Mathematics - 2017-06-19 (page 4 of 7)

Secret

12:00

Indeed, the rigorous statement is $\Bbb{Q}$ is dense in $\Bbb{R}$. A few minutes ago, however we are talking about how mathematical objects are illustrated when communicating them to the public

which is why the discussion tone becomes the intuitive tone

I wonder if any software can plot the following discontinous everywhere function:

SteamyRoot

If you're implying that "communicating to the public" should mean you can just do everything "intuitively", I heavily disagree. Whatever you say or show to the public can be intuitive or in an intuitive tone, but you should be able to back everything in a mathematically rigorous way.

Secret

That's what I am thinking. Intuition first, then the rigor (since past experience they tend to get either bored or scared of the rigor if presented first). I am still learning how to do the balance...

Leaky Nun

@Secret linearly plot all the rationals on a line?

Can you plot them quadraticly?

SteamyRoot

@Secret Actually, no, this is what I disagree with.

Rigour first, then explain it in an intuitive way.

Leaky Nun

I would say that it depends on the branch, and that intuition can also be important.

Secret

12:10

@SteamyRoot But how to keep them from getting bored (or even scared) because you are showing equations first on the screen?

SteamyRoot

@Secret You don't have to show the rigorous part.

Leaky Nun

Oh, it's about communicating to the public. In that case, I would say that it depends on the audience.

SteamyRoot

You can leave it all behind, but you need to have done it for yourself.

Akiva Weinberger

You can also biject the rationals (in an order-preserving way) to the set of intervals "missing" from the Cantor set. (Meaning, the connected components of its complement of finite length)

Leaky Nun

Every rational?

Akiva Weinberger

12:12

Yeah

Leaky Nun

That's interesting.

Akiva Weinberger

It's easy to biject it with the dyadic rationals ($\frac n{2^d}$)

Secret

@SteamyRoot Ah I see, I initially thought you mean to do both the rigor and the intuition in front of the audience

Akiva Weinberger

but it turns out that you can biject the dyadic rationals with the rationals in an order-preserving way as well

(You can derive this by staring at the Ford circles. The bijection is called the Minkowski question mark function.)

SteamyRoot

@Secret Ah, no. That definitely won't go well with certain audiences.

Akiva Weinberger

12:13

https://en.m.wikipedia.org/wiki/Minkowski's_question_mark_function

Secret

@SteamyRoot which is why sometimes when I think about how to communicate maths to the public and make them not so scare of it and realise it is interesting, I get my brain tied to knots

Leaky Nun

@AkivaWeinberger ?

Akiva Weinberger

@LeakyNun Indeed.

Secret

because you don't want to go all intuition because people will otherwise see you as handwavy, but you also don't want them to be scared away by formulae and stuff

SteamyRoot

@Secret Well, it's okay to be handwavey sometimes. But if a question from the audience comes, you have to be able to justify it.

Akiva Weinberger

12:16

If you draw Thomae's function with the vertical line segments, you can write the name of each rational on top of its line

and then it looks like you just have a bunch of line segments pointing from the name of the rational to its location on the real line

Secret

@LeakyNun I suspect that will not work, because there are always a rational between any two rationals, so you still basically plotting more or less a dense set (I think the rigorous version will be, the image of the rationals under the map $x\mapsto x^2$ will still give a dense set)

Akiva Weinberger

(You could draw the labels at different sizes in such a way to fit them all)

(Specifically, translate each Ford circle upwards by the value of Thomae's function at that point, and make sure the label fits inside the corresponding circle)

Secret

@SteamyRoot Of course, if one is going to be doing a public presentation, they will be ready both intuitively and rigorously

Leaky Nun

@Secret you took it seriously... it was meant as a ridicule on the choice of word "linearly plot"

Akiva Weinberger

In any case, I don't see any good way to visualize the _ir_rational numbers other than just saying "the limit points of the graph of Thomae's function"

Leaky Nun

12:20

Dirichlet function anyone?

