2-node-supercomputer.net 2021-05-08

Science Quantifies Uncertainty

Philosophy demands irrefutable truth. Ideology demands unquestioned faith. Science deals with the murky ground between these two extremes.

What do I mean? A philosopher will never be satisfied by a finite number of experiments. After all, the next time you perform the experiment, it may have a different outcome. There is no way you can be 100% sure it will end the same.

An ideologist, on the other hand, will be satisfied after running the experiment just a single time, as along as it confirms their beliefs. If it doesn't confirm their beliefs, then the ideologist will proclaim the experiment was performed badly or is invalid in some other way.

That is, an ideologist will keep their beliefs even in the event of counter evidence, and a philosopher will never be sure of anything but the most limited statements.

The scientist, however, is content with a good description of the world, even if he knows it is not perfect. In fact, a good scientist will quantify their uncertainty. (And a great scientist will work to reduce that uncertainty.)

For example, we observe the Sun rising. On the first day, the scientist may proclaim: "That's interesting! I have no idea if it will rise again tomorrow."

On the second day, they observe the Sun rising again. Now the scientist will proclaim: "That's interesting! On both days that I have been around, the Sun rose! I will give it a 66%1 chance that it will rise again tomorrow."

On the third day, the Sun rises again. The scientist proclaims: "That's interesting! The Sun has risen on all three days I was here to observe. I give it a 75% chance that it will rise again tomorrow."

Days pass. The Sun rises and rises and rises. Every day.

On the 99th day, the Sun rises yet again. Now the scientist proclaims: "That's interesting! I have observed the Sun rise on all of the 99 days that I have been observing. I am 99% certain that it will rise again tomorrow."

The more observations the scientist gathers, the more certain they become that the Sun rises every day. Of course, there are pitfalls here. Maybe the scientist has talked to other people that have seen more sunrises, or some other people that speculate that the Sun cannot be rising forever, perhaps because they haven't seen a sunset, yet, or because they have a theory that the Sun will stop burning in a few billion years. The scientist combines all this data to come to an uncertainty quantification of the theory that the Sun rises on any given day.

That is, science quantifies the reliability of ideas. Interesting science concerns itself with those models that have high reliability.

Does this mean that science quantifies the truthfulness of an idea? Maybe, and I would say that is certainly a goal of science, but I don't know how to quantify the uncertainty on that.

  1. One can quibble with these percentages. My reasoning is that if you observed only one sunrise, then that could really just be an anecdote. It's like trying to estimate both mean and variance from a single data point. In essence, the scientist must establish the domain of possible answers and the probability from that one observation. Thus, after one observation, the probability should be 50% for the next day. I'd be happy to hear a more formal argument here.