The Grove

Prince North Læraðr

12:22 AM

in The Sphinx's Lair, Nov 10 at 18:54, by Deusovi

this is nala! she only has three legs but we don't think she's realized it

Literally

The exact

Same

Words

Except for "yet"

Also found this jewel by Deusovi

in The Sphinx's Lair, Jun 23 '17 at 17:38, by Deusovi

her name is Nala, but we sometimes call her Tripod

Sciborg

12:34 AM

To be fair, I've made the same joke about my dog for years verbatim when i have to go home and walk her ("we have to go back home to the Queen now")

Prince North Læraðr

1:25 AM

@bobble or anyone else- can someone explain heavyside functions for me? I'm kind of confused

I have the general idea but confused on a couple questions

maybe @Deusovi if you're free?

bobble

I'm not sure what a "heavyside" function is

Prince North Læraðr

It's a type of piecewise function

bobble

Heaviside step function

The Heaviside step function, or the unit step function, usually denoted by H or θ (but sometimes u, 1 or 𝟙), is a discontinuous function, named after Oliver Heaviside (1850–1925), whose value is zero for negative arguments and one for positive arguments. It is an example of the general class of step functions, all of which can be represented as linear combinations of translations of this one. The function was originally developed in operational calculus for the solution of differential equations, where it represents a signal that switches on at a specified time and stays switched on indefinitely...

do you mean this?

Prince North Læraðr

Yeah

bobble

okay, what are your specific questions?

Prince North Læraðr

1:27 AM

I'm not sure how to graph them when you have multiple heavysides

Like

H(x-1)+H(x-2)-2H(x-3)

bobble

well can you graph them individually?

Prince North Læraðr

Yeah

bobble

and then add those graphs up?

Prince North Læraðr

Urm

well, no

That's the solution but ya know, it's kind of confusing to tell what's going on

bobble

hmm, let's try this

Prince North Læraðr

1:30 AM

What's up with the pluses and minuses?

bobble

you don't have to split them up just at their turning points

Dmihawk

heck, that's a bit of mind-bender to get your head around

Sciborg

i'm just as confused by all of this

bobble

H(x - 1) = 0 when x < 1, 1 when 1 <= x < 2, 1 when 2 <= x < 3, and 1 when 3 <= x

Prince North Læraðr

right but what's up with all the + and -? What am I supposed to do with that?

bobble

1:32 AM

well, that's saying that when x is 2 <= x < 3

the first two Hs are giving 1, so 1 + 1

and the third is giving nothing, so 0

so 1 + 1 = 2

I'm trying to achieve the same thing by splitting up the piecewises extra

H(x - 2) = 0 when x < 1, 0 when 1 <= x < 2, 1 when 2 <= x < 3, and 1 when 3 <= x

2H(x - 3) = 0 when x < 1, 0 when 1 <= x < 2, 0 when 2 <= x < 3, and 2 when 3 <= x

adding all of those up now

Prince North Læraðr

wait does the + or - tell you if the next heavywise is moving up or down, basically?

bobble

0 when x < 1, 1 when 1 <= x < 2, 2 when 2 <= x < 3, 4 when 3 <= x

the + and - are just adding up the values that the Hs are spitting out

Prince North Læraðr

Oh, I see

Dmihawk

does that help?

Prince North Læraðr

A bit confusing but I think I get the gist

bobble

1:36 AM

oh wait the last is negative

drat

basically Breaking Stuff Up For The Win

Prince North Læraðr

So the (x-n) tells you when the function is switching, and the + and - tell you if the function will be moving up or down by some x amount

bobble

yes

Deusovi

1:57 AM

(i'm around now, hello)

Sciborg

Hi Deus!

Deusovi

just saw the ping - looks like you have things worked out here

Prince North Læraðr

Yea

Questions actually:

If f(n)=n/n+1, what is f(n+1) expressed as a function of f(n) itself?

Dmihawk

(n+1)/(n+2) ?

Deusovi

well, what is f(n+1) expressed in terms of n?

and then can you find some way to manipulate the expression to "find" f(n) in there?

