Mathematics - 2017-08-18 (page 3 of 3)

Little Rookie

19:23

What does it mean by " $P(X=\infty)$ " , where $X:\Omega \rightarrow \mathbb{N} \cup \{\infty \}$

Tobias Kildetoft

@LittleRookie Same as it would with any natural number in place of $\infty$

Alessandro Codenotti

Hi chat

Tobias Kildetoft

@AlessandroCodenotti Hi

Little Rookie

Oh, so a random variable can take a value that is infinite?

Will Hunting

It means what it means.

Leaky Nun

19:30

@LittleRookie only in this context

because the codomain is $\Bbb N \cup \{\infty\}$

Little Rookie

I see, why would the codomain be $\mathbb{N} \cup \{\infty \}$ instead of $\mathbb{N}$ ?

Tobias Kildetoft

@LittleRookie Because you defined to be that

Ted Shifrin

Hi @Alessandro

Little Rookie

what is the set $\{ \infty \}$ ? It's my first time seeing it.

Tobias Kildetoft

@LittleRookie For the purposes here, $\infty$ is more or less just a symbol for some element which is not itself a natural number

Alessandro Codenotti

19:35

I have a couple of abstract algebra questions that are giving me an headache, can I bug you with them? @Tobias

Tobias Kildetoft

@AlessandroCodenotti Sure, may as well warm up for when the teaching starts

Akiva Weinberger

What's a Haar measure

Little Rookie

it says $P(X=\infty) = 1- P(X<\infty)$

Alessandro Codenotti

Kunen, in a set theory book, writes that "it is a (fairly easy) abstract algebra question to determine which abelian groups are the additive group of a field", but I'm not finding it fairly easy at all

Little Rookie

Does $\infty$ refers to a number that is bigger than any natural number here?

Tobias Kildetoft

19:38

@AlessandroCodenotti Woops, read that as multiplicative rather than additive

@LittleRookie Well, not a number, but they may well mean for it to be an added element with that property

Leaky Nun

@LittleRookie just treat it as any other symbol

Tobias Kildetoft

@AlessandroCodenotti The additive group is the same as the one for a suitable vector spaces, which is easy to describe

Little Rookie

But why it is then stated that $P(X=\infty) = 1-P(X<\infty)$ ?

Semiclassical

huh, that was weird.

for a few minutes, my browser kept redirecting me to the area51 SE whenever I tried to go to a chat page.

Akiva Weinberger

Oh that's what it is

Little Rookie

19:44

Mine too

Alessandro Codenotti

Same here @semi

Leaky Nun

@AlessandroCodenotti I'm interested in an abelian group that isn't the additive group of a field

Semiclassical

ah, so must've been something global.

Leaky Nun

3

Q: All chat.SE links redirected to Area 51

All chat.SE links redirected to Area 51 starting from the last minute... bug? (Just click any chat.SE links)

bug

3

Q: Going to chat.stackexchange.com takes me to Area 51?

If I type chat.stackexchange.com into my browser, it resolves as area51.stackexchange.com. The same happens if I click the chat link from the dropdown on a site, as well. This just started within the last couple of minutes. I'm using Chrome, if that matters any.

bug status-completed chat

Alessandro Codenotti

$\Bbb Z$ @LeakyNun

Leaky Nun

19:45

5

A: Going to chat.stackexchange.com takes me to Area 51?

I broke it. I just unbroke it. Sorry!

Little Rookie

@LeakyNun if $infty$ is just a symbol, why is $P(X=\infty) = 1-P(X<\infty)$ ?

Semiclassical

That's probably the best short answer I've seen.

Leaky Nun

@LittleRookie because the complement of $\{\infty\}$ under the codomain is every finite number

Semiclassical

Though I guess you could shorten it to: "Oops-Fixed-Sorry!"

Tobias Kildetoft

@LittleRookie You had not said anything about that until now. But yes, that means that for this purpose, $\infty$ is an element which is greater than all naturals

Leaky Nun

19:46

@TobiasKildetoft scroll up

Akiva Weinberger

So $\Bbb Z$ no, $\Bbb Q$ yes, $\Bbb Z_2^2$ yes, $\Bbb R^3$ maybe

Not anything whose multiplication operation is continuous

Little Rookie

I see, thanks.

