Mathematics - 2011-10-15

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robjohn

00:00

Oops, there go my 6 minutes :-)

It's a new day on MSE.

J. M.

Nah, I think it's more me than you guys... :)

robjohn

I added the Conclusion so that it would be more obvious that I was answering the question, but that didn't seem to help.

@J.M.: you back from work?

I'm trying to remember everyone's timezone, but failing I think.

You are 12 hours different so your Saturday morning is just starting, right?

J. M.

No, I just woke up. :)

Right, it's Saturday morning here.

robjohn

8:05

J. M.

Yeah.

robjohn

00:05

15 hours actually

I wonder if there is a clock app in which I can put names under a series of clocks, one for each regular chat member.

J. M.

Make it like those things they use for newscasts... :D

robjohn

Yeah or have in airports.

I have to run some errands and take the dog for a walk before dinner. I will be back after dinner.

J. M.

See you.

4 hours later…

robjohn

04:06

user image

4 hours later…

A T

08:04

maths is raging me

J. M.

08:15

Mind elaborating?

robjohn

08:41

I guess no elaboration

1 hour later…

Gortaur

10:06

@robjohn send me the link if you find it

robjohn

10:46

@Gortaur what link?

Gortaur

on clocks )

2 hours later…

robjohn

12:22

@Gortaur: The clock widget for the Mac allows multiple instances. I just made one for Jeruusalem, Amsterdam, and Manila. I will add more as the need arises.

J. M.

Add one for Zurich. ;)

robjohn

who's in Zurich?

J. M.

t.b.

robjohn

Ah

didn't know

And Zurich :-)

Zurich is the same timezone and Daylight Savings settings as Amsterdam

J. M.

Ah... that's my fault for not looking at a map... :D

robjohn

12:35

I had to look on the web to find out they were the same

t.b.

13:11

Hey guys, greetings from Zurich! Yes, there is only one time zone in most of continental Europe (except Portugal and some countries far in the east). However, @JM, Switzerland is an exception in that we don't have Euros, but still Swiss Francs (see the nice little island in grey at the heart of Europe, that's us separatists :))

J. M.

Just like the Brits... okay. :)

t.b.

We're different, we don't even pretend to participate in the European Union...

J. M.

The neutrality does look to be a long-standing tradition...

t.b.

Yeah, that's what the right wingers try to sell us... However, looking more closely, the "neutrality" would more appropriately be called "opportunism": call yourself neutral and collaborate with the evil powers as far as they need you to and they'll pardon your quirks and even let you call yourself neutral...

Anyway, that's my impression

J. M.

Ah, reminds me of the story of the bat...

t.b.

13:20

exactly, we certainly do have teeth...

Gortaur

13:50

@tb more about russian emoticons. Schrodonger one is :):

J. M.

I'd call that the bipolar smiley...

Gortaur

JJust saw it on bashorg

J. M.

Man, I wasted days on that site years ago... :D

Asaf Karagila

I just called JDH's question "The Ultrafinitists Nightmare" :-)

J. M.

@Asaf: I just *knew* it'd be a "Nice Question" in a few hours...

Asaf Karagila

13:57

@JM: Do you have a good bread recipe?

This time I have prepared yeasts :-)

J. M.

Oh, with yeast? Hmm...

You want something spiced up, or would something plain do?

Asaf Karagila

Well, I'm gonna add olives, tomatoes, onion...

But that can be added to pretty much any given bread.

J. M.

Hmm, hmm... the notebook for my recipes is in another house, but let me check if there's anything on the Internet that's similar...

Asaf Karagila

k

J. M.

I think this is the nearest to mine, except I don't use olive oil... the prices for that are sort of steep here.

Asaf Karagila

14:08

I wouldn't use any other oil for something like bread, actually :-)

J. M.

Well, you can afford olive oil, so by all means use olive oil! :D

No need to shackle yourself with the limitations I have...

(my dirty secret: I use clarified butter in place of olive oil.)

