## Space – the Final Front Ear

Sorry about the fabricated mondegreen, which obviously references the Star Trek series of films and TV shows. Captain Kirk saw space, or more correctly distance, as a barrier, but it really is one of the factors that determines the structure or shape of our Universe.

It is interesting to me, that, although the Universe is finite, if it derived from a Big Bang, there is a human urge to explore outwards, as if it were infinite. That is probably one of the factors that led scientists such as Fred Hoyle and others to support a Steady State Theory of the Universe.

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Personally, I believe that there is no such thing as a steady state in anything. When we see something which appears to be in a steady state or equilibrium state we should look for the feedback factors that are keeping it that way. For example a pendulum hangs straight down when at rest because any deviation from that position results in gravitation forces pulling it back to the rest position.

If friction is low the pendulum will actually pass through the equilibrium position and swing to the other side, whereupon gravity will slow it and draw it back towards the equilibrium position again. Eventually friction will slow the pendulum down and the pendulum will again hang vertically.

So we have two forces, gravity and friction, resulting in the pendulum returning to the equilibrium position. No pendulum lasts for ever, as the pivot will wear out or an elephant may step on the thing, so the equilibrium will only exist for a finite time, but it will last long enough for us to use in clocks or in scientific experiments.

Space is itself expanding as I understand the theories and some of it is out of our sight, over an event horizon, which is a locus where everything is moving away from us at the speed of light. That doesn’t much our location special – it is true of any point in the Universe. LGM on a planet around a star that is over the event horizon from us have their own event horizon, and while they may be able to see a star inside our event horizon and we in theirs, we cannot see each other.

Space separates us form the LGM, but it also separates from things local to us. Ben, our dog, is over there, about 3 metres away. My cup is mere centimetres away. It is fair to say, I think, that this is the essence of space – it is hard to conceive a universe which doesn’t incorporate a spacial concept. Or rather, a separation concept to allow things to be different from one another.

Space is not the only “separation concept” that I can think of. Things can also be separated in time, so two different bodies can exist in the same spacial position, but just not at the same time. Time is so connected to space that Einstein and others were able to link time and space into a complex space/time concept.

The similarity between the space dimension and the time dimension is striking. You can even measure distance in time units as astronomers do when they talk about light years. We also do it when we say that a distant town is three hours away.

We less frequently talk of time in distance units, for example, when we say things like “six laps later”, to describe the time between two events in a car race. At some level we acknowledge that time and the space dimension have a lot in common.

Space in the sort of concept that everyone knows and experiences but no one thinks deeply about. There’s no doubt that space separates events from one another. You can’t have two solid objects occupying the same space at the same time, without catastrophe ensuing. Scientists have been trying to achieve this for years, with the aim of harvesting the energy generated from the ensuring nuclear fusion.

Space appears on the macro (normal) level to be continuous. We appear to move smoothly from one location to another when we walk, incidentally forcing the air out of way as we do so. There is no sudden jumps that we notice, we don’t hop from point to point like a chess piece on a board.

The philosopher Zeno came up with a number of paradoxes related to movement, that is getting from point A to point B. For instance, the athlete Achilles could not overtake a tortoise in a foot race, because Achilles would need first to reach the tortoise’s starting point, by which time the tortoise would have moved on. Achilles would then have reach the point that the tortoise had reached now, by which time the tortoise would have moved on. And so on, ad infinitum.

Of course Achilles does overtake the tortoise, and I believe the main issue in this case is related to the summation of an infinite number of decreasing distances, which intuitively one might this would sum to an infinite distance. In fact the sum of the distances is a finite number. If Achilles runs 10 times as fast as the tortoise and they start 10 feet apart then Achilles overtakes the tortoise after he has travelled 11 and 1/9 feet exactly.

Zeno’s paradoxes still inspire debate, but his conclusion was that movement, the smooth transition of something from one place to another is an illusion. One of the assumptions used is that distance is a continuously varying property, but it may be that it is not, and there are hints of that at the quantum level. The Planck length is the smallest distance about which statements can usefully be made and it is impossible to determine the difference between two locations less than one Planck length apart. Perhaps we do hop from place to place like chess pieces, or at least our atoms and their constituent particles do.

