Mathematics - 2016-05-04 (page 2 of 5)

@Brody keep in mind that this is not entirely a "non-problem". it is not (and cannot) be a theorem that ZFC is consistent. one could, in principle, prove that it's inconsistent by showing that from ZFC follows some absurdity.

but it's pretty unlikely someone's going to find one.

Forever Mozart

yes that's how most people feel

Brody

but most are pretty confident in its consistency no?

at least so far I haven't seen any strong reservations about zfc or anything weaker

Forever Mozart

either that or they don't care... most of the axioms are so intuitively simple that platonic ideas can be expressed without worrying about them too much

Balarka Sen

@MikeMiller: I am looking at the Kronheimer's lecture on the four color theorem & instanton homology right now. That's a pretty crazy idea.

Mike Miller

there were two, is that the first?

Balarka Sen

6:32 AM

Right, the first one.

Mike Miller

gotcha

Balarka Sen

He's defining the Tait coloring as a homomorphism from $\pi_1(\Bbb R^3 - G) \to \Bbb Z/2 \times \Bbb Z/2$. And suddenly he embeds the Klein 4 group into $SO(3)$.

Mike Miller

sure

Balarka Sen

Let's see how quickly it gets too technical for me.

Forever Mozart

obviously

Balarka Sen

6:36 AM

Ah, just two slides.

Mike Miller

what did he do to you

Balarka Sen

It took two slides till we got to "Chern Simons", "Morse Smale" and "Morse homology"

I stopped watching.

Mike Miller

seems hard to learn something by not doing so :)

i remembered the lectures being quite lucid but i'm probably not allowed to have opinions on that

Balarka Sen

I fast forwarded ahead a bit and figured it was a genuine technicality. He didn't explain what he did to me there. So I am really stopping watching, perhaps for the greater good.

Mike Miller

I don't know what a "genuine technicality" is.

Forever Mozart

6:43 AM

the greater good

will kill us all

Brody

if it makes you feel better, one slide gave me a mild palpitation

but tis all french to me

Balarka Sen

@MikeMiller He took the "character variety" of reps of $\pi_1$ into $SO(3)$, realized it as critical set of "Chern Simons functional", something something "Morse Smale" and voila compute it's "Morse homology" to get the instanton homology of the embedded web (if I remember it right). The only mild genuine technicality about this particular slide is that I don't know what any of that means ;)

Technicality is relative, I realize, though.

Mike Miller

I don't know what genuine means, is all.

Sometimes one believes things and moves on. It is not natural to expect one will understand everything in a talk.

But sure.

Balarka Sen

oh, that he doesn't explain this in later slides, that's all.

do you truly want to encourage me to see the whole talk? ;)

Mike Miller

This is general advice.

Balarka Sen

6:54 AM

Ah, Ok. I agree with what you said.

Mike Miller

It also applies in this scenario. As you are a human being with agency and whatnot, you may choose to do what you want here.

Balarka Sen

I do realize. I was merely joking.

I am not watching the rest of the talk because I don't want to. I'll rather get some sleep or get more work done.

Brody

another season may yield more fruit

or rather, preferring quality over number, fatter and juicier fruit

Balarka Sen

@Brody mmhmm.

Forever Mozart

what

Brody

7:02 AM

turns out cramming for a morning final at 3 am wasn't such a bright idea

Mike Miller

Cramming is rarely a good idea.

Forever Mozart

i did it as an undergrad. thats how it goes

Brody

earlier fruit comment referring to you watching the lecture, of course @balarka

Forever Mozart

my students probably all hate me. fk em

Brody

mozart had some predilection toward poo poo

Balarka Sen

7:06 AM

I know. I interpreted it as "may appreciate the talk more if I watched it later".

Brody

was thinking more mechanically, like absorbing information

but yea that too

Forever Mozart

lol what?

Brody

@ForeverMozart < mozart liked poo poo

Forever Mozart

how?

Balarka Sen

@Brody You should head to bed if you don't want to fall asleep on your exam!

Brody

7:08 AM

Mozart and scatology

Wolfgang Amadeus Mozart displayed scatological humour in his letters and a few recreational compositions. This material has long been a puzzle for Mozart scholarship. One view held by scholars deals with the scatology by seeking an understanding of the role of it in Mozart's family, his society and his times, while another view holds that such humor was the result of an "impressive list" of psychiatric conditions from which Mozart is claimed to have suffered. == Examples == A letter of 5 November 1777 to Mozart's cousin Maria Anna Thekla Mozart is an example of Mozart's use of scatology....

