Mathematics - 2017-06-14 (page 1 of 9)

TheGreatDuck

00:03

@AkivaWeinberger

tazdingo

Hello!

i have a math question haha :)

Akiva Weinberger

Ask

tazdingo

so we have that for a Normal distribution (u,o^2) the density is the integral from -inf to +inf, is this http://sites.nicholas.duke.edu/statsreview/files/2013/06/normpdf1.jpg

Ok, that integral integrates 1. But if i change that -(x-u)^2 to -(x-(u+o^2)) is still the desity of a normal distribution??

nitsua60

00:19

@tazdingo Is your last sentence right? Notice that you've got terms quadratic in x in your first term, but linear in x in the second term.

tazdingo

sorry, i mean -(x-(u+o^2))^2

nitsua60

So you're asking "if $e^{-\frac{(x-\mu)^2}{2 \sigma^2}}$ is normal, is $e^{-\frac{(x-\mu+\sigma^2)^2}{2 \sigma^2}}$ also normal?"

tazdingo

yeah, in that integrate, if i change that term, to $e^{-\frac{(x-\mu-\sigma^2)^2}{2 \sigma^2}}$, i want to know if that still can be a density of a normal distribution. Sorry for english i'm not a native speaker, i know i might be difficult to understand me

nitsua60

No worries on the language. Yes, that'd still be normal, just with a different location for the center.

Anything that's in the form $e^{-x^2}$ will give you a Gaussian (normal) distribution. Writing it in the form of the linked image just makes it easy to see the mean and deviation at first sight.

(And the leading coefficient just normalizes the integral over all x.)

tazdingo

Excellent!! Thank you so much!

nitsua60

00:41

@tazdingo Glad to help =)

LegionMammal978

Would it be true that $\lim\limits_{x\rightarrow\infty}\left(1+\frac1x\right)^x=\lim_{x\rightarrow 1}x^{\frac{1}{x-1}}=e$?

@nitsua60 MathJax just does that randomly sometimes ¯\_(ツ)_/¯

Semiclassical

01:05

First one is definitely true. @LegionMammal978

Second one looks right too (and Mathematica agrees)

Secret

02:08

Last night dream: I was at a desktop computer in the middle of the night running some kind of 3D/4D modelling. Akiva was nearby as a looped shape with a spherical envelop is displayed on the screen. He mention how he observed there are 3 looped geometries within. Meanwhile as I take a closer look I realised that that's no loop, those are (simple) knots. The geometry shape is also indexed by the ordinal $\omega^{\omega^{\omega^{\omega^{\omega}}}}$, visible faintly rotating with the geometric obje

ct

(Rough drawing of the shape will be available later)

Faust7

02:22

...

what?

Leaky Nun

@Faust7 you'll get used to it

he likes to share his dreams

Faust7

lol

Leaky Nun

@Secret shouldn't $a_0(0,2) = 3$?

Faust7

anyone know of any universities in Canada that offer summer math classes of the third and 4th year variety?

Secret

@LeakyNun Nope because a_0(0,1)=1 and a_0(0,2) is the number after 1, which is 2

Btw simple art also camp up with an Veblen looking operator that does similar things

Leaky Nun

02:26

@Secret I mean, the motivation behind is hyperoperation, right?

or, why did you choose $a_0(0,1)=1$ instead of $=2$?

Secret

Yeah, except they are not really hyperoperation due to have add almost no rules on how to manipulate its algebra, which is why it behaves more like a notation generating function

Theoretically, I can extend its definition so that ordinal collapsing functions can be plug into it to give some really crazy looking notations

The a function is more efficient at running across tiers, but the ordinal collapsing function is better at enumerating fixed points and mixed terms

(As Well the only notation that can go beyond the large Veblen ordinal)

LegionMammal978

02:41

I've never understood ordinal collapsing functions very well

Faust7

Whats an ordinal collapsing function

LegionMammal978

Ordinal collapsing function

In mathematical logic and set theory, an ordinal collapsing function (or projection function) is a technique for defining (notations for) certain recursive large countable ordinals, whose principle is to give names to certain ordinals much larger than the one being defined, perhaps even large cardinals (though they can be replaced with recursively large ordinals at the cost of extra technical difficulty), and then “collapse” them down to a system of notations for the sought-after ordinal. For this reason, ordinal collapsing functions are described as an impredicative manner of naming ordinals....

Faust7

the only thing i understood of that was "projection function" and as far as context

>>.

user76284

03:14

An absorbing state is a state that, once reached, will always lead to itself. What do you call a state that, once reached, will never be reached again? Transient?

roscoe_casita

how will it not reach itself again?

i have a question, was hoping to ask for some help ~

a polynomial encoding, that represents and exponential encoding (replace encoding with set?)

if you generate an encoding that is polynomial, in polynomial time, that represents all of the exponential solution encodings, no more, no less,

is that beinging to border on the P=NP | P!=NP argument?

user76284

Consider the transition system $\{a \rightarrow b, b \rightarrow c, c \rightarrow c\}$.