Akiva Weinberger

I mean, in practice, I just imagine a dotted line of some sort. Maybe drawn in a very dark ink to show that it's measure $1$ per unit.

Secret

What happens if we attempt to plot the following (known to be nowhere continuous) graph:

$$f(x)=\left\{\begin{matrix} 1\text{ if }x=0 \\0\text{ if }x=\frac{p}{q},gcd(p,q)=1 \\ x \text{ otherwise}\end{matrix}\right.$$

Akiva Weinberger

That's just $x$ times Dirichlet's function?

Leaky Nun

@AkivaWeinberger no, it's 0 at rationals

...and x at irrationals

@Secret you get a graph of y=x... juxtaposed with a graph of y=0... and the point (0,1)

Akiva Weinberger

Oh, redefined at the origin

Secret

12:26

41 mins ago, by Akiva Weinberger

@Secret As I mentioned, the set of isolated points in any subset of space is countable. So an approach along the lines of Thomae's function is guaranteed not to work.

Akiva Weinberger

The $\gcd(p,q)=1$ adds nothing.

Secret

Basically, I swapped some of the lines in the definition of the Thomae function, and noting that this new function should be nowhere continous since wikipedia gave a proof that a continuous at rational but discontinous as irrational function is impossible

More explicitly:

and I think Leaky is correct in what the resulting graph might look like

(so that is not helpful in visualising the irrationals...)

Akiva Weinberger

Nice way of writing the letter $x$

That is in my top three favorite ways of writing the letter $x$ in math

Waiting

@Justwinbaby long time no see. :-)

@Secret how is it going?

I just considered a break from work (8 hours or so of ceaseless work)

Astyx

Is there only one way to define the square root function on the positive reals such that it is a group morphism ?

Just win baby

12:35

Hello @Waiting :-)

Waiting

@Justwinbaby how are you doing these day? :-)

Secret

Nothing much:
1. Chemistry: Have read how to use a 2nd program in my PhD, and I just sent some calculations in, hopefully they will run smoothly

2. Chat crawling: Currently at 13/2/2015

3. Maths: We are discussing higher dimensional geometry, then discuss about communicate maths with public and now the structure of irrationals and how to visualise them, as well how a maths person should balance between rigor and intuition

Akiva Weinberger

@Astyx How else would you define it?

Leaky Nun

@Astyx Well, if you specified the function, then there is only one way

I mean, you basically told us what each element maps to.

Just win baby

Fine thanks @Waiting how are you?

Leaky Nun

12:36

Oh, you haven't specified the group operation.

Akiva Weinberger

It's strange how we jumped from visualizing the fourth dimension to visualizing the rationals (or irrationals)

Leaky Nun

$\sqrt{f_1(x,y)} = f_2(\sqrt x,\sqrt y)$

Astyx

I meant : does there exist a unique group morphism R from the positive reals to the nonzero reals such that R (x)^2=x

Leaky Nun

It seems plausible that the functional equation above has infinitely many solutions @Astyx

@Astyx oh...

Akiva Weinberger

$R:\Bbb R_{>0}\to\Bbb R^\times$

Waiting

12:37

@Secret Intuition means a lot to me. Actually I think it's even more than that, sometimes I feel the mathematical thoughts come to me in a special way but don't ask me to give you more details, I feel mathematics.

Leaky Nun

@Astyx No, because $R[\Bbb R^+] = \Bbb R$, and then I don't know what negative elements are supposed to map to.

Secret

@AkivaWeinberger Because they both fell under the same umbrella: chat.stackexchange.com/transcript/message/38217000#38217000

Akiva Weinberger

@LeakyNun The range could be a subset of the reals

Astyx

^

Secret

@Waiting I have intuitions too, though most of them are visual. What I lack is non-visual intuition, and I suspect as I continue to expose to more fine art and practice, I think I will soon get that

Just win baby

12:39

Chat crawling? @Secret

Leaky Nun

@AkivaWeinberger oh, sorry

Waiting

@Justwinbaby Not that bad, thanks. I'm working around some mathematical ideas of approaching some new integrals, never done before in the literature.

