We cannot define anything precisely. If we attempt to, we get into the paralysis of thought that comes to philosophers, who sit opposite each other, one saying to the other, "You don't know what you are talking about!" The second one says, "What do you mean by know? What do you mean by talking? What do you mean by you?"

Science is what we do to keep us from lying to ourselves

A very great deal more truth can become known than can be proven.

We absolutely must leave room for doubt or there is no progress and there is no learning. There is no learning without having to pose a question. And a question requires doubt. People search for certainty. But there is no certainty. People are terrified — how can you live and not know? It is not odd at all. You only think you know, as a matter of fact. And most of your actions are based on incomplete knowledge and you really don’t know what it is all about, or what the purpose of the world is, or know a great deal of other things. It is possible to live and not know.

I am a successful lecturer in physics for popular audiences. The real entertainment gimmick is the excitement, drama and mystery of the subject matter. People love to learn something, they are 'entertained' enormously by being allowed to understand a little bit of something they never understood before. One must have faith in the subject and in people's interest in it.

So, ultimately, in order to understand nature it may be necessary to have a deeper understanding of mathematical relationships. But the real reason is that the subject is enjoyable, and although we humans cut nature up in different ways, and we have different courses in different departments, such compartmentaliz ation is really artificial, and we should take our intellectual pleasures where we find them.

Thus we can get the correct answer for the probability of partial reflection by imagining (falsely) that all reflection comes from only the front and back surfaces. In this intuitively easy analysis, the 'front surface' and 'back surface' arrows are mathematical constructions that give us the right answer, whereas .... a more accurate representation of what is really going on: partial reflection is the scattering of light by electrons inside the glass.