Tobias Kildetoft

@AkivaWeinberger the final one sure, assuming choice

Leaky Nun

@TobiasKildetoft how? oh, it is isomorphic to $\Bbb R$ under choice

Akiva Weinberger

Right

because it's isomorphic to $\Bbb R$ as an additive group then

Leaky Nun

19:48

@AkivaWeinberger I got sniped

Alessandro Codenotti

@TobiasKildetoft hmm, I agree but I'm missing the easy description

Akiva Weinberger

Yeah. Under choice, $\Bbb R$ and $\Bbb C$ are isomorphic groups.

(Which is weird)

Tobias Kildetoft

@AlessandroCodenotti So it is a direct sum of a suitable number of copies of either cyclic groups all of the same prime order, or it is a direct sum of some number of copies of the rationals

Akiva Weinberger

@AlessandroCodenotti What about $\Bbb Q^2$?

Alessandro Codenotti

(The next question is how many nonisomorphic fields are there with additive group $\Bbb R$ by the way)

Leaky Nun

19:50

@AkivaWeinberger same as $\Bbb C \cap \Bbb Q^2$ which should be a field

Akiva Weinberger

True. $\Bbb Q^3$?

/kju kjubd/

Alessandro Codenotti

@AkivaWeinberger what's the question?

Akiva Weinberger

Is it the additive group of a field

Leaky Nun

@AkivaWeinberger hey, the two /ju/ are from the same source, and hey, someone who can speak IPA!

Hatshepsut

"How can a stick that is r units long be cut into four pieces to form a rectangle with the greatest possible area? Since it is a rectangle, there will be two pieces of length a and two pieces of length b. The constraint can be expressed as 2a+2b=r or 2a+2b−r = 0; we wish to maximize ab, the area of the rectangle. The Lagrangian multiplier problem, then, is expressed as ab−λ(2a+2b−r)."

What is the "problem" in the last phrase, expressed in a complete sentence?

Tobias Kildetoft

19:51

@AlessandroCodenotti Hmm, I think there are infinitely many fields with additive group isomorphic to the reals

Leaky Nun

@Hatshepsut function, probably

but really, using Lagrangian is overkill

@AkivaWeinberger both are from /y/ borrowed from French :p

Hatshepsut

im trying to understand lagrangian using this example

Tobias Kildetoft

@AkivaWeinberger I am fairly certain all of the groups I described are the additive groups of fields

Alessandro Codenotti

I think I can construcy countably many of them, I suspect there's either $2^{\aleph_0}$ or even $2^{2^{\aleph_0}}$

Akiva Weinberger

@TobiasKildetoft Right, but what field is $\Bbb Q^3$ the additive group of?

Tobias Kildetoft

19:53

@AkivaWeinberger what do you mean?

Leaky Nun

1 min ago, by Tobias Kildetoft

@AlessandroCodenotti Hmm, I think there are infinitely many fields with additive group isomorphic to the reals

This statement doesn't make sense without further constraints

Akiva Weinberger

@LeakyNun It's easier when they're on my keyboard :P

Tobias Kildetoft

@AkivaWeinberger Take your favorite extension of the rationals of degree $3$.

Alessandro Codenotti

Are $\Bbb Q^2$ and the additive group of $\Bbb Q[\sqrt{2}]$ isomorphic? It feels weird

Leaky Nun

I mean, "doesn't make sense" -> "is a tautology"

Tobias Kildetoft

19:54

@AlessandroCodenotti Why does that feel weird? The isomorphism is pretty direct

Leaky Nun

@AlessandroCodenotti yes it is, because people need to stop thinking about vectors as something carrying direction

Akiva Weinberger

@TobiasKildetoft Oh. Duh. Thanks.

Hatshepsut

In the Lagrangian multiplier problem, is the question "Maximize this function ab−λ(2a+2b−r)"?

Leaky Nun

@AkivaWeinberger oh, direct sum of $\Bbb Q$, 3 times, lol

Akiva Weinberger

/ˈkibɔɹd/

Leaky Nun

19:55

@AkivaWeinberger typical American rhotacism :p

Akiva Weinberger

I am a typical American.

