Everything is a matter of perspective, but to put things in perspective it is useful to have a sense of scale.
For scientists, when we talk about the world around us and the universe beyond, we often speak in terms of orders of magnitude.
This is an approximate scale, but it allows us to gain some perspective on things. It allows us to talk in terms where each order of magnitude represents an increase or decrease in scale by about a factor of ten.
For example, from a scientific point of view we might say that the numbers two and 13 are about the same order of magnitude, but it really depends upon what you are counting.
If you are talking about molecules of water, then whether you have two molecules or 13 is not so important.
On the other hand, if you are talking about an endangered species, the difference between two and 13 is a lot. Indeed, for endangered species, when the numbers get to this order of magnitude, you are likely talking about extinction regardless of the exact number.
However, if we consider the numbers two and 113, they are different orders of magnitude. Regardless of what you are counting, there is a difference between two and just over 100. For endangered animals, the larger number could represent a successful breeding population.
Of course, while this way of thinking about things may be useful for scientists, it sure plays havoc when trying to balance a cheque book.
When looking out at the universe, an order of magnitude approach is a convenient way to think of distances. For example, a typical person is just under two metres tall (even someone only 1.5 metres tall is equal to two metres when you are talking about an order of magnitude) whereas a tough par three golf hole might be 200 metres.
This is an increase of 100 times in distance or two orders of magnitude. It provides some perspective. That is, the length of a good par three golf hole is about 100 times the length of a typical person.
Add another order of magnitude and you have two kilometres, a distance that would be a nice evening stroll, provided the weather co-operates.
Add another order of magnitude and you have 20 kilometres, which is a healthy jog or a comfortable bike ride.
Add two more orders of magnitude and, at 2,000 kilometres, you are about a third of the way across Canada or a third of the way to the centre of the Earth. In either case, distances of this magnitude begin to look substantial from a human perspective. A distance of 2,000 kilometres is about six orders of magnitude larger than we are or about a million times our size.
With two more orders of magnitude, we have a distance of about 200,000 kilometres. That is about halfway to the moon (380,000 km) and again gives a sense of perspective. After all, it would only require 200 million humans standing on each other's shoulders to get to the moon, although that is not practical.
Three more orders of magnitude and we have, at 150,000,000 kilometres, the Sun.
Again, from a human perspective, this is a tremendous distance - about 11 orders of magnitude greater than our normal human scale, but in interstellar terms it is a baby step. To measure interstellar dimensions, we use light years.
In order to measure how far apart things are in space, distance is measured by the time it takes light to travel it. A distance of 300,000 kilometres (the distance to the moon) is one light second. The distance from the Sun to the Earth is eight minutes and 20 seconds at the speed of light or put another way, the Earth is 500 light seconds from the Sun. Five hundred light seconds is only about 11 orders of magnitude longer than the distance between your nose and your toes.
Proxima Centauri, our closest interstellar neighbour, is about five orders of magnitude further from us than the Sun at a distance of 4.3 light years (136 million light seconds). Our galaxy, the Milky Way, is about 100,000 light years across or another five orders of magnitude. And present estimates of the age of the universe tell us it is 27.5 billion light years in diameter or five more orders of magnitude.
So, all told, from human scale distances to the width of the universe is only 26 orders of magnitude. That amounts to ten to the 26th power or a one trailed by 26 zeros.
A huge number, but not really that far if you think in orders of magnitude. Indeed, thinking this way kind of puts everything in perspective - at least, to within an order of magnitude.