Asaf Karagila

This is a dirty secret indeed! :-)

J. M.

At least it is still tasty. I would imagine using olive oil would make for better bread... but all I can do is imagine.

Asaf Karagila

Take a trip to Israel once.

J. M.

Maybe some day. :)

Asaf Karagila

14:14

Yuck.

Multigrain?! Whole wheat?!

J. M.

That's for those who feel they don't have sufficient fiber...

I use wheat.

not the multigrain. I'm not dieting... :P

Asaf Karagila

Well, this is the same recipe I found in Hebrew, modulo garlic, tomatoes and that stuff. Which I was gonna add anyway.

I'll let you know how it went.

J. M.

If you can, take a picture.

...on another note: at last, everybody on the first page of the Users page is 10k+...

Asaf Karagila

14:40

Hm.

I just realized it.

Tomorrow we're going to visit my girlfriend's parents. No use baking a loaf of bread.

t.b.

@Gortaur: This strikes me as a schizophrenic smiley :)

There are so many lazy questions here recently. Many of them are simply answered by entering the title into Google...

smanoos

Hello

I am glad I could join this room

J. M.

14:55

I'm not sure people have a good realization of "effort typing into Google" versus "effort typing into m.SE"...

Asaf Karagila

@JM: What sort of yeast-to-flour ratio I should use?

Calle

O hai.

J. M.

@Asaf: How puffy do you need it to be?

Asaf Karagila

Hardly, but not completely dry.

Calle

You're baking mathematical bread?

Asaf Karagila

15:02

I'm gonna use about 1 cup of flour, and fresh yeast.

Calle

Make a bread with genus 3.

J. M.

What sort of yeast do you have again?

Asaf Karagila

Fresh. They come in this cube of yeast...

J. M.

@Calle: three-hole doughnuts have been done a lot of times...

Calle

Make a loaf with genus infinity then!

J. M.

15:03

Wait, what? Cube? Not something powdery?

Calle

We have cube yeast here.

Asaf Karagila

It's a cube of fresh yeasts. Powdery, but not too dry I think.

J. M.

Hmm, okay. A teaspoon or so to three cups of flour should be fine.

Asaf Karagila

So... if I'm gonna go with one cup of flour, about a third of a teaspoon?

Or is there an amount which is "too little" for the yeasts to start ferment?

J. M.

If you use too little, it'll take a while to rise...

Calle

15:07

Or how about bread with the shape of a Julia set?

Asaf Karagila

Okay, I found the ratio. 50g fresh yeasts (which is what I have) is about 25-30g dry yeast.

J. M.

Oh! Apparently I didn't see you type "fresh". No wonder I was confused.

Asaf Karagila

:-)

J. M.

So with that conversion... you need about two teaspoons for three cups.

Asaf Karagila

Right.

cracks his knuckles. It's bakery time!

J. M.

15:11

:D

Asaf Karagila

Oh wait.

Before I start with that...

How much sugar/yeast?

J. M.

Ah, what sort of sugar are you using?

Asaf Karagila

White, usual, whatelse sugar.

Although I have brown sugar as well.

J. M.

Something I should've asked first: have you proofed your yeast already?

Asaf Karagila

Proofed? No. I handwaved them :P

Calle

15:17

Proof by yeast.

J. M.

:D I mean you need to test your yeast first.

Asaf Karagila

I figured that.

How do I do that?

J. M.

You mix up a teaspoon of sugar and two teaspoons of yeast into warm water.

Calle

If it's new yeast it's not really necessary.

J. M.

wait a bit, and check for bubbles.

@Calle: you never know... ;)

Asaf Karagila

15:19

k.

robjohn

@Calle How much butter would you need for bread in the shape of a Julia set?

J. M.

Sorry, was on the phone. Anyway, usually, you don't have to add sugar anymore; the yeast can feed on the carbohydrates in the other ingredients.

You just need to knead really well.

@rob: I'm not even sure the shape would stay nicely with oven heat... :)

Calle

@robjohn: Dunno, I have not tried it.

robjohn

@J.M.: I some Julia sets are connected. I wouldn't think you would want bread in the shape of Julia dust.

