Describe how the albums have aged with time using mathematical functions!

[perfectchaos180]

So being the nerdy engineer, I thought this would be a neat topic, basically describe how the graph for each album would look when time is on the x axis of a graph and how much you like the album is on the y axis.
For example, I would describe Octavarium with a cosine wave, my liking of it oscillates, started out liking it

When Dream and Day Unite: y = (1/30)*x
(the more I listen to it the more I like it, it just grows very very slowly)

Images and Words: y = sqrt(x) + 1000
(its growing but the growth slows down over time and is getting fairly asymptotic, the +1000 is because I started off liking it)

Awake: y = ln(x)
(didn't like it much, but then it grew like crazy, now is becoming asymptotic)

Falling Into Infinity: y = x - 2
(steady growth, didn't like it much at first)

Scenes From a Memory: y = e^(10x) + 1000000000000000
(tremendous growth, started off really liking it)

Six Degrees: y = e^x
(exponential growth, wasn't a big fan at first)

Train of Thought: y = e^(-x)
(started off liking it, then it started dying and I don't like it much now )

Octavarium: y = cos(x)
(oscillates like crazy, started off liking it)

Systematic Chaos: y = e^(-x) + u10(x) - u20(x)
(started off liking it, started dying, got a pulse and started liking it again, then that pulse died and I don't like it much now, thus the step functions)

Black Clouds and Silver Linings: y = 0 
(never liked it, still don't)

[Adami]

We're getting some weird threads around here it seems.

[zxlkho]

Adami is right. This is the weirdest thread I've seen in a while...


(for shits and gigs) I&W: y = ∞

[j]

I lol'ed at this thread.  Especially Octavarium.

-J

[kirbywelch92]

I liked Octavarium, both for its lol factor and for nuggetz.

[Phantasmatron]

This is a...creative...thread idea, I'll admit...but I dont even

[YtseJamittaja]

Well...


WTF!?!?!?!

[Perpetual Change]

I'll use everything I know about math to give this a go.

When Dream and Day Unite:  a;_=lsg;m g6s8g4--==654-6-+
Images and Words: 2-2=
Awake: Best Them
Falling Into Infinity: 這個沒有特別好
Scenes- 1928 + 2-2=
6 Degress- 6+8x2 8=6
Train of Thought- 0198471904871904871239048719048712309487124
Octavarium- 5/8/5/8/5/8/5/8/5/8/5/8/5/8/5/8/5/8/5/8/5/8/5/8/5/8/5
Systematic Chaos- 2534985gvmo5yi nq-t5vii3pcv2590236890vup298526bup
Black Clouds and Silver Linings= r0r0r0 + r0r0r0 = .00000000000ra

[Weymolith]

I'll use everything I know about math to give this a go.

When Dream and Day Unite:  a;_=lsg;m g6s8g4--==654-6-+
Images and Words: 2-2=
Awake: Best Them
Falling Into Infinity: 這個沒有特別好
Scenes- 1928 + 2-2=
6 Degress- 6+8x2 8=6
Train of Thought- 0198471904871904871239048719048712309487124
Octavarium- 5/8/5/8/5/8/5/8/5/8/5/8/5/8/5/8/5/8/5/8/5/8/5/8/5/8/5
Systematic Chaos- 2534985gvmo5yi nq-t5vii3pcv2590236890vup298526bup
Black Clouds and Silver Linings= r0r0r0 + r0r0r0 = .00000000000ra

HERO

[Metabog]

Awesome... levels... approaching... critical.

First person to approximate DT's popularity growth with a Taylor series wins.

[cthrubuoy]

https://www.wolframalpha.com/

otherwise, WUT.

[tri.ad]

We need the name of the new drummer.

[Metabog]

Do I REALLY have to spend today doing Matlab graphs for this forum?

[Zorander]

Do I REALLY have to spend today doing Matlab graphs for this forum?

Yes!

[Jamesman42]

perfectchaos, you should give the reasoning for your given functions in relation to the respective albums (lolpun that probably few will get there).

But hey:

WDADU: y = 1 ---(very meh)
IaW: y = (n!)^2 ---(it's awesome, it "contains" higher values of awesome)
Awake: y = (n+1)! ---(also very awesome, factorial grows fast)
FII: y'' + y = 0 ---(second derivative plus the original function...they took a new spin on their sound, but =0 because I'm not digging the whole album)
SFAM: y = e + x ---(kind of meh, so linear)
SDOIT: y = (n!)^3 ---(Yes, the album is amazing, tremendous growth here)
ToT: (x-5)^2 = 12(y-19) ---(a shifted, skinny parabola? but yeah, very good, even if they narrowed down their style a lot to straight up metal with some progressiveness)
8VM: x^2 + y^2 = 58 ---(double references FTW...one is obvious, the other one isn't, can you guess it?)
SC: x = 2 + t, y = t ---(really hit or miss, thus the parameter t)
BC&SL: y = e^(10x) ---(big growth here as well)

Done nerding out here.

[Sir GuitarCozmo]

A graph for how it would look?