Forever Mozart

scatological means poo poo

?

Brody

@balarka no u

"we all know how our own bodies work, i think"

Balarka Sen

It was a friendly suggestion.

Forever Mozart

dont hate on Balarka

I'll be back in 10 minutes...

Brody

sorry balarka, i appreciate your concern

Balarka Sen

7:10 AM

Nah, it's ok.

FYI I haven't slept all night and it's 1 pm.

Brody

it's later morning, so i'll still get 6+ hrs

o wow @balarka

that's kinda bad

Balarka Sen

That's the point.

Brody

okay mr. sen, i'm convinced. god willing i will see you another time

perhaps you can get some rest too soon

Balarka Sen

Does that mean I might die and you may never see me again, or you might die and I will never see you again, or we both might die and never see each other again? I am confused.

Brody

death is sufficient but not necessary

Balarka Sen

7:18 AM

Good luck on your exam, in any case!

Brody

i may just decide on a whim to burn all my possessions and journey the kodak

Balarka Sen

That's your plan when you fail your exams? ;)

Brody

yep

Balarka Sen

I'd say that's a pretty thin chance of happening then.

Brody

will a pastoral hiatus make me a better mathematician?

Balarka Sen

7:20 AM

Something tells me I don't want to know what that is.

Brody

living off the land and my cows. will my cows give me groundbreaking epiphanies?

Balarka Sen

Who knows.

Brody

mmm at least you seem pretty contained for being so sleep deprived

Balarka Sen

Practice.

Brody

People don't know that descents into insanity are often willful in some sense

Like a child exaggerating their emotional state to elicit reaction

But that's just the initiative. At a point you'd convince yourself of the fabrication and become truly insane

Balarka Sen

7:27 AM

Not sure the context in what you mention those. Sometimes your metaphors are hard to interpret.

Brody

ambiguity is the intellect's breast milk

Balarka Sen

...

Mike Miller

i like this guy

Brody

the last one was pretty clear

Balarka Sen

that's twice i heard an appreciative statement about somebody from you today, Mike. what is wrong with you? are you even the real one?

Brody

7:31 AM

it also speaks of itself

"haha that's soooo meta bro"

BACK

going to bed. gn all

g'night.

burnin the midnight oil

if you want a good book to help you sleep, I suggest Albert Camus "The Plague"

put on the audiobook

Balarka Sen

Interesting. I'll note that down.

Forever Mozart

7:39 AM

that is my favorite book

because it shows you how different people choose to live amongst death

it's an allegory

Balarka Sen

sounds like something I'd want to read.

Forever Mozart

have you ever read Camus?

Balarka Sen

no, not really.

Forever Mozart

The Stranger is his most famous book

it is short but devastating

Balarka Sen

sounds like an existentialism guy

Forever Mozart

7:42 AM

oh yes, one of the leaders

in 40's France

Balarka Sen

I have only ever read one such thing which may be labelled as existentialism, but it's pretty dense.

It's also my favorite.

Forever Mozart

Sartre? Dostoyevsky?

Balarka Sen

Beckett, Waiting for Godot :) I haven't read Dostoyevsky's existentialism stories.

But I'd say "Dream of a Ridiculous Man" was my favorite short story.

Forever Mozart

oh, I bought that once but never read it

Balarka Sen

I strongly recommend it.

Forever Mozart

7:45 AM

its a play

Balarka Sen

Mhm.

you read anything surrealistic/symbolic?

Forever Mozart

i dont think so

Balarka Sen

ar, alright.

you haven't read Gogol then, I suppose?

Forever Mozart

no

Balarka Sen

gotcha

Algebra 2015

7:57 AM

hello

I have this linear transformation:

imgur.com/I5xsYnO

a is a real number

linear transformation A is from real polynomial space of degree to into R3

How to write the matrix corresponding to L.T. A in standard basis of both spaces ?

Tobias Kildetoft

@Algebra2015 Well, what does the map do to the standard basis?

Algebra 2015

hm, "increase" it ?