Leaky Nun

I thought one would reduce the last syllable

Akiva Weinberger

I distinguish the vowels in price and prize, and I merge phrases such as Saturday and sadder day.

(And cot and caught.)

Leaky Nun

@AkivaWeinberger is "prize" more open?

Alessandro Codenotti

@TobiasKildetoft in $\Bbb Q[\sqrt{2}]$ I can find $2$ elements $a$ and $b$ such that for all nonzero integers $c$ and $d$ $ac+bd$ isn't an integer, but there are no $2$ such elements in $\Bbb Q^2$

Akiva Weinberger

19:56

@LeakyNun Yeah

Alessandro Codenotti

My internet is acting weird tonight, I sent a message twice

Tobias Kildetoft

@AlessandroCodenotti And why is that weird?

Hatshepsut

@LeakyNun anyway, so that lagrangian function, what do you do with it? maximize it by manipulating a and b?

Akiva Weinberger

pr/ʌɪ/ce and pr/aɪ/ze, roughly

Leaky Nun

@AlessandroCodenotti alternative definitions of integer?

I mean, $a=(1,0)$ and $b=(0,1)$ if you only consider $(x,0)$ as integers

@AkivaWeinberger because of the voicing?

Alessandro Codenotti

19:59

Oh, nevermind, I see the isomorphism and why it works now

I was being dumb

Hatshepsut

@LeakyNun i dont think that's the reason; spider/tiger

Leaky Nun

@AlessandroCodenotti just use vector space ^^

@Hatshepsut which one is more open?

Hatshepsut

@LeakyNun tiger

Leaky Nun

@Hatshepsut interesting

Akiva Weinberger

@LeakyNun Yeah, though I'm suffering a minor existential crisis because I just realized I've been raising the vowel in "spider" (and not "rider") all this time

Leaky Nun

20:01

@Hatshepsut pronounce sider and cider @AkivaWeinberger

Akiva Weinberger

and "tiger"

Oh shit sniped

I promise I wasn't looking at Hatshepsut's comment :P

Alessandro Codenotti

My idea to construct fields with additive group $\Bbb R$ was to take uncountable extension of $\Bbb Q$ and then for each $n$ construct one which has exactly $n$ independent numbers without a square root

Akiva Weinberger

@LeakyNun Hm… different for some reason? Though I mean 'sider' isn't a real word I don't think

Or maybe it is

"Slider" definitely is, though, and I don't rhyme it with "spider" or "cider"

Leaky Nun

@AkivaWeinberger sider-cider split

reddit.com/r/linguistics/comments/1qtt7y/…

Hatshepsut

@LeakyNun yeah i have that split

Leaky Nun

20:04

all these years of learning English and hearing American accents I never noticed such a random split

although my Hong Kong accent has that split, on different words

Tobias Kildetoft

@AlessandroCodenotti I was just thinking of taking rational functions on the reals, since these still have the same dimension over the rationals as the reals themselves

And doing this in various number of variables

Leaky Nun

can someone give me a list of simple words for me to see which words I pronounce which way

Alessandro Codenotti

Rational functions means the field of fractions of $\Bbb R[X]$, right?

Tobias Kildetoft

@AlessandroCodenotti Yeah

Hatshepsut

@LeakyNun en.wikipedia.org/wiki/…

Leaky Nun

20:07

@Hatshepsut no, I'm not asking for a list of splits

I'm talking about this specific split

Canadian raising

Canadian raising is an allophonic rule of phonology in many dialects of North American English that changes the pronunciation of diphthongs with open-vowel starting points. Most commonly, the shift affects or , or both, when they are pronounced before voiceless consonants (therefore, in words like price and clout, respectively, but not in prize and cloud). In North American English, /aɪ/ and /aʊ/ usually begin in an open vowel [ä~a], but through raising they shift to [ɐ], [ʌ], or sometimes even [ɜ] or [ə]. Canadian English often has raising in words with both (height, life, psych, type, etc....

