Monday 7 October 2024

The Maher Paradox (Conjecture)

(with tongue placed loosely in cheek)

I’ve decided to invent my own paradox, The Maher Paradox. The Maher Paradox states:

All so-called paradoxes are, on closer inspection, not in fact paradoxes.

Which I know isn’t really a paradox, but then many so called paradoxes aren’t paradoxes to begin with and are even less so on closer inspection. Maybe a more accurate title might be, The Maher Paradox Conjecture.

First, the obvious question to ask: what is a paradox?

At its most basic level, a paradox is a statement which seems to contradict itself, as in the sentence, I always lie. If the statement is correct then I can’t be lying, rendering the proposition untrue as I have told the truth about always lying and therefore can’t always lie. But this means the statement is in its own way a truthful statement about my lying in that I am true to my word in saying that I am always lying. By making a statement that is in fact true, I have lied about always lying and therefore the statement is in an important way correct. Which is again a paradox. Oh what a tangled web we weave when first we learn to paradox.

At a deeper level, paradoxes are mathematical, physical or philosophical statements that say something about the absurdity of the world or the absurdity of competing theories for the way the world works.

Schrödinger’s Cat, for instance, is a paradox. Erwin Schrödinger created his infamous cat in a box that is both alive and dead until you observe it as a pastiche of the idea of quantum superposition, where a quantum system can be in a super-state of possible configurations until it is ‘observed’ and the system then collapses into one state or another. It was meant to be a criticism of quantum theory, but was repurposed and became an illustration for how quantum theory works. I’m sure it is to Schrödinger’s eternal chagrin that his eponymous cat has become synonymous with quantum mechanics and science communication the world over. If only he was spinning in his grave, that would be a form of perpetual motion; which is also a paradox.

The thing about these second kinds of paradox is they are often idealised mathematical models for a world that actually have no basis in reality. Though we should also allow that they are often used as reductio ad absurdum, pushing a theory to its logical limits.

The prime example of this is Russell’s Paradox. Russell’s Paradox is an important innovation in the development of set theory, but the quasi-real world example that Bertrand Russell used to illustrate his theory employs Ancient Greek Barbers:

Russell’s Paradox: A barber shaves only those men who do not shave themselves.

The paradox then arrives from asking, who shaves the barber? If he doesn’t shave himself then he should be the one to shave himself, but then he would be shaving himself, so he can’t shave himself, but then he isn’t shaving himself so he can shave himself, so then… and this is where we find ourselves stuck in a feedback loop of infinite regress.

Again, this has a much more technical implication in considering the set of all sets that are not members of sets themselves, which is beyond the scope of this discussion (and, incidentally, the expertise of the writer). The real world manifestation of Russell’s Paradox is easy to unpick. Few communities only have one barber and who exists in a vacuum. Two barbers who shave each other is enough to render the paradox unparadoxical.

Indeed, few barber’s or other hair cutting establishments have only one barber, with many hairdressers working freelance at one particular location. I’m sure this would have been true even in the ancient world. As to the set of all sets that are not members of themselves, this can be lumped in with considerations of infinity, to which we return later.

The same considerations can be made about Zeno’s Paradox. Zeno actually formulated a number of paradoxes, but here we are specifically interested in his paradox of motion, which is what most people understand by Zeno’s Paradox. Achilles and the Tortoise is often how Zeno’s Paradox is framed, but I want to use another common example for simplification of explanation.

There is a frog on a lily pad at the centre of a pond. In order to reach the bank of the shore, the frog must hop halfway across the pond. Then it must jump half the remaining distance, which, is to say, a quarter. Then another half of the distance left, which is an eighth, and then a sixteenth and a thirty-secondth. In this way, the frog will never reach the bank, as it will be jumping forever through smaller and smaller intervals.

Of course, if frogs really moved like this, the entire frog population would have gone extinct a long time ago. This is not how real world objects behave. The frog will reach the bank in a handful of jumps. Maybe even a single jump. Frogs are also amphibious and can swim for shore. Achilles will in fact catch up with the tortoise in no time, no matter what length of a headstart he gives it (within reason).

These are all clever examples to get us thinking about mathematical objects which tend towards infinity or zero, but they have little real world analogue. In learning about calculus, we learn about the idea of a mathematical gap tending towards zero, but it is important that the limit never actually reach zero. If it did, calculus would in fact become useless, because any number multiplied by zero is zero.

It is the same way that smaller and smaller decimal numbers divided by a whole number will tend closer and closer towards infinity (1/0.5 = 2, 1/0.25 = 4, 1/0.001 = 1000 etc.). This is because if you divide any number by a fraction, 1/½, 1/¼ etc., you in fact take the denominator of the fraction, move it to the top of the equation and multiply it by the number, which in our examples is always 1. 1/½ becomes (2x1)/1, which is to say, 2. As the denominator of the fraction doing the division becomes larger and larger, the result of the calculation becomes equally large.

The implication here is that as the decimal number hits zero, the result of this whole number division will be infinity, which is why if you try to divide any number by zero on a calculating device, it will return an error message. Yet as soon as the decimal number hits zero, the impossibly large number will reset. The result of 1/0 isn’t infinity. It is in fact zero

We know this from calculating trigometric functions. The value of sine starts as 0 when an angle is 0. It then rises to 1 at 90O, returns to zero at 180O and drops to -1 at 270O, before returning to 0 at 360O. The cosine function cycles in similar fashion, but is 90O out of phase, such that it starts at 1, drops to 0 at 90O, drops further to -1 at 180O, before climbing back to 1 at 360O, through 0 at 270o.

The Tan function is mathematically identical to dividing the sine function by the cosine function. We start with: 0/1 at 0O, which is to say 0. The value of Tan then rises asymptotically (i.e. getting closer and closer to a number at smaller and smaller increments without ever actually reaching it) towards infinity. But at 90O, where sin = 1 is divided by cos = 0 (1/0),  Tan becomes 0. A similar rise is seen between 90O and 270o, where the value of Tan rises from -∞ to ∞. It should be noted, however, that mathematicians set the value of Tan at 90O and 270o to zero for ease of calculation. However, they were right to do this, because the value of any number multiplied or divided by zero is in fact zero.

Leaving mathematics for awhile, another paradox that isn’t really a paradox to begin with is The Fermi Paradox. The Fermi Paradox asks why, if the universe is teeming with intelligent life, we haven’t found any of it yet. Many explanations are put forward to try and resolve this paradox, but few of them are very satisfactory because they seem to be bourne out of human arrogance. i.e. the question asked honestly is, if the universe is teeming with life, why wouldn’t it want to immediately contact us?

