Suppose there are 10,000 investors, each randomly deciding whether to buy or sell stocks. Even if none of them has any predictive ability, some may still achieve extraordinary returns for ten consecutive years. People might call these survivors investment geniuses, when in reality, they may simply be the lucky ones in a random process. In Fooled by Randomness, Nassim Nicholas Taleb uses this example to illustrate his central argument: people frequently mistake luck for skill, randomness for patterns, and are naturally inclined to invent explanations for random events, overgeneralize from them, or mistake them for causal relationships.
This example is well known, but it is not what I want to discuss today. Selecting 10,000 investors at random while ignoring their individual backgrounds and contexts is a way of approaching the problem from the perspective of the world as a whole. I am not particularly interested in predicting the world or approaching questions from such a perspective.
Instead, I want to offer a conditional probabilistic perspective.
I am inclined to believe that the choices people make do not have predetermined, absolute outcomes. Rather, their possible outcomes follow probability distributions. Whenever we make a choice, we are effectively rolling a die and sampling from the corresponding distribution. This means that randomness is always present. Good intentions can lead to terrible outcomes, and our actions may produce unintended butterfly effects. But probability distributions can change, and indeed, they are constantly changing. A person’s abilities, personality, genes, memories, upbringing, past experiences, and many other factors I have yet to mention collectively determine the probability distribution of the outcomes they may experience under particular circumstances. Luck, meanwhile, determines where a person ultimately lands within that distribution.
I shared this perspective with ChatGPT, and it asked me:
“Do you believe that this randomness is inherent to the world itself, or does it merely arise from our inability to fully observe and model all the determining factors?”
It then introduced two kinds of randomness:
- Epistemic uncertainty. If we knew a person’s complete genetic makeup, neural state, memories, environment, and all external conditions, their future would, in principle, be determined. We simply lack the ability to calculate it.
- Ontic randomness: Even with complete knowledge of every relevant condition, there would still be genuine, irreducible randomness in the future.
I replied, with all due respect, I adopt neither position.
Here is what I think.
I am inclined to believe that if we knew a person’s complete genetic makeup, neural state, memories, environment, and all external conditions, then their future would indeed be determined, even if we were unable to calculate it.
But, and I want to emphasize this but, I believe that either:
(i)We can never possess all the information. This is not a matter of our physiological limitations. I suspect it has more to do with something along the lines of Gödel’s incompleteness theorem.
(ii) Or perhaps the conditions themselves, including neural states, genes, memories, and environments, exist only as probability distributions.
(iii) Or, more boldly, I propose the following:
Either we can know the exact values of some conditions, rather than merely their probability distributions, or we can know the probability distributions of all conditions, rather than their exact values. We cannot have both complete information and complete precision (well, prolly reminds you of Heisenberg).
ChatGPT misinterpreted my argument. Or perhaps, more precisely, it kept trying to identify the parts of my argument that overlapped with theories and references it was already familiar with.
It asked:
“Do you believe that the universe objectively possesses a complete and precise state that no observer can access? Or do you believe that such a ‘complete and precise state’ does not exist in the first place, and that probability distributions are the most fundamental descriptions of reality?”
I responded:
Suppose we have a completely deterministic universe. In such a universe, I would argue that we necessarily cannot have an observer capable of accessing its complete state. Therefore, I do not believe that any observer, not merely a human being, but anything capable of observation, can obtain all the conditions that determine the universe. Any observer existing within the universe must necessarily be unable to access the complete set of conditions determining its state.
And this impossibility does not arise from limitations in human perception, intelligence, instruments, or computational power. It is a more fundamental limitation, one that may be logically necessary.
I see three possible ways of formulating this idea:
- Incompleteness of information. An observer can access only some of the conditions, never all of them. This is where I draw a connection to Gödel’s incompleteness theorem.
- The probabilistic nature of conditions themselves. What we ordinarily regard as definite conditions, such as genes, memories, neural states, and environments, may themselves need to be represented as probability distributions.
- The mutual exclusivity of precision and completeness. We can either know the precise values of some conditions or know the probability distributions of all conditions. We cannot simultaneously obtain the exact values of every condition.
Let me give an example.
Suppose I want to predict whether I will eventually study philosophy, physics, or computer science. The moment I attempt this prediction, I become an observer of myself. Now, I am myself an enormous collection of probability distributions, with countless priors. I have my personal history, academic background, preferences, upbringing, present environment, genetic makeup, interests, and so on. Suppose we want to calculate the probability that I will choose to study philosophy. For simplicity, imagine a number line representing a binary decision. On the left is “Yes, I will study philosophy” and on the right is “No, I will not.”
Now, suppose every contributing factor can take one of two forms.
The first is a probability distribution, from which we must roll a die, so to speak, to sample a particular value. The second is an exact numerical value, which acts like a vote or a weight that can be placed directly on our number line, pushing the decision toward either yes or no.
Under my proposed framework, there are two possibilities.
I may know the probability distributions of all the relevant factors, including my experiences, genes, interests, and upbringing. I would then sample values from these distributions to determine an outcome. Alternatively, I may not know all the probability distributions. However, for certain factors, I may know their exact numerical values, which I can place directly on the number line.
I am proposing that the tradeoff between completeness and precision is a universal constraint on observation itself.
ChatGPT eventually said it understood my point. It described my argument as a universal limitation on the knowledge available to observers, rather than a limitation of human cognitive ability.
But it continued:
“In your conception, the universe may possess a completely determined state and laws of evolution, even though no observer within it can simultaneously obtain precise information about all the relevant conditions.”
It then concluded:
“This means that whether the world itself is deterministic and whether the world can be known completely and precisely are two different questions.”
I disagreed with this distinction.
My objection may initially sound like a version of the familiar philosophical question: If a tree falls in a forest and nobody is there to hear it, does it make a sound?But I think I am trying to argue something more fundamental than that. I do not believe that the determinacy of the world and the possibility of knowing it completely and precisely can be treated as two independent questions. The world does not possess a state independent of observers.
The world exists only relative to observers.
And by “observer,” I do not mean only a conscious, thinking human being. A tree, a cell, or any other system capable of entering into some form of observational relationship with its environment may also be considered an observer.
My reasoning is as follows:
i) There is no world independent of observers.
A universe without any observers is not an objectively existing entity waiting to be discovered. Such a universe simply does not exist.
ii) No observer can access the exact values of all conditions.
This is a universal limitation instead of a consequence of insufficient observational or computational capabilities.
iii) Therefore, a universe with a completely determined state and laws of evolution cannot exist.
The universe exists only relative to observers, and for any observer, such complete determinacy is necessarily impossible. In other words, I reject the assumption that there is an observer independent reality whose complete, precise state exists somewhere beyond our reach.
Probability is not merely a tool that observers use to compensate for incomplete knowledge of an independently existing, deterministic world. It may be the fundamental form in which the world exists relative to an observer.