Alessandro Codenotti

Nice one, it should work

(The fact that $\Bbb R[X]$ and $\Bbb R$ are isomorphic as additive groups is much weirder than $\Bbb C$ and $\Bbb R$ in my opinion)

Leaky Nun

words that I pronounce with a more closed vowel include nice, height, life, type

Akiva Weinberger

@LeakyNun Wow. Also weird that both lists there put "tidy" under "always raised"… I never raise it. I think.

Leaky Nun

@AkivaWeinberger you might be confused by the word "raised"

hint: it doesn't mean open

Akiva Weinberger

No I pronounce tidy like the vowel in "wide"

Not like the vowel in "white"

Leaky Nun

20:10

I also don't raise "tidy"

Akiva Weinberger

Tiger is raised for me

Leaky Nun

not for me

Akiva Weinberger

I have no idea what's going on

Leaky Nun

although "tight" is raised for me

Akiva Weinberger

Same

Leaky Nun

20:11

I'm having a hard time knowing what accent I'm using

Akiva Weinberger

This is the weirdest thing. How could I have not known how I talk

I apologize to anyone in the chat whose conversation on abstract algebra I've derailed

Leaky Nun

@Hatshepsut I think you're suppose to find its partial derivatives

Alessandro Codenotti

LoL

Let's talk about abstract linguistics

Leaky Nun

webcache.googleusercontent.com/search?q=cache:http://…

Pronunciation Features of Hong Kong English

[aɪ]

The diphthong [aɪ] is usually replaced by [ʌɪ].

e.g. light, mice, rite, site, tight, twice

Akiva Weinberger

Those are all raised for me as well

Wait are you saying "Canadian raising" exists in Hong Kong?

Alessandro Codenotti

20:15

I have a great proposal for a better than English international language, its only problem is the uncountable alphabet

Leaky Nun

@AkivaWeinberger I think it's just before unvoiced consonants

@AkivaWeinberger this is strange

en.oxforddictionaries.com/definition/white

en.oxforddictionaries.com/definition/wide

Do you hear a difference?

This is British Accent... Looks like it isn't unique to Canadian?

> As a native of East Yorkshire, England, this difference has always interested me. In that area, we have the same difference in diphthong-length between, say, 'site' and 'side' as in RP English. But in WEST Yorkshire, they're both pronounced long.

3

A: Whence came the different varieties of long /i/?

As a native of East Yorkshire, England, this difference has always interested me. In that area, we have the same difference in diphthong-length between, say, 'site' and 'side' as in RP English. But in WEST Yorkshire, they're both pronounced long. I'd always thought that it was semantically uni...

Akiva Weinberger

I kinda hear a difference in vowel quality, but mostly in vowel length

Leaky Nun

@AkivaWeinberger this is strange

Because I pronounce [aɪ] in side, wide, ride, and I

Akiva Weinberger

As do I

…As do /aɪ/

But that follows the "rule" with the voicings

Alessandro Codenotti

I don't want to discourage you, but I'm afraid making sense of the mess that English pronunciation is is not a task mankind is ready for

Semiclassical

20:23

Language be weird.

English in particular.

Akiva Weinberger

I think today's xkcd is just messing with us

Semiclassical

Pretty sure that's the joke, yes.

Akiva Weinberger

@AlessandroCodenotti We need a language with no vowels, so there's no chance of them moving around and changing!

Semiclassical

(pretty sure)

Leaky Nun

@AkivaWeinberger there is a language with only two vowels

Also relevant:

Akiva Weinberger

20:25

Oh weeird

I mean

Semiclassical

So vowels, plural, are relatively modern.

Akiva Weinberger

We can't ever know for sure, I assume

Leaky Nun

2 days ago, by Leaky Nun

Our reconstructed Proto-Indo-European only had one vowel

Akiva Weinberger

@Semiclassical In this language family, at least.

Leaky Nun

2 days ago, by Leaky Nun

(it is the hypothetical ancestor of the Indo-European languages including Sanskrit, Greek, Latin, German, and English)

@Semiclassical "relatively"

talking about something like 2kBC (really rough estimate)

Semiclassical

20:26

Right.

