So Ryan asked me yesterday night if I believed in fate. I don’t know if he expected a binary answer yes/no, but being that I’m insufferably nerdy I’ve always thought of it as “not quite so” so here’s a bit of a mathematical/philosophical thought exercise that draws on simple calculus, general systems theory, Gödel’s theorem and law of thermodynamics.
Suppose we’re working with linear time, this means that events are ordered in a sequenced manner so event 2 comes after 1, etc, and we could find a model which given x1, x2… xn number of variables would produce the prediction of an event y with a significant degree of accuracy so that f(x1,x2… xn) = y
We’re gonna work under the hypothesis that events in time are linked so that the effects of previous events would affect the outcome of our model - I initially said that we’d have to feed either previous outcomes (y1,y2…yn) to the model but that’d require different models for each moment in time
Since i’m working under the hypothesis that there’s only one model that can explain all, i’m just gonna use the same number of variables and thus the number n of variables remains constant, but the thing is all models like any system degrade over time - entropy, if you will, because if we suppose that for every computation there’s a margin of error, however small it may be, that error is gonna pile up until the system becomes unstable and is unable to make predictions anymore. Because we keep feeding our system the results of previous computations, and because of the number of variables we’re gonna use, which approaches to infinity, it is reasonable to assume that this deterioration of the model would happen in an incredibly short amount of time.
Now the real question is, the only true argument against fate is the level of perfection of the model that describes events - aka whether there’s any error at all or not
But the definition of error is the deviation from an expected outcome - which ultimately brings up the question, who decides what’s the expected outcome?
And more importantly, it’s also worth noticing that the error at n time can only be calculated at (n+1) time - the future, because you need to compare what you predicted to what actually happened
Therefore, should there be a margin of error, there wouldn’t exist such thing as fate because the ordering of events couldn’t be ascertained until it actually happened
So necessarily the model has to have a 0 margin of error - it has to be perfect. but if it was perfect, under the premises of gödel’s incompleteness theorem, we’d have to question whether something inside existence can actually describe existence as the model would need to be a perfect closed system
Only outside of existence there can be something that encompasses the entirety of existence therefore the model doesn’t exist
So my final answer is: there is no such thing as fate, but you can get close to determinism in a short term