Space and time enable events to happen uniquely, and without collisions. Events may happen in the same place as long as they happen at different times. It may be that events of different probabilities happen at the same place and time, so long as the sum of the probabilities of all events is one. It may therefore be that probability is a dimension with the same sort of status as the space and time dimensions. This would require that our view of probability, of one event out of many being the one that actually happens is an illusion and that events of all probabilities happen in a sense.

## Considering the Universe

(Once again I wrote this on Sunday, but forgot to post it on Monday)

When we are considering the Universe we are considering something that we are part of, and of which we share the characteristics, such as, for example, existence. We can exist only because the Universe exists and the Universe exists, at least in part, because we exist. It is conceivable that in some way a universe could exist with nothing in it, much like a mathematical empty set but it would be pretty boring.

Or would it? Maybe I’m applying some anthropocentric reasoning to that statement. After all, the concept of a mathematical empty set is very useful in mathematics, and but then again, “useful” is a human concept.

A universe may be non-empty, but have no life in it. We, from another universe can conceive of such a universe, but there can be no perceiving of that universe if we rule out the possibility of visiting it from our Universe. We can’t even tell if such a universe exists, so some would argue that the question of its existence is meaningless.

That’s a valid argument, but then again, out Universe was not perceived by any entity in the billions of years prior to the evolution of life. Of course the question of the early  existence of our Universe before the coming of life, is not meaningless to us – we know that it must have existed for us to exist.

Of course, we can conceive of other universes other than our own, but do other universes exist in any real sense, apart from our own. A universe is self contained in the sense that there is no logical reason to conceive of anything outside of it. It is all of physics, all of existence.

One definition of universe is:

a distinct field or province of thought or reality that forms a closed system or self-inclusive and independent organization

This is a pretty good description of what I am writing about I’d say. The key word for me is “closed”. If something is closed it contains whatever it contains and the outside is irrelevant so far the contents are concerned.

Though now I come to think of it, maybe that is not true. If we have a can of beans, we know what is inside it by the label, and we can open the can with a can opener. Maybe the contents of our Universe are visible on the outside, on the label as it were.

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Our Universe has laws, or appears to have laws. The laws appear to be universal – that is, they apply everywhere in our Universe without exception. An atom here behaves the same as a similar atom here would and conceptually swapping them would make zero difference.

We do not know all the laws but we humans believe that we can know all the laws and I believe this to be true, even if it might take longer than the life of the Universe for use to discover and understand them all. By laws, I mean “how stuff works” and even if the ultimate answer is “because that’s the way the Universe works” and there is no deeper meaning than that, I’d still consider them laws.

``` http://www.gettyimages.com/detail/492250290 ```

One bizarre possibility though, is that there is no order and the Universe is totally random, and only appears to have order. When we look at an expansion of the number Π we mostly find what seems to be random digits. Occasionally however we find runs of digits which look like they are non random, such as a lengthy series of the digit “3”, but eventually the random appearance returns.

This feature of the number Π can be used for amusement, such finding one’s own name “encoded” in Π, or any other string. Maybe our Universe is like a very long encoded string in the number Π, which seems to be ordered but actually isn’t. Maybe at some future instant things will revert to the real random state that the Universe is its real state.

Some physicists and cosmologists postulate alternate universes to account for some of the weirder facets of Quantum Physics, but in the broader sense we can consider universes which are similar but different and unrelated to ours. Would we want to visit such universes? Could we conceivably do so?

It seems to me to be unlikely that we could visit other universes, as the only methods that we could use are physical ones and our Universe encapsulates its physicality. That is, the physical laws pretty much define it. A frog can leap from a pond, since frog, pond, the air and the surroundings of the pond are physical, but simple leaping cannot take the frog to another universe, no matter how hard he jumps. A human can use physics to travel the Universe, but using physical means it doesn’t appear possible for us to jump out of our pond.

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Would we really want to visit other physics-based universes? The other universes would have to be pretty much the same physically, our physical bodies would suffer – imagine for an example a universe where protons decay in minutes instead of in aeons. We would die in seconds.

Our best prospects for universe-hopping would be those universe which are probability neighbours. That is, they share the same physics as our Universe, but some events happened differently. For example, one can contemplate a universe where slaving never happened or where France’s hegemony dominated the early USA and French language and culture dominate in the North Americas.

Of course, we are used to a physical Universe, but it is conceivable that other universes may be not physically based. It’s extremely difficult to even talk about such universes, should they (in some sense) exist, and my mind keeps trying to populate such conceptual universes with things, and things are presumably physical entities, and would not be able to exist in a non physical universe. Probably!

Perhaps our physical nature hampers us in understanding the real nature of things. Perhaps we can only conceptualise things based on our nature. After all our thoughts are the end result of physical processes evolving over billions of years and are implicit in the history of our Universe and encoded in a way in the Big Bang.

## Time Travelling

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Time stories have been around for years, and yet we have seen no time travellers. If there are time travellers, then they are hiding from us. That would be pretty hard, since society and language are changing all the time, and they would most likely look out of place.

If they came from the past, their mannerisms, clothing and use of language would likely give them away. Imagine someone from the time of Sir Francis Drake appearing in the current era. He would quickly be spotted.

