

do you guys think I should add this line explaining why we care about $\Delta_E \neq 0$ ?

Ted Shifrin

Good exercise, DogAteMy.

Kaj Hansen

Unless you're referring to Ted's pic :P

Ted Shifrin

Yes, Karim.

Mike Miller

2:49 AM

I was

Kaj Hansen

hahaha

Mike Miller

I feel uncomfortable about teaching at a SLAC b/c it seems to me I'm mainly contributing to education inequality

Ted Shifrin

smacks Kaj for good measure

what's SLAC?

Semiclassical

southern los angeles college? guessing

Akiva Weinberger

@Adeek "Have"?

Mike Miller

2:50 AM

small liberal arts

Ted Shifrin

DogAteMy has a better occupation: editor.

Adeek

have ?

Semiclassical

I guess part of my other motivation in all of this is the sense, from the last election, that there's such a huge disconnect within US culture.

Adeek

@AkivaWeinberger have where ?

oh

nvm

has no repeated roots.

Akiva Weinberger

In the theorem

Yeah

Ted Shifrin

2:50 AM

But you would not be happy teaching at a state 2-year college, Mike.

Mike Miller

would I not? that's definitely more important work.

very proud of a friend of mine from undergrad who did that. she's a great teacher doing good.

Ted Shifrin

I agree, but I'm not sure you've got the patience.

Semiclassical

@TedShifrin The thing I always find awkward is when people hear "I liked working with students as a TA" and respond "oh, so you want to be a teacher"

I love interacting with students, but I am -not- responsible enough to be in education.

Ted Shifrin

Huh? @Semiclassic ...

Mike Miller

yeah, that's probably fair...

meow-mix

2:51 AM

hi everyone

Akiva Weinberger

Hey

Ted Shifrin

There's @meow!

I would not call you irresponsible based on what I know, @Semiclassic.

Semiclassical

Um

Akiva Weinberger

We were discussing politics, which in turn is something that is discussed in toxicology probably

Secret

yeah same, I cannot teach because I cannot handle barrage of questions, despite I like to ask a barrage of question myself back in my student days

Semiclassical

2:52 AM

You do realize you're talking to someone who is still in limbo precisely because he can't be arsed to get his oral exam done?

Mike Miller

@Semi We should actively poke each other to write

& do our oral exams

Semiclassical

Yeah.

Right now, what I should be doing is grading lab reports.

Ted Shifrin

I think MSE chat is the downfall of many of you.

Akiva Weinberger

Someone poke me to read the thirteen pages of history textbook I need to be reading

Ted Shifrin

Go away!

Mike Miller

2:53 AM

@AkivaWeinberger who wrote it and what's it about

Semiclassical

Eh. I question that logic.

Akiva Weinberger

@MikeMiller Who wrote the textbook??

meow-mix

@TedShifrin whenever i'm on, you're not on, and vice versa :P

Semiclassical

More generally, I question the logic of people who treat the distraction as the problem when it's the distractibility that's the real issue

Akiva Weinberger

Uh, Divine, Breen, Fredrickson, and Williams according to the cover

Ted Shifrin

2:54 AM

Not exactly, @meow. So what's your question? Before I go cook dinner?

Akiva Weinberger

(Of course, Uh wrote most of it)

meow-mix

so it's about exercise 4

Ted Shifrin

OK ... I looked it up.

meow-mix

by a line do you mean a line in $\mathbb{R}^n$? or in projective space

Semiclassical

I do want to do some writing about the Griffiths-Dwork stuff I partially understand now

Ted Shifrin

2:55 AM

No, I mean a line in $\Bbb P^2$.

meow-mix

ok

Ted Shifrin

We're talking Lemma 2.5.

Semiclassical

Though I'd still like to figure out that question I posed earlier

Mike Miller

@Akiva read it then go read some Hegel

Semiclassical

Psh, read Kant

(don't actually read Kant directly, it's painful)

Akiva Weinberger

2:56 AM

I kan't

Ted Shifrin

Not to mention Heidegger. ... (I am not a philosophy person.)

Hesitantly ducks

smacks DogAteMy

There we go

Indeed.

2:56 AM

Oh Lord Hegel....

Akiva Weinberger

I'd rather read some Conway

Kaj Hansen

"The self-same consciousness which repels itself from itself, becomes aware of being an element existing in itself. But to itself it is this element to begin with only as universal reality in general, and not as this essential reality appears when developed in all the manifold details it contains, when the process of its being brings out all its fullness of content."

Akiva Weinberger

or Euler

Semiclassical

About the only thing by Kant that I know of as easily readable is his lectures on ethics, and that's something that was transcribed by one of his students.

Mike Miller

actually I really strongly recommend zizek's less than nothing

Semiclassical

2:57 AM

Zizek is weird

Ted Shifrin

Ethics ... Lack thereof brings us full circle back to politics.

Semiclassical

though if you mention Lacan I'll have to eye you dubiously

Akiva Weinberger

OK bye I'm reading history now

Ted Shifrin