mathematics, probability

A Doubt

My mother in law has been struck by lightning and bitten by a snake. She survived both.

Now, what are the probabilities of those events occurring? According to some Google search results, 1 in 10 thousand for each, perhaps 1 in 100 thousand. Which implies she is one in 100 million to one in 10 billion with both experiences!

This is a very uncomfortable for my worldview.  It shouldn’t have happened. Unless of course, if for example the snake wasn’t real. She didn’t see the snake, only a small painful wound which the doctor interpreted as a snake bite.

There is another explanation. She is a very outgoing person, and for this kind the statistics may be very different, perhaps even more so in this part of the world. Additionally we are not talking about two independent events here. Among lightning struck people a snake bite may be quite common. Think about Bear Grylls for example; some people keep pushing their luck against all the natural elements.

Unfortunately, all such apparent mysteries are not as easy to explain. Niel Armstrong had a problem, I am not sure he was aware of. He should of asked himself – what’s more probable: that I am to be the first man on the Moon, for which the odds are at least one in 100 billion, or that I am just a lunatic with a delusional memory? The odds for the latter are about one in a million.

Here Andrei Kolmogorov and his complexity comes to the rescue. Armstrong had photos and movies, not merely memories. Other people would have to have conspired with him, when he was telling his space stories. Therefore, the complexity of a possible illusion/conspiracy would be much greater than 47 bits. Much, much more. So, Armstrong, as a rational man, ought to believe he was indeed the first man on the Moon.

The alternative was much less probable.

This is also why you don’t need to believe that you are a materialized Boltzmann brains. A picture like the one you are looking at with your eyes just now, would come with only a tiny minority of all Boltzmann brains.

Always go with the shortest possible bitstring when you are in doubt. The shortest complete explanation is always the most probable.

Almost always.