``` http://www.gettyimages.com/detail/127681134 ```

For someone travelling from the past, the issue is that he or she would not know what to expect as the present is the future of times past, so they would not be able to prepare themselves for the future, as they would consider it.

If a citizen of the future where to travel to the current time, he or she could presumably prepare his/herself for what would be the past to him/her. The time traveller could learn about our era and equip him/herself with clothes, money and other things from our era and would be able to learn the idioms of the language of the current time, as well as the ethics and morals of the era.

There are web sites on the Internet which claim to have proof of time travel (I’m not going to link to one – a Google search will bring up many of them). In most cases the evidence is far from compelling, relying on blurry photographs and dubious eye witness accounts.

I’ve recently been scanning my old photographic slides and in one of them, from the early 1980s or late 1970s, the person in the picture appears to be holding an iPad! What in fact she is holding is a place mat, with a cream coloured border and relatively dark picture on it. This demonstrates how easily “evidence” of time travel can be found if you look hard, and if you strongly believe that time travel is possible.

Every person, every object, even every elementary particle has position which can be measured (leaving aside the issue of Heisenberg’s Uncertainty Principle and Quantum Physics for now) at any moment in time. The four dimensions, three of space and one of time uniquely identify an event in the life of the person, object or particle.

These four coordinates represent a single point in a four dimensional space. Since we find four dimensions hard to visualise, this space/time is usually represent by a depiction of a three dimensional space of two space and one time coordinate axes. The path of a person, object or particle through life consists of a single unbroken line in the four dimensional space.

Note that in time dimension, if time travel is not possible, for every value of the time coordinate there will only be one point of the person’s life line. In other words, while the person could visit and revisit the same three dimension spot in space many time, they will only pass through a particular time once and once only. A person’s now is unique.

Time travel means that a person could pass through the same moment in time multiple times, and the possibility arises of loops in time. It seems obvious that the same event could not appear on the time traveller’s life line. In other words the loops in a life line would not cross.

To get from one event in space/time to an earlier event in space/time, the person could either travel through the intervening times or just jump from the first event to the second. In other words time travel if it is possible would be represented by a line going backwards in time or it could be discontinuous, with a break the in the person’s time line.

From the point of view of an observer, a discontinuous time line for the time traveller would be seen as a sudden appearances from nowhere and a later sudden disappearance. If the time line is contiguous, the observer would again see a sudden appearance of the time traveller, and then two instances of the time traveller both apparently travelling into the future at one second per second.

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One will be the time traveller doing just that, and the other will be the observer’s view of the time traveller as he travels backwards in time. Eventually the observer will see one of the instances (people!) merge with another instance of the time traveller and disappear. Since we don’t normally observe such sudden appearances and disappearances it’s very tempting to say that time travel does not happen.