Calle

I think ducks would like it.

robjohn

15:29

but yeah, with rising the gaps wouldn't survive.

Calle

You have to plan ahead. It should look like Julia set after you take it out of the oven.

robjohn

@calle it would work great for bread crumbs

Asaf Karagila

I think I used too much water in this proof.

There's a little bubble in the middle, but that's about that.

robjohn

That's right, its called Fatou dust when the Julia set is for a point outside the Mandelbrot set.

J. M.

Just a cup of warm water... ;)

Asaf Karagila

15:36

Well.

What do I do? Are the yeast proofed or do I need to run another test, or what?

Aha! The yeasts are fine. The water bubble up slowly.

J. M.

Ah, there you go.

Asaf Karagila

So now I take a teaspoon, about a 1/3rd cup of water and a teaspoon of sugar, mix it, prepare the flour with some salt, and then pour the water on the flour?

J. M.

Nono, you can skip the sugar...

Asaf Karagila

k

J. M.

and, don't mix the salt with the yeast at once

Asaf Karagila

15:44

I know I know.

Mix the salt with the flour first.

J. M.

Okay, I think you've got it down... :)

Asaf Karagila

I will be back.

Asaf Karagila

15:56

So I put the yeast in the water, and added water into the salt/soda carbonate/flour.

Do I wait 10 minutes, or do I mix it right away?

J. M.

Ah, hmm... shouldn't need that long a wait...

Gortaur

hoho, I found baharat

this arabic shop is really cool, they have also rice for piloff

Asaf Karagila

Great.

J. M.

only about the time it took to proof your yeast...

Asaf Karagila

Took me about 15 minutes before they started bubbling.

J. M.

15:59

wait, what?

really, 15?

Asaf Karagila

Well, it could have been that I used too warm water, or something. Not sure really.

J. M.

It's the kind of "warm" that you can dip your fingers into...

Asaf Karagila

Yeah, I used that kind of warm for this batch.

robjohn

@Gortaur: you've been looking for baharat for a while now. I'm glad you've found it.

Is it the kind you like?

Gortaur

yes

J. M.

16:04

@Asaf: Anyway... you did say you have fresh yeast; ideally you only need to have the yeast sit for five or so minutes before kneading.

Gortaur

I used it in Russia in fact

we call it chmeli-suneli

J. M.

I would understand ten if like me you use dry yeast...

robjohn

@Gortaur: I will keep my eyes open to see if they have any here.

J. M.

My eyes are drooping already, so... see you guys.

Gortaur

@robjohn what's more cool - they have carnation

robjohn

16:14

@Gortaur Carnation baharat?

or just Carnation products in general?

Gortaur

google translate betrayed me

Cloves (Syzygium aromaticum) are the aromatic dried flower buds of a tree in the family Myrtaceae. Cloves are native to the Maluku islands in Indonesia and used as a spice in cuisines all over the world. Cloves are harvested primarily in Indonesia, India, Madagascar, Zanzibar, Pakistan, and Sri Lanka. The clove tree is an evergreen that grows to a height ranging from 8–12 m, having large square leaves and sanguine flowers in numerous groups of terminal clusters. The flower buds are at first of a pale color and gradually become green, after which they develop into a bright red, whe...

robjohn

Ah, clove. :-) We have a good supply of that, we overbought last winter when we made a lot of mulled cider.

I will have to pull up our recipe. It's getting time to start making more.

We make a very tasty mulled cider.

1 gallon cider
1/2 c. firmly packed brown sugar
4 to 5 whole cinnamon sticks, break into pieces
10 to 15 whole allspice
20 to 25 whole cloves
1 sliced lemon

In covered 6 quart kettle, bring cider, brown sugar, and spices to a boil;
add sliced lemon. Uncover and simmer on low heat for 1/2 hour.

