Mathematics - 2017-04-03 (page 3 of 3)

10:05 PM

@MikeMiller, @PVAL-inactive: Do you guys have any recommendations regarding reference management software?

Mathjax not showing up

Oic, you click see full text

Simply Beautful Art, I already see $a#b$ occuring twice above, you are already larger than the smalllest grammar of your symbol alphabet that includes operators and letters.

I recommend trying to understand $F3\#3\#3$ before moving on to involve the @ symbol

Therefore your expression is not optimal

Why not compress that string further?

Heck no, its not meant to be optimal, its meant to be simple, beautiful, and somewhat of an art

Oh

10:09 PM

@Danu no

Aiming for a simple technique that produces large numbers is better than optimizing little things, especially when using it for actual purposes

Yes, but smallest grammar by definition is at least as simple as string unless smallest grammar is string (approximately)

@MikeMiller You don't use any?

no

Unfortunately, I cannot immediately grasp the effect of what you are saying. My question in return is this:

Given some $Fa\#\dots\# b$, is better to use your idea or add a few more characters like $Fa\#\dots\# b@c\# d$? If my notation easily captures yours, then there is no point. See the beauty and simplicity behind this?

It is like the argument "well multiplying an exponential function by five will make it bigger" but the truth of the nature is that the exponential function multiplied by a constant is not 'much bigger' as in it can still be easily rewritten using exponentiation alone.

10:13 PM

@MikeMiller Who needs references when you can prove it all yourself, I guess ;-)

with a small shift horizontally. Now doing a constant raised to the exponential function is a whole different matter...

Oh, Ic, if you can encode mine with yours and make a smaller string, then you win?

Well I already did that, son!

@SimplyBeautifulArt

:|

I use references, just not a reference manager

LOL

10:14 PM

my bookmark bar is a form of reference manager i guess

Balarka Sen

lol

What do you mean? @FruitfulApproach

Ted Shifrin

Balarka, you're supposed to be un-sleeping.

@MikeMiller I was joking.

Balarka Sen

@Ted Like the unknot?

10:15 PM

If you have expressions $UsU$ occuring such that $|U| \geq 3$ then there exists a smallest grammar of smaller size than your string, that represents your string perfectly.

Ted Shifrin

un-knot-sleeping?

I'm fairly certain I can make a function that grows way faster than anything you've got in mind. This function is only an introduction type thing for something I'm working on

Balarka Sen

sounds like "I'm not sleeping"

But if you include the LHS and $\rightarrow$ symbols in your size of the grammar then perhaps $|U| \gt 10$ or somethign

@MikeMiller It kind of gets out of hand for me though... I've already got like 50 papers collected... Just keeping them in folders is getting too messy.

10:16 PM

@FruitfulApproach Well, your just reusing my notation aren't you? Isn't that a tad cheating?

Plus, eventually you'll need a bib(la)tex file to compile your paper...

No, it's a general approach for any alphabet, you can apply it to any stage with data

Yeah, but that's then and this is now.

#hashtag

@SimplyBeautifulArt Why redo your work, when it can be improved upon slightly?

10:17 PM

How do you propose to optimize this then? (Using only the given letters and such)
$F5\#5@5\#5$

If you wanted to calculate the absolute smallest you would need to prove that some algorithm can do this, but this algorithm is really difficult to code I've found

I guess you can just make the bibtex file by hand.

That is easy:

Of course its difficult! *shakes his head*

$A \to 5 \# 5$

10:18 PM

And you want to write $FA@A$?

Final grammar is $ |s| - 1$ where $s$ is your string

But you're right somewhat

if You include your definition of grammar size (which for your purposes sounds like you would), then what I said is not true, and you would need either 7-10 + $5\#5$ 's

or a longer string, longer than $5\# 5$

That doesn't make any sense, as I've defined my array function, having variables involving $\#$ is not well-defined (yet)

Then I would be right

Hey @AkivaWeinberger

I can look at your full text, paste it here

And see if I can compress it

10:20 PM

I made a simple function that is awesome

15 mins ago, by Simply Beautiful Art

Fast-Array-Iteration-Leaping (FAIL):

$$?,d=0\text{ or anything using @ symbol}\\Fa=a+1\\Fa\#\dots\#b\#?=Fa\#\dots\#b\\Fa\#b\#\dots\#c=F[a]a\#b-1\#\dots\#c\\F[1]a\#b\#\dots\#c=Fa\#b\#\dots\#c\\F[k]a\#b\#\dots\#c=F[k-1](Fa\#b\#\dots\#c)\#b\#\dots\#c\\Fa\#?\#\dots\#?\#1.0\#b\#\dots\#c=Fa\#?\#\dots\#?\underbrace{\#0\#\dots\#0}_a\#a\#1@0\#b-1\#\dots\#c\\Fa\#?\#\dots\#?\#d@0\#b\#\dots\#c\\=Fa\#?\#\dots\#?\underbrace{\#O(d)@a\#\dots\#O(d)@a}_a\#a\#d@0\#b-1\#\dots\#c\\O(a)=a-1\\O(d@0)=O(d)@a,\text{ where $a$ is the first number in FAIL}\\O(d@e)=d@e-1\\Fa\#?\#\dots\#?\#d@e\#b\#\dots\#c\\=Fa\#?\#\do…

Please click the "15 minutes ago" button to see original full message

@AkivaWeinberger By awesome I mean it produces large numbers without transfinite ordinals

@FruitfulApproach I think that when you see the full force of my function, you will realize why it is near impossible to make any significant improvements

@FruitfulApproach By the way, I'm still not done with my function

I have plenty of notation that translates currently into $\underbrace{a@\dots@a}_a$ or something like that.

Also, be careful when expanding... it will probably simplify slower than you want it to

If you can produce a better system that produces numbers so large they can not effectively be expressed using the current notation, then do enlighten me. @FruitfulApproach

11:09 PM

A mixing blade on a food processor extends out 3 inches from its center. If the blade is turning at 600
revolutions per minute, what is the linear velocity of the tip of the blade in feet per minute?

I did 600rev/1 min * 2 pi rad / 1 rev * 60 mins/1hr

got 72000 pi rad

I don't know how to convert it into feet

V = ωr = 600 * 3 = 1800 in/min = 150 ft/min

oh nvm I didn't have to convert at all

@MATHASKER Your profile is out-dated

@SimplyBeautifulArt tru lol Imma change it

@MATHASKER Don't you feel like you have something to be proud of to put on your profile?

11:23 PM

@SimplyBeautifulArt not really

just saw a weird question in functions

low level but..

:O Neat name @IPAddress

Semiclassical

@MATHASKER Simplest thing is not to go into radians. Instead, how far does the blade turn in one revolution?

given a result of a composite function you have to write it in terms of the individiual functions (you are given these functions)... however it can only be done by comparison

360 degrees

11:26 PM

individual*

@SimplyBeautifulArt thank you

Semiclassical

Well, that's the angle. But what distance does the tip of the blade move?

can it be done in a method other than comparing?

idk 2pi maybe?

A gas-driven lawnmower had a blade that extends out 1 foot from its center. The tip of the blade is
traveling at the speed of sound, which is 1,100 feet per second. Through how many revolutions per
minute is the blade turning?

v = 1100 ft / 1 sec

and the radius is 1 ft

1100 ft / sec = w * 1 ft

should i multiply it by 2 pi rad / 1 rev?

I don't know what to do im stuck

thats physics

circular motion

11:41 PM

oh, we're doing it in pre calc right now