Mathematics - 2017-06-21 (page 9 of 11)

Akiva Weinberger

17:00

*stack

Typhon

*stock

Akiva Weinberger

Stock Exchange is the thing with all the stocks and shares and stuff

Semiclassical

*stroke

Secret

*snoke

Akiva Weinberger

I've seen the NYSE building, but I've never been inside

Zee

17:00

Spoke

Akiva Weinberger

I hear it's nice.

Secret

Spook

Typhon

@AkivaWeinberger yeah. this is the stockings exchange

Balarka Sen

steak

Akiva Weinberger

Er, nyse.

Semiclassical

17:01

Stoke

Zee

Break

Typhon

everyone give me your stockings

Icche Guri

hello I am facing a problem

Typhon

NAOW!

Akiva Weinberger

gives stalk of corn

Typhon

17:01

XD

Semiclassical

well, this took a turn.

Secret

@IccheGuri details?

Zee

@Typhon totally not gibberish

Typhon

@Semiclassical rerouting destination

Semiclassical

assuming direct control

Typhon

17:02

we are now going to the moon

@Semiclassical DC outlet activated

Semiclassical

fly me to the moon, let me play among the stars...

Typhon

XD

Balarka Sen

freak out in the moonage daydream, oh yeah

Akiva Weinberger

Wut

Typhon

@Zee sends you to Mars

Semiclassical

17:03

pretty sure the scanners clip is again relevant for the chat as whole right now

Zee

Eva

Semiclassical

because we're just all over the place

Balarka Sen

@Akiva youtube.com/watch?v=LaqMwE5NKaM

Icche Guri

I have 6 boxes

Akiva Weinberger

Nice

Can I have one

Six is too many for one person

Typhon

17:03

@Semiclassical Nooooo! I don't wanna be scanned!

Icche Guri

THe no of choclate in boxes are respectively :

6 8 3 1 1 4

Balarka Sen

i'm listening to that song right now. i dunno why but i am

Zee

Me too

Alright am gonna go play video games to wake my brain up

Balarka Sen

i really wonder how much cocaine one needs to take to dress up like that and waltz around on stage with that much self confidence

Akiva Weinberger

$1_0^2~1_1^2\mid6_{-1}^2~1_1^2\mid7_{-1}^2~7_0^2\mid 7\sharp_{-1}^2~5_0^14_0^1$

Typhon

17:07

@Zee I'm gonna go work on my game to wake up.

Secret

@AkivaWeinberger what key?

Akiva Weinberger

@Secret $A$ minor

Icche Guri

I want to take some chocklate from one box and place these choclate in another box

Secret

harmonic A minor?

Akiva Weinberger

@Secret Well, there's both a $7$ and a $7\sharp$ so I dunno

Icche Guri

17:09

I like to solve this problem .

hackerrank.com/contests/101hack50/challenges/even-and-odd-boxes/…

Akiva Weinberger

When it's a $7$ it's the normal one

(forget what it's called)

Typhon

@IccheGuri I'll take box $2^{sin(\frac{\pi}{2})}$ please

Icche Guri

what is the reason to choose this ?

Secret

Oh (censored), I cannot handle combinitorics problems. Guess you need to ask someone else

Typhon

gives everyone in chat a piece of chocolate

Icche Guri

17:09

@Typhon

Typhon

yes???

Akiva Weinberger

@IccheGuri He was joking

Typhon

^^^

Icche Guri

made my day

Typhon

it had 8 pieces in it (the most)

Icche Guri

17:11

but I can not finding the logic behind this problem .

Typhon

so im taking that box and giving everyone some chocolate

Icche Guri

Can you help me ?

Typhon

i have no clue

Akiva Weinberger

Find the ones that are opposite the parity they're supposed to be

and move chocolates among them

Icche Guri

Ok Simply let me state the problem first

Akiva Weinberger

17:14

$1_0^12_0^13_0^14_0^1\mid \underbrace{7_{-1}^4\mid 7_{-1}^4}\mid3_0^2~2_0^2\mid 1_0^2~7_{-1}^2\mid \underbrace{1_0^4\mid 1_0^1}\emptyset^3$

RE60K

$$\sum_{t=0}^k\binom{n-t}{r-t}$$

Akiva Weinberger

@Secret I realized I didn't decide how to do ties (notes that are longer than a measure)

So I did that ^

(Again $A$ minor)

That's what measure theory is, right? /s

RE60K

how to find a closed form for $$\sum_{r=1}^k\binom{r+9}r$$

Akiva Weinberger

Dunno but my first instinct would be to look at Pascal's triangle @RE60K

Semiclassical

Sounds like hockey stick

Typhon

17:23

@RE60K what makes you assume it has a closed form?