Akiva Weinberger

@Semiclassical And it's possible whatever came before PIE had lots of vowels, and they just all got lost somehow

Alessandro Codenotti

@AkivaWeinberger "Equinox (solstice in British English)" is genius

Akiva Weinberger

Oh, they're opposites of each other, aren't they @AlessandroCodenotti

I only realized this just now

Alessandro Codenotti

They're 3 months apart

Semiclassical

I'm not sure what should count as 'modern' when it comes to language tbh.

Leaky Nun

20:27

@Semiclassical I've seen estimates like 10k BC

Akiva Weinberger

The Germanic branch of languages has an abnormally large vowel inventory, I've heard.

Semiclassical

Though I'm not sure anyone else does either.

Leaky Nun

@AkivaWeinberger just English, I've heard

Semiclassical

Language, by its very nature, isn't something we can have archeological data on.

Leaky Nun

Proto-Germanic is mainly /a/ /e/ /i/ /o/ /u/

i-mutation (umlaut) gave us two mores

Akiva Weinberger

20:28

@LeakyNun Really? How much does, say, Swedish have

Krijn

Dutch has a lot I think

Akiva Weinberger

Or German

Krijn

We combine like o and e to get oe

Semiclassical

Best one can have is writing, and I imagine that's both rare and not really relevant.

Alessandro Codenotti

We cut the consonants in Italian, our alphabet has 21 letters

No need for j,k,w,x and y

Leaky Nun

20:29

1 min ago, by Leaky Nun

@Semiclassical I've seen estimates like 10k BC

no, not 10k BC. more like 100k BC.

Akiva Weinberger

I mean Norwegian has AEIOUÆØÅ (as I write this I realize I forget what Swedish does)

Semiclassical

Interesting. In that sense, 2kBC really would be modern.

Akiva Weinberger

So even without spelling irregularities that's 8

Semiclassical

It does seem like a question that will remain mysterious: How and when did human language arise?

Tobias Kildetoft

@AkivaWeinbergerSwedish has å, but not æ and ø

they have ä and ö instead of those

Leaky Nun

20:31

> The large inventory of vowel qualities is a later development, due to a combination of Germanic umlaut and the tendency in many Germanic languages for pairs of long/short vowels of originally identical quality to develop distinct qualities, with the length distinction sometimes eventually lost. Proto-Germanic had only five distinct vowel qualities, although there were more actual vowel phonemes because length and possibly nasality were phonemic.
In modern German, long-short vowel pairs still exist but are also distinct in quality.

Akiva Weinberger

@Semiclassical You can try looking it up online, but everything kinda looks like "We have no idea" + more words

Semiclassical

That it happened is plainly evident. But the research tools seem just so limited and speculative.

Tobias Kildetoft

(similarly to German)

@AkivaWeinberger Also, y is considered a vowel in the Nordic countries

Akiva Weinberger

Spanish (like Italian EDIT: no) has five. Well, you can also form some diphthongs out of those five, I don't know if those count

Semiclassical

@akiva Ignoramus et ignoramibus

Leaky Nun

20:32

@TobiasKildetoft umlauted /u/ (i.e. /y/)?

@AkivaWeinberger Italian has 7

Akiva Weinberger

@TobiasKildetoft Really? I knew about Finnish (completely different language family), not the others

Leaky Nun

open/close e, open/close o

bene vs beve

Tobias Kildetoft

@LeakyNun No, none of the Nordic countries have ü

Leaky Nun

(@AlessandroCodenotti can confirm)

Alessandro Codenotti

@AkivaWeinberger according to wikipedia u,i,e,o all have 2 different pronunciation in Italian

Akiva Weinberger

20:33

Hm weird

I think I heard somewhere Arabic has three.

Tobias Kildetoft

I don't think any Danish vowels have less than two ways to pronounce it

Akiva Weinberger

/a/ /e/ /u/

I'm glad we're focusing on vowels, because there are some languages in the Caucasus that totally have us beat on consonants.

Like 60 consonants or something.

Leaky Nun

9 mins ago, by Leaky Nun

@AkivaWeinberger there is a language with only two vowels

Akiva Weinberger

That's from there isn't it

Leaky Nun

yes, many consonants and 2 vowels

Krijn

20:35

That just seems unnecessary

Leaky Nun

@AkivaWeinberger Arabic definitely has "i"

Akiva Weinberger

Oh

Leaky Nun

hijab

jihad

islaam

Alessandro Codenotti

Here. Also the "h" is completely silent in Italian, it took me a lot of time to learn how to read the English "h" at the beginning of a word and I still mess it up now and then

Leaky Nun

wait, where is /e/?

