Probability is 1
The probability of an event occurring in the future is always 1. A value less than 1 signifies our ignorance.
As provocative as this statement may sound, let me reason with you like I did with Partha Bhattacharya & let you decide for yourself if it is a useful perspective for you to look at things in the future.
What if my event is defined as “the event where X never happens”? That too is 1. X was never supposed to happen P(X) = 0.
The claim here is that any & all events in the future are deterministic and knowable.
In classic probability theory, A and A’ are known as complementary events if one of them happening is defined as the event of the other one not happening in that case if we apply classic probability axioms -
One can prove that P(A) & P(A’) can not be 1 simultaneously.
Yes, true. The claim is that “for events of the future, its not the uncertainty of that event happening that causes its probability to become less than 1, its our lack of knowledge that makes it so”.
Let me give you an example -
Say you put an hand in a box full of red and blue balls in a 1:1 ratio and you pick red
Your chances of picking red was 1 and blue was 0. You just didn’t know that before hand and hence you may have said 50%
As a counter, you may argue that - 1 is defined in probability as P(R|R) and the second one which is 50% is P(R). First is called conditional and second is called marginal. Conditionals have lower entropy than marginal, yes. Although there are notions in probability like “almost surely” and “infinitely often” they do not match my initial claim of the probability of occurrence to be a solid, definite 1 or 0.
Think about this, increasing the amount of information does change the probability of an event of occurring. P(X) = 1% whereas P(X|Y) can be 50% and P(X|Y|P) can be 90% and P(X|X) = 1.
Think about it in another way, if I ask you to calculate the probability any event in your past, you’d be confused for a while but always come back with an answer of “1”. P(X|X) = 1. Probability of X given X is 1.
This is not to say or claim that anything can happen in future. In fact its quite the opposite. It is not to say that probability of some outcome never happening is 0. There will be scores of events about the future in your mind all of which has non-0 and non-1 probability numbers associated with it - if you increase the amount of information you have about any of these events you’ll inch closer to near “1” or “0” values about it happening.
There are two ways to think about events of the future, “(fully) deterministic and knowable” and “indeterministic and unknowable”. Numerically both of them are represented in the same way but they imply drastically different things.
If you think, that the events are deterministic & knowable, you’d shift to an internal locus and try finding new information about those events of interest and finding their “1” or “0” values. But if you think later is of use then you’d relegate outcomes to an unreliable component of “chance” & claim “I think there is a 50% chance of that happening”.
Both 1 & 0 are states of complete knowledge & there are pretty good theories on what are the theoretical limits of ignorance. Generally ignorance is maximized at p= 1/K where K is cardinality of the event space.
I’ll rest mathematics here and draw you attention to how thinking about events of the future in above perspectives be useful to you in all avenues that you’d like to apply it to. If you chose to think that “Well that event is going to happen for sure, I just don’t know about it?” you’ll exert effort in developing more knowledge about it. (this statement is same as saying “That event is not going to happen for sure, I just don’t know enough about it?”) rather than resting at “That’s probably going to happen with a 50% chance”. Try this experiment & share what’s different?
All of this also has an interesting branch on “predictability of data” and why some data streams can not be compressed, but that’s for a different day.
My invitation here is to chose to think about events in the future as deterministic and knowable rather than indeterministic and unknowable and see how it changes your locus of action on things of importance (and keep on ruminating in 2X2 of determinism and knowledge ).
Further reading:
- Information Theory: https://en.m.wikipedia.org/wiki/Information_theory
- 12 Virtues of Rationality: https://www.yudkowsky.net/rational/virtues (“That which can be destroyed by the truth should be.” — P.C. Hodgell - one of my all time favorites)
- Richard Hamming’s Lectures : https://www.youtube.com/playlist?list=PL2FF649D0C4407B30