RE60K

It telescopes , I had solved it in past

unfortunately I lent out my old notes

Akiva Weinberger

Yeah it probably does

Semiclassical

@RE60K I'm pretty sure that'll be covered by the hockey-stick identity

RE60K

It becomes $$\frac{k+1}{10}\binom{k+10}{k+1}-1$$

Akiva Weinberger

Is it called Pascal's identity, when two binomial coefficients add to another one?

Semiclassical

17:24

As discussed in this question here: math.stackexchange.com/q/1490794/137524

Akiva Weinberger

Use the symmetry of the coefficient

RE60K

No it has fixed bottom in binom

found it math.stackexchange.com/questions/398771/…

None of the answers use telescoping unfortunately

Semiclassical

You have $\binom{r+9}r=\binom{r}{9}$

RE60K

Oh!

Semiclassical

So yours can also be expressed with a fixed denominator

TBH, though, I started by visualizing where those binomial coefficients would be on Pascals triangle

And remembered the connection to hockey-stick from there

Akiva Weinberger

17:30

@Semiclassical Wait

$\binom{r+9}9$

RE60K

$$\binom{n+k}k=\frac{(n+k)..1}{k..1}\frac{((n+k+1)-k)}{(n+1)}=\frac1{n+1}\left[ \frac{(n+k+1)..1}{k..1} - \frac{(n+k)..1}{(k-1)..1}\right]$$

something like this

Semiclassical

With that in mind, I searched again and found this:

4

A: Telescoping series of form $\sum (n+1)\cdot...\cdot(n+k)$

Hint: $$ \sum_{n=k}^m\binom{n}{k}=\binom{m+1}{k+1} $$ A generalization is discussed in this answer. The equation above is equation $(1)$ with $m=0$. Telescoping sum To turn the sum in the question into a "telescoping sum", we can use the recurrence for Pascal's Triangle: $$ \binom{n+1}{k+1}=\...

Secret

C major (actually I should have used D major, but renumbering this under D major is a headache thus will do that next time...)
$$4\sharp_0^14\sharp_0^14\sharp_0^11_0\sharp^{\frac{3}{2}}6_0^{\frac{1}{2}}4\sharp_0^{\frac{3}{2}}1_0\sharp^{\frac{3}{2}}6_0^{\frac{1}{2}}4\sharp_0^{2}\emptyset^11_1^11_1^11_1^11_1\sharp^{\frac{3}{2}}1_1^{\frac{1}{2}}3_0^{\frac{3}{2}}1_0^{\frac{3}{2}}6_0^{\frac{1}{2}}4\sharp_0^{2}$$
See if you recognise it

Semiclassical

Which appears to be the desired proof of H-S by telescoping @RE60K

Balarka Sen

what am I going to do now

Leaky Nun

17:33

@Secret star wars imperial march?

Secret

bingo

Balarka Sen

@Semiclassical teach me electrostatics man

Semiclassical

What do you want to know?

Said in this tone of voice: youtu.be/7udsYPVhl6Y

Secret

@LeakyNun actually, how are you able to read so fast?

Leaky Nun

@Secret I just sound each note in my head, and after the first six notes I pretty much figured it out

oh, and I ignored the other numbers, just the notes themselves

Secret

17:36

I see

Semiclassical

(Mostly for the end of that bit, heh)

Akiva Weinberger

@Secret The second half looks off but I might be wrong

Balarka Sen

@Semiclassical I probably don't have a specific question lol. I am reading capacitors now.

Akiva Weinberger

$\emptyset^{273}$ @Secret

Dodsy

my life sucks

Akiva Weinberger

17:51

Recognize this? @Secret $\emptyset^15_0^15_0^15_0^1\mid 3_0^4\mid\emptyset^1 4_0^14_0^14_0^1\mid2_0^4$

Secret

also C major?

Akiva Weinberger

Anything minor

Leaky Nun

@AkivaWeinberger should it be $3\flat$?