To see what I mean, take a piece of paper and draw a line from top to bottom with a look in it. Now horizontal lines across the page represent time as seen by the observer. If you move a ruler down the page, at first there is a single line, the time line of time traveller. But at the point that the time travellers has travelled back to, suddenly there are (apparently) three lines travelling down the page. At the point that the time traveller travels from, two of the lines merge and disappear.

If time travel is discontinuous the observer would first see one instance of the traveller, and then another instance would pop into existence. The two would coexist for a time, and then one instance (the original one) would disappear, with the second continuing to exist.

As I said, it’s tempting to say that this proves that time travel is not possible. Certainly, a macro level we don’t see people appearing and disappearing so it is definitely very unlikely, though reasons for this not to be noticed can be constructed.

At an atomic level though, we do see spontaneous generation of particles, into a particle and its anti-particle. If the anti-particle the meet another particle and they annihilate one another, this could be construed to be a single particle with the anti-particle being the particle travelling back in time.

This is bad news for time travellers. To travel back in time by this method, the time traveller would have to be zapped into a burst of energy and an anti-traveller who would then travel back in time to the earlier time when a burst of anti-energy would be required to zap the anti-traveller into another instance of the time traveller. These occurrences would be likely to destroy the integrity of the time traveller’s body. That is it would destroy it.

## The Negative Universe

If cosmologists are to be believed the Universe came from nothing and is likely to return to nothing. This is odd as there seems to be an awful lot of it! There are between ten to the power 78 and ten to the power 82 atoms in the observable universe, according to some estimates. There’s also a huge amount of energy out there in the universe, and as Einstein said, this is equivalent to matter, according to his famous equation.

It is likely that the enormous amount of matter and energy that we see out there is balanced by an equivalent amount of “negative” matter and energy somehow. “Negative” is in scare quotes because it may not describe what is actually going on. Anyway, the negative matter and energy may be incorporated into this universe somehow, which means that on average half the universe is this sort of energy. We can’t see it anywhere so far as I know, so it is a bit of a puzzle.

We can see evidence everywhere for “normal” matter and energy, and we should be able to see evidence of “negative” matter if it is anywhere near us. As I understand it, “negative” matter would behave differently to “normal” in various ways and should be detectable. I’m not sure in what ways it would be different – I can guess that there could be a gravitational attraction between particles of “negative” matter, just as there is between particles of “normal” matter, but there could be a gravitational repulsion between “negative” matter and “normal” matter for example.

But my ignorance is almost total. I do believe it is true that “negative” matter should be detectable.) Since we can’t see or detect “negative” matter within our locality (ie “the observable universe“) it may be grouped elsewhere in the universe. If so, it may not have any observable effect in our neck of the woods, but inevitable it will have an effect at some time in the astronomical future.

The reason that I say this is that the universe doesn’t seem to be expanding faster than the speed of light so any effect such as (possibly) gravity which does appear to have a “speed of light” effect will eventually affect our corner of the universe. But the situation is complex, and as the Wikipedia article says,

Due to the non-intuitive nature of the subject and what has been described by some as “careless” choices of wording, certain descriptions of the metric expansion of space and the misconceptions to which such descriptions can lead are an ongoing subject of discussion in the realm of pedagogy and communication of scientific concepts.

In other words, there are many misconceptions and misinterpretations around this topic. However any effect of the possible existence of “negative” matter on our little neck of the universe is likely to be felt a long time in the future, even on a cosmological time scale, I feel. “Negative” matter could have created a negative universe, I guess, which mirrors this universe.

In a negative universe at least one dimension would be reversed but all other dimension would have the same polarity as our universe. If an odd number of dimensions were reversed, would all but one cancel out? I’m not sure but a cursory mathematical examination would indicate that this would not be so, but I lack the time to explore the concept in depth.