What would $a$ and $b$ be called?

roscoe_casita

hmm, I don't know the right name, I'm software engineer

do you discard $a$ and $b$ after you use them?

user76284

What do you mean discard?

I'm talking about an abstract transition system: en.wikipedia.org/wiki/Transition_system

It's just a directed graph.

roscoe_casita

hmm, interesting, i've worked with finite autonoma before.

user76284

03:25

Yeah, like the state diagram of a finite automaton.

roscoe_casita

aye, so you have 'transient' states? that makes sense to me

user76284

In my example, I believe $a$ for instance is called a "garden of Eden" state because no states lead to it.

roscoe_casita

the start state ~ ?

user76284

I'm not choosing any particular state as a start state.

roscoe_casita

I'm probably asking this in the wrong chat room

Semiclassical

03:33

The trouble with the word 'transient' is that while it implies that you don't remain in the state, it doesn't capture the fact that you never return to it either.

I'm not sure there's a word that captures that, though.

Dodsy

@Semiclassical So, I decided that my gameplan to study for this test will be going over 42 questions from my homework that I don't think I can currently answer.

And by doing that, I'm hoping that I will have reviewed enough content to be able to write the test well.

Semiclassical

Sounds like a plan.

Dodsy

For the last test, I only studied the practice test.

roscoe_casita

ephemeral, temporal, evanescent

Faust7

Anyone know whats up with math profs and puns?

MarksCode

04:01

Hey guys, I'm looking at a proof right now that's handwritten and can't figure out what one of the symbols is. Does anybody know what the letter on the left is here: imgur.com/e3h9B7z

Faust7

sorry im not sure from that context

MarksCode

steady markov chain

steady state

Faust7

sorry nfi maybe someone else will know

MarksCode

i think its lambda but im not sure

Mike Miller

@anon that discussion on G^N was pretty helpful

thanks

MarksCode

04:10

This class makes me want to drink

Faust7

been there i took a class on Differential geometry

MarksCode

Like I have the answer for this problem right in front of me yet I can't figure out what I'm even looking at

Faust7

i can honestly say i understood about 3% of the testbook by time i finished the course

MarksCode

Does anyone here know anything about queuing systems/ markov chains?

Faust7

maybe im just an idiots but that was with like 20-30hrs a week of hw on the subject

i know some stuff about markov chains but i dont know what that says, you could try linking the entire proof

MarksCode

04:16

The question is this: imgur.com/a/bCiya, and the answer is this: imgur.com/a/54dBt

I friggen have the answer but cant figure out what it means :(

Semiclassical

Only thing I notice is that $p_n=p_0 (\rho^n/n!)$ in that answer i.e. a Poisson distribution.

(because that's literally the definition of a Poisson distribution)

MarksCode

heh, poisson... cause this thing is literally killing me

Semiclassical

lol

I mean, they are setting up a recurrence relation and obtaining $p_n$ as the solution to that.

MarksCode

I feel like this solution is so simple for someone who actually knows what the heck this means.. but for someone dumb like me its so confusing

Faust7

it looks like it might actually be lambda

its def a RR

Semiclassical

04:20

Well, do you see how they're getting that recurrence relation?

TheGreatDuck

@Semiclassical I'm trying to think of a way to get around an efficiency issue I'm having. I think your advice might be useful here.

Semiclassical

Eh, I'm dubious. But sure.

TheGreatDuck

ok so I'm generating a list of blocks that represent this shape: indiedb.com/games/block-builder/images/…

MarksCode

anybody here want to play chess?

TheGreatDuck

my problem is that the the structure's general frame by frame workings are efficient

it's the generation itself that takes forever

any advice?

Faust7

04:22

@MarksCode know how to play Go?

MarksCode

if anybody wants to pay chess against me lichess.org/2BIFPndm

TheGreatDuck

^^this thing

Semiclassical

Huh. No, I'm afraid this is beyond me.

MarksCode

@Faust7 yes but I'm very inexperienced

Faust7

ah i havent played ina long time but i enjoy it more than chess ^^

TheGreatDuck

04:24

@Semiclassical fair enough. Seemed like a stupid man's problem if you know what I mean. By that I mean no offense. I mean that it seems like a problem that just needs a general inexperienced eye (inexperienced with the code that is).

Semiclassical

gotcha

TheGreatDuck

I suppose that a long load time for a level isn't real bad

Faust7

what are you tring to do with that duck

TheGreatDuck

my concern is when it gets to 5-10 minutes

@Faust7 it's a bit complicated

indiedb.com/games/block-builder

^^moving this to surface geometry (in a few spots)

i felt like making some special levels. :-)

MarksCode

wow nobodys accepted my chess game invite

I feel like such a loser

Maybe its a sign I shouldn't distract myself

TheGreatDuck

04:26

@MarksCode I think people got entranced by the surface geometry.

