Physics and Numbers

We began this introduction by talking about how physics began as philosophy, a sort of thinking that tries to understand things more deeply, and doesn't have a results-oriented focus. But soon the first natural philosophers crossed a divide which continues to separate physics and all the sciences from philosophy. This divide has three hallmarks: experimental observation of nature's actual behavior, complete control over experiments including the ability to repeat them at will, and always using numbers to describe nature. We started by talking about experimental observation, and more recently discussed the focus on experimental control, how it results in a corresponding narrowing of "scientific truth" to those things that can be controlled and repeated at will, and how it unfortunately can be part of a vicious cycle which focuses on power and abuses both man and nature. Now we will turn to the third hallmark of natural philosophy: its focus on numbers.

Numbers and the things we can do with them will be the daily bread of the rest of this blog. (That's why I discussed this hallmark last.) But before we get to know numbers I want to point out that there is a great mystery here: why are numbers useful for describing nature? Certainly this doesn't seem like a mystery today, when the success of numbers is a fact of life. The movie reproductions we watch via DVD or high definition television are composed of billions of numbers; indeed any image can be represented by numbers, as are the voice signals that we listen to on our cell phones and the songs we listen to on CDs. Mapquest and GPS have quantified our moving around: 5.3 miles north, then turn right and 1.4 miles east. And time also: we watches to tell the exact date and time. Clearly numbers have been very very successful, but their success alone does not explain why you're successful. If we think that the utility of numbers is obvious, it is only because we are prejudiced by our daily experience.

Control Over Experiments

We started out by introducing philosophy, and then saying that natural philosophy (physics) made a break from other philosophy by emphasizing three things: scientific experiments, control over experiments, and numbers. We have just finished discussing scientific experiments, which involve a real attentive observation of nature and readiness to be both surprised and wrong, which has some similarities to love between people. However the analogy to loving relationships is not complete,: the second major characteristic of natural philosophy (physics) is its emphasis on repeatability and total control.

Natural philosophers restrict their inquiries and do not study a lot of things, saying by definition that many things are just not their problem. This may come as a surprise to many who understand that science gives explanations of everything and considers the whole world as its domain. This is not really true: scientists restrict themselves to studying things that they can repeat at will, things that they can make happen over and over again, and that their colleagues can duplicate. For instance, if I fill a balloon with cold air and then heat it, the balloon will grow bigger. I can repeat this many times with many balloons, and it will never happen that heating the balloon would make it shrink. Moreover my friends, my neighbors, and even you my reader can fill balloons and heat them and observe the same behavior. The balloons are fully under our control: we can keep them at a particular temperature as long as we like, and measure their size, temperature, composition, etc.

Natural Philosophy

Of course natural philosophers - physicists - have the same philosophical bent. As a case in point, consider the efforts to come up with a Theory Of Everything, or a Grand Unified Theory. In those efforts physicists are trying to understand something that is far beyond human experience, with almost no connection to the real world, so that we have to build billion dollar machines if we want to hear even the slightest whisper from nature about these matters. Not practical at all.

But going back to the natural philosophers, you can imagine how it looked at the time when a person asked whether heavy things really fall faster than light things, or debated the commonplace knowledge that vacua can not exist in nature, or claimed that everything is made out of very small invisible indivisible pieces. This last was proposed by the Indians and Greeks but had no connection with real world evidence until two millenia later. These people clearly had an unworldly bent, the sort of attitude that is epitomized in so many pictures of Einstein.

But there was something a bit different about these natural philosophers, which made them far different from other philosophers, and still lies between the two like a canyon. The natural philosophers emphasized numbers, experimental verification of their ideas against nature's actual behavior, and complete control over experiments. I'll expand on all three.

The Beginning - Philosophy

We'll start at the beginning, and the beginning of physics is philosophy. For a long time we called ourselves "natural philosophers." In fact the first physicists were just philosophers. So, a few words about philosophy, because I think that most people dislike it or feel very disassociated from it, think of it as something repellant like the number of angels on the head of pin, and think it belongs to the past. Whether or not I'm right about a common dislike for philosophy in the populace at large, I am right about a dislike for philosophy among today's physicists. Many physicists look down on philosophy; Feynman had some choice words about it of basically total disdain. So let's unearth the truth about philosophy and what it's about, and then see how physics grew out of that.

There is a very practical way of approaching life - one that emphasizes getting things done. This is the mode that most of us spend most of our time in. I know how to walk, the sky and what that tells me about how to keep myself warm and safe from the weather, how to use a sponge, soap, and water to scrub and clean dishes, how to make my room beautiful, how to communicate with others and participate in family ties, the rules for my local government/groups and how to work those rules to get things done, and many many other things. At every stage in history most people have been engaged in getting things done. It's still that way today. We put a lot of thought into it and are constantly challenging ourselves and learning more into order to get new things done. It requires immense time and talent, and the majority of people have focused on this sort of life and work, and many have lived very satisfying lives doing so.