Secret

Beethoven's 5th Symphony

►

I initially get the wrong key (I started with A minor hence 1 is A), but the pattern of the melody allow me to recognise it

[Random]

Akiva Weinberger

@LeakyNun I meant for it to be in a minor key, so that it's already a minor third

but otherwise, sure

Secret

17:56

${\Large\emptyset^{\omega}}$

Akiva Weinberger

@Secret Do… do you have perfect pitch?

(Also, I probably should have made each note like twice as fast)

Secret

I think not, it took me some years before I can get the pitches right from audio to text form of anything, I think it's just practice makes perfect for me

Akiva Weinberger

Ah, upon listening, I got the rhythm completely wrong, didn't I

Leaky Nun

@AkivaWeinberger how does your notation work?

Dodsy

What is this game

Secret

17:59

@AkivaWeinberger you are just 2 times slower than the original, I think

Leaky Nun

@AkivaWeinberger because any notation I know would use 6712345#6 for minor

Dodsy

lmfao

Akiva Weinberger

(Ooh, harmonic minor!)

Leaky Nun

...and is it in minor?

Dodsy

what's this notation called?

Leaky Nun

18:00

Numbered musical notation

The numbered musical notation (simplified Chinese: 简谱; traditional Chinese: 簡譜; pinyin: jiǎnpǔ; literally: "simplified notation"), is a musical notation system widely used in music publications in China. Not to be confused with the integer notation. It dates back to the system designed by Pierre Galin, known as Galin-Paris-Chevé system. It is comparable to the Gongche notation from the Tang Dynasty. It is also known as Ziffersystem, meaning "number system" or "cipher system" in German. It should be noticed that some other unrelated musical notation systems are also called cipher notations. The...

Akiva Weinberger

@LeakyNun Just specify a scale and then use the numbers for that scale. So if I specify minor, then $12345678$ is (for example in the key of $A$ minor) $ABCDEFGA$

If I specify major, then $12345678$ is (for example in the key of $A$ major) $ABC\sharp DEF\sharp G\sharp A$

(I think?)

(Yeah)

Leaky Nun

I would seriously use 6712345#6 for minor

Akiva Weinberger

I would find that confusing, to be honest

Leaky Nun

Read my link

Akiva Weinberger

$123\flat456\flat7\flat8$ would be better, perhaps

Secret

18:01

I actually prefer the base to be letters, that way it is much clearer what key is

Dodsy

this is the best beethoven song ever

Beethoven "Moonlight" Sonata op 27 # 2 Mov 3 Valentina Lisitsa

►

Leaky Nun

> The notation uses a movable Do (1) system. The key signature defines the pitch of "1". So 1=C means "C major". Minor keys are based on the natural minor or the Aeolian mode, and the key signature defines the pitch of "6" of the minor key's relative major. So 6=A means "A minor", the tonic of which is written as 6. Naturally, the Dorian mode of D should be marked as 2=D and based on 2. Some people prefer to write "Key: C" or "Key: Cm" instead.

@AkivaWeinberger actually, in sol-fa, you still use la as the first note of the minor

Akiva Weinberger

Oh, that's an interesting link

I didn't know that existed

Astyx

Rehi chat

Akiva Weinberger

Thanks for sharing

I was just having subscripts say which octave and superscripts say how many beats

Leaky Nun

18:03

@AkivaWeinberger well it's a Chinese thing so

Dodsy

reeeely?

Akiva Weinberger

@Secret But I don't know what key most things are in

I don't have perfect pitch

and it's too much hassle to open up the piano app on my phone :P

(And I'm nowhere near my actual physical piano at the moment)

$1\sharp~2\flat ~1\sharp~2\flat{{}:}\|^\infty$

Leaky Nun

@AkivaWeinberger what?

Akiva Weinberger

There we go

Dodsy

Right now I'm learning Erik Satie's Gymnopedies No. 1

very satisfying piece to play

Akiva Weinberger

18:07

@LeakyNun It's the most pointless trill

Leaky Nun

@AkivaWeinberger I wouldn't say that it's a trill

Secret

Jaws theme!!

►

Akiva Weinberger

It's the most pointless… thing

Ever time I sing an A, there's a 25% chance it's actually a C triple flat

Hm. I just realized:

In a sense, $\aleph_0$, $\Bbb N$, and $\omega$ are "enharmonic."