Just win baby

cool :-)

Akiva Weinberger

But yeah, Secret essentially said that the only math topics that the public likes that they can't visualize are higher dimensions and infinity. I said that's nonsense, you can totally visualize infinity.

Waiting

@Secret Yes, exposure is definitely mandatory. I agree with what you said.

Secret

12:41

@AkivaWeinberger and then Akiva showed me rationals representations I did not knew previosuly

Astyx

I'm basically asking wether there exists a morphism $\Bbb R \to \Bbb Z /2\Bbb Z$ unless I'm mistaken

Akiva Weinberger

Yeah. And then that's where we are now.

Secret

and that's how we end up in irrationals as according to my mind's tendency to wander to topics in the direction of increasing mind screwiness

SteamyRoot

@Astyx Group morphism? Ring morphism?

Waiting

@Secret I also think you have to work continuously without skipping days. I mean one has to work very hard daily and profoundly.

Akiva Weinberger

12:41

@Astyx Probably not without the axiom of choice.

Astyx

Group

Akiva Weinberger

@SteamyRoot Group, on $\Bbb R_>$

Or on $\Bbb R$, they're isomorphic

Secret

@Waiting Consider I dream of maths a lot, I think I am not worried about that since even my sleep is utilised for maths and my other subjects

SteamyRoot

Only the trivial morphism then, no?

Astyx

That's my question

Waiting

12:42

@Secret That's nice.

Astyx

Why is there no other morphism ?

SteamyRoot

Try to map something to $1$ and check if it's still a morphism

Akiva Weinberger

Oh, yeah

Yeah, if $f(x)=\bar1$, then $f(x/2)=?$

Secret

http://chat.stackexchange.com/transcript/message/38208092#38208092
Waiting: For example

Akiva Weinberger

This is for the domain being $(\Bbb R,+)$

Astyx

12:44

Damn I'm dumb

Waiting

@Secret Then you have to be extremely powerful mentally. No matter what you choose to do, there is that possibility to hear that what you do is something silly, stupid.

Astyx

Thanks for the help

Akiva Weinberger

No prob

@Astyx Nah

Astyx

Same goes for Q then I guess

Akiva Weinberger

I guess the way to write this is ${\rm Hom}(\Bbb R,\Bbb Z_2)=0$

Secret

12:45

@Waiting I am not terribly worried about that. My true self is the ability to convince ordinal people to join me into the world of bizarre and weirdness

(ordinary, too many ordinals in my mind recently...)

Akiva Weinberger

(or $=1$, they're the same in group theory anyway)

@Secret lol!

Waiting

@Secret That's great.

SteamyRoot

@AkivaWeinberger Technically, you write $0$ for abelian and $1$ for non-abelian.

Secret

For example, division by zero algebra is pretty much the most nosensical possible thing one will hear in the maths community, yet a couple of professors and my friends found my work quite interesting

Akiva Weinberger

@SteamyRoot Same group, though

Waiting

12:47

@Secret Turn every hit you get into power to reach more and higher objectives.

Akiva Weinberger

Different categories, but whatever

SteamyRoot

But $\operatorname{Hom}$ is in general a groupoid rather than a group, so usually we refrain from either and use $\{0\}$.

Akiva Weinberger

Oh.

Yeah, I guess that makes sense

Secret

Always remember, ideas mix, and always remember, I have 6 years of track record of infecting my weirdness to many people I have interacted with real life or not

Waiting

@Secret it's not just silly motivational text, this is if you want to reach a top in anything you do. Very, very powerful mentally.

SteamyRoot

12:48

It's a pretty standard convention for the $1$ and $0$ being Abelian and non-Abelian, though. It's not uncommon to see exact sequences like $0 \to \mathbb{Z}^2 \to \Gamma \to S_3 \to 1$

Akiva Weinberger

This is like that nonsense with $D\sharp$ and $E\flat$

Astyx

And finally $\Bbb Z/p\Bbb Z $ ?

