Thoughts on Probability

What is probability? Is probability subjective or objective? Here I will write down some of my thoughts on probability. I hope you can correct them more.

First, let's give an example. He had no idea about the weather outside and asked him how likely it would be to rain, he may answer 50% (apparently this is a guess ). If you let him look outside, he will discover the dark clouds and the storm will come. Then, ask him what is the probability of rain, and he may answer 90%. Either it's raining or it's not raining. There are only two answers to this question. What does 90% of the probability mean? According to the definition of probability, it is based on the previous situation that this person encountered, 90 of the 100 such dark clouds were raining.

Rain or rain does not shift from human will, but people's subjective guesses about rain are different. Based on the increase in information, the probability of subjective judgment also changes. Is there an objective probability of rain (that is, there is a real probability, which is not transferred by human will )? My point of view does not exist. All probabilities are subjective. Increasing subjective probabilities indicates that uncertainty is eliminated. When uncertainty is completely eliminated, the probability is 1. At this time, one thing can be completely determined. But we know that nothing can eliminate all its uncertainties, just as drinking water may also lead to death.

We will continue to discuss the issue of weather forecast, from 50% to 90%, which means that this person thinks that uncertainty has been reduced. If he says the rain is 100%, it means that he is a very confident person and his self-confidence to uncertainty has been completely eliminated, but this is just what he thinks. Objectively, can we completely eliminate uncertainty? If you have a computer with unparalleled computing power, then you know the state of all particles in the universe (why do you want to go to the level of the universe? From a very detailed perspective, the Galaxy rotation will have a slight impact on the weather on the earth.) theoretically, you can calculate the weather at a certain time point, you can even figure out the future of everything. In this way, there will be no uncertainty. You can directly answer the question whether it is raining or not. But in reality, humans may never have the power to simulate the entire universe.

This seems like discussing philosophical things. In fact, probability is closely related to philosophy. The deterministic viewpoint of philosophy is that everything is definite. As Einstein said, God does not roll the dice. In my opinion, the future is definite, but unknown. It is impossible for us to simulate the capabilities of the entire universe, so even if we are certain about the future, we are also unknown.

Back to the weather forecast, it is still not raining. In fact, it is confirmed tomorrow, but we do not know, so we need to use a computer for simulation calculation. After simulating 100 times and 80 times of rain, the meteorological station will be able to announce that it will rain tomorrow.

If all the particles in the universe know that this nonexistent computer is used to repeat the computation for 100 times, it will be the same result for 100 times because it calculates the future, it will tell you exactly whether it will rain or not tomorrow. What humans can do is to infinitely reduce the uncertainty of things and predict things more accurately to improve our lives.

Here is another example of throwing a dice. A six-sided dice: What is the probability of a six-sided face? The answer must be 1/6. If I tell you that all six faces of this dice are 6? The answer must be 1. At this time, the uncertainty has basically been completely eliminated (because we don't consider the situation where one side of the dice is standing ).

This means that with the increase of the information obtained, the uncertainty is gradually eliminated, so that the last infinitely close to 1, the uncertainty can be basically eliminated. This may be why conditional probability is so important and explains why the application of Bayesian probability is so amazing.

In short, the probability we calculated is based on the prior knowledge plus some formula derivation, the obtained number can tell us the possibility of things. Even if the future is definite, we are also unknown. It is precisely because of unknown that we are full of expectations for our lives. Instead of carefully calculating the future, it is better to start the struggle now. If you are in a daze on the screen, it is better to wait for the coming tomorrow ~~