Scale

Sometimes we have to compare certain things in order to understand how they are related to each other. For example, comparing how big a room is compared to a tile (or vice versa) so that we can figure out how many tiles we need to tile the floor in that room. To be able to do such comparison, we have to understand something called ‘scale’. Not the scale which gets deposited on bathroom tiles or the scale we use to weigh ourselves but the scale which refers to measurement and orders of magnitude. Measurement is a fundamental concept in Physics. So fundamental, in fact, that everything we do in Physics starts with observation and therefore being able to measure things.

So what is scale and what can we do with it?

Scale: to allow the same physical quantities to be comparable when they are of different orders of magnitude. For instance, the atom is something which is extremely small compared to everyday objects, like a football. If we want to understand the structure of the atom, it helps to be able to visualise how it is. Now, a simple way to put it is that the atom is composed of two parts: a central part and an outer, orbiting part. Somewhat like a car which keeps going round and round a roundabout. The roundabout being the central part of the atom, the car, the outer part. We’ve given names to these two parts: the central part is called a nucleus, the outer part, the electron (or electrons) if there is more than one. Just as you can have several cars going round and round the roundabout at the same time. But, there can only be one nucleus, one roundabout.

So that picture or model of an atom is easy enough to visualise. It might not be exactly what it is like in reality but it is close enough in order to be able to grasp the basic idea of the atomic structure. Now, as the car goes round the roundabout, it makes a circle, with the centre of the roundabout being the centre of the circle and the distance from that centre to where the car is moving being called the radius of the circle. Twice that radius is the diameter of the circle. Similarly, as the electron goes round the nucleus, it draws a circle round the nucleus. The diameter of the atom will give us an idea of the size of the atom.

Roundabouts are big. We do have small ones but typically, they are big. Maybe 9 metres in diameter. So the radius of the roundabout is 4.5 metres. Now the car will be moving round that roundabout at perhaps 1 metre from the edge of the roundabout. Altogether, this makes the radius of the circle which the car draws equal to 5.5 metres. The diameter will therefore be 11 metres.
How does the diameter of the atom compare to the diameter of that circle? The circle drawn by the car will be ten billion times larger than the atom! That is a huge number. It is difficult to imagine such big numbers. Even though we can talk of the world population being 7 billion people or banks making billions of dollars of profit, to actually be able to picture such large quantities is hard.
The reverse is also true. To picture very, very small quantities is also difficult. How small is a thousandth of a millimetre? We can just about do with a millimetre, maybe even a tenth of that. But a hundredth, let alone a thousandth, is just humanly impossible. So to be able to visualise the atom, at a millionth of a millimetre in size (roughly), we find it easier to scale it up to the size of things we can picture easily. By making the atom ten billion times bigger than it is, we make it comparable to a roundabout.

We can also scale things down if they are too big to imagine. Let’s take the Solar system, for example. In this case, the Sun is the centre of the massive circle and the furthermost planet, the edge of the circle. This huge circle is about 1100 million kilometres in diameter. That makes it a 1000 billion times the size of the circle of the car-roundabout system. To picture something of that magnitude is hard. So we scale it down. We bring it to a scale which is more manageable for us to visualise.

This is what we mean by scale. To size things up or down so that they become comparable to things with which we are more familiar or to make different systems to be more similar in certain aspects so that we can compare their structure or some other property.

This scaling up and down business comes with a caution. It is not necessary that some characteristics will remain the same when we move from one scale to another. For example if we were to compare how a bee flies to an airplane then it cannot be a direct comparison. At the scale of the bee, the air relative to the bee appears to be a much denser medium than how air appears to us or to an airplane. Which means, that the bee flying through air will find it more difficult, because of the “thickness” of the air around it. The airplane has other difficulties to overcome when it flies but the “thickness” or “stickiness” of air isn’t one of them.

So, using the concept of scale allows us to put things in perspective and compare similar quantities and even better visualise objects or things which would otherwise be mindboggling.

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