Secret

I cannot sing perfect pitch, but music played under slightly different keys will feel off to me

Akiva Weinberger

They're the same set but spelled differently.

Leaky Nun

18:10

D major: $3 - - - | - - - - | - \underline{6 4} \underline{2 1} \underline{7 1}| 7 - \underline{6 5} -$

Akiva Weinberger

What are the dashes, again?

Leaky Nun

extension from the previous note

so the first note is 9 beats long

Akiva Weinberger

Ah, I see

Leaky Nun

and $|$ are the barlines

Akiva Weinberger

I don't think I recognize that tune

Wait

I misunderstood the underlines

Those make them shorter?

Leaky Nun

18:12

D major: $3_1 - - - | - - - - | - \underline{6_1 4_1} \underline{2_1 1_1} \underline{7_0 1_1}| 7_0 - \underline{6_0 5_0} -$

@AkivaWeinberger yes

Akiva Weinberger

I don't recognize it, no

user107952

This is not a math question. This is just an announcement. For the past year, I have been considering myself the most mathematically and logical rigorous human alive. I consider myself more rigorous than even Fields Medalists like Timothy Gowers and Terrence Tao. I feel like Bill Gates all the time. In fact, I don't think even Bill Gates feel this happy and on top of the world all the time. But I do.

Leaky Nun

@AkivaWeinberger Air on the G String

Akiva Weinberger

Oh, never heard it

Ah, Bach?

Leaky Nun

@user107952 and then?

@AkivaWeinberger yes

user107952

18:15

@LeakyNum I want to tell this annoucement as many human beings as I can in my life. I want to tell everyone how happy and confident I feel.

Akiva Weinberger

@user107952 Nice to know

user107952

Timothy Gowers is foolish compared to me.

Secret

theguardian.com/notesandqueries/query/0,5753,-2859,00.html

32

Q: Does it really make difference to play a song in a different key?

I hear sometimes players and composers say that this song won't sound good in F Major for example, and you should play it or write it in G Major (this was just an example). In other words, it seems that they assign aesthetic attributes to keys. My question is that, imagine a baby growing up in ...

So no, a key sound weird does not imply perfect pitch

Akiva Weinberger

@LeakyNun If you're doing something in minor, where do you mark the octave changes?

Like, is it $6_07_01_12_13_1$, etc.?

Leaky Nun

sure

Akiva Weinberger

18:20

OK

6=? $~6-6'-\mid 4-6'-\mid 5-5'-\mid5\sharp-3'2'$

(prime mark = next octave)

Not an actual song, I just think it sounds cool

Leaky Nun

I see

user107952

Even Timothy Gowers and Terry Tao should consider it an honor to shake hands with me.

Akiva Weinberger

Do I have to listen to you, or do I also have to agree with you

Secret

Prove using set theory that the following is true:

$$\int_0^{\infty} e^{-x^2}dx=\frac{\sqrt{\pi}}{2}$$

(anyone else (you know who you are), continue on the musics)

user107952

@Akiva Weinberger, I just want to know what you think of my claims. And yes, even you should consider it an honor to shake hands with me.

Secret

18:28

typo: Forgot the [random] before the word "Prove"

Akiva Weinberger

I think, no matter how good I get, I would never feel comfortable saying the things you just said.

And I'm suspicious of anyone who is.

@Secret Using… set theory??

Secret

@AkivaWeinberger don't worry about it, that one is totally random. However, I suspect such a proof will be very long

Akiva Weinberger

Oh, like, from basic principles ZFC?

I'mma pass, then.

Astyx

No one likes those

Leaky Nun

Jun 15 at 11:23, by Leaky Nun

To me, "ZFC is a basis for most mathematics" seems like "Quantum physics is a basis for the design internal combustion engines" - yes, you could build up from quantum physics to derive how an internal combustion engine works, but usually you don't bother. — immibis Jul 1 '16 at 13:36

Secret

18:32

Hint: Unlike most [random] this one is actually triggered by a ★. I will let you guys figure out what it is

hence that footnote: anyone else (you know who you are), continue on the musics

user107952

Given the fact that I am the most rigorous human, it logically follows that I am more rigorous than even the mathematician who proved the abc conjecture. So, I should be able to rigorously verify the correctness of the abc proof. I might need to learn some definitions first, but once I do, it should be easy. I would be doing the mathematical community a huge favor.