Akiva Weinberger

@SteamyRoot O_O

What's $\Gamma$?

@Astyx I feel like $\Bbb R\to\Bbb Z_3$ should be doable…

SteamyRoot

Well, any group that fits the exact sequence. I just took an example of my research where I use $\Gamma$ alot :P

Akiva Weinberger

Ah, OK

Secret

12:49

then I am already doing it daily. It's part of my nature already

SteamyRoot

@Astyx Map something to $1$ again?

Leaky Nun

@AkivaWeinberger not really nonsense if you don't use equal temperament.

Akiva Weinberger

@LeakyNun Huh. Never thought about it like that.

That explains double sharps as well, I guess

Leaky Nun

indeed it does.

Akiva Weinberger

And… triple sharps?

I'm gonna go ahead and guess that that never happens

Secret

12:51

(ok now where was I in 2015... Will deal with irrational visualisations later...)

Waiting

$$\sum _{k=1}^{\infty } \sum _{n=1}^{\infty } \frac{\Gamma (k)^2 \Gamma (n) }{\Gamma (2 k+n)}((\psi ^{(0)}(n)-\psi ^{(0)}(2 k+n)) (\psi ^{(0)}(k)-\psi ^{(0)}(2 k+n))-\psi ^{(1)}(2 k+n))$$

Akiva Weinberger

…No

No, I refuse

@Waiting

Leaky Nun

@AkivaWeinberger never seen it. No keys require it natively.

Akiva Weinberger

Do not want

Harmonic minor uses both flats and sharps occasionally, which is interesting

Waiting

@AkivaWeinberger Then you can use it, say, to take a selfie with it ...

Akiva Weinberger

12:53

Here's a fun scale, if you care about such things @LeakyNun

Leaky Nun

@AkivaWeinberger I do.

Akiva Weinberger

The harmonic minor is white notes starting on A but with a $G\sharp$, yeah?

Leaky Nun

@AkivaWeinberger yes

Akiva Weinberger

Do the same but starting on $E$

so $E,F,G\sharp,A,B,C,D,E$

Dominant Phrygian, I think it's called. Sounds very Eastern European.

Leaky Nun

Interesting.

Akiva Weinberger

12:54

Despite the major third, it sounds very minor

So it's like a minor scale but with a flat second and sharp third

Leaky Nun

because of the minor second?

Akiva Weinberger

Yeah

Astyx

Wait I made a silly confusion for Q, since the group of squares of Q^* is not isomorphic to Q itself

Secret

@Justwinbaby .

21 hours ago, by Secret

2 days ago, by Secret

(NB For those who wonder why I am digging up very old messages: I am currently backing up all my messages left throughout the SE network in order to prevent another information loss disaster similar to the fall of Mos Eilsey to happen)

:: We _*cannot* tolerate anymore information loss! ::

Akiva Weinberger

What happened to Mos Eisley?

The chat or the fictional city?

Astyx

12:55

I guess there are more than one square roots for Q

Secret

@AkivaWeinberger The chatroom. There was a flame war broke out involving some abusive users, and the SE team decided the room has to be deleted

Leaky Nun

@AkivaWeinberger Oh I know why it sounds very minor: it's just $A$ harmonic minor starting from $E$

Akiva Weinberger

@LeakyNun Also, $E,F,A,B,C$ makes a pentatonic scale. Not the pentatonic scale, but a pentatonic scale. It (and modes of it) sounds very Japanese.

Secret

so the scifi SE started a fresh chapter with a new chat

Akiva Weinberger

(Modes meaning just starting on a different note in it, so like $A,B,C,E,F$)

Leaky Nun

12:57

@AkivaWeinberger Fun fact: the five black keys form a pentatonic scale.

Astyx

There are as many square roots on Q as there are primes

Secret

Since my rep is not high enough to see deleted chat rooms, the messages and ideas I temporary stored there is basically lost

Akiva Weinberger

@LeakyNun Yup

Astyx

Now on to $\Bbb Z/p\Bbb Z$

SteamyRoot

It's really just the same for the $p = 2$ case.

