Different cultures have different ways of expressing common concepts. One of the most interesting aspects of this cultural relativism arises when it comes to notions of number, small sets, plurals, and so on.

Prague Astronomical Clock

For example, in English, we have the concepts of singular and plural. If there is one of something, it is singular; any more, and it is plural.

One stone; two stones.

Russian, on the other hand, includes a concept of “twoness” before moving on to the more generic plural. It is as if we had a construct like…

One stone; two stonae; three stones.

One finds other differences, especially when cultures are viewed historically: how the concept of number and measure has changed over time. As is well known, it took a long while for the concepts of zero and infinity to be invented.; Roman numerals are particularly difficult to use to do math; the mathematical community needed many years to come to grips with the notion that the square root of a negative number could in fact be a pretty useful concept (if you didn’t let its inherent weirdness bother you too much).

Even in modern times, some isolated cultures haven’t developed any concept of identifiable number beyond three, so in counting, they are only able to produce the sequence, One, two, three, many…

It is difficult not to feel a certain sense of superiority over such cultures, and we like to think in the Western world that we have reached some pinnacle, some sort of “completeness”, when it comes to our concepts of singular, plural, number theory, symbolic math, and so on. It is as though we believe the set is complete.

But this complacency is somewhat ill-placed, and despite the fact that the mathematical concepts exist, few people have a reasonable grasp of them. If we look at something like the concept of large numbers, we find very quickly that most people’s visions of such things are rather limited.

Nowhere is this more important than when we are considering long periods of time, as we shall in these essays, as we look at the history of the Cosmos, or the evolution of Life. For example, it is commonly accepted that the dinosaurs died out about 65 million years ago, and that the Sun is about 4.6 billion years old, and that the Big Bang occurred about 13.7 billion years ago.

We all know these are big numbers, but how big are they really? How much bigger is one than another? How can we get a grasp on them? More to the point, when discussing time lines and history, how can we arrive at a meaningful understanding of long periods of time, like “65 million years”?

Let’s have a go, as follows:

First of all, picture a millimetre: it is a pretty small thing (maybe the width of the two l’s in the word “millimetre” itself), and there are 25.4 of them in an inch, which is very roughly the length of the last joint of your thumb.

Let’s imagine that one year corresponds to 1 millimetre. Once we make that association, we can build a “time ruler” and start measuring periods of time as various lengths or distances. This helps us get an idea of how big some of these big periods really are.

So, if you live to be 100 years old (good luck on that), on the millimetre-per-year scale, your whole life would measure 100 millimetres, which is about the length of a small smartphone, or the width of the palm of your hand. The period from birth, through your childhood and on to the end of your teens would correspond to about the width of your index finger.

Looking back from the present, Shakespeare was writing about 450 years ago, so he’s half a metre away from us, at least in terms of our time line. The purported birth of Jesus at approximately 0 AD (commonly thought to be about 4 BC) would be about 2 metres away.

In order to grasp this properly, we need to keep in mind at all times that a year is still just a millimetre. So by the time we start taking about the change to the Common Era, those years have started to add up, into a considerable length; indeed, we are getting to the point where the term “distance” seems more appropriate. The Great Pyramid of Giza was completed about 2,500 years BCE, and the birth of agriculture is thought to have occurred about 10,000 years ago.

So these two events, measured with our ruler, would be about 5 and 10 metres away, respectively. All of a sudden, we are talking well across the living room.

So much for civilization and culture; but how long have human beings walked the Earth?

Although there is much conjecture around this question, and given that there are many ways to define human, it is thought that anatomically modern humans – someone you might see on the street and not think twice about — arose very roughly 200,000 years ago.

Prague Astronomical Clock – Sun and Moon

Whoa! We suddenly have taken a huge jump here: Remembering that the whole of your 100 year lifespan measures about the width of your palm, modern humans have been around for a length that measures 200 metres. About two football fields. Two-thirds the height of the Eiffel Tower. Further than you can run without being winded…

And modern humans, by evolutionary standards, have been around for just the blink of an eye.

As said earlier, it is thought the dinosaurs died out about 65 million years ago, which by our measure is 65 kilometres. That’s very approximately the distance between London and the South Coast, 650,000 of your palm-width lifetimes ago, the distance from Toronto to the tip of Lake Simcoe.

Several studies have shown that many people in the Western world have a very poor grasp of time lines when we are talking evolutionary scales. Large proportions of the population of America, for example, believe that humans and dinosaurs were for a time contemporaries. (No doubt some pretty poor black and white science fiction films were enough to cement this misconception.) Our distance time-line puts the lie to this: Humans have been around for about 200 meters; the dinosaurs died out 65 kilometers ago.

And that’s when they died out. In fact the dinosaurs reined for about 100 million years (100 km on our measure), and life, obviously, had been around a long time before that, in order to have evolved such incredible beasts. So how far back do we have to go to get to the origins of life on Earth?

This question is not so simple to answer, as the further back in time we go, the simpler and smaller life forms get (and so don’t get fossilised well or at all), and of course the more time there has been for those fossils that do get created, to be eroded away. Moreover, even the time of our earliest fossils doesn’t go back far enough, as the creatures that made them would have needed time themselves to have evolved. Nonetheless…

Nonetheless, the earliest microbe-like fossils we know of date from about 3.5 billion years ago. That’s billion, not million, so we are going to have to move to a whole new scale of distance measurement. Measured as a distance on our time ruler, the origin of Life occurred between 3,500 and 4,000 km back in time, which is very roughly the coast-to-coast distance across America.

So we soon arrive at the point where expanses of time are so vast that even our one-year-per-millimetre tool starts to produce distances that are tough to get our heads around. The Big Bang occurred 13.7 billion years ago, which by our measure is 13,700 km, and which is somewhat more than the average diameter of the Earth.

And that, at a scale where the whole of your life would fit in the palm of your hand.

It is a wonder.