In a celebrated remark in the case Jacobellis v. Ohio (1964) involving “hard core pornography”, US Supreme Court Justice Potter Stewart said that “I shall not today attempt further to define the kinds of material I understand to be embraced within that shorthand description; and perhaps I could never succeed in intelligibly doing so. But I know it when I see it.”

This is a common problem that we all face. There are things that we “know” in a general sense but which we cannot strictly define. Pornography is just one of an infinite class of problems for which we have broad brush definitions (i.e. we think we know it when we see it) but which almost always break down under close examination, and exceptions to the definitions we create can always be found.

I am becoming convinced that this is a general feature of life. Questions have simple answers only when we don’t examine them too closely. Suppose, for example, I asked the question “What is the length of my desk?” you would expect that there is a definite length to it and that there should be a straightforward way to get the answer.

At the simplest level, you could take a ruler and measure it and call this the length. But is that the most accurate measurement? A ruler is, after all, a pretty coarse measuring instrument. You could get fancier and use more sophisticated devices such as laser beams and high precision timers to get increasing levels of precision. But at some point you reach a limit to precision because at a fundamental level, because of Heisenberg’s Uncertainty Principle, the length of the desk is not a well-defined quantity. This is because although the desk looks like an object with sharp boundaries, when you get to the sub-atomic level, we know that the atoms on the surface are quantum mechanical systems and so the edges of the desk are not sharply defined but instead are fuzzy and a blur. How do you measure the length of a blur?

At the large scales with which we normally work, we can ignore this and think of the desk as having a definite length but that is because we are not looking too closely.

For another example, although we all have a general intuitive idea about what is science and non-science, I have previously discussed how, when you look closely at the question, it is hard it is to strictly demarcate science from non-science. This is because the problem of finding necessary and sufficient conditions that demarcate one class of objects from another class of objects is very hard, and perhaps impossible.

While in everyday life we tend to be coarse-grained in our outlook, universities tend to be places where things are examined in fine-grained detail This is partly the reason why universities have received the label of “ivory towers.” To those outside the university it can seem like academics are engaged in research at a level of detail that seems pointless and the ‘ivory tower’ label is sometimes intended as an insult. But the reality is that universities are one of the few places where people try to examine things closely, to see how far we can go in defining things before we reach the limits at which things break down. While to outsiders this may seem like nitpicking, it is important to do this because the consequences of such fine-grained analyses can have practical consequences.

For example, most people have a clear idea of (say) what is alive and what is dead, of what is human and what is not. But those classifications are not as clear-cut as they can seem. What is considered dead for example, has changed over time, from ‘heart dead’ to ‘brain dead’ to ‘persistent vegetative state.’ Knowing the precise limits of knowledge in this area has important practical consequences. (See part 1, part 2, and part 3 of that series.)

It seems to be the case that as much as we might like to have certainty, we can never have it. At some point, we reach a level of detail where we have to make a decision, a judgment, as to what something is and what we need to do. This is why we often delegate to people (judges, doctors, academics, and other experts in each field) who have studied these things the right to make such judgments on our behalf. It is not that they are infallible and cannot be wrong, but because at least they work with an awareness of the limits of knowledge and of the ambiguities that exist at the fine-grained level.