# Uniqueness and uniformity

If everything were completely unique, we would have no way of identifying them as to what they are. If everything were completely identical, or uniform, we would have no way of distinguishing them. We conclude that the world is somewhere in between: everything is a combination of the unique and the uniform.

If all events were completely independent, or unrelated, we would have no way of identifying them as to what they are. If all events were completely identical, we would have no way of distinguishing them. We conclude that all events are a combination of the independent and the identical.

So it is not possible to have two completely unique or identical individuals. Nor is it possible to have two completely unrelated or identical events.

In statistics, we assume the least about events we don’t know about: we assume they are independent and make the least possible inference. We assume we know nothing other than what we are given in the data. We take multiple trials and use the law of large numbers to infer safe conclusions. Or we adopt a maximum entropy prior distribution as a minimal assumption.

In natural science, we assume the most about things we don’t know about. This is based on an assumption of the uniformity of nature. The natural world that we don’t know is like the natural world we do know about. We assume that what we don’t know about is the same as what we do know about. That is, we assume everything we know is all we need to know – until we know more. Then we revise and make the same assumption.

If we begin natural science with no prior knowledge and pick up a rock, we conclude that everything is rock. If we then step in a puddle, we conclude that everything is a rock or a puddle. If we let go of the rock and it falls to the ground, we conclude that all rocks fall to the ground just like that rock.

In history, the less we assume about events we don’t know, the better. Events are assumed to be unique though somehow related to other events. Through historical study we infer the relation of events. So history is more like statistics than natural science.

Natural history takes the approach of natural science toward studying the past. It assumes that all events in the past are like events in the present. So the past and the present are alike and history is the repetition of similar events. This is an anti-historical approach to history because it ignores or downplays the uniqueness of events.

2008