Tobias Kildetoft

What? I mean write down the actual value it takes on each of the standard basis elements

Algebra 2015

$$\left( \begin{array}{ccc}
0 & 1 & 0 \\
3 & 1 & 1 \\
3 &3/2 & 1\end{array} \right)$$

i do not understand how the values of this matrix were calculated

poynom is: $ax3^2 + bx + c"

and I understand that R3 has 3 dimensions

Tobias Kildetoft

@Algebra2015 Well, that is clearly wrong as it has forgotten $a$

Algebra 2015

8:10 AM

1. what does this mean, how to use it, how to calculate it:

imgur.com/I5xsYnO

since A must be linear a=0

Tobias Kildetoft

@Algebra2015 Did we not go over a practically identical question here some time ago?

Algebra 2015

no

similiar

but quite different

pls help

Tobias Kildetoft

Why quite different? Did that one not also ask for the matrix in the standard basis?

Algebra 2015

but for other input data

since I would understand

tjank you

Tobias Kildetoft

that does not make it quite different.

You need to do precisely the same thing here, just with a different map

Algebra 2015

8:12 AM

thank

how from $ax3^2 + bx + c" get this matrix:

$$\left( \begin{array}{ccc}
0 & 1 & 0 \\
3 & 1 & 1 \\
3 &3/2 & 1\end{array} \right)$$

?

Tobias Kildetoft

@Algebra2015 You don't. Just like last time you first write up the standard basis

Algebra 2015

for polynom : is it 1, x and x^2 ?

Tobias Kildetoft

yes

Algebra 2015

and now ?

Tobias Kildetoft

then you write up what the map does to each of those

Algebra 2015

8:14 AM

how to get numbers of the matrix?

Tobias Kildetoft

@Algebra2015 I think you really need to look up what the matrix of a linear transformation in a given basis is before you try to do any more problems

Algebra 2015

p'(0) = c ?

2p (0) = 2c ?

p(1) = a+b+c ?

Tobias Kildetoft

@Algebra2015 Why is there a $c$ there? You are not supposed to do this for an arbitrary polynomial but just for the ones in the standard basis

Algebra 2015

pls help

Tobias Kildetoft

@Algebra2015 ignoring everything I say and then saying "pls help" is not going to make me want to help you

Algebra 2015

8:17 AM

i do not understnad, really

Tobias Kildetoft

@Algebra2015 you are also not doing as I say

Algebra 2015

i did read

but still do not get it

Tobias Kildetoft

@Algebra2015 There is nothing to "get". I asked you to input the standard basis elements into the function and you have yet to do that

Algebra 2015

i do not know which elements do u mean an how

Tobias Kildetoft

@Algebra2015 I asked you to write up the standard basis and you did this correctly. How can you then not input these into the function?

Algebra 2015

8:22 AM

p'(0) of 1 = 0 ?

Tobias Kildetoft

yes

Algebra 2015

or how.really i do not understant

p'(0) of x = c ?

Tobias Kildetoft

no, there is no c in the polynomial x

Algebra 2015

?

we have ax^2 + bx +c

Tobias Kildetoft

the polynomial is just $x$. There is no $c$ anywhere.

Algebra 2015

8:25 AM

why is than important this: ax^2 + bx +c

?

then

Tobias Kildetoft

@Algebra2015 Forget that thing for now, as you clearly do not really understand what it is.

Algebra 2015

i need to do it

Tobias Kildetoft

@Algebra2015 you need to apply the function to the polynomials $1$, $x$ and $x^2$

Algebra 2015

p'(0) of polynom x is 1 ?

Tobias Kildetoft

nowhere here will any $a$, $b$ or $c$ appear

yes

Algebra 2015

8:26 AM

ok

p'(0) of polynom x^2 = 2 or 0 ?

p' of x^2 =2x

Tobias Kildetoft

so when you set $x=0$ you get?

Algebra 2015

since x = 0 , then also p'(0) of polynom x^2 = 0 ?

right

I get 0

great

8:28 AM

so

correct me

rtathe 1 st line in the matrix : 0 1 0

reffers to calculations: p'(0) of polynom 1 = coefficient 1

p'(0) of polynom x = coefficient 0

p'(0) of polynom 1 x^2= coefficient 0

?