Leaky Nun

@Secret yea sure: not a ★, but seven ★s

Secret

@LeakyNun nope, it's not me.

I post [random] regardless of stars

Leaky Nun

@Secret what?

@user107952 you may find the following article a good read:

Dunning–Kruger effect

In the field of psychology, the Dunning–Kruger effect is a cognitive bias, wherein persons of low ability suffer from illusory superiority when they mistakenly assess their cognitive ability as greater than it is. The cognitive bias of illusory superiority derives from the metacognitive inability of low-ability persons to recognize their own ineptitude. Without the self-awareness of metacognition, low-ability people cannot objectively evaluate their actual competence or incompetence. As described by David Dunning and Justin Kruger, the cognitive bias of illusory superiority results from an internal...

Secret

@LeakyNun well, assume I get you right, currently the only item in the visible starboard that has 7 stars is my random bunch of symbols, which is why I think you might be referring to me

Leaky Nun

18:37

@Secret yes

Secret

but I can clarify that it is not me, why would I post a troll sounding [random] (that set theory integral) given that I don't really care about how many stars I get?

and because most of you knew me well, you know that question is not directed at you

@user107952 Ok. I have an actual question for you that logic might be used. Prove or show counterexample, that there exists no model theoric object that will allow division by zero to be nontrivial. NB I am not sure how to proceed that proof

Balarka Sen

@user107952 "lol"

Secret

@user107952 we knew that that is impossible for rings because of the 0x=0 axiom, but it seems for more general structures the question remains open. Given that you said you are rigorous and careful, perhaps you might be able to help me to find a proof or counterexample that I otherwise don't know

user107952

@Secret, I am a rigorous proof verifier, not a proof maker. I ask very clever questions, as my math stack exchange questions reveal, but I am bad at doing proofs. Although, if P=Np is true, a rigorous proof verifier can be converted to a proof maker.

Secret

ok noted

Astyx

18:46

It's easy, just check every possible setting

Semiclassical

@user107952 Sorta like how I feel about chess. If someone gives me a chess problem, I feel like I can more or less understand the thinking there.

Mats Granvik

With this iterative formula:
$$x=2 \pi \exp \left(W\left(-\frac{-c n+\frac{\vartheta (x)}{\pi }+\frac{x \log \left(\frac{2 \pi e}{x}\right)}{2 \pi }+2}{e}\right)+1\right)$$
we can find these points:

user107952

Since I am the most rigorous, I consider it my life mission to teach people rigor. I will tell you all a secret very, very few humans know. The argument "I am the most rigorous human. H is a human. Therefore, I am more rigorous than H." is invalid. You need the additional premise, "H is not me." Consider yourself all honored to learn this secret from the most rigorous human.

Gregor Perčič

Any thoughts on IUT (Inter Universal Teichmüller Theory) of Shinichi Mochizuki? Even with my academical experiences, this is unlike anything I've seen before. Truly marvellous.

Mats Granvik

of the Riemann zeta function.

Semiclassical

18:51

But that's tactics. By contrast I have much less sense for strategy, of seeing the big picture and how everything should develop.

Mats Granvik

$c=\frac{1}{4}$

Semiclassical

@GregorPerčič my thought is: It's hard enough to appreciate math where there's only a handful of people who know enough to make progess. It's another level of difficulty entirely when there's only a handful of people can evaluate that progress.

Balarka Sen

My thought is that I can't distinguish a random paragraph from his IUT papers with a random paragraph from a mathgen paper.

Semiclassical

So I guess I prefer to leave such matters alone in favor of stuff I can actually do meaningful work on. (Not that IUT is anywhere near my subjects of interest to begin with.)

user107952

So now, I have made you all more rigorous.

Gregor Perčič

18:57

@Semiclassical True. Still, I know enough to recognize a great work. It still haunts me: we, with our ordinary brains even after years of labor can't catch a brink of genius that simply manifests and leaves us with the uneasy feeling of smallness.

Semiclassical

Eh, it's a glimpse into an alien viewpoint about mathematical reality

Whether that viewpoint is inspired or delusive is beyond my capacity to evaluate

Gregor Perčič

@user107952 Gödel's two incompleteness theorems have your rigor beat. They are the equivalence of mathematics committing philosophical suicide (AKA there are limitations to what we can prove with rigor).

Transcript for

$Mathematics$ Mathematics