We sometimes use orange and lemon

Gortaur

16:29

1/2 c in gramms how much is it?

robjohn

that's a volume: 1 cup. let me look up the conversion to cc

1 US cup = 236.588237 ml

approximately ;-)

Gortaur

))) like in europe

who is allspice

robjohn

1 gallon = 3.78541178 liters

allspice was mentioned in the recipe I found for baharat I think

Allspice, also called Jamaica pepper, pepper, myrtle pepper, pimenta, or newspice, is a spice that is the dried unripe fruit ("berries") of Pimenta dioica , a mid-canopy tree native to the Greater Antilles, southern Mexico and Central America, now cultivated in many warm parts of the world. The name "allspice" was coined as early as 1621 by the English, who thought it combined the flavour of cinnamon, nutmeg and cloves. Several unrelated fragrant shrubs are called "Carolina allspice" (Calycanthus floridus), "Japanese allspice" (Chimonanthus praecox) or "wild allspice" (Lindera benzoin...

I guess it wasn't in the recipe for baharat. I was thinking of the nutmeg I think

robjohn

17:08

@Gortaur: thanks for the upvote (I assume it was you).

Gortaur

17:58

@robjohn: thank you as well. I liked your answer so much that I would put a bounty on it - but I don't know if it allowed here to put bounty a posteriori to a particular answer

with regards to allspice - we just call it 'fragrant pepper'

robjohn

18:44

@Gortaur: From the name, I never knew that allspice wasn't a mixture of other spices until I looked it up a couple years ago. :-)

Gortaur

but you can see that it is just one kind of spice when you look at it, right?

robjohn

when it is not ground, yes

I think when I was a kid, I only saw ground allspice.

Then I don't think I used it myself, unground, in anything until the mulled cider

Gortaur

how? you eat soups without it?

robjohn

without allspice?

sure

Gortaur

though since you usually saw it grounded

robjohn

18:54

when I have actually used it it was ground

Gortaur

from my childhood I usually found 5-6 pieces of allspice in my plate of soup

robjohn

until we used the whole allspice in the cider

Gortaur

and eat couple of them like my father did :-D

robjohn

that is like crunching on a peppercorn

clears the sinuses

Gortaur

I had sinusit wen I was young and I know now that you meant the part of the nose

rather then math function

I never clear math function I mean )

robjohn

18:57

:-)

when something is really spicy or intensely aromatic, we say it clears the sinuses

perhaps the idiom is not worldwide :-)

Gortaur

but the effect is

though I don't know if you ever tried true mustard

robjohn

Seeking explanation for this apparent paradox **shaking** the grand pillars of mathematics.

lol

@Gortaur I think I have.

Gortaur

I do not know how can we compare

sareptian one

robjohn

I know we have fields of mustard here, but there are probably different kinds.

Gortaur

that is my fear

that is what I am afraid of

that are my nightmares

robjohn

19:03

gonna go get lunch with my wife. see you later.

Gortaur

bon appetit

with regards to mustard, we have one sort there called thermonuclear. That clear sinuses for sure without and idiomatic meaning

3 hours later…

robjohn

22:05

quiet time.

Gortaur

22:22

yeah

Bullmoose

hi folks

Gortaur

)

hi

Bullmoose

hi @Gortaur

is there any chance any of you feel like helping me check some very simple arithmetic.... it's driving me nuts, and there is noone here in the lab besides me...

Gortaur

let's try

Bullmoose

basically, i derived an expression, getting rid of an integral, but evaluating the integral numerically in MATLAB gives a different result from the expression i derived...

thanks...

so, this is a very simple lower bound for a mixture of two normal distributions...

for entropy of a mixture of two normal distributions...

differential entropy is $-\int f(x)\log f(x)dx$

wth does the chatroom not display math?

Asaf Karagila

22:31

Yeah, there's no mathjax for the chat.

Jeff said that they are not planning on that feature anytime soon too.

Bullmoose

oh no... hmmm is there some kind of workaround you guys use?

Asaf Karagila

Yes.

We discuss cooking and alcohol most of the time.

Bullmoose

oh

Asaf Karagila

These things don't really require mathjax active.

Bullmoose

the i guess my subject is not appropriate here...