MarksCode

Its ok I cancelled the game, going to stare at this markov chain thing for a longer

Faust7

@MarksCode i dont remeberhow to play chess played too much go

TheGreatDuck

@MarksCode granted, idk if any of us are real chess buffs. I'll play it once in a blue moon, but it's more of something to do with the family irl.

and even then it has been yeeeeeaaars.

MarksCode

chess is so fun

Semiclassical

chess is one of those things i can only appreciate at the level of tactics

I've no head for strategy.

TheGreatDuck

04:29

@Faust7 if I had a convenient way to make gifs I'd show you the actual structure in action but it's basically 2d minecraft on surface geometry... in this case tubes. The generation of the surface and all of it's little bells and whistles is a bit... slow.

MarksCode

I like everything about the game

its so complex... like a woman

Faust7

what kind of function are you using to generate the helix?

well helix with a disc roated around it ^^

TheGreatDuck

@Faust7 the function isn't the issue but I'm using f(x) = <5cos(x),5sin(x),2x>

Faust7

hmm ok

TheGreatDuck

if you meant "what is generating the structure"... about a 2-3 hundred line piece of code.

Faust7

04:32

lol

TheGreatDuck

well it's not just a tube plot model

each square is an object with references to the adjacent blocks.

and has 4 points (obviously)

the bottleneck is probably the allocation if I'm to guess.

perhaps the way to do it would be to print out all of memory and load it back in manually

Faust7

intresting

TheGreatDuck

granted, that would be in very bad taste.

it's the sort of language where you have to write your own allocator

and hope nothing breaks

Faust7

hehe coding doesnt like me

TheGreatDuck

coding likes me very very much

MarksCode

04:35

im a computer science student... coding is fun :)

Faust7

That being said it does look intresting

TheGreatDuck

i just have a tendency to go beyond the performance capabilities of modern computers

MarksCode

except for C

screw C

Faust7

C+ is the only thing i ever learned

TheGreatDuck

@Faust7 the 2D version is efficient barring too massive levels, but that was fixed by choosing not to draw things that are offscreen.

MarksCode

04:36

u mean C++?

TheGreatDuck

it's the 3D surface geometry that is tricky

Faust7

wasnt fond of it

MarksCode

welcome zee

TheGreatDuck

both the construction of the surfaces and the efficiency of doing so

Faust7

if your a computer science majour youd know better then i would

TheGreatDuck

04:37

technically the core engine of it is almost done.

MarksCode

I'll teach someone coding if they teach me math! :)

TheGreatDuck

@Faust7 I'm a computer science major and a math major

Zee

@MarksCode what coding so you do?

MarksCode

@Zee Nope, was just being polite :)

Faust7

the only thing i know how to do nowadays is run a VB with python to do calculations when they get too ugly

TheGreatDuck

04:38

@SimplyBeautifulArt I think that high school kid helping me with the game is going to hate me later.

^^that's actually a surface the game will take place on if I get it working more efficiently.

Semiclassical

Just to be clear, the issue is one of building that helix in an efficient way?

Faust7

are the squares rounded edges or squard points?

TheGreatDuck

@Faust7 the squares are all polygons of four points.

Faust7

if there rounded thats alotof calculations

TheGreatDuck

technically not squares as that rarely happens

Faust7

04:40

but you still calculate those 4 points for every square?

TheGreatDuck

@Semiclassical building the 3D model itself is efficient so i think the issue is in building all the squares as individual little objects and linking them all to each other

Semiclassical

Hmm.

Faust7

is there some way you can simply cut the surface up without calculating the points?

TheGreatDuck

the point calculations aren't the bottleneck

Faust7

ic (sorry just throwing out my thoughts however irrelivant) ^^

TheGreatDuck

04:41

:p

it's probably because for the squares I have to allocate point objects and square objects and there's probably something wasteful somewhere

tbh, it would probably be more efficient to dump the heap space into a file and load the file at runtime

Semiclassical

Am I right in thinking that 'polygons' are the name of the game here, in that those are what you have available in building up your helix?

TheGreatDuck

@Semiclassical 3D modeling is built from triangles with textures, but the underlying block data structure can be whatever i choose. It's homemade.

I'm choosing to have blocks of the following nature:
//point 1
//point 2
//point 3
//point 4
//adjacent square 1
//adjacent square 2
//adjacent square 3
//adjacent square 4
//blockType
//removable

^^that's what each block holds

Semiclassical

Hmm.

TheGreatDuck

I'm gonna write up a thing to dump out a string to reload the memory stuff I have.

it's all packed into one array

0

A: How can I build a data structure that will persist across saves/loads in GameMaker?