$\varphi(px) = p\varphi(x) = 0$ for all $x$.

Secret

12:58

It's not very disastrous though, since I only have stored 2 ideas in there and I recall what they are, but imagine, for an unspeakably small probbaility it happens in the h bar or the maths chat, that's a year worth of my highly unique ideas loss in the drain

Akiva Weinberger

@SteamyRoot Oh. Duh.

So $\varphi(x)=p\varphi(x/p)=0$.

Right. So no maps from $\Bbb R$ to torsion-y things.

Secret

(NB, people cannot really steal my ideas except the time travel theory because all idea ideas of mine are unreadable/illegible without the weirdness personality of mine (even with explanation), which is possess by only a handful of people who have interacted with me long enough)

6

Just win baby

:-)

Astyx

I'm asking for a morphism $(\Bbb Z /p\Bbb Z)^{2*}\to (\Bbb Z/p\Bbb Z)^*$ where $^{2*}$ means the group of squares right ?

SteamyRoot

Well, no surjective morphisms at least.

Akiva Weinberger

13:01

The set of notes $B,C,E,F,A$ sounds really interesting to me for some reason

(Same octave, so going up in pitch)

@LeakyNun

Leaky Nun

I kind of like how there are 12 keys. That makes nice groups.

Oh, and of course $G$ is a generator, which makes it a cyclic group.

(Well, duh, it's just the $\Bbb Z_{12}$ group.)

Secret

Mbira music on a torus

►

Akiva Weinberger

@LeakyNun Microtonal music is a thing.

Leaky Nun

Sure.

Akiva Weinberger

People have divided the octave into other amounts (like 15 equal pieces) and played music with it

It sounds… weird

If you want to listen to a good microtonal artist, look up Sevish.

(He's got a channel on YouTube)

Waiting

13:06

I'm out, maybe return in a few days, very hard work here is still needed to finalize some ideas (actually to turn them into practical tools).

@Justwinbaby bye

Secret

Sevish - Xenomic (microtonal music)

►

It's waaaaaavvvvvvyyyyyyy

Akiva Weinberger

Hm, idea for LaTeX musical notation: superscripts say number of beats, subscript says which octave

$A_3^1 C_3^1 E_3^1 G_3^1$

Secret

that might conflict with currently accepted usage of subscripts if I recall (which is to precisely notate which note in a (forgot word) scale you are at)

Akiva Weinberger

$F^1~E^1~C^{1/2} D^{1/2} B^{1/2} E^{1/2}$

@Secret Oh, didn't know that

Secret

Scientific pitch notation

Scientific pitch notation (or SPN, also known as American Standard Pitch Notation (ASPN) and International Pitch Notation (IPN)) is a method of specifying musical pitch by combining a musical note name (with accidental if needed) and a number identifying the pitch's octave. Although scientific pitch notation (SPN) was originally designed as a companion to "scientific pitch" (see below), the two are not synonymous, and should not be confused. Scientific pitch is a pitch standard—a system which defines the specific frequencies of particular pitches (see below). SPN concerns only how pitch names are...

To be precise

SoumyoB

13:30

@Astyx It's been a long time since I last read up Markov inequality. Could you elaborate a little on exactly how you're taking the exponential?

Just win baby

Bye @Waiting nice chatting with you :-)

SoumyoB

13:45

Firewall - Sincere (Lange Vocal Mix)

►

I just can't seem to get enough of this song

Astyx

Hi @SoumyoB ! Yeah so the problem I was talking about specifically was about random walks, that is $S_n = \sum_{i=1}^n X_i$ where each $X_i$ follows a Rademacher random variable, and all are independant. The using Markov inequality on the $e^{tS_n}$ for $t\in \Bbb R_+$ we get upper bounds that work wonders to prove some results. (eg $P(S_n \ge \epsilon) = P(e^{S_n} \ge e^{\epsilon}) \le \dots$).

