About 2 months ago I wrote about oscillatory reactions that are so weird that the original research paper was rejected for decades because it was in a collision with the Second Law of TD (it wasn't...).
There will be some math, but I'll try to make it interesting and philosophical.
I will call @abigail-dantes to tell me if there is something similar known in psychology.
You are probably wondering what software will be used.
Well, it's Paper&Pencil 3.7. It's a freeware...
Let's start with the simple equation that describes the formation of the product (P) from the starting substance (A) via intermediary product (X) and describe the evolution of x in time.
It's becoming interesting because the following equations could be simplified.
Now we have only 2 parameters: κ which is constant and boring and λ that depends on the concentrations of the initial substance A and the product P. It evolves in time in some cases.
If the system is opened, and the concentrations of A and P are constant - x will be related to λ in a linear way. That's the ideal life. You decide how much you want to invest (money, time, struggle), you decide the outcome (wealth, health, happiness, love...). And you can predict your current state of mind,
In the real world, in a closed system, it will be linear for some values, excluding the extremes. Still - nothing special.
But for some values, there will be the "S" curve.
And this is the moment when the philosophical questions appear.
First, you need to invest your time and willingness (A) in some process of learning, so you can have a successful career (P). You go to college (λ1), you graduate (λ2) and you start working. Now you want some change, but you can't simply jump from one point to another. Or maybe there is a new balance between your willingness to change something and the outcome you achieved.
Now you are turning back (the upper line) via the pathway defined by the products you made (P) and the amount of your will (A). Then you start learning again. Not from scratch, but from the λ1 point (sharp fall). And it will be bad until you reach λ2 when you will jump again.
You can have a very different outcome of your current state (X) for the same λ.
It's strange. And it also means one more thing. Even with the same personality, the same devotion, the same everything, the outcome (your current state) will be different because you passed the checkpoint.
It looks similar to the relationships. You are investing your time, emotions, efforts and Boom! you are in love.
Now you are riding on the upper line, you are still kind, you are still trying to do the best and your current state of happiness is higher (you have sex with your partner, you have a stable companion) but instead of rising to the goal (lower line), you are falling down. You are standing from a better position (higher value of x) but you are doomed!
The only way to stay on the upper line is to be "right" from λ2. And sometimes you are not controlling all the parameters. Yes, you are doomed - but that's not bad. It's the law of math.
And the best thing is... There are many more parameters in complex systems. Not only λ. If you neglect them, you will be in that λ loop forever.
If you want to shoot yourself because the "life is not fair" and you are putting way too much effort and the results are constantly going down - just break the loop and start all over again.
You can't fix everything in order to remain happy (current state of x).
And go away from that attractor, that infinite loop, so you could explore different dimensions and get the unimaginably high values of x.
Get out from your comfort zone, bad marriage and that job you hate.
Yes, it's scary, the inevitable fall will hurt but keep in mind there is dt in the equation. And the t (time) you have is not infinitive.