# The Problem with Causality

## On Causality, Certainty, Process and Time

What do we mean when we say that “A caused B”?

We usually mean that there was some process, governed by a set of rules, that links A to B. And that A happened before B.

Hence, “causality” depends on two factors:

- Time
- A process, governed by a set of rules

# The Problem with Process

How do we know if processes happen? We “know” because of laws we’ve inferred about the universe. When we say that “A caused B”, there are some laws that say that A must cause b.

Some of our “laws” are about abstract things. Like the laws of mathematics. If the two shorter sides of a right-angle triangle are of length 3 and 4, such a mathematical law says that the longest side must be of length 5.

Other laws about concrete things (like physical nature, biological systems, medicine, psychology, economics) base on empirical observations. When we observe many instances of A happened and then B also happening, we define a law that says “A causes B”.

Strictly speaking, in the latter cause, we don’t know if “A causes B”. Our empirical observations only imply that “A correlates with B”. This is the problem with process. There are no concrete processes where we know with certainty. Our knowledge of processes is purely correlation. Not causation.

# The Problem with Time

Physics defines time as the direction in which disorder in the universe increases. Or more intuitively, the direction in which information increases. For example, before you toss a fair coin, you don’t know what the outcome will be. But after you toss the coin, you know (heads or tails). Hence, after the coin-toss, the amount of information in the universe has increased by one bit. This is the “pure” definition of time.

Now consider the following “points of time”.

- Before A has happened
- After A has happened, but before B has happened
- After both A and B have happened

We can see how “information increases” with time when we observe what we know at each point in time.

- We don’t know the answers to either question, “Has A happened?” or “Has B happened?”
- We know the answer to the first question, but not the second
- We know the answers to both questions

Now suppose that “A always and only causes B” is some universal law of nature. Then if A happens, we know that B will happen. Not necessarily instantly, but eventually. Hence, if we know the answer to the question “Has A happened?” we know the answer to the question “Has B Happened?”. Hence, “After A has happened” we have all the information about the universe as if B has also happened. Thus, “purely speaking” there is “no passing of time” between A happening and B happening. We might as well say “B caused A”.

Note, the more uncertainty, the more time. The less uncertainty, the less “passing of time”.

# The Paradox

Hence, at one extreme we have “perfect certainty” where “A always and only causes B”. In which case, there is no time. At the other extreme, we have perfect uncertainty, where there is time, but we can’t say if “A causes B”.

This is the problem with causality. Either there is perfect certainty, in which case there is no time, and hence no causality. Or else, there is no certainty, in which case the “process” that results in causality is flawed. In the middle we have an uncertain “no cause’s land”.

Conclusion?

Either,

**“A and B cause each other with certainty, at the same instant of time.”**

Or else,

**“The relationship between A and B is uncertain. We can’t draw any “causal” inferences.”**