I get we have to take the exponential to apply Markov since we need something positive. But it's seems magical too me that it works so well

Semiclassical

14:02

A quick subjective question: Suppose I want to produce a square with the same perimeter as the unit disk.

That's not hard; the unit disk has perimeter $2\pi$, so a square of side-length $s=\pi/2$ will have the same perimeter.

I say that, but then I produce the result in Mathematica:

user193319

I have a quick question about a certain term, but here is some context: Let $X$ be compact Hausdorff. Let $\mathcal{A}$ be a collection of closed connected subspaces of $X$ that is simply ordered by proper inclusion.

SoumyoB

@Astyx gimme some time, I'll be back and will see your question

user193319

My question is, what exactly does "simply ordered by proper inclusion"?

Semiclassical

No matter how I look at that, I can't convince myself visually that the two figures have the same perimeter :/

Alessandro Codenotti

@user193319 for every pair of sets $U$ and $V$ in $\mathcal A$ either $U\subseteq V$ or $V\subseteq U$

with both holding iff $U=V$, so we actually have a linear (simple) order

user193319

14:09

@AlessandroCodenotti So, if I wanted to show that $\mathcal{A}$ has the finite intersection property, then I could just take the set among a finite collection that is contained in all the other ones and show that the intersection is simply equal to the smallest set?

Alessandro Codenotti

yes

(I should learn how to read, I missed the "finite" part :P)

user193319

@AlessandroCodenotti Haha! Don't worry: I have a tendency to read things too quickly, too. Thanks, by the way!

Astyx

14:29

@SoumyoB Alright, thanks for your time !

Abcd

14:44

What does uncertainty in uncertainty principle mean?

Leaky Nun

@Abcd "the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa"

Uncertainty would be referring to the fact that you cannot know a quantity precisely.

Abcd

@LeakyNun Thanks. I had created a room for us. Did you see that?

Leaky Nun

@Abcd I didn't

Abcd

@LeakyNun I got confused because its denoted by delta

@LeakyNun :( . I had invited you.

Leaky Nun

I found it

Abcd

14:49

@LeakyNun Please send me the link. I am unable to find it

Leaky Nun

$Mathematics$ Maths

Maths

Soham Chowdhury

I remember.

19

Q: When is it ok to use \newcommand and \DeclareMathOperator?

As some of you may know, you can use \newcommand and \DeclareMathOperator to create new TeX macros. For example, $\DeclareMathOperator{\cosine}{cosine}$$\DeclareMathOperator{\cosine}{cosine}$ allows you to write $\cosine$ and see $\cosine$. Unfortunately, using either of these commands affects th...

Abcd

@LeakyNun Could you explain a question related to it to me? I know how to solve and get the answer but don't understand what the question means.

Leaky Nun

@Abcd just ask; don't ask to ask

Abcd

@LeakyNun I an atom, an electron is moving with a speed of 600 m/s with an accuracy of 0.005%. What is the certainty with which the position of the electron can be located?

Leaky Nun

14:56

Do you know the uncertainty principle?

Abcd

@LeakyNun Yes. $\triangle x\triangle p = \frac {h}{4\pi}$

Leaky Nun

and do you know any quantity in the equation?

Abcd

@LeakyNun delta x is uncertainty in position delta p is ....in momentum

Leaky Nun

$\Delta x \Delta p = \frac h {4\pi}$

@Abcd and do you know any of those?

Abcd

@LeakyNun I know how to solve> I just want the explanation of the question

@LeakyNun I know how to solve

Leaky Nun

14:59

I'm not sure whether that is $\pm 0.005\%$ or $\pm 0.0025\%$

Abcd

@LeakyNun former

Leaky Nun

@Abcd then that's what it means

Abcd

@LeakyNun There's a crucial assumption in uncertainty principle derivation: electron travels with speed of light. Is that acceptable? Is it correct?

Leaky Nun

the precision is 0.005%

@Abcd really?

Abcd

@LeakyNun sorry sorry sorry. I meant in De broglie's wavelength

Simply Beautiful Art

15:06

I got a series problem if anyone wants to try.