Yet there are any number of reasonable explanations that human beings perhaps don’t want to think about because they remind us of how utterly unimportant we are at a universal, or even a galactic scale. We have been broadcasting radio signals for barely a century. Travelling at the speed of light, those first broadcasts have reached out to a sphere of one hundred light years distance from the Earth and will probably be so weak that they have became lost in the background noise of cosmic radiation. Even then, a hundred light years is a tiny fraction of the way across even our own galaxy. The vast majority of visible stars in the night sky, even when seen from a location relatively free from light pollution, are within about four thousand light years from Earth. Which, again, is a tiny fraction of the volume of the Milky Way.

Moreover, the Milky Way is but one galaxy of two trillion that exist in the observable universe. Some astronomers think even this might be an underestimate, when you consider all of the galaxies that are too dim to be seen or are blocked out by other objects. If we think about the galactic disk of dust that makes up the central bulk of the Milky Way, it is blocking out a significant portion of the sky (including, importantly, much of the other half of the Milky Way, which could be teeming with life for all we know). There could then be twice as many galaxies than we know about in the observable universe, swelling the number to four trillion. And even the observable universe is thought to account for only around fifteen percent of the entire universe, the rest of which has expanded beyond the point at which its light can ever reach us. Meaning there might conservatively be as many as twenty trillion galaxies in the entire universe, each containing hundreds of billions of stars. At this point, the human brain’s ability to understand truly astronomical numbers has long since broken down.

At these scales we are dealing with probability and statistics. There will necessarily be many galaxies in the universe that are teeming with life and, conversely, those that are entirely sterile or home to a handful of technologically advanced civilizations during their entire lifespan. There is no reason why we couldn’t be living in one of these second kinds of galaxies and will never be able to communicate with another society within the Milky Way because they simply do not exist in the here and now. If we were able to peer inside that galaxy five over from our own, we might find a place similar to the world imagined in Star Trek, with a number of space faring civilizations coming together to form a federation of planets. Ten galaxies over in the opposite direction, there is a galaxy like Star Wars (not so very, very far away after all). In another galaxy within out local group there is a planet on which exist things we would recognise as dragons. Here we sit (maybe) on a desert island surrounded by rain forests on all sides. If only we had the skills, tools and material to build a boat. A device able to hold us in stasis for thousands of years would also be a help.

The point is the Fermi Paradox isn’t a paradox, but a statement about the enduring arrogance of humanity and its need to always place itself at the centre of things. We used to believe Earth was the centre of the universe. Then we replaced Earth with the sun. When galaxies were discovered, we placed the Milky Way at the centre, until we then found out about the Big Bang and realised that the universe in fact has no centre. The Fermi Paradox is in its way a further attempt to place Earth back at the centre by assuming that any advanced civilization would immediately want to make contact with us before anything or anyone else. The implication is then that because they haven’t made contact, they must not exist,, Thus then makes humanity unique in the universe and finally replaces Earth at the centre of things.

The Fermi Paradox isn’t a paradox and there are any number of answers to the question that require no convoluted solutions or explanations rooted in solipsistic navel gazing. The Milky Way might be relatively deserted at the present epoch. Or maybe the half we can’t see on the other side of the galactic disc is a hotbed of intelligent, space faring life that will always remain invisible to us. Or communication between star systems remains impractical due to the distances involved and the power required to direct a broadcast at one particular star system. Or maybe there is a way to communicate which requires no electromagnetic communication (radio waves, etc.), which prevents anyone else listening in (Ursula Le Guin and Liu Cixin, amongst  other sci-fi writers, include such devices in their novels). Or maybe, just maybe, humanity just isn’t that interesting. Maybe we have been visited many times by other civilisations, but they always move on after scanning us because worlds like ours are ten a penny. Whatever the solution, it certainly isn’t a paradox.

Another thorny issue in the general area of paradoxes concerns infinity. Human beings have been struggling with the concept of infinity for thousands of years and it seems to have driven us mad in the process. One thinks of the Total Perspective Vortex in the Hitchhiker’s Guide to Galaxy; a punishment device in which its victims are shown the unimaginable scale of the universe compared to themselves, an invisible dot on an invisible dot, next to a sign, saying, You are here. The experience fries the mind. Thinking about infinity has sent more than one mathematician into the mouth of madness.

The sciences contain two schools of thought about infinity. Physicists encounter infinity and assume something must be wrong with their calculations. At the edge of the big bang or at the centre of a black hole, the equations break down and the theorists conclude something must be missing from their calculations, or there is something we don’t know about these extremes, where general relativity and quantum mechanics interact. Knowing more, say through some kind of Grand Unified Theory, would make the infinities disappear.

Pure mathematicians, on the other hand, invent different types of infinity, which is a paradox. One of the classic examples is the idea of an infinite integer number line. In other words, a two dimensional line of all the whole numbers stretching from plus infinity on one side to minus infinity on the other.

But then we can say that between each whole number is a half number. Between 0 and 1 is 0.5. And between 1 and 2 is 1.5. On an infinite integer number line, there must also be an infinite number of half numbers. Moreover, between 0 and 0.5 is 0.25. And between 0 and 0.25 is 0.125. And between 0 and 0.125... well, you get the idea. So there are, so the theory goes, an infinite number of subdivisions on an already infinite number line. An infinite number of infinities. An invisible dot on an invisible dot.

Except an infinite integer number line is a paradox and The Maher Paradox Conjecture states that all paradoxes are not paradoxes. The problem with declaring some finite thing infinite is that we are comparing apples with oranges, only it is much more complicated (and you don’t even get a fruit salad at the end of it). To explain why this is so, it is useful to think about the work of Descartes.

Rene Descartes (1596-1650) was a genius. In many ways, he was the last person to be both a great mathematician and a great philosopher. The two disciplines separated not long after his death and have continued to be estranged from one another for much of the last four hundred years (though Bertrand Russell arguably filled a similar niche). Descartes gave us both Cartesian geometry (at its simplest, graphs containing a Y and an X axis), and also Cogito Ergo Sum. I think therefore I am.

Most people have some level of awareness of Descartes’s most famous conjecture. I think, therefore I am, remains a masterful piece of reasoning from first principles and real world evidence. Unfortunately, Descartes was subject to, if not directly influenced by, the religious dogma of his day, and when he turned his attention to the existence of God, the same reason failed him.

God, Descartes said, is infinite. There nothing you can do to add anything to him. God is the alpha and omega. He is all. He is everything. Then Descartes states, apropos of nothing,  that God is also infinitely good. But more than that. Descartes also says that God cannot be evil. He is beneficent and merciful. He is without fault or flaw.