Prince North Læraðr

2:01 AM

@Dmihawk Not a choice

Dmihawk

ah, then ignore me :P

Prince North Læraðr

That was my initial thinking too

Dmihawk

I'll go back to inventing my new counting system :)

Prince North Læraðr

Hehe

Deusovi

(disclaimer: i have no idea if that'll actually work. that just seems to be the most natural way to approach it for me)

Sciborg

2:02 AM

The all-new patented Dmihawk Counting System, now with extra base-12

Prince North Læraðr

These are my choices

Dmihawk

well, I'm quite proud of it, but know that Deus will probably crack it in like 3 seconds O_O

Deusovi

ooh sounds like a linguistics-y puzzle

@PrinceNorthLæraðr there's the "right" way to solve the problem and there's the "this is a multiple choice test" way to solve the problem

Prince North Læraðr

Hm, well my test is all multiple choice soooo

I cna do the "multiple-choice way" via process of elim

Dmihawk

may be working on a puzzle where I only have pixels to work with cough Density™ #3 cough

Deusovi

2:05 AM

ooh, exciting

i really like the density concept - i'm a big fan of completely abstract puzzles like that. reminds me of The Witness

@PrinceNorthLæraðr the multiple choice way is "just expand each answer, and check against your f(n+1)"

Dmihawk

oh yes, I loved The Witness :D <3

Sciborg

The Witness is awesome, it was pretty much made for PSE people

Dmihawk

first game I ever played was when my Dad introduced me to Myst at age 4

Deusovi

i've been working on a thing inspired by it for a long time. no idea when i'll finish, or even if it would get released on PSE

Dmihawk

sorry North, I'm not trying to bury your question, I'm just as stuck on trying to solve it as you are :'(

Prince North Læraðr

2:08 AM

@Deusovi My thoughts exactly

Sciborg

Myst is an oldie - i've only ever played emulated versions. the first games i played as a kid were on Windows XP

the main thing i remember about Myst is that most people never made it off the first island

Deusovi

i also never made it off the first island!

Sciborg

It's a beautiful and culturally significant game, just horribly unintuitive :p

Dmihawk

I think it gave birth to my love of puzzle-solving, the sequel (Riven) was even more challenging!

Deusovi

i've heard it's very good, but the initial "puzzle" as i remember is literally just "make sure you have a precise count of these things that appear basically everywhere. also their levers start in random positions so good luck"

Sciborg

2:12 AM

Probably one of the first adventure-puzzling games of its type :D

The initial "puzzle" is indeed a nightmare

there are a couple really awesome interviews with the creators on YouTube, where they explained how they made it and how it kicked off their whole careers with the unexpected success - really inspiring.

Dmihawk

perhaps one of my future puzzles will have to be Myst-inspired :)

Sciborg

That would be a rad puzzle idea

Dmihawk

oh :( I've done that already apparently :P

1

Q: Name the Game #1

This is part of a series of puzzles where you must identify the name of a video game In my books you must read About a ship, clock and tree One path is red, the other is blue Which one you free is a choice made by you Name the video game

video-games

I'll have to make a better one!

Sciborg

Maybe you could have it where the solver is trapped on the Myst island and needs to solve the puzzle to escape :p

Dmihawk

oooh that sounds neat!

Sciborg

2:20 AM

If only PSE supported point-and-click puzzles...

Dmihawk

haha then I'd get really carried away!

I custom-built a room escape game (IRL) for my Mum's birthday last year

about a month in, I realised how much harder real-life puzzles are vs. digital ones :P

Sciborg

That's awesome, i do some game dev on the side and making small games for friends and family is the best part IMO :) always fun to make people happy!

Dmihawk

totally agree :)

Sciborg

but if you're anything like me, you probably suffer from the scope of projects getting way bigger than at the start because you get too excited about it and start adding more stuff :p

Dmihawk

unfortunately, all that does it lend itself to the theory that we're both part of Deus' neural network :P

(that's totally me in a nutshell)

Deusovi

2:25 AM

@Sciborg i definitely do that

Sciborg

the multiple-personalities-of-Deus conspiracy thickens :P

Dmihawk

Wife: what are you doing?
Me: I'm just gonna clean the bank up a little bit...

one week later...

Sciborg

oh my lord

Dmihawk

Sciborg

you have a little garden??? that's awesome!

Dmihawk

2:29 AM

in my defense, I did clean up the bank...