The solution is to use C-style dynamic memory allocation which is essentially the idea of a struct based programming language. In this sense memory within an array is allocated (for instance 5 indices) and those indices act as your individual node, list, graph or what-have-you. Pointers in this c...

^^this is how i store my data structures

Semiclassical

The only halfway clever thought I have is that, if you view that (curled up) checkerboard pattern

MarksCode

04:45

all these squares make me want to play chesss....

Faust7

lol

Semiclassical

Then in some sense it seems like you only need 'half' the squares.

TheGreatDuck

technically there are no squares on the inside

they just have backsides

Faust7

like the halfway clever thought

Semiclassical

sure.

I wasn't meaning inside/outside

TheGreatDuck

04:46

ok?

Semiclassical

I guess I mean something like this.

MarksCode

I have no clue what you're doing @TheGreatDuck, but if the pattern is repeating can't you just generate one "row" then keep rotating it and placing it ontop of the last row

TheGreatDuck

@MarksCode the issue is the creation of each stone. it would probably be just as slow if all of them were shoved on (0,0)

granted, that's a guess

Semiclassical

Suppose I have a square and its four adjacent neighbors.

TheGreatDuck

alrighty?

oooh

i know what you mean

the adjacent neighbors are pointers

I'm not storing that many duplicates :p

Semiclassical

04:48

yeah. If I know the coordinates points for the four adjacent neighbors, then I don't need to know the points for the square inside separately.

I mostly wonder if you're storing more info than you actually need.

Actually, let me say it like this. Suppose I have four squares in a square pattern

`ab`
`cd`

sigh.

[a] [b]
[c] [d]

that'll have to do.

TheGreatDuck

memory isn't a concern

but I see what you mean.

:-)

Semiclassical

Ah. Oh well.

TheGreatDuck

The issue is efficiency

as in raw speed

Faust7

like if you have a chess board

Semiclassical

Yeah. You technically only need to know, say, the lower-left corner for each square.

Faust7

04:50

and i tell you where all the black squares are

TheGreatDuck

not really

Semiclassical

You can infer the other corners from its neighbhors.

TheGreatDuck

the walking algorithm works better if they each know their four corners

Semiclassical

Well, you need to know what the neighbors are as well.

Hm.

TheGreatDuck

but yeah, juggling the references a little different would be good later on

granted, if I choose to do a memory dump and reload it...

I can hand-optimize that

Semiclassical

04:52

I don't quite know what efficiency means here, though.

TheGreatDuck

the speed at which it takes to build it

it takes about 30 seconds

with a 4 block circumference and 20 block length

Semiclassical

Seems like that's a hard and fast boundary.

If you want all the squares on screen at once, you need to take the time to build them.

TheGreatDuck

no the graphics aren't slow

that only takes about a second

fits in one frame in fact as it gets regenerated each frame

it's the blocks that are slow

i.e. the level generation

but it's fine

Semiclassical

I'm afraid I don't follow what you're getting at very well.

TheGreatDuck

I figured out a workaround

Semiclassical

04:54

mmkay

TheGreatDuck

the way I figure, the allocation of the blocks is really slow

so it would be faster to just dump a literal list of all the values in that local memory

MarksCode

I dont get why $\pi$ is used to represent states in a queue system, did they run out of symbols or something

TheGreatDuck

and just one by one assign those values back in

faster than trying to worry about making it more efficient (it might just be the limit)

Faust7

pi and phi are common for those kind of things

MarksCode

my birthday is on pi day :D

Faust7

04:56

theres a quazi rulebook for what kind of symbol you use

MarksCode

my birthday is irrational!

Faust7

my birthday is two prime numbers

MarksCode

3/3?

7/7?

Faust7

07/13

2 is prime

:p

TheGreatDuck

@Semiclassical think of it this way, why bother doing all the mathematical calculations when you can just print out the memory and load it back in?

should be loads faster

MarksCode

04:58

wait

Semiclassical

makes sense.

MarksCode

@Faust7 is your birthday in 1 month?

Faust7

july 13th

07/13

MarksCode

oh damn, nice!

Faust7

oh yes

its in one month exactl ylol

TheGreatDuck

04:59

@Semiclassical plus, since each block is only 10 memory slots, it shouldn't even be that much code. Just a matter of cutting out any dangling pointers I might've left in there. Granted, who cares at that point. :p

Semiclassical

lol

TheGreatDuck

i mean, each memory slot probably gets touched 3 or 4 times

Semiclassical

I should point out that my knowledge of programming is basically at the level of "how do I compute X thing"

TheGreatDuck

ah

my knowledge goes down to the lowest level

Semiclassical

anything in the realm of actual programming e.g. pointers etc. is nil

TheGreatDuck

04:59

(well, except for hardware)

Transcript for

$Mathematics$ Mathematics