Skipping over such obvious questions as, how can an infinite being be only male (a woke question to ask, I’m sure), or passing a cursory eye over the Bible to see how merciful and forgiving the Old Testament God truly is, we arrive at the idea of infinite goodness. Infinite goodness is another way of saying, all types of goodness. So what about evil? Good and evil are human concepts and have as little objective meaning as hot and cold, or light and dark. These are dualities, which are only important to sentient beings, with an arbitrary line of demarcation between them (when does a cold thing become hot and vice versa? – depends who you ask). Without one, there can be no understanding of the other.

As such, evil is a subset of good. Good is the absence of evil. Evil is the absence of good. The two are inseparable. An infinite amount of good would therefore also include an infinite amount of evil. If God were infinitely good, they would also need to be infinitely evil. Because, to be clear, there is a world of difference between having a lot of one quantity or substance and having an infinite amount of that one thing. At the point of infinity, any one finite thing spills out into everything else.

We can see this with the infinite integer number line. We can try to imagine a number line that stretches before and behind us for as far as we can see; for as far as our best telescopes can image. But an infinite integer line would merge to include all things that are not integers. An infinite amount of something includes all the things that are not that thing, because not being something is a subset of being that thing when viewed at an infinite scale.

An infinite integer number line also includes all irrational numbers (√2). All transcendental numbers (π and ex). And yes, all decimal numbers between the gaps. Also, every possible shade of red, every possible species of rose, every variation of Batman, Dr Who, Miss Marple, Romeo and Juliet, including anthropomorphised animals and alien species and an infinite number of things besides. Mixing a finite property like whole numbers or Shakespearean characters with the totality of infinity is a fruitless endeavour. Mathematics claims there are many different types of infinity, but there is in fact only one. Infinity is binary. There is infinity or there is not. And given that all possible events are not currently occurring simultaneously at all places in time and space probably means that infinity has never and will never exist.

One way to think about infinity, though it is probably as useless as every other attempt to visualise the invisibly infinite, is as a circle, inside of which sit all possibilities. All the mass of the multiverse, all its energy, all those shades of red and varieties of rose and all numbers, rational, irrational and transcendental, all people and all animals and alien species having a turn at being Batman, Bond, Dr Who, Hamlet, Desdemona, Anne Bennett, Daisy Buchanan, Milady, as well as everyone singing their versions of My Way, Summertime, Yesterday and Hallelujah to add to every other version that already exists, as well as an infinity of other possibilities besides.

This is an interesting thought experiment because of a curious factor of mathematical infinity. If you add any number to infinity, you still get infinity. ∞ + 1 = ∞: ∞ + ∞ = ∞ Yet if you think of infinity as a circle that contains all possibilities and things, you could argue that the reason why ∞ + 1 = ∞ is because ∞ already contains the concept of oneness. Nothing new is being added to infinity from outside circle (because there is nothing left out there) and so the total weight remains infinite. You could equally say that ∞ + Crayola Red = ∞. Or ∞ + Ian Watkin-Jenkins as James Bond = ∞. ∞ + Frensicllsenfordbablecox from Fornax 12 as Scarlet Witch = ∞. It would make as much sense.

Another paradox connected to this misunderstanding of infinity is the Hilbert Hotel. The Hilbert Hotel tries to say something about these paradoxical rules of addition when dealing with infinity. There is a hotel with an infinite number of rooms, each of which are occupied with an infinite amount of guests. But hold on a minute. We should be good enough at spotting non-paradoxical paradoxes at this point to see the problem already. If there are an infinite number of rooms, how can there be any energy left in the universe/multiverse to also have an infinite number of guests? Where has this new mater come from? If we have somehow found some extra matter and energy to create an infinite number of guests, can there really have been an infinite number of hotel rooms to begin with?

It gets worse, because Hilbert’s thought experiment continues by then having a new guest arrive at the hotel. Where has this person come from? Nothing remains outside the circle, so from what imagined realm has this guest arrived? “It don’t work”.

David Hilbert (1862-1943), who created the Hilbert Paradox, also imagined the Hilbert Curve, which is a geometric shape that can be replicated at smaller and smaller scales with more and more iterations until it, theoretically, can be replicated an infinite number of times inside a finite space. The problem with imagining any infinite thing inside finite space is that the limits of the real world will always prevent infinity from being reached.

If we were to trace out a Hilbert Curve using a pen or on a printer, at a small enough scale the line of the curve would be smaller than the width of a molecule of ink. If we could somehow continue the tracing using smaller and smaller wavelengths of light, through to gamma rays, we would at the very most hit the width of a single photon and be unable to progress any further. Even smaller orders of magnitude and we reach the Plank length, the smallest theorised physical length that can exist due to the limits imposed by quantum theory. A Hilbert Curve might theoretically tend towards infinity, but the limits of the physical world prevents it from actually happening and even by the time Hilbert’s curve banged up against Plank’s length, it would still be as far from infinity as when it started.

Infinity is probably impossible anyway, but it is almost certainly impossible in two dimensions or higher. Probably even then. Again, this bangs up against the limits of my intelligence and when I try to explain the following, I can’t quite illuminate what is dimly lit in the deep recesses of my mind. But it goes something like this:

It has to do with calculating the area of a larger and large two dimensional space. One simple way we learn at school is by multiplying the length of a space by its width. This is simplified when the length and width are the same, because then the area is equal to the length of one side, squared. A = x2. The area gets bigger and bigger the larger x is. 12 = 1; 22 = 4; 32 = 9; 42 = 16 etc. The numbers not only increase, but the space between them gets bigger and bigger: 25, 36, 49, 64, 81, 100. The gap between them in fact increases by an odd number each time, increasing by two from the previous gap= 1 – 4 = 3; 4 – 9 = 5; 9 – 16 = 7; 16 – 25 – 9.

Then, and this is where the fog creeps in, we can ask about the numbers that aren’t part of this results in this sequence. What about 2, 3, 5, 6, 7, 8, 10, 11, 12, 13 etc.? The point here is that in considering a two dimensional space that continues to increase in size, there are numbers that are excluded. If we were to expand this to three dimensions, where A = x3 ( and I’ll save you from having to consider cubes of a number sequence), even more numbers are excluded. So how can infinity exist in three dimensional space, when even a simple geometric sequence excludes numbers between the spaces? Infinity means everything and yet in more than one dimension, things are quickly excluded. Space is, for the most part, empty. The frog doesn’t make smaller and smaller jumps to reach the shore.

Here, I am sure fans of Zeno’s Paradox would argue that infinite regress is a factor, but again, the world does not behave like this. In theory, a handful of mating rabbits could produce enough offspring to entirely cover the surface of the Earth in a handful of years. And yet they don’t. Not once. Ever. There is always something that will prevent infinity from being reached because infinity is not a thing. It’s nice in theory, but so is democracy and cheap, affordable fusion power and they will probably never be truly achieved either.