Sciborg

Judging from the stakes do you grow tomatoes?

sure do :)

Nice!!

Look at all those happy little plants

Dmihawk

2:32 AM

clockwise from bottom left - tomatoes, corn, beans, carrots

Sciborg

Now it really is "The Grove" in here :D

Dmihawk

do you get up to any gardening/landscaping?

Sciborg

Unfortunately I'm in an apartment, so can't garden much - i do have some nice little houseplants though :)

Dmihawk

oh yup, nice to have some greenery

Prince North Læraðr

man, what a weird room this has become e:P

Can someone help with a function thingy?

Sciborg

2:34 AM

But we're on topic, "The Grove" = plants right? :p

Dmihawk

go for it North!

Prince North Læraðr

Ooh, should I kick you for being "off-topic"? :P

Dmihawk

:(

Sciborg

Sorry, sorry, we'll do math from now on i promise

Prince North Læraðr

I'm just joking lol I don't care

Sciborg

2:36 AM

I'm not so good at abstract math anymore, but we'll see what we can do to help :D

Dmihawk

F(tomato) + F(dirt) + F(water) = y (where y = 'yum'!)

Prince North Læraðr

For function f defined by x=/=0, f(x)+2f(1/x)=2x^2. What is f(sqrt(2))?

Dmihawk

oof, gimme a sec to write that out by hand, so I can read it

Prince North Læraðr

Let me snip it so it's easier

Sciborg

Will have to write this down also, one sec :p

Prince North Læraðr

2:37 AM

disregard how weird that sqrt looks. It's a sqrt

The answer is 3/2. I have no clue how to get to that solution

Sciborg

hmm, so this is one of those weird "self-defined" function problems

where you're kinda defining a function with itself

Prince North Læraðr

ugh, I hate abstract functions. I think my teacher said none of it is on the test tho so

stupid finals

Sciborg

there's a way to simplify these i think

Prince North Læraðr

It's like a trauma just passed first quarter only to revisit it all over again

Sciborg

isn't this inverse functions?

Prince North Læraðr

2:40 AM

well is f(1/x)=f^-1(x)?

No

not always, I don't think

Sciborg

yeah, that's not it, i'm just trying to remember things

Prince North Læraðr

Hm

I'm not sure how to take the inverse of f(1/x) so that it's f'(f(1/x))=x

merrybot

@PrinceNorthLæraðr did a quick wolfram alpha on this ... it thought f was just a variable

Sciborg

yeah, disregard the inverse stuff - i don't think that applies here

Prince North Læraðr

@merrybot No, f means function

@Sciborg I'm just going to skip it for now. If it's not on the finals, it's not worth my time

Sciborg

2:42 AM

hang on, hang on, there might be a way to solve it - what if you just replaced (1/x) with, like, a "b" or something

merrybot

@PrinceNorthLæraðr i know that, but it seems wolfram alpha doesn't know that in context

Sciborg

so that you have f(x) + 2f(b) = 2x^2

and then you can say well, f(x) = 2x^2 - 2f(b), that's my function

so then f(sqrt(2)) = 2(sqrt(2))^2 - 2f(b)

and you can turn 2(sqrt(2))^2 into 4 right? 2*2

so f(sqrt(2)) = 4 - 2f(1/sqrt(2))

yeah?

and then from there you just solve recursively down

or maybe you do something with limits, i dunno

Prince North Læraðr

shrugs

Sciborg

that's probably not the intent at all, no clue

just skip it

Deusovi

plug in √2 and 1/√2

that gives you a system of equations in the variables "f(√2)" and "f(1/√2)"

Sciborg

2:50 AM

ohhhh, and then you solve the system?

Deusovi

yep

Sciborg

now this is coming back to me, that's how you're supposed to do it North.

plug in the number and the inverse, and then use the system of equations

treat it like a variable

Deusovi

in general, if you have something you want to figure out, a good idea is to get multiple independent pieces of information about it, and that might narrow it down

here you want f(√2). you can get information about it if x=√2 or if x=(1/√2)

Sciborg

Makes sense

North do you want to try doing that?

Prince North Læraðr

oh I can do that?

I have a lot of stuff left to cover still, so I'll pass

Sciborg

2:59 AM

tried it on my own and i got -3/2, so i messed up somewhere, hang on