I will start this blog by talking about why statistics are pretty much the coolest domain of math. To sum up, it’s because probability is the language of reason in a stochastic world.
You might be surprised by my thesis: isn’t logic the true language of reason ? Logic is indeed a language of reason, but one that only applies to deterministic worlds ! Logic is perfectly suited to the realms of mathematics, in which everything is determined by absolutely rigid rules from which you can’t escape.
However, if we need to reason in a world in which relationships are not completely deterministic, we need a language which has more expressive power than logic, and this is where probabilities and statistics come into play. These two are very related, but if we really want to make a distinction, we could say that probabilities deal with saying how we should act to accomplish a goal efficiently (eg: what is a good poker strategy), whereas statistics deals with what we should believe in (eg: is this pattern I’m seeing significant or not). Not only are statistics a language that works at describing inferences in a stochastic world, one can also show that Bayesian statistics actually contain logic as a special case.
Statistics thus has a very important role to play in the scientific method. Most of science is basically trying to find patterns and checking whether established patterns hold up in new situations. For example, if you wanted to test whether Newton’s theory of gravitation is a better account of reality than Einstein’s, you would design an experiment in which the two theories give different predictions, collect data, put on your statistician hat and check which theory the data agrees with (if it agrees with any).
But statistics actually play a much wider role in this world: every human on earth (and most animals) is an intuitive statistician, collecting data about the regularities of his environment, and trying to act on those. This statistical knowledge is a fundamental component of the behavior of every being on this planet. For example, you know intuitively about what’s normal weather in the city you live, and you can probably predict the weather for the next few days because you have observed the regularities of the weather throughout your life; you know intuitively how your friends and family react to a wide variety of situations because you have lived through a wide variety of situations with them, and even for a person you’ve just met, you can guess how he would act, because he’s most likely going to act like somebody you already know ! Our world is filled with patterns, and it seems like it was particularly beneficial for animals to recognize those in order to increase their survival. A lot of animals thus seem to have “learned” (through evolution) intuitive statistics, through the prism of which they interpret the world.
To conclude, when we study statistics, we are studying the fundamental language of reason, which is not only at the heart of science, but also inside the head of every creature and of every human of this little earth. If that’s not cool, then I don’t know what is.
If you want to read more on this, I can only recommend E.T. Jaynes’s book, which is absolutely awesome, and which makes this point much better than I ever could.