I should state here that I love math(s). And mathematician(s). Mathematics created and has crafted the modern world since the time of the Industrial Revolution. Yet it has its limits (which is a kind of maths joke). Infinity is certainly at the edge of those limits and many of the paradoxes we have considered come about from confusion over infinity and considering it a real thing. Or considering it an infinite number of things. It is one or it is zero and it is almost certainly zero. Though there is also an argument to be had over whether there is ever really nothing. Zero is itself a kind of paradox in that by describing nothing it is in fact something. I will return to this idea at the end.

We should also, I suppose, talk about one of the most famous paradoxes, The Grandfather Paradox. In the Grandfather Paradox, you invent a time machine, go back in time and kill your own grandfather, who is now never born, so your father/mother doesn’t exist and now neither do you. So you can’t go back and kill your grandfather, because you don’t exist, so now your grandfather does exist and so do you, so you can go back and kill him. Then he doesn’t exist and neither do you… And on and on it goes, ad infinitum. Infinite regress.

The Grandfather Paradox is part of a group of Temporal Paradoxes, where future objects prevent past events, which prevent the future event affecting the past in the first place. Physicist, Joseph Polchinski, was one of the first to think about this kind of paradox. He used the example of a billiard ball that heads into a time machine, emerges a few seconds in the past and strikes its past self, deflecting it from the direction of time machine and preventing itself from traveling back in time in the first place. And, well, we know how this dance goes.

When thinking about temporal paradoxes, I often marvel at the lack of imagination or artistic licence demonstrated by the framers of these thought experiments. I would like to blame the straight laced minds of scientists, but the man who developed the Grandfather Paradox, Rene Barjavel, was in fact a science fiction writer. Of course, the most obvious resolution to the Grandfather Paradox is that time travel is impossible and that is that. No paradox occurs. Which is the point of the Grandfather Paradox. Time travel creates paradoxes, ergo time travel must be impossible QED. But can’t we do better than that?

I love sci-fi, but one of my beefs with time travel stories is how they are always predicated on the idea of their being one, inviolable timeline that the heroes must restore to equilibrium. Star Trek, Stargate, Dr Who, even El Ministerio del Tiempo (The Ministry of Time, a romp though Spanish history, which includes nearly fifty years of fascist rule under General Franco), all must correct some wrinkle in the fabric of spacetime to return things to exactly how they were before.

Yet if we consider the Many Worlds Interpretation of Quantum Mechanics, for which no evidence so far exists, there is a possibly (slim, I admit), that for every quantum event that occurs, every other possibility also takes place, splitting reality into many parallel worlds. For instance: A sheet of glass is half silvered so that photons fired at its surface have an exactly 50/50 chance of passing through the glass or bouncing off it. The Many Worlds Interpretation of Quantum Mechanics states that each photon does both, bouncing off in one world and passing through in the other. If we scale this up to the macroscopic world, it means that for every decision or event that happens in a person life, every alternative is also played out in some parallel reality. Think Sliding Doors, if you must.

So let’s consider our patricidal time traveler. If every possibility is truly played out then there is already a reality in which the killer’s grandfather was killed and his mother/father was never born. Moreover, we could argue that there is a reality in which a time traveler came back in time and killed the man. The time traveler therefore creates no paradox, but fulfills a role. By killing his grandfather, he transitions into a world in which his grandfather was killed. The universe in which the man went on to have children and grandchildren is not prevented from existing, it mere plays out in parallel, but with the killer now stuck in the alternate realty in which he never existed and yet exists. He is also now, presumably, on the run from the police.

As to the billiard ball, I have a sense that as infinity is impossible and there is nothing to say the same event always has to play out the same way every time, my feeling is that the ball would bounce back and forth for a while, maybe for millions of years, but eventually the feedback loop would erode and the whole system would come to a stop. Like the way a camera pointed at a screen displaying the camera image creates a feedback loop of repeated images of itself, but is seen to be degraded at the rear, loosing colour and fidelity. Maybe a freak collision would send one or other of the billiard balls flying through the air, killing the scientist who started the experiment, preventing events from taking place in the first place.

I admit that time travel seems pretty unlikely and even if it is theoretically possible, it would require so much energy to achieve that no society, no matter how advanced, is ever going to be able to achieve it. However, I would suggest that the reason we don’t see time travelers popping back from the future to have a look at us is because we have yet to invent time travel. If we consider the theorised resolution to the Grandfather Paradox just discussed, it seems to me that anyone who travelled backwards in time would immediately enter a parallel dimension separate from our own with no hope of return. The mere displacement of air caused by a time travel device appearing in the past would be enough to change things, however slight. As soon as one started turning up to witness historical events, the drift would be even greater. And when you started changing things, like saving Diana or killing Hitler, you really would be adrift, like a raft caught in the gulf stream.

Which brings up another important question. Is time travel really possible even by travelling back in time? If your presence in the past affects the past, then it is not the past you know anymore. Kill Hitler and you change the world, and not necessarily for the better. Germany would still be rancid with anti-Semitism after the First World War and the Weimar Republic. Another leader might not make the mistakes Hitler did, while all of the other architects of the Holocaust might still be in power. Either the way, the world would be a totally different place, populated by totally different people. My grandparents, for instance, married at beginning of the war and then my grandfather went away with the Navy and my grandmother didn’t see him again until VE Day. My mother and aunt were born the following year. If they had lived together sooner than this then either my mother would never have been born, or she would have been born years earlier and not met my father.

There is almost a variation on Heisenberg’s Uncertainty Principle going on here. Just as a measurement of a particles position makes its momentum less knowable and vice versa, so witnessing events of the past changes the future. If you take a passive role in the past, the future continues as before, but you play no part in its development. Even betting on sporting events, a la Biff in Back to the Future 2, would probably affect the course of events in some way.

Yet even if you travelled back in time and remained in orbit, observing events from a distance, it is unlikely that events would proceed in exactly the same way for a second time. Time travel is essentially like creating a carbon copy of the universe and expecting it do everything the same way twice. Like Jeff Goldblum’s drop of water in Jurassic Park, the path of the water is unlikely to follow the same path twice. Maybe there are certain events, like World War Two, that we can’t avoid and are always likely to occur no matter what you do. The outcomes might be different, but the cause would be the same.

Perhaps the biggest objection to time travel is actually that it would involve making a copy of the universe and how do you make a copy of anything that big? But no matter who won the Second World War, the universe would continue just as it always has. Some events are unavoidable. A different outcome in 1945 wouldn’t prevent the Boxing Day Tsunami of 2004. Subjective reality would have to have some kind of locality, where sentient beings create their own separate version of the universe  and then we really are getting into pseudo science and science fiction. It is interesting to ask if the universe existed before we built telescopes to observe it, but it is not a question we can ever answer and it is useless to try.

