Elon Musk’s argument: “the probability that this universe is base reality and not a computer simulation is one in a billion” is a sound and logical argument. (If you’re not aware of his full argument, google the video)

However, the argument seems to lack an understanding of meta-probability. Understanding meta-probabilities allows us to better contextualize/interpret the argument.

A quick example:

1. What is the probability that a fair coin toss results in heads? 50%

2. If you are told a red team is playing a blue team at soccer this afternoon, and you are asked to predict the result - what is the probability that the blue team will win? 50%

3. If you are now told that the “blue team” is the French national soccer team, and the “red team” is made up of local school children, what is the probability that the blue team will win?…. Now that we have more information, it’s no longer 50%… it’s now more like 99.999%

What’s going on here? Whilst in examples 1. and 2. both probabilities are 50% at face-value, they are actually quite different. The problem stems from the fact that when stating a probability, the uncertainty of the probability is rarely stated. The reality, when comparing the probabilities of a fair coin toss with a random soccer game (1. and 2.) looks like this:

As you can see above, whilst both probabilities are stated as 50%, the meta-probabilities are shown by the curves. The curves reveal that the coin toss result is known to be a 50% chance fairly accurately, but the soccer game result is known to be 50% with a large amount of uncertainty.

In example 3. we acquire more information about the teams playing, and this allows us to make a better prediction of the result. In other words: The less information we have about the system/process we are trying to predict, the greater the uncertainty in our probabilities.

So whilst I agree that: “with the information we have at present, it seems logical that there is a one in a billion chance that we are not in a simulation”, the information we have about the universe is but a speck of the total information available about the universe (the entire system/process). We mainly know a lot about ourselves and Earth in this time-period. This is highly likely to skew predictions and give them bias.

I’m not pretending to know whether we live in base reality or in a simulation. But I can say that the uncertainty in Elon’s probability is so great that it is no longer a meaningful/reasonable prediction.