Certainty and Accuracy are Inversely Proportional

Imagine a very simple and boring game involving Player 1 and Player 2. The two players stand opposite each other and toss a ball to each other every second. There is no other point to the game; they just pass the ball back to each other every second forever.

If someone were to ask us to predict how this game will play out, we could very easily — it is Player 1 and Player 2 passing a ball back and forth each second. If someone were to ask us how certain we are that that is the nature of the game, we could say 100% — it is a very simple game with just one rule (passing the ball back and forth), so we have a very, very high degree of certainty that we understand the game.

Now let’s make the game more complicated by saying that one player can at any moment decide to stop playing for any reason. If we observe a game ending, we can say with absolute certainty that a player stopped the game, but we can’t necessarily say who stopped it or why.

This is because we have added an extra dimension to the game, making it more complex.

And it isn’t the only way we can make the game more complex. We could, instead, change it to have ten million players with the same rule: one player tosses a ball to another every second and, like the first game, no player can stop for any reason. However, there are now ten million players, so we can’t necessarily know who passes the ball to whom at any given point without observing it. Suddenly our certainty has declined due to there being many players to the point where we cannot with certainty say that, say, Player 1 passed the ball to Player 2, or Player 532, or Player 5,235,124. Our certainty has fallen.

This might sound obvious, but this principle doesn’t apply to just a very simple game. When we try to communicate with others, we often feel certain that we know what they are thinking, what they are feeling, or why they are doing what they are doing. But if we can’t be certain with a simple ball game with two rules, how can we be certain about another human being with a rich, complex inner life?

There is a general rule here that we can not only state with confidence, but formulate mathematically: certainty of a structure is inverse to its accuracy and this scales with the structure’s complexity. Or:

C = k/AX

Where C is certainty, A is accuracy, and X is complexity, with k being the proportional constant.

We cannot ever be certain of the thoughts or feelings of another person, let alone the makeup of a society or culture. In fact, the more complex the person or the society or the system, the less certain we should be of our accuracy when we think we have “figured it out”.

Furthermore, this applies to non-human parts of the world, too. Animals have complex natures of their own accord, giving us far less certainty than we naturally assume since we often compare our understanding of animals to a baseline understanding of humans; since animals are simpler, we surely can understand them more. And this is obviously true, but if our understanding of other humans is really much smaller than we think it is, it follows that our understanding of animals is smaller as well.

For physical phenomena, this applies as well, with the complexity of the structure dictating the accuracy of our a priori systems of explaining the structure. This is well documented and expressed in multiple ways in philosophy, mathematics, and science; I don’t need to relitigate such an obvious truism here.

For the universe itself, the problem reaches infinity. The universe’s complex makeup, and our own limited snapshot-based understanding of the world is a massive barrier towards understanding. We do not see the entire universe and all of its constituents operating at all times and at all points in space, so our certainty in understanding the universe as a whole must be the lowest of any other certainty we have of any other thing.

Anyone who believes they have figured things out is wrong and self-deluded.

Anyone who claims to have things figured out is selling something.

Anyone who tries to understand the world more, knowing it is a futile and pointless exercise, will lose certainty over time and, as a simple mathematical function, their accuracy will rise as well.

This is why philosophy values humility above all else.

This is also why, as Harry G. Frankfurt said, sincerity is bullshit.