## The number of the universe.

Anything that can be measured can be encoded in a single number. Take for instance the trajectory of a stone thrown into the air. Its position in relation to the point of launch and the time it has taken to reach that point can be encoded into a set of numbers, three for the spacial dimensions and one for the time dimension. This can be done for all the points that it passes through. These individual numbers can then be encoded into a single number that uniquely identifies the trajectory of the stone.

Or, a physicist can describe the motion of the thrown stone by using generic equations and plug in the starting position and starting velocity of the stone, which can then be encoded, probably in a simpler fashion than the above point by point encoding.

If we can imagine a set of equations that describe all the possible physical processes (the “laws of nature”?) and we can imagine that we can measure the positions of all the particles (including photons,’dark matter’ and any more esoteric things that might be out these), then we could encode all this in a huge number which we could call the ‘number of the universe’. Such a number would be literally astronomical and I do mean ‘literally’ here.

The most concise expression of the state of the universe over all time is probably the universe itself and the laws that govern it. Each individual particle has its own attribute, like charge, mass, position and so on as well as things like spin, charm and color. Some of these change over time and some are fundamental to the particle itself – if they change so does the nature of the particle. The rest of the universe consists of other particles which have a lesser or greater effect on the particle, all of which sum together to describe the forces which affect the particle.

There are a couple of things which might derail the concept of the number of the universe. Firstly there is Heisenberg’s Uncertainty Principle and secondly there is the apparent probabilistic nature of some physical processes.

What follows is my take on these two issues. It may make a physicist laugh, or maybe grimace, but, hey, I’m trying to make sense of the universe to the best on my abilities.

People may have heard of the Uncertainty Principle, which states that there are pairs of physical properties which cannot both be accurately known at the same time. You may be able to know the position of a particle accurately, but you would not then be able to tell its momentum, for example.

It is usually explained in terms of how one measures the position of something, which boils down to hitting it with something else, such as a photon or other particle. The trouble here is that if you hit the particle with something else, you change its momentum. This is, at best, only a metaphor, as the uncertainty principle is more fundamental to quantum physics than this.

Wikipedia talks about waveforms and Fourier analysis and an aspect of waves that I’ve noticed myself over the years. If you send a sound wave to a frequency analyser you will see a number of peaks at various frequencies but you cannot tell how the amplitude of the wave changes with time. However, if you display the signal on an oscilloscope you can get a picture of the shape of the wave, that is the amplitude at any point in time, but not the frequencies of the wave and its side bands. Err. I know what I mean, but I don’t know if I can communicate what I mean!

The picture above shows a spectrum analysis of a waveform. I don’t have the oscilloscope version of the above, but below is a time-based view of a waveform.

In any case, the uncertainty doesn’t imply any indeterminacy. A particle doesn’t know its position and momentum, and these values are the result of its properties and the state of the rest of the universe and the history of both. This means that the uncertainty principle doesn’t introduce any possible indeterminacy into the number of the universe.

On the second point, some physical processes are probabilistic, such as the decay of a radioactive atom. I don’t believe that this has any effect on the number of the universe. The number incorporates the probabilistic nature of the decay, including all the possibilities.

There is an interpretation of quantum physics called the “Many Worlds Interpretation“, where each possible outcome of a probabilistic process splits off into a separate world, resulting in an infinity of separate worlds. I don’t believe that this tree of probabilistic worlds is a useful view of the situation.

No, I think that there is a probabilistic dimension, just like time or space. All the things that can happen, ‘happen’ in some sense. The probability of you throwing 100 tails in a row with a fair coin is very small, but it is possible. As I see it the main objection to this view is the fact that we only see one view of the universe and we don’t appear to experience any other possible views of the universe, but this is exactly the same with the dimensions of space and time. We only experience one view of space at a time as we can’t be in two places at the same time. While we could be in the same place at two times they are two distinct views of the universe.

In any case the number of the universe encompasses all probabilities so if you still adhere to the single probability model of the universe, our universe and all possible universes are encoded by it. The question then becomes how you can extract the smaller number that encoded the single universe that we experience. I believe that that is not a question that needs to be answered.

The question that does remain open is – why is that number the number of our universe? Why not some other number?

## Nothing

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!