[cthrubuoy]

SFAM :    (x^2 + y^2 -1)^3 = x^2 y^3

[Jamesman42]

SFAM :    (x^2 + y^2 -1)^3 = x^2 y^3

[TAC]

We're getting some weird threads around here it seems.

[lithium112]

perfectchaos, you should give the reasoning for your given functions in relation to the respective albums (lolpun that probably few will get there).

But hey:

WDADU: y = 1 ---(very meh)
IaW: y = (n!)^2 ---(it's awesome, it "contains" higher values of awesome)
Awake: y = (n+1)! ---(also very awesome, factorial grows fast)
FII: y'' + y = 0 ---(second derivative plus the original function...they took a new spin on their sound, but =0 because I'm not digging the whole album)
SFAM: y = e + x ---(kind of meh, so linear)
SDOIT: y = (n!)^3 ---(Yes, the album is amazing, tremendous growth here)
ToT: (x-5)^2 = 12(y-19) ---(a shifted, skinny parabola? but yeah, very good, even if they narrowed down their style a lot to straight up metal with some progressiveness)
8VM: x^2 + y^2 = 58 ---(double references FTW...one is obvious, the other one isn't, can you guess it?)
SC: x = 2 + t, y = t ---(really hit or miss, thus the parameter t)
BC&SL: y = e^(10x) ---(big growth here as well)

Done nerding out here.

Man, this was good, but c'mon - if you're nerding you gotta go all out. First of all, you haven't defined your parameters. I assume y is enjoyment, but what are n, x and t? What metric of time are you using? Clearly n must be whole numbers but is that in decades, or years or hours?

I liked how you explained stuff though. Made it more interesting. Though, for reference y'' + y = 0 isn't really a function (could be a number of functions (y = cos(x), y=0...)) and I liked your 8VM nuggetz (full circle ftw) except a circle is technically a function and not a relation.

All in all - lol DT + math = <3

cool thread OP.

[Jamesman42]

I figured, from the OP, that y was enjoyment. The variables are whatever. I didn't feel like defining things (not good for math, I know!). I guess I used those variables to define how fast the function is growing, so the fastest growing ones are the best (except 8VM is my favorite, but I had to do the circle formula).

y'' + y = 0 is a differential equation, and I figured I'd use that because they used a bit of their own sound and went in a different direction (hence the second derivative).

Yeah, the circle is not a relation, but I am not limiting myself to functions relations here. Heck, I could have gone a bit crazier with some 3-D functions, complex functions, crazy differential equations, matrices, cylindrical or spherical equations, or some long proofs. I just chose to keep it a bit simple.

[Sir GuitarCozmo]

[Silver Tears]

Wow this thread 

[jdprsaga]

No time to think of all graphs but i must say..

if the Like Hiperplane Y represent the likeness in the space "I" then the closest albums to the gradient are:

SDOIT followed really close by FII.

[ddtonfire]

d(enjoyment of WDaDU)/dt = 0 (Haven't listened to this one for a while)
d(enjoyment of Images and Words )/dt = 0 (pretty steady)
d(enjoyment of Awake)/dt = 1/((1+x)^2) (it is increasing slowly from some finite value toward some value)
d(enjoyment of FII)/dt = δ[t] (i enjoy it more each time I listen to it, but when I don't listen to it, I don't care)
d(enjoyment of SFAM)/dt = δ[t] (each listen is a breath of fresh air)
d(enjoyment of 6DoIT)/dt = k*(enjoyment of 6DoIT) (my love is like a bacteria culture)
d(enjoyment of ToT)/dt = 1
d(enjoyment of 8va)/dt = -(1/2)Sin(x/2)  (the interest wavers)
d(enjoyment of SC)/dt = -1/((1+x)^2)  (it is decreasing slowly from some finite value toward some value)
d(enjoyment of BC&SL)/dt = -(1/2)Sin(x/2)  (the interest wavers)
d(enjoyment of DT11)/dt = null

[Jamesman42]

John Petrucci plays x^x^x^x^x^x notes per second.

[LCArenas]

[Sir GuitarCozmo]

John Petrucci plays x^x^x^x^x^x notes per second.

Kill-Zone Mode or World Domination Mode?

[glaurung]

It never ceases to amaze me what kind of wacky thread ideas people come up with on this side of the forum.

[The Letter M]

The Majesty Demos - 24 (almost old enough to rent a car!)
WDADU - 21 (old enough to drink!)
IAW - 18 (old enough to vote!)
AWAKE - 16 (old enough to drive!)
FII - 13 (old enough to see PG13 movies!)
SFAM - 11
SDOIT - 8
TOT - 7
8VM - 5
SC - 3
BC&SL - 1

-Marc.

[ddtonfire]

Octavarium is potty trained by now!

[dethklok09]

uh i dont think highschool algebra 1 and geometry a (first trimester, only a couple of weeks so far) are gonna help me out

[Rafael Guerra]

Octavarium: y = cos(x)

Mine is more like y= 2sin(x-4)+1

[Kosmo]

My face: 

[Nic35]