All of which is to say that there are any number of solutions to the Grandfather Paradox that prevent it from being a paradox. If I was going to write a fictional variation on the Grandfather Paradox (The Grandfather Paradox2), I’d make is so the Fates are so annoyed with the killer messing with causality, that every time he kills his grandfather he is born into a new family and then has to travel back in time to kill his new grandfather. Then he is born to a new family and the whole thing goes on and on in a variation of infinite regress, until he eventually shoots himself and the Fates are satisfied.

Paradoxes are paradoxical for a reason. They either show us the limits of our mathematical models and explanations for physical processes, or they demonstrate to us the limits of our understanding. Like physics’ version of infinity, we should recognise in a paradox a manifestation of some misunderstanding of the way the universe works and seek answers to resolve the paradox. Which, to be fair, is why many paradoxes are framed. But even where something like the Grandfather Paradox seems to disbar the prospect of time travel, we should find other solutions to disconnect between what we imagine would happen and what might actually happen. Whether or not time travel is possible, we should prepare for the possibility of paradox and look to proactively resolve it.

Other paradoxes seem to occur because we try to impose the concept of infinity on a finite universe. Yet infinity is not real. It is the imagined limit of our understanding (silly, arrogant humans); the boundary at which reason breaks down and the universe ceases to make sense. Once we loosen our grip on the concept of infinity, its paradoxes soon melt away.

One paradox remains and that is the universe itself. Is it forever or did it have a beginning? Here I am using a more general sense of the universe, more like the idea of a multiverse. We know the universe we inhabit had a beginning, although these days many scientists reject the idea of the universe started from a point of infinite energy (for reasons discussed above). It probably still started from a mass of highly dense energy, but occupied a finite space. So where did it come from?

It is almost an entirely pointless question, because there is no way to prove a theory one way or another. And even if we could show that our universe was spat out from another universe or ripped from the womb of a black hole, or was caused by two other universes interacting on the theorised brane of a multiverse, the question would still remain, then what created that universe/multiverse?

The question of the age of creation is a paradox, because if we accept that existence isn’t infinite, then what was there before everything was set in motion? Like the astronomers of old, we are tricked into invoking a Prime Mover: the force that set the heavens in motion. But then what set the Prime Mover in motion? Infinite Regress stalks us like Death itself.

Whatever the answer, it is one that is almost entirely unintelligible to sentient beings at our level of understanding. Is time meaningless outside of a universe such as ours?  Even without time, wouldn’t there still be cause and effect? Maybe cause and effect evolved like everything else in existence. Still the question remains, how do you get something from nothing? Even by invoking God, you still have to explain their existence. The paradox remains.

Every rule has an exception. Of course, people misunderstand that particular phrase. A rule seems to have an exception. You investigate the exception, find a solution to it and the rule becomes all the more respectable. Like the particle experiment at CERN a few years ago that seemed to break the barrier on the speed of light. Particles appeared to be moving faster than light, but it turned out the detectors were faulty and the speed of light is safe (for now). The exception to the rule turned out not to be an exception at all.

If we ever work out how the universe began, The Maher Paradox Conjecture will be proven once and for all. I'm not sure I'll still be around to gloat.


 

Life, the Universe and Everything: The Philosophy of Douglas Adams

Douglas Adams is principally remembered as a writer of comic fiction. His science fiction series, The Hitchhiker’s Guide to the Galaxy is the thing for which most people still know him today. This is partly because H2G2, as it is abbreviated by fans, appeared in many different formats. It started life as a BBC radio series, then a series of books, a play, a text based computer game, BBC TV series, and finally a film in the years immediately after Adam’s untimely death in 2001.

Yet Douglas Adams had many other strings to his bow. He was enthusiastic about technology and its potential to make the world better, presenting a number of radio and television series on the subject. He was a committed conservationist. His book, Last Chance to See, co-written with zoologist, Mark Carwardine, as they travel the world in search of endangered species, remains a classic.

Adams was also a guitarist and music aficionado. Pink Floyd’s final studio album, The Division Bell, was named at the suggestion of Adams to his friend, guitarist David Gilmour. Not to mention Adams’s early work co-writing sketches with Graham Chapman for the final series of Monty Python’s Flying Circus. If anyone can be considered the seventh Python, it is surely Douglas Adams.

Because of his perception as a comedy writer, the contribution of Adams to a number of disciplines of philosophy is perhaps neglected. Not that Adams ever wrote a philosophical treatise, or couched his work in purely philosophical terms. Yet many a true word is spoken in jest. While H2G2 contains any number of circular arguments presented for comic effect, there are also ideas featured in the books and radio scripts which cast a serious eye upon the human world.

Science fiction has always been about taking contemporary issues and ideas and removing them to a place sufficiently distant in space or in time to be able to explore them with greater objectivity. H2G2 is no different than any other work of science fiction in this regard. In the sections that follow, we will look at five disciplines of philosophy, including economics and politics, to examine what Douglas Adams had to say.

Political Philosophy

The president’s job – and if someone sufficiently vain or stupid is picked he won’t realize this – is not to wield power, but draw attention away from it.

As quoted above, the Hitchhiker’s Guide to the Galaxy is referring to a Galactic President. More specifically it refers to Zaphod Beeblebrox, former galactic president, and one of the principal characters in all variations of H2G2.

However, it is hardly a great stretch of the imagination to see this as a satire on the President of the United States. The initial radio series and the first two of the five books were released during the presidency of Jimmy Carter. At the end of 1980, the USA elected Ronald Regan to become its 40th President. The age of the stupid had begun.

There is a tradition in Russia that the leader of the country must alternative between hairy and balding men. If the previous president or king was hirsute and bearded, the next leader must be balding and beardless. They take this very seriously. Something similar might be argued for America in line with Adams’s comments on presidents. Republicans tend to elect stupid leaders; the Democrats vain leaders.

The analogy doesn’t always hold, but considering Ronald Regan and George W Bush on one side, Bill Clinton and Barrack Obama on the other side, it is good enough. The forty fifth President brought stupidity, ignorance, and basic bigotry to it apotheosis (or is it its nadir? – neither words he would understand). Obama was probably the most accomplished President since Lyndon Johnson, but had more in common with John F Kennedy, in that he was adept at giving speeches which were big on gravitas, but light on actual substance. The writer and presenter Sandi Toksvig described Obama as sounding like the pre-printed messages in Hallmark greeting cards. It’s hard to argue with this assessment.