In our universe things tend to a state of disorder. If one partition of a closed system contains all the matter (in the simplest case, as a gas) and the partition is removed then eventually the matter is eventually dispersed through the whole system. In a negative universe, possibly the opposite would apply – gas dispersed through a system could tend to bunch up in one part of the system. Maxwell’s demon could watch benignly without lifting a finger.

Our view of this is that it is extremely unlikely – would a glass spontaneously rise from the floor, gathering the scattered wine and land on the table complete with wine? Perhaps this is a parochial view, only true in our universe. In some alternate universe, this may be the normality – entropy may tend to decrease, order may tend to increase. Such an entropy twin may simple be the time reversed twin of the original universe. Or the original universe perceived from a time reversed perspective.

If the universe sprung out of nothing, then the sum of the universe is zero. Any object has its anti-object. Any event has its anti-event. Maybe the universe has a partner, an anti-universe if you like, or even a mirror universe. Time in our universe runs from the zero moment into the positive future. In a mirror universe would presumably (and debatably) run in the opposite direction from the zero moment and all spacial dimensions would be reversed.

This would correspond to a point reflection in time and space, which may or may not be the same as a rotation in time and space. I’m not sure. Some of complexities can be seen in this Wikipedia article on “parity”. In particular some interactions of elementary particles may display chirality, which means that they come in left and right handed versions, like gloves or shoes. All of the above means that if a person were to be point reflected into an anti-universe and all the elementary particles of his body were switched with their anti-particles, there may be no way for the person to tell that the switch had occurred.

Sure, time would be reversed, but so would literally everything else, so a left-handed glove would appear, in the point reflected world, to still be a left-handed glove even though, if we could see the glove it would appear to us, from our point of view to be right-handed. Of course I’ve assumed for much of the above that the reflection that transforms a universe to its anti-universe is a point reflection.

In mathematical terms that means that all variables are reversed. That is x is replaced by -x, y by -y, z by -z and so on. It may be that the reflection may be in a line and the x dimension stays the same while the others are negated. Or it may be a reflection in a plane (a mirror reflection) where 2 dimensions are unchanged. Or it may be a reflection in a higher number of dimensions.

As you can see, the subject is complex and I’ve not got my head around it (obviously!), but I believe that if we were switched into the anti-universe (including all out particles) it would not look any different from this universe. In fact we would probably find ourselves discussing our anti-universe, which would be our original universe. In fact it would not matter which universe we called “the original” because they both would have come into existence at the same time and there would be no meaning to the term “original”.

## Synergy and Emergence

I’m fascinated by the phenomenon of synergy. Wikipedia defines it as follows:

Synergy is the interaction of multiple elements in a system to produce an effect different from or greater than the sum of their individual effects.

One man might be unable to move a heavy load, but two men working together might be able to move it easily. Ants individually can only move very small objects, but working together can build very large structures, their nests. Synergy is related to emergent phenomenon, where a complex system shows behaviours which are not apparent in the system’s constituent parts. For example a water molecule cannot said to have the property of “wetness”, but a large collection of water molecules does have that property. Wikipedia defines it as follows:

Emergence is the way complex systems and patterns arise out of a multiplicity of relatively simple interactions.

Synergy and emergent systems are found in all levels of physical and biological systems. In fact the whole of biology could be considered to be an emergent system from physics – animals, plants and other living things are after all, only collections of molecules, and molecules are not, of themselves, alive.

At the highest level of all, consciousness is an emergent system of the synergy of astronomical numbers of brain cells. At the lowest level, all of physics is an emergent system of the state of the universe at the beginning, the Big Bang.

After I wrote that I looked up “emergence” on Wikipedia and found this:

Biology can be viewed as an emergent property of the laws of chemistry which, in turn, can be viewed as an emergent property of particle physics. Similarly, psychology could be understood as an emergent property of neurobiological dynamics, and free-market theories understand economy as an emergent feature of psychology.

The writer of the Wikipedia article is obviously on the same page as me!