Akiva Weinberger

20:36

@LeakyNun Oh, I see, turns out it was

Modern Standard Arabic has /a/ /i/ /u/, plus vowel length

(long and short)

and of course tons of regional variation

Leaky Nun

@AkivaWeinberger i see

Akiva Weinberger

Inuktitut has the same vowel inventory IIRC

Leaky Nun

@AkivaWeinberger yes, confirmed

and then Japanese has only a e i o u, just like Spanish

Akiva Weinberger

Is it possible to teach children to reliably distinguish all vowels of the IPA?

Guess: no

(Side note, I don't actually know how to write down most of the vowel sounds I make)

(in the IPA)

Leaky Nun

Danish has 32 vowels :o

Akiva Weinberger

20:40

WHAT

Leaky Nun

@AkivaWeinberger in which language?

Tobias Kildetoft

@LeakyNun I would not be surprised to know we have that many vowel sounds :)

Akiva Weinberger

> The vowel system is unstable, and the contemporary spoken language is experiencing a merger of several of these phonemes. The following vowel pairs may be merged:

etc

@LeakyNun English.

Leaky Nun

32 vowels, and 0 diphthongs.

Akiva Weinberger

Where are you gettin 32

Leaky Nun

20:42

@AkivaWeinberger eh, long and short, sorry

Akiva Weinberger

Oh

Well that's 30 using the above chart (/a/ and /upside-down v/ don't have variable lengths)

But still, wow

Tobias Kildetoft

I have no idea which of those correspond to which sounds

Leaky Nun

@TobiasKildetoft the position in the trapezium is supposed to tell you the position of your tongue

Akiva Weinberger

> Unstressed [ɪ, ʊ, ə, ɐ] are not shown.

Damn

Tobias Kildetoft

@LeakyNun I am not sure how much I feel like trying out all the vowel sounds to see where my tongue is when :)

Akiva Weinberger

20:46

> /syns sønˀs sœns/ synes, synds, søns

Leaky Nun

IPA recognizes 39 vowels (ignoring length etc) so Danish is not even half

Akiva Weinberger

Well that's three

Tobias Kildetoft

@AkivaWeinberger are those three the words with those sounds? Because the first one can be pronounces in two ways depending on the meaning

Leaky Nun

Danish only has 21 phonemes, even including length

Tobias Kildetoft

And the second one is not a word on its own

Leaky Nun

20:49

@TobiasKildetoft ('seems', 'sin's', 'son's')

Akiva Weinberger

OK I thought I knew how to pronounce IPA but this passage broke me

(The text sample on the bottom of the page)

Tobias Kildetoft

@LeakyNun Yeah, the second one only becomes a word as part of a composite (and the first one would probably be pronounced in only one of the two ways except in very rare cases)

Akiva Weinberger

In any case, I'm sorry, Tobias, but I will not learn Danish any time soon.

Tobias Kildetoft

@AkivaWeinberger Not a very useful language to learn anyway

Leaky Nun

@TobiasKildetoft how is your name pronounced?

Akiva Weinberger

20:53

Send us a Vocaroo link

Tobias Kildetoft

@LeakyNun vocaroo.com/i/s0H39kRmdQvF

Leaky Nun

@TobiasKildetoft so the "d" is silent?

Tobias Kildetoft

Yes, though it would have been pronounced differently without the "d" there

Effectively, the d is pronounced as another l

Leaky Nun

interesting

Tobias Kildetoft

I usually pronounce the d when I introduce myself to people who don't speak Danish, as it is much easier for them

Leaky Nun

20:58

fwiw Danish has one of the most irregular spelling systems

Tobias Kildetoft

It was kinda funny last time I gave a talk, since that was in Sweden, and the chair pronounced my name correctly, except he pronounced the k in my last name as one would in Swedish, where it is more like an "sh"

Yeah, we like us some irregularities and strange and isolated special cases

Leaky Nun

@TobiasKildetoft like the "ch" sound in German "ich"?