Asaf Karagila

22:34

Especially if you don't have any choice. :P

Gortaur

@AsafKaragila +1 we should remember it

Bullmoose

i know nothing about cooking besides taking stuff that my girlfriend made for me during the weekend and putting it into microwave.... i do like beer though

allright, thanks guys -- then i'll continue

Asaf Karagila

I baked bread for today's dinner.

Bullmoose

I'll do my best to keep formulas readable...

so entropy formula has a log(x) inside it... which i bound by taking (x-1) instead.

this yields the following lower bound for entropy: -int (p(x)*(p(x)-1)dx

this then simplifies to 1-int (p(x))^2 dx, because integral over the entire domain of a p.d.f is 1

so far so good..... now, my p(x) is a mixture of two Gaussians, both with zero mean but different variances....

Gortaur

@Bullmoose: ask it as a question, it would be more simple

Bullmoose

22:41

well, when i work everything out i get the following formula:

1 - (1-e)^2/(2*sqrt(pi*s1))-2*e*(1-e)/sqrt(2*pi*(sigma1+sigma2)) - e^2/(2*sqrt(pi*sigma2))

where the variances of the Gaussians are s1 and s2, the the weights for each are 1-e and e...

Asaf Karagila

+1 on Gortaur's suggestion.

Bullmoose

when i plus this into MATLAB with s1=1, s2=2, and e=0.2, I get 0.7378

when i use numerical integration of the original lower bound (containing integral), I get 0.7567

Asaf Karagila

I think that I have baked this loaf on too high of a temperature at first, but then I cut it to pieces and toasted the slices (as I intended to do anyway) so it worked out great.

I minced tomatoes and olives into the dough as well.

Then I cut cucumbers, tomatoes, more olives, and salty cheese, we had pesto and some dried tomato paste, and some other fitting cheese... it was great.

Oh snap, I'm about to get a silver tag badge.

Bullmoose

i did try different numerical integration routines, and i did "slice" up the integration.... still the same result.... i guess my question is where did i go wrong in my derivation... i'm pretty sure i did all my steps correctly, and i re-did them thrice.

robjohn

23:03

user image

That came out pretty small.

Asaf Karagila

insert "that's what she said joke" here

Bullmoose

still readable.... and that's precisely what i got as well

robjohn

:-p

Bullmoose

ok, so i am not crazy

MATLAB is

robjohn

@Bullmoose I tried to copy what you wrote above

I don't know where it came from, so I just copied.

Asaf Karagila

23:06

I sure hope there won't be many questions in the next three days.

We're going to my girlfriend's parents, and they don't have wifi and the keyboard on her brother's computer just suck. Not to mention a CRT monitor. Yes, you read it right - CRT.

robjohn

@Asaf: at least you could all huddle around the monitor and keep warm.

Gortaur

@AsafKaragila ?

robjohn

and perhaps see images of your skeletons.

Asaf Karagila

I can look at the mirror and see my skeleton... BMI 18 for the win.

robjohn

@Gortaur: he was referencing my comment about the imported image.

That came out pretty small.

@Gortaur: I responded to a question you asked in August. It might be just the sort of answer you didn't want. :-)

yayu

23:13

my problem got solved.. thanks @j.m for the suggestion

Asaf Karagila

I will take credit on his behalf, since he is not here and I am the Koenig.

robjohn

@yayu: what question?

yayu

i had asked here what to do about some serial downvotes

robjohn

what did you do?

yayu

@robjohn ^

Asaf Karagila

23:17

I prefer the older interface of parallel downvotes.

yayu

i mailed the team

as the script had failed to detet it

Asaf Karagila

It had bigger cables, even if the capacity was smaller.

robjohn

@Asaf: but that messes up the capacitance.

or the resistance, or both.

Asaf Karagila

I'm a set theorist, I don't have to care.

yayu

parallel downvotes, hmm.. a single downvote for multiple questions?

Asaf Karagila

23:19

No. It's downvotes in parallel universes.

robjohn

or downvotes that never affect the same question.