Each water molecule has a myriad of properties, none of which is “wetness”. However “wetness” can be explained by considering the behaviour of the various types of bonds that would be formed between water molecules and a consideration of how the molecules would move around each other, and react to other molecules such as those of the surface that the water is placed on. On some surfaces (such as the surface of a leaf) the molecules will organise themselves into “beads”, on others the water will “wet” the surface.

Obviously molecules don’t have volition, and the way I expressed the idea above is much too anthropomorphic, and indeed the behaviour can be described by referring to the physical behaviour of the water molecules, and there is nothing particularly mysterious about this, at least at the level at which I am pitching my suggested explanation.

There are other emergent phenomena that are more difficult to explain. Life, for example. Living organisms are made up of various more or less esoteric chemical compounds, including some really, really large molecules. These large molecules (DNA) are made up of a small number of much smaller molecules (bases) which are strung together in the famous double helix. This double helix is folded in complex ways into truly enormous (at a chemical level) structures called chromosomes. These structures encode all the information necessary to create the organism.

This in itself is a paradox – a small part of the organisation contains all the information necessary to construct the whole organism. It resembles a bootstrap situation. It seems to me that much of the genetic information  has to be instructions for constructing the information and not a detailed description of the organism.

Cells are complex and are individually alive, in some sense, since they are created, produce offspring and eventually die, but with some exceptions (unicellular organisms) a single cell can’t live on its own.

But to get back to the subject, I’ve described (probably pretty badly) a lot of chemistry, but I haven’t been able to describe where life comes from. It’s difficult, but possible, to describe how cells function in a mechanical, chemical sense, but it is not easy to say what it is that makes them alive. You can tell from the over use of bold that I’m having difficulty expressing my meanings here!

Living cells make copies of themselves, but so do some mechanical or chemical processes. Crystals and snowflakes spring to mind. Living cells consume chemicals from their surroundings and so do some complex non-living processes (I’m thinking of weather systems that circulate water and air, but that’s maybe not a good example). Living cells are self organising, altering surroundings to suit themselves, it’s true, but they are simply little complex chemical factories. Where’s the life in that?

In spite of the argument above, it is undeniable that life exists and practically, it is relatively easy to distinguish living things from non-living things. There are some “edge cases” though. Is a virus a living organism or merely a result of a chemical process. At the other end of the scale, is a rain forest a living organism? It certainly contains living organisms, but can the rain forest as an entity be described accurately as a living organism? My answer would be “probably yes” in both cases.

The other example of emergence that I want to consider is “consciousness” and its cousin “mind”. We are conscious and we have minds, but are we the only animals that are conscious and have minds? I find the idea unlikely but possible. Animals have evolved over many millions of years and every feature of our bodies has been evolved gradually and incrementally. Our brains have evolved from one or two neurons in one of our ancestor’s bodies and have been incrementally expanded over a long long time.

But our ancestor was not a human being and many animals with varying sized brains. Our pets and the bird outside the window have evolved from that animal. Consciousness and mind are related to the brain, so it is highly likely that as the brain evolved, so did mind and consciousness, which implies that our pets and the bird in the tree and all other animals with brains has a greater or lesser consciousness and mind.

It is possible, but unlikely that there is some threshold where an increasingly complex brain becomes conscious. My dog acts as if it were conscious and has a mind, but that could be merely a mechanical function of the brain. Personally I doubt it. I think that lower animals like dogs are conscious, have a mind and are self-aware, but at a lower level than humans.

There is no test for consciousness so far as I know. Oh, if an unconscious person’s eyelids flicker, we might say that he is “coming round”, but it could be that these mechanical processes could have no consciousness behind them. A similar argument is the “android” argument – if a man is replaced by an android, which has no consciousness or mind, and the android completely emulates the behaviour of a conscious and minded person, how would we tell, and by emulating the behaviour, would the android in fact possess a mind and consciousness?

That’s another way of putting the question “what is this emergent phenomenon called consciousness, and how does it arise from the way that the brain works”. I’ve read some discussion of this issue by various philosophers, and I still have no opinion on the matter.

This article has expanded to well over my self-imposed target of 1000 words. It is however a subject that I find interesting, and I hope that any readers do so too.

## 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!