Of course Great Britain is hardly in a position judge. Not when David Cameron and Boris Johnson have both been Prime Minster in recent years. Men who remind us that the best education money can buy cannot instil intelligence in people who didn’t have any to begin with (or, with which to begin, as their private education would argue, incorrectly).

The UK has also seen Tony Blair as Prime Minister; a man who could give Narcissus lessons in vanity. Vain leaders are arguably more dangerous than stupid ones. And when a vain leader joins forces with a stupid one, disaster is bound to follow. I’m sure the people of Iraq would have something to say on the subject.

Democracy is a good idea in principle, but was hijacked a long time ago. Increasingly politicians the world over fail to represent their constituents and instead represent only themselves and the narrow interests they serve in order to reap the financial benefits for which their treachery is rewarded. American politics is predicated on raising funds to run a campaign, which is open to corruption from the very start. Britain is different, but still guilty of prioritising rich interests over those of the most in need. Untendered government contracts worth billions of pounds can be given to Tory party donors, but the same people will let the children of the poorest members of society go hungry with apparent relish. Or watch with barely concealed glee as they drown in dinghies crossing the English Channel. All while claiming to be followers of the Christian faith.

Douglas Adams summed this all up in typically succinct fashion:

To summarize: it is a well-known fact that those people who most want to rule people are, ipso facto, those least suited to do it. To summarize the summary: anyone who is capable of getting themselves made President should on no account be allowed to do the job.

To summarize the summary of the summary: people are a problem.

Hair, no hair. Which explains a lot.
Economics

Shoe shops! In every road, on every street corner, in every city shopping precinct, shoe shop after shoe shop!

Adams’s main contribution to economics is The Shoe Event Horizon. Although, I think he might have been depressed at how one of his most beloved tech companies, Apple, has become as ruthless as any conglomerate to which his imagination gave birth.

The Shoe Event Horizon appeared in episode five of the second series of the original radio incarnation. It reappears in the second novel, The Restaurant at the End of the Universe. It works like this. The commercial centres of a planet are flooded with shoes shops. Hundred of them. Thousands. Then fashion is introduced into the mix. The types of shoes that are sold are upgraded each season. Moreover, the shoes sold are of such poor quality that they fall apart almost at once. Hence they need to be constantly replaced due to changing fashions and inferior manufacturing, increasing public dependence on the shoe companies (all owned by the same company), until the financial situation reaches a point of critical mass:

The shoe event horizon. The whole economy overbalances. Shoe shops outnumber every other kind of shop. It becomes economically impossible to build anything other than shoe shops.

The Shoe Event Horizon takes its name from the event horizon of a black hole. This is the point around a black hole at which gravity becomes so strong that nothing, not even light, can escape. The Shoe Event Horizon is reached at the point in a target planet’s economy where it is impossible to build anything other than shoe shops. A comic idea, to be sure, but one which has real world analogues in western capitalist societies, as well as emerging economies in the developing world.

One of the things the Shoe Event Horizon foretold is something that has come to be known as Planned Obsolescence. This is the very idea that products for sale are deliberately designed to break after a specific length of time, forcing consumers to spend money on replacements at regular intervals. Anyone who has ever bought jeans or shoes from a supermarket knows they are often so badly made that they develop holes and broken stitching in a few months. The Dolmansaxlil Galactic Shoe Corporation would be proud.

The worst culprits though are the tech companies. Their products are often designed to fail after a certain time. Either that or newer operating software is not available for older products, preventing applications from updating so that they can no longer be accessed.

All this serves to drive up profits for the tech companies, depleting the world’s resources, and killing off the competition in the process. Not to mention the dubious working conditions for the people who manufacture the products in Chinese sweat shops, as well as the wars they help to perpetuate in countries where raw materials like bauxite and cobalt are mined.

Ironically it is Apple, of whom Douglas Adams was a big fan, being one of the first people in the UK to own an Apple Mackintosh computer, who have become the exemplar (if exemplar is the right word: spoilers – it isn’t) of Planned Obsolescence and, by extension, The Shoe Event Horizon. One day it might become economically impossible to build anything other than Apple stores.

The Shoe Event Horizon is ultimately a satire on capitalism itself. Those who lionise Capitalism speak in reverent tones about things like market forces and Adam Smith’s invisible hand guiding the market. Capitalism is the antidote to the evils of Communism, so we are told. In reality they are two sides of the same coin. In Communism, the state owns the means of production. With Capitalism, the means of production instead owns the state. Both moving inexorably towards one and the same destination, just one moving clockwise and the other anticlockwise. One political party or one corporation, the end is the same.

Socialism is lumped in with Communism as a great evil to be avoided, but the truth is that Capitalism is just as socialist as Communism. It’s just that with Capitalism, socialism is only extended to the very rich. Banking, farming, the arms industry, oil companies, and the tech industry all receive hand outs and bails outs and pay as little tax as possible. National infrastructure is placed under more strain by them than by the average citizen. Yet little is contributed to the general upkeep of roads and environmental protections and the like. When socialism is spoken about as being undesirable, this is equivocation, with the end of the statement left unspoken. Socialism is undesirable for individuals and the poor. There is always money available for wars and bail outs. Not so much for libraries or to pay nurses anything other than lip service. Clapping NHS workers is cheaper than bothering to fund its services properly. Or repeating slogans like Support the Troops and Help for Heroes, when ex service men and women are left to beg on the streets once their usefulness has ended.

Yet as the Shoe Event Horizon reminds us, this kind of naked profiteering is unsustainable. Capitalism treats society like a Jenga tower, pulling out more and more blocks from the bottom and placing them on top until the entire structure becomes unstable. In this it is not so different from the Soviet structure, which was not so much defeated by the west as it collapsed in on itself after years of corruption and neglect. All top heavy structures topple over eventually.

If all the people who make things and grow things and do the actual work died tomorrow, the very richest would die of neglect within a few weeks. If the owners and operators of all the world’s corporations suddenly expired, it would be some time before anyone noticed. As another famous science fiction writer, Kurt Vonnegut, famously wrote: So it goes.

 
Teleology

The Answer to Everything...

Yes...!

Life, the Universe and Everything...

Yes...!

Is...

Yes...!

IS...

Yes...!!!

Forty two.

Teleology is the study of the end of things: The purpose or point of things. And what could be more important than to work out the purpose of the universe?

Yet in a certain sense, the question is meaningless. It is also self-serving and self-deluding, given that what we really want to know when we ask about the purpose of the universe is, what is my place in the universe? Or rather, give me an answer to the question that highlights my importance within the function of the universe. Our quest for a meaningful meaning to the universe is rarely objective , but often subjective in even formulating the question.