SteamyRoot

It's going to be rather hard for an electron to travel at the speed of light.

Simply Beautiful Art

Show that $f(s)$ is analytic on the entire complex plane where $$f(s)=\lim_{x\to-1^+} \sum_{k=1}^\infty\frac{x^{k+1}}{k^s}$$

Leaky Nun

@Abcd what does it have to do with this problem?

Abcd

@LeakyNun It's a separate question.

Akiva Weinberger

@Secret That's the same use that I was doing (although they change octaves from B to C rather than from G to A)

It says which octave you're using, not where in the octave you are

Secret

15:09

Ah ok

Akiva Weinberger

So I guess the only real difference is that I was adding superscripts for note length

Secret

I think so, I don't recall classical notation has numerical superscript

Akiva Weinberger

I was saying that was my addition

$A_3^1~C_4^1~E_4^1~G_4^1\mid F_4^1~E_4^1~C_4^{1/2}D_4^{1/2}B_3^{1/2}F_4^{1/2}$

(is the thing from earlier but switching it so that octaves change on $C$ instead of $A$… for whatever reason…)

If they're all from $A_3$ to $G_4$, I don't really need the subscripts, to be honest

$A^1~C^1~E^1~F^1\mid D^1~F^1~A_4^1~G_3^1$

Oh. Oh, one of those notes is wrong, whoops.

Secret

and I suspect by note length, you mean something like this?

Note value

In music notation, a note value indicates the relative duration of a note, using the color or shape of the note head, the presence or absence of a stem, and the presence or absence of flags/beams/hooks/tails. A rest indicates a silence of an equivalent duration. == List == == Variations == The breve appears in several different versions, as shown at right. The first two are commonly used; the third is a stylistic alternative. Sometimes the longa or breve is used to indicate a very long note of indefinite duration, as at the end of a piece (e.g. at the end of Mozart's Mass KV 192). When a stem...

Akiva Weinberger

Yeah. So a quarter note is $1$, and eight note is $\frac12$, etc

Cookie to whoever can sing/play the above thing and see which note is the error.

Then repeat the first two measures and add $A_4^1~G_4^1~F^1~D^1\mid E^2~A_3^2$.

Leaky Nun

15:16

@AkivaWeinberger the $G$?

Akiva Weinberger

Which one?

Oh, I messed up the octave, didn't I

Fourth measure should end in $G_4^1$, not $G_3^1$

That's not the one I was thinking of

Secret

Hmm, I can see how an advantage of this is that you don't need the harmony package to type music in latex, and also that the note value becomes a number makes it more flexible.

However part of the aesthetic of music and how people recognise it is musical writing came from the way the notes are written, though I guess that's a minor, cultural thing and that the society just need to adapt to a new convention so it shoudl be fine

Akiva Weinberger

It's not about throwing away the old convention, it's about how MathJax doesn't support proper music notation and that makes me sad.

So this is an alternative.

Secret

Makes sense

Semiclassical

Ooo, uncertainty

Akiva Weinberger

15:20

I mean, I suppose I could just record myself singing in Vocaroo and post the link?

You know what, major improvement, specificy what scale you're using and then just use numbers

so if I specify I'm in a minor scale, the root minor chord would just be $1^1~3^1~5^1$.

(Broken chord.)

Secret

that's quite compact and concise

Akiva Weinberger

And then the dominant phrygian thing I mentioned earlier is $1~2\flat~3\sharp~4\mid 5~6~7~8$ (again with the numbers in a minor scale)

Secret

what is middle C in this scale? (I usually rely on middle C to find where I am)

Akiva Weinberger

Rests are… $\emptyset$, maybe?

Secret

Do we use $0$,$-1$ and so on?

Akiva Weinberger

15:24

@Secret Well, this would move around based on key… but if you're doing it in $A$ minor (which seems a natural choice) it would be $3$

@Secret Not sure. Maybe $7_{-1}$?