Tobias Kildetoft

@LeakyNun Sortof, but not exactly

Also, how precisely it is pronounced is somewhat regional

(and don't get me started in the Swedish pronunciation of "sj" and the endings "tion" and "sion")

Leaky Nun

@TobiasKildetoft ok, I won't get you started

Faust7

22:27

Blargh

Does Blargh mean yes?
(): Blargh?

(): See Blargh means yes.

Akiva Weinberger

@Faust7 In Polish, "tak" means "yes". In Indonesian, "tak" means "no".

Unhelpful: "Are you speaking Polish?" "Tak."

Paradox: "Are you speaking Indonesian?" "Tak."

Faust7

=)

that makes me happy and i learned two things thank you

Akiva Weinberger

Also look up the flags of Poland and Indonesia

Poland:

Will Hunting

@AkivaWeinberger You seem to be a polyglot.

Akiva Weinberger

Indonesia:

Faust7

22:40

Polands great they invented the toilet seat you know?

Akiva Weinberger

They're the same but upside-down!

@WillHunting I know some languages. Polish and Indonesian are not among them.

I just know this fun fact

Will Hunting

I only know English reasonably well.

Faust7

Took the French to put a hole in it; but whos perfect?

Morning @TedShifrin

Ted Shifrin

Good afternoon, Faust.

Faust7

Excited for September?

I talked to my adviser today

less worried

Ted Shifrin

22:49

Um ... Should I be? Oh, and ...

No point worrying, so long as you work hard.

Faust7

Yeah he said that

was trying to get idea what grads i needed to get into the masters program

Ted Shifrin

Good.

Faust7

took him awhile to explains that its not "just" about grades

and he said i could defer the honours project off till the winter semester if i dont know what i want to do so ima do that and try and contact that other prof in September and see if we can work out an agreement to do something in dif geo

Will Hunting

23:31

@Faust7 I didn't know you are a math student.

Faust7

@WillHunting not a particularly good one

but i am at UVIC in canada

dsillman2000

Any chance someone could quickly help me take a matrix derivative?

Faust7

what size is it?

lets just say yes

dsillman2000

It's quick

but I don't know too much about linear algebra calculus

Faust7

link /post

We all have to start somewhere

dsillman2000

23:45

$\frac{\partial }{\partial \mathbf{y}}\left[ \left(\mathbf{x}\cdot \mathbf{y} \right ) \cdot \mathbf{z} \right ]$

where none of the matrices are the same size

so just taking out y would yield $\mathbf{x} \cdot \mathbf{z}$ which are not compatible sizes

x is compatible with y

and their product with z

but not x and z

Faust7

your notation is alittle confusing

dsillman2000

ohh hang on

y doesn't get replaced with a scalar $1$ does it?

It gets replaced with a matrix of $1$'s the shape of y, right?

Faust7

Well y is eitheir a vector a matrix by definition

dsillman2000

Matrix

Faust7

and the derivative is with respect to the second variable

not the derivative of the y matrix

dsillman2000

23:49

Yeah

It's the derivative of the expression

with respect to the y matrix

Faust7

normally with given values you'd calculate the dot product then take the derivative of the sum

dsillman2000

Yes, which is achievable by simply making y a matrix of ones in the shape of y, correct?

Faust7

for example $ y * y^2$ the derivative of this with respect to y is $3y^2 $ not $1* 2y$

dsillman2000

Because then the dot product would yield the sum of all of the contents of x

Faust7

so im not seeing how you can take the derivative of one of the matrices terms before calculating the dot product?

dsillman2000

23:52

You can symbolically

It simply depends on the order in which the dot product is presented

Like the derivative of the expression with respect to z

is just $(\mathbf{x\cdot y})$

Faust7

Ic, im afraid you need someone more adept in there understanding of what you are doing

dsillman2000

i'll see if my newfound hypothesis works in the program

Faust7

^^

sorry i couldnt help

dsillman2000

It's cool

you helped more than you know ;)

Faust7

Im glad lol, gotta move a computer brb

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$Mathematics$ Mathematics