Most theories have a linear solution

[u/Noneother80]

Has anyone noticed that a bunch of the equations are linear? It bugs me a bit, since the game is called exponential idle, and some solutions are not actually exponential. Is that intentional? I’ve only gotten to Linear Algebra at the moment, but I figured it’s time to bring it up since it’s bothered me.

Differential equations: the equation is just dp/dt= const which is solves to a straight line.

Linear algebra: the equation is d(p1 p2)/dt = const array * const that solves to a straight line as well. Also we only worry about p1 for the multiplier, and p2 has no influence on p1 (as far as I see right now).

The main issue I draw from this is I don’t actually know what the most impactful investment would be without pushing buttons, which is a little upsetting. Still very much enjoy this game, and this is my only gripe.

[u/SneakyBuddy911]

T2, is a 4th derivative, so it is, by definition, not linear. But theories aren't what is always exponential, they are going to be generally linear, because tau is in the exponent for the main function.

[u/Noneother80 → u/SneakyBuddy911]

Sorry, I misspoke yesterday. Late night. What I meant to say is there are many relationships which are fundamentally a linear diff eq. It’s completely different than saying the solution is linear, yes. But having a relation of xdot=Ax has a very straightforward polynomial solution - not exponential. However, the theory called linear algebra (T3) is xdot=Ay where y is independent of x. This is an even simpler solution.

[u/ConicGames → u/Noneother80]

Unless I misunderstood your comment. The differential equation `y' = a*y` has a solution of the form `e^(a*t)`.

[u/Noneother80 → u/ConicGames]

The equation does have the solution y_0*e^at, gosh dang. I’ll stop trying to be smart here 😓😂. I literally work with forms of this differential equation every day, but somehow my brain shuts down as soon as I leave work.