(Or I'd you're doing it in $C$ major it would be $1$)

Secret

Let me just double check, so suprscript is note value, subscript is which octave, and the base is the note pitch?

Akiva Weinberger

Yeah

Minor scale: $1^{1/2}5^{1/2}~\emptyset^{1/2}5^{1/2}\mid 6^{1/2}0^{1/2}2\flat^{1/2}3\sharp^{1/2}$ repeat from start a bunch of times

Secret

ok, so using the 12 (forgot name) scale system, the base can only be 1 to 8, thus I think the number 0 is free to be used as a base, we can thus use that to denote rests and then the superscipt will be note value of the rest, consistent to how superscript used in this notation

Akiva Weinberger

(Warning: That's stupidly difficult to sing for some reason)

I just used $0$ as the note before $1$ there.

Secret

If I recall, each octave has 7 distinct note pitches. Since we have subscripts to deal with octaves, it means we only need 7 symbols for the base

Akiva Weinberger

15:29

(Minor scale $02\flat3\sharp$ is a diminished chord, for the record)

@Secret Fair. Though if it doesn't move around a lot we could use $0$ and $8$ to save space or clutter

Secret

Right, then $\emptyset$ will be a good rest notation then

Semiclassical

oh, and hi chat

Akiva Weinberger

4 mins ago, by Akiva Weinberger

Minor scale: $1^{1/2}5^{1/2}~\emptyset^{1/2}5^{1/2}\mid 6^{1/2}0^{1/2}2\flat^{1/2}3\sharp^{1/2}$ repeat from start a bunch of times

Only repeat three times, add a $1^12\flat^1\mid3\sharp^14^1$ climb, and then modulate up a fifth and start over

(And then climb back down)

Secret

In other news: My calculation does not seemed to save an archive file after it finishes, or I don't know where it is inside the whole computer cluster

This is why I really don't like to navigate witin supercomputing clusters, all these data structures are so confusing

I'ma gonna chat crawl this month and then cool myself off with ordinal collapsing fnctions

Akiva Weinberger

15:46

I just got my music theory book for next year. As you can imagine, I'm pretty excited

@Semiclassical What?

Secret

What music instrument do you play?

Akiva Weinberger

Piano

Alessandro Codenotti

Music theory is on my list of things I should learn

Akiva Weinberger

(And voice, if you want to count that)

Secret

Ah same, I played the piano roughly 10 years ago, before uni kicks in and I stopped

Akiva Weinberger

15:49

I don't do piano as much as I should

Secret

though my music sense is still retained

Akiva Weinberger

I've gotten much worse

Liad

it's true that $S \ ^ n - \{x\} $ homeo' to $S \ ^ n -\{y\}$ for all $x,y, \in S \ ^ n$ ?

i think it is but im not sure how to build the homeo'

i proved that $S \ ^ n - \{(0,\dots,1)\}$ is homeo to $\Bbb R \ ^ n$ and now i want to conclude that $S \ ^ n -\{x\}$ is also homeo' to $\Bbb R \ ^ n$.

SteamyRoot

Just rotate them into eachother?

Liad

yea. how :P

SteamyRoot

15:54

By... rotating.

Like, take the plane spanned by the origin, $x$, and $y$.

Faust7

morning

Secret

Chemistry: Ok, I think I knew what is going on. The script said if any error is encountered in the run, all contents are dumped to dev/null, that is why I don't get my archive file. The issue is then I need to figure out how to make a copy of the script so that I don't end up modifying the global, communal one

SteamyRoot

How do you get $x$ to $y$ ?

Liad

rotating it :P

how can i write it down explicitly? @SteamyRoot

Semiclassical

@AkivaWeinberger I was hearing the other conversation re: uncertainty

SteamyRoot

15:57

Uhhhh... Picking a decent coordinate system would probably make it easy.

Start with the plane I mentioned, and build the other coordinates around it.

Akiva Weinberger

@Liad There's a general theorem saying all connected manifolds are homogeneous, though that's not necessary here

$Mathematics$ Maths

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$Mathematics$ Mathematics