For instance, when people say that they say, I believe in a God (see below), what they are really saying is, I believe that I am important. I believe any teleological explanation for the existence of the universe must place me at its absolute centre. That I, one small part of one ordinary planet, orbiting one ordinary star in one ordinary galaxy in what is, in all likelihood, one ordinary universe, am somehow still special. That I am the centre of a universe in which no centre exists. Or, in the inverse, but equally valid cosmological view, a universe in which every point is as central as any other. Either way, the universe is as devolved and decentralised as it is possible to be.

Yet the question, as we say, is meaningless. After all, why should the universe have any point, other than the one from which it began its existence at the big bang? What if the meaning of life is that life is meaningless? Which may be a depressing answer, but that doesn’t prevent it from being true. After all, the trans Atlantic slave trade and the holocaust are depressing, but they still took place (no matter what idiots think).

Conversely, maybe the question has an extremely simple answer. Something like, the purpose of the universe is to expand and create. That is what the universe does at face value at least. From some form of singularity, an unfathomable amount of energy was thrown out to create an expanding universe. Out of that energy, matter was created, stars and galaxies were formed, giving rise to habitable planets on which sentient beings arose to look into the night sky and ask from where all of this creation came.

From this we might derive a similar drive for human existence. The meaning of life is to expand one’s awareness and to create, either through basic biological reproduction, or by outpourings of artistic expression. Or both.

This is some lefty, liberal hippy shit, to be sure, but few other ideas sit so well in the habitable zone between finding an answer to life, the universe, and everything that speaks to the human condition, while retaining something of the reality of the universe. Rather than interpreting the wishes of an irrational, contradictory god that exists largely in our heads and tells us what we want to hear, at least the existence and actions of the universe play out above our heads in nightly repertoire. If only someone would bother to turn off the lights.

What does any of this have to do with Douglas Adams? A good question. Nothing, except that Adams appreciated the meaningless of searching for a meaning to life. Perhaps the most famous section of the Hitchhiker’s Guide to the Galaxy is that of Deep Thought. Deep Thought is a giant supercomputer built by an ancient civilisation to come up with an answer to the question of life, the universe, and everything. He mulls it over for seven and a half million years and finally announces that the answer is forty two. An even bigger computer, the Earth, then has to be built to figure out what the actual question is for the answer to make any kind of sense.

This is cyclical nonsense done for comic effect, as with much of Adams’s writing (see, below), but the answer Deep Thought gives is as meaningful and valid as any teleological explanation humans have developed for the purpose of the universe.

In many ways Deep Thought is a grand skit upon the function of religion, particularly the various Christian schisms. Speculative questions are developed to the try to fit the answer to a question (How many roads must a man walk down? Forty two.). They are no less nonsensical than the attempts to try and resolve the various contradictions and absurdities found in the Bible.

Deep Thought and Forty Two reinforce the universal truth that if one asks a stupid question, one will get a stupid answer. That absurd axioms can only lead to further absurdities. Humanity is not the be all and end of the universe and any ideology attempting to place human beings at its centre, let alone select human minorities, are doomed to failure and are right to be ridiculed. As such, forty two is as valid an answer to the absurd question of life, the universe, and everything as anything else. Other valid answers include: the square root of minus one, mauve, a slice of lemon (wrapped around a large gold brick), the dodecahedron, or a liquid which is almost, but not quite, entirely unlike tea. 

"It was a tough assignment."

Theology and Metaphysics

"I refuse to prove that I exist,'" says God, "for proof denies faith, and without faith I am nothing." "But," says Man, "The Babel fish is a dead giveaway, isn't it? It proves you exist, and so therefore you don't. QED."

Perhaps the most famous proposition in all of philosophy is Rene Descartes’s statement: Je pense donc je suis. This is usually presented in Latin (Descartes originally wrote it in French): Cogito Ergo Sum. However, we know it from its English translation: I think, therefore I am.

Reading Descartes’s rationale in reaching this conclusion is still impressive nearly four hundred years after it was first developed. What can I really know? Descartes asks. I know that my senses do not faithfully reproduce the sensations of my surroundings. Sometimes they deceive me and make me see things that are not really there. One thinks of Scrooge in A Christmas Carol, when the ghost of Marley asked him why he doubts the evidence of his eyes:

"Because," said Scrooge, "a little thing affects them. A slight disorder of the stomach makes them cheats. You may be an undigested bit of beef, a blot of mustard, a crumb of cheese, a fragment of an underdone potato. There's more of gravy than of grave about you, whatever you are!"

Moreover, how can I know that what my senses tell me about the world around me are in any way accurate? This might all be a grand illusion. I might be a brain in a jar hooked up to some artificial reality. I might be living in the Matrix or some other form of virtual reality. This might be a simulation. Descartes of course did not quite think in these terms.

The only thing that I can say with any confidence is that as I am able to think and ask such questions as, how do I know that I exist, I must, on some level, exist. Everything that I see and experience around me may well be part of one grand delusion, but there is some part of me that is able to think, which is evidence for some form of existence, whatever form that existence might take.

Er, excuse me, who am I?

Hello?

Why am I here? What’s my purpose in life?

What do I mean by who am I?

Calm down, get a grip now … oh! this is an interesting sensation, what is it? It’s a sort of … yawning, tingling sensation in my … my … well I suppose I’d better start finding names for things if I want to make any headway in what for the sake of what I shall call an argument I shall call the world, so let’s call it my stomach.

It is a brilliant piece of reasoning, which makes what follows it all the more depressing. In my Penguin Classics copy of Discourse on the Method and the Meditations, Descartes turns his attention to the existence of God. Apropos of nothing, Descartes argues that God must exist. He has already successfully argued that the senses deceive us into believing the existence of things that are not there. We hallucinate and daydream and fully dream when we close our eyes at night and slip into unconsciousness. Yet this rationale does not translate into Descartes’s thinking for things that remain entirely invisible and unknowable to us.

Whether you believe or do not believe in God (I am very much in the later camp), is irrelevant in this matter. God is in many ways a collective hallucination for people who believe in such things, but one which is no more verifiable than whether human existence is one big computer simulation. If we are unable to confirm the evidence of our eyes, how can we say anything about the thoughts in our head? Which is what beliefs are: Desires for how we wish the universe to act and to be like, but without any empirical evidence to support those wishes. The same often applies for political beliefs or support for one particular sports team.

To be fair to Descartes, he was living at a time of great religious persecution, where to even suggest that the existence of God might be a matter for doubt could have landed him in serious trouble with the religious authority of his day. As such, he had to make an argument for the existence for God, even if he did so in such a haphazard fashion that it is difficult to take seriously. Yet it is also an example of how theology does not conform to the rigours of the scientific method found in other branches of philosophy and the sciences.