Tobias Kildetoft

except you got some of the switched around there compared to what you got before

Algebra 2015

I now explained the 1st line of this:

how from $ax3^2 + bx + c" get this matrix:
$$\left( \begin{array}{ccc}
0 & 1 & 0 \\
3 & 1 & 1 \\
3 &3/2 & 1\end{array} \right)$$

did I do it ok ?

Tobias Kildetoft

@Algebra2015 you still really need to stop trying to put those $a$, $b$, $c$ into this. They are nowhere in the problem and will appear nowhere

Algebra 2015

ok

2 p(0) + p (1) of polynom 1 = coefficient 3 = 2*1 + 1 = 3 ?
2 p(0) + p (1) of polynom x = coefficient 1 = 2*0 + 1*1 = 1 ?

2 p(0) + p (1) of polynom x^2 = coefficient 1 = 2*0 + 1*1 = 1 ?

Tobias Kildetoft

right

Algebra 2015

8:36 AM

3 integral of polynom x = coefficient 3/2 = 3*1/2 = 3/2 ?

3 integral of polynom 1 = coefficient 3 = 3*1 = 3 ?

Tobias Kildetoft

@Algebra2015 you need to actually calculate the integrals here

Algebra 2015

integral of x^2 = x^3/3

coefficient 1/3

*3 =1

Tobias Kildetoft

@Algebra2015 what coefficient? You are taking integral from $0$ to $1$

that this works out to one of the coefficients is a bit of a coincidence

Algebra 2015

I am right for presenting all alculations for the 9 numbers of the matrix:

$$\left( \begin{array}{ccc}
0 & 1 & 0 \\
3 & 1 & 1 \\
3 &3/2 & 1\end{array} \right)$$

?

integral of x = x^2 /2

*3 = 3/2

Tobias Kildetoft

@Algebra2015 I would not be convinced by your calculations for the last row

Algebra 2015

8:40 AM

this i called coefficinet or number to be put into matrix ?

why not ?

integral of 1 = x

=

?

*3 =3

??

Tobias Kildetoft

@Algebra2015 because you don't seem to understand why it works out to just one of the coefficients

Algebra 2015

pls explain

why is 3, 3/2 and 1 wrong ?

Tobias Kildetoft

@Algebra2015 Not sure what there is to explain. You are asked to calculate an integral from $0$ to $1$ and you reply with one of the coefficients of the indefinite integral. You never explain why it happens to equal this coefficient

Algebra 2015

why is 3, 3/2 and 1 wrong ?

Tobias Kildetoft

they are not, but your explanations for them are not convincing

Algebra 2015

8:43 AM

aaaa

ok

Algebra 2015

8:53 AM

how to interprete this matrix ?

btw how to be here shown picture from imgur correctly?

imgur.com/znTvoUo

i calculated and I got 500

since it is skew symetric

Tobias Kildetoft

I have no idea what you are talking about. The matrix you linked is symmetric, not skew symmetric. And calculated what?

Algebra 2015

ok

which numbers are to be put in blank space, also without dots

a-s and zeros ?

here is my question

n is a natural number

a is thoug a real number

what is the result for the nxn determinant

?

is 4*a^3 ?

Eric Stucky

9:11 AM

That seems pretty unlikely; you mean that no matter how big that matrix is you'll always get 4a^3 ?

Surely that isn't true if it's only 3x3.

Algebra 2015

(n-1)*a^(n-2) ?

Eric Stucky

i dunno, why do you think that?

Algebra 2015

ok. how then to calculate it?

Eric Stucky

I guess I would start by trying to just use the definition of determinant

That looks pretty tedious, though, so maybe some row operations first would help

Algebra 2015

this is symetric determinant

or ?

imgur.com/znTvoUo

Eric Stucky

9:16 AM

The matrix is symmetric, yes.

As Tobias already told you

Algebra 2015

so... how to tackle it

Eric Stucky

I already told you what I think?

Do you think this won't work?

Algebra 2015

I am asking...

have no idea

Eric Stucky

Quote:

I guess I would start by trying to just use the definition of determinant

That looks pretty tedious, though, so maybe some row operations first would help

Endquote.

Algebra 2015

is it ok for n=even equals to 0

anf for n=odd equals to (-1) ^(n/2)

Tobias Kildetoft

9:58 AM

To summarize the latest referee report I got: "This is a very interesting, original and inspiring paper. Here are some comments that show I did not understand what the paper is really about".

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$Mathematics$ Mathematics