Nothing is an interesting concept with many different aspects. Maths, science, philosophy and many other fields of endeavour have their own overlapping concepts of nothing, zero, null or just the absence of anything.

Some computer languages have a concept of ‘null’. This is not the same as the concept of ‘zero’. To use the usual analogy of pigeonholes, numbers and other things in computers are conceptually stored like objects stored in pigeonholes. Each pigeonhole must have a location, sort of like ‘third row down, fourth hole in the row’. A pigeonhole could be empty or it could contain a number or a string of characters or more complicated objects that the computer recognizes. It could optionally have a label so that it can be found quickly.

A computer moves things around and in the process it manipulates them. Given this analogy, what is ‘nothing’ to a computer? It could mean several things. It could mean the number zero, stored in a pigeonhole or it could refer to an ’empty string’ stored in a pigeonhole. (An ’empty string’ is like the object ‘where’ when the individual letters ‘w’, ‘h’, ‘r’, and the two ‘e’s have been removed. It is represented by two ). It can be a more complicated object that hasn’t been completely set up. Alternatively it could refer to an empty pigeonhole. It could even refer to a label which has not yet been allocated to a pigeonhole. Pity the poor programmer who has to keep all these ‘nothings’ separate in his or her mind (and a few others that I’ve not mentioned!).

In mathematics we have the concept of zero, but this is a fairly newly introduced concept. Some number systems, such the Roman Numeral system do not have a zero, and it was a big conceptual jump to add zero to the mathematical number systems. After all, what do you hold when you have two oranges and you give them away? Nothing! You can’t see zero oranges in your hands, unless you are a modern mathematician of course.

So mathematically ‘nothing’ is zero then? It could be, though ‘nothing’ could be integer zero, ‘0’, rational zero, ‘0/any number’, real number zero, ‘0.0’, complex zero, ‘0 + 0i’, or many many other versions of zero. Maths also has a concept of a set, which is just a collection of objects, which can be pretty much anything. An analogy often used is to liken a set to a bag which contains any sort of object. Statisticians are fond of sets which comprise a set of balls which can be of more than one colour but are usually otherwise identical. If all the balls are removed from the bag, what do you have? A bag with nothing in it! It is usually referred to as an ’empty set’. Note the similarity with the ’empty string’ mentioned above. There’s nothing coincidental there.

There are other sorts of ‘nothing’ in mathematics. A mathematical ‘function’ is a way of relating ‘variables’. The details don’t matter, just the fact that functions have ‘zeros’. They may have one or more zeros or they may have none. Having no zeroes could be considered a sort of ‘nothing’, in a way, though the functions in question are no less proper functions than any other. I’m sure that there are other more esoteric ‘nothings’ in maths.

In physics things should be clearer, right? In physics a vacuum is created is all matter is removed, leaving … nothing. Except that it appears to be impossible to actually remove everything from a container leaving nothing. Even the best pumps will leave a considerable numbers of atoms floating around inside the container. Other methods of emptying the container may reduce slightly the number of atoms in it, but we can’t even reach the very low densities found in the gas clouds visible to astronomers. Even in the depths of space between the galaxies we still find the occasional atom, usually of hydrogen.

Maybe we should look between the atoms for nothing? Most people have an image of an atom as a sort of miniature solar system with the nucleus standing in for the sun and the electrons standing in for the planets. Unfortunately the analogy breaks down if you look closely. Electrons are only found in certain orbits around an atom and even that is an over-simplification. Their location depends on a probability function and in some views this means that the electron is sort of smeared out in space and doesn’t have a strict location and you can’t say specifically that it is ‘there’ at a particular location, only that it has a particular possibility of being there.

One consequence of this is that you can’t say that is** isn’t** at a particular location, so it is impossible to declare that there is nothing at a particular point in space at any one time. If you consider all the particles in the universe, they all have a probability of being there, so you might be surprised not to find a particle there at a particular moment in time.

In addition to this, I have read article which describe ’empty space’ as a seething mass of pseudo particles or virtual particles. These come in pairs of particle and anti-particle which are continually coming into existence, mutually annihilating each other out of existence again. Viewed in this way it is difficult to describe ’empty space’ as containing nothing, so we still haven’t found ‘nothing’. Although physics has the concept it is hard to find a physical instance of it.

Cosmologists talk about the “Big Bang” when everything came into existence. Before the Big Bang, they say, there was nothing. Nothing! But what does this mean. I like to think of it by analogy. If you take a piece of paper and draw a circle on it, you can consider this circle to contain all space and time and everything that exists in space and time. If you draw a line horizontally through it you can label the big inside the circle as ‘time’. Note that the line should not extend beyond the circle.

The point where the line reaches the left hand side of the circle is the Big Bang. The point where the line reaches the right hand side of the circle is the point where everything collapses on itself and space and time cease to exist.

Some cosmologists think that there will not be a collapse, so the curve is not a circle but a curve open to the right. This doesn’t affect my argument – everything and every time is included inside the curve.

If you now draw a line vertically, not extending beyond the curve, and label it ‘space’. If you move the line to the left, the graphical distance between the top point and the bottom shrinks. Moving the line to the left moves it back along the time axis and represents an earlier state of everything. When the line just touches the curve the point of intersection of the two lines represents the Big Bang.

What about the points outside of the curve? This is where the analogy breaks down. Since we have included all space and time inside the curve the points outside the curve do not represent real points in space and time at all. In short, they do not exist. We could loosely say that nothing exists outside the curve of space and time, but that is not true. ‘Nothing’ is a concept based on space and time, being the opposite of ‘something’ or the potentiality for ‘something’ and as such needs a space-time framework to mean anything. If there is no space and time, there can be no ‘something’ and therefore ‘nothing’ is meaningless. Beginners in science and astronomy might ask what is beyond the boundary of the universe, but the question doesn’t mean anything. The universe contains everything.

If there were other universes, with their own space and time, they would have to be right alongside our universe (that is an analogy of course – language fails us in this situation) as there is nothing to be between the two universes. If you were able to travel from one universe to the other, a concept which I don’t believe stands up to examination, you probably wouldn’t notice the difference. Maybe nothing is a sort of inability to be. But that language implies an intent, which implies a lot of other things and maybe leads to pantheism and I don’t wish to go there.

Well, I’ve used over 1300 words to talk about ‘nothing’, so I will stop here. What comes after the end of this post? Why, nothing, of course!