The Law of Large number tells us that as we increase the number of samples, the average becomes more reflective of the population. The best way to explain this is to talk about a coin flip.

I asked a three people to suppose there was a coin between. I prompted: suppose I flip the coin, what is the probability the coin flip results in heads versus tails? All three responded with 50/50. And I could imagine most people might think that. However, the answer is wrong. The answer is technically $50% \pm 100%$ — which is the same as saying “try it and find out”.

The Law of Large Number tells us that we need close to 1,000,000 coin flips to occur before we could say with high confidence that the result of a coin flip resuling in heads is 50/50. I’m not spending my time flipping coins, so the next best thing is to assign an amount of precision — or confidence.

I won’t belabor the post with math; you can search on google or with an AI tool to learn more. The point is: precise beliefs about what might be true or happen require large amounts of data. As the amount of high quality data comes in, so to can your confidence in the belief; little-to-no data should translate to “it’s nothing more than a coin toss at this point, let’s see how it pans out.”

I use this thinking as a mental-health improvement hack My views on the world tend to feel more or less certain by the amount of quality data I collect and analyze. My confidence in a restaurant being good may be informed by the number of reviews, a claim about world events being true may require to source news from multiple differing sources, that a musical idea works needs multiple performances and validations each time. As more data comes in, confidence in my beliefs about the world rise. Paradoxically, it’s that lack of confidence in my beliefs that reduces anxiety, reduces perceptions of being slighted or that I’m being attacked, and enables me to feel more grounded and content.

Yes — as I become less and less certain, I become more and more grounded. I am not a contradiction. I am simply not large enough, and if that realization isn’t good for my mental health, I don’t know what is.

Last modified on 2026-02-11