Asaf Karagila

Or just downvotes from users that never met and never will meet.

robjohn

o|` turn those downvotes upside down o|`

those notes came out badly

yayu

or casts a vote and assigns a probability...

then server computes the expectation value

Asaf Karagila

Hey, that could be an interesting test. The server tries to compute the probability for you to upvote a post.

Based on your votes history and some other nonsense.

yayu

23:22

meanwhile the question would remain in a state of -1 and +0 at the same time

robjohn

acceptances without upvotes. The answer is correct, but not very good?

what does it signify? :-o

Asaf Karagila

Some users are not aware that it is polite to upvote useful answers, in particular the accepted one.

And many times these users ask questions that hardly anyone looks at.

And when people do look at it, they are usually too lazy or unfamiliar with the subject to judge the quality of the content of the question and the answers.

Thus, you have questions with answers, and an accepted answer, and all those have zero votes.

yayu

i have done this sometimes

robjohn

I have seen some answers with votes, but the accepted answer with no votes.

yayu

for example.. this question

the answer cited references which dealt with the problem

but either did not have the access to or background to understadn the reference

but from the abstracts i could tell that they dealt with the problem.. so it was a correct answer

Asaf Karagila

23:29

The only reason I did not vote for an answer to a question I'd asked is that it was completely not useful.

yayu

what is the number (6358) below my gravatar

robjohn

I answered a similar problem in a summer course where the instructor gave it as a counter intuitive induction problem. The answer was 1,2,4,8,16, then 31. I computed the actual answer, but he simply ignored it thinking I couldn't have solved it.

Asaf Karagila

lol

robjohn

@yayu: your reputation

yayu

my reputation is less than a third of that

Asaf Karagila

23:31

It's your overall SE reputation.

robjohn

I think it was the number of regions a disk is divided into when connecting n points on its boundary.

1->1, 2->2,3->4, etc

@yayu: chat.stackexchange.com/users/12072/yayu

your rep there is 6K+

Hey, my rep is bigger than the one below my gravatar

yayu

yeah .. a result of linking too many SE sites and getting +101 on each by default

robjohn

My gravatar says 5736, but I am at 6092.

yayu

i see the number as 6092

strange

robjohn

Hmm. I see 5736 beneath my gravatar. Odd.

I see 6400 beneath yayu's gravatar.

and you said you see 6358

yayu

23:36

i see 6358

robjohn

weird.

yayu

yes

robjohn

perhaps we are in parallel universes.

yayu

well, you're about to gain 250 in rep

Asaf Karagila

You should refresh.

The chat server does not fetch the reputation continuously.

robjohn

23:41

Wow. I just went up to 6092 when I refreshed. Thanks Asaf! :-)

Asaf Karagila

Yeah, I had a similar jump from 14.9 to 15.2 a few days ago :-)

yayu

can anyone tell me where i can find an accessible proof of schur's lemma

Asaf Karagila

Do you read Hebrew?

yayu

no.. though ive been in israel :)

Asaf Karagila

Well, I could have pointed you to some great representation theory lecture notes if you'd read Hebrew.

yayu

23:51

is there literature which treats rep theory assuming a background of only linear algebra and groups

Asaf Karagila

I have no idea. I studied it in a course, I think that we used Serre or Lang or possibly Folland.

yayu

ok.. can someone help me with a linear algebra concept?

Asaf Karagila

Maybe.

yayu

what is the relation between the kernel of a linear map and its invertibility

Asaf Karagila

A linear map is invertible if and only if its kernel is trivial.

robjohn

23:54

If the kernel is {0}, then it is invertible

what he said :-)

yayu

yes.. if there is a no trivial kernel then the map is invertible...

how do i prove this

Asaf Karagila

Well, if the map is invertible then it is 1-1.

robjohn

If there is a non-trivial kernel, it is not invertible

Asaf Karagila

Just show that a linear function is 1-1 if and only if its kernel is trivial.

Assume Tx=Ty, then T(x-y)=0.

Therefore x-y in Ker(T)

yayu

ahh

get it

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