Douglas Adams references such lack of rigour in interviews he gave in his lifetime. He notes his education at Brentwood School, where scientific and philosophical concepts were taught with careful attention, using reason to elucidate the journey from first principles to a consistent and provable theory. Yet, as a Church of England school, when the focus turned to religious education, those same rigorous methods were nowhere to be found. Here reasoning seemed to rest on the simple axiom of: just because. Like Descartes justification for the existence of God, Adams’s teachers built theological arguments on castles made of sand (or Jenga blocks) and apropos of nothing.

This mindset is then parodied in the Hitchhiker’s Guide rationale for the non-existence of God. God cannot exist, because the existence of the Babel Fish proves he exists and proof denies faith, which is all that religion and the belief in God are based upon. It is a paradox (see below), but one which pokes fun at the idea that it is impossible to prove a negative. You can’t prove that God doesn’t exist, but you can prove that he does exist, which for religion would be almost as bad. If God were real and the Bible was literally true, many people in religious authority would be in a lot of trouble.

We cannot prove the non-existence of God, but we can show that his existence solves nothing metaphysical. The philosopher Bertrand Russell learned this lesson early in his young life, turning him from a believer into a lifelong atheist. God is invoked as the creator of the universe; the prime mover that gave movement to the universe and set the planets and stars in motion. But then the question becomes, but who created God? Theology tells us that God just is. But if God can just be then we can equally argue that the universe just is. There is nothing special about the existence of a God’s role in the universe that cannot equally be said for a universe that arose all by itself. A godless universe doesn’t solve anything, but it also doesn’t complicate the vexed question of the origin of the universe. Indeed, it simplifies matters considerably.

Douglas Adams described himself as a radical atheist. A Dawkinsist, as he often called himself, in reference to his friend, the biologist, Richard Dawkins. Adams famously said of religion and the supernatural, “Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?”

Yet he could also write books that feature UFOs, ghosts, time travelling college rooms, séances, and electronic monks. Adams recognised that fiction operates under different rules to non-fiction. It is possible to consider the mythical and the mystical when writing escapist tales. Which is where they should remain. Such things have no place in considering real world solutions for real world phenomena.


Paradoxes

“The ships hung in the sky in much the same way that bricks don't.”

Paradoxes. Many philosophers have paradoxes associated with them. Mathematical paradoxes, like Zeno’s Paradox. Logical paradoxes, like Russell’s Paradox. The Socratic paradox that all I know is that I know nothing. Or Epimenides, a Cretan philosopher, who said that all Cretans are liars. The paradox is often used by philosophers to test the limits of knowledge or logic, or to examine the general limitations of language to convey useful and internally consistent information.

Douglas Adams’s work is littered with paradoxical ideas and aphorisms. We have already seen in the previous section the idea that proof that God exists is ultimately a logical proof for his non-existence. There are many other examples.

One such example is the story of the Improbability Drive. This is a space propulsion drive that uses improbability as its powering force. The drive itself is invented by a student who recognises that such a machine is virtually impossible, so he works out just how improbable it is and inputs that number into a computer. He then creates the drive out of thin air and is killed by his contemporaries for being a smart arse.

The tale of the Improbability Drive can in part be seen as a satire on the study of cosmogony, the study of the beginning of the universe, as well as theology. In any explanation for the beginning of the universe, there is the problem of infinite regress. As we saw in the previous section (see above), for anything that creates the universe, whether it be God or the Big Bang, there is then the question of what created the creator. One solution is that our universe is one of innumerable universes sitting on a manifold called a brane. But then what created the brane?

This is an old philosophical chestnut that has been incorporated into many an apocryphal tale. The classic one is found in Stephen Hawkins’s A Brief History of Time. An old lady attends a cosmological lecture by a philosopher about the nature of the solar system and the universe at large. At the end of the lecture she objects, saying that everyone knows that the Earth in fact sits on the back of a turtle. The philosopher smugly asks her what does the turtle then rest upon. The woman replies, “It’s turtles all the way down.”

An improbable invention that is created by calculating how improbable is its existence is one very clever way around the idea of infinite regress. Perhaps one day science or philosophy will develop a theory quite so deft to explain the existence of the universe.

In the third Hitchhiker book, Life, the Universe and Everything, Arthur Dent learns how to fly by teaching himself to the throw himself at the ground and miss. The paradox is that one cannot do it voluntarily. The trick is to distract oneself at the crucial moment so that one is unaware the ground is looming up below. The idea that one can perform the impossible, even miraculous, by simple virtue of being unaware of what one is doing is highly paradoxical. It serves as a plot device in the third and fourth books in the Hitchhiker’s Guide to the Galaxy series.

Another paradox, that is never explained, is how Zaphod Beeblebrox is great grandfather to his own great grandfather. That is to say that he is from a long line of Zaphod Beeblebroxes, of which he is the first and his great grandfather is the fourth. All we are told is that it involved a contraceptive and a time machine.

This, of course, is a variation on the Grandfather Paradox, where a person goes back in time and kills their own grandfather before he can sire a son and so the grandson is never born to go back in time and kill their grandfather. But then the grandfather isn’t killed, the grandson is born and can go back in time to kill their grandfather. At this point we encounter our old friend, infinite regress.

Although one of the ways out of the Grandfather Paradox is to introduce the idea of parallel worlds. That as soon as one goes back in time and changes anything, one creates a different version of reality that exits in parallel with the original universe. The grandfather is killed in the new version of reality, but continues to exist in the first reality and no paradox is required. Indeed, if the Many Worlds interpretation of quantum mechanics holds true, both universes already exist and killing one’s grandfather would simply move one from one universe into the other.

Another broadly paradoxical idea that plays into this is the idea of an artificial universe. A writer for the Hitchhiker’s Guide has set up an artificial universe in his office so that he can research stories in the galaxy, but still go to parties near the guide’s offices at night. In The Restaurant at the End of the Universe, this is used to protect Zaphod Beeblebrox.

Beeblebrox is be executed by being placed in the Total Perspective Vortex, a device which shows its victim the entire, infinite enormity of the universe and their place in it, frying their brain in the process. However, when Beeblebrox is subjected to the Vortex, he has entered the artificial universe and not left it.

This alternate universe, it turns out, has been set up for the sole purpose of protecting Beeblebrox from the Total Perspective Vortex. So when he is shown the sheer scale of the universe, he realises that he is the most important object in it (which in the alternative universe, he is). Not a good idea for a man of Zaphod’s already massive ego. He in all other respects continues to interact with the real universe and its inhabitants. Only when he has successfully survived his exposure to the Vortex is the universe turned off and he can get on with his real mission.

The real mission is to find the man who rules the galaxy. He is a lonely old man who doubts everything; even his own existence. The galactic government keep him out of the way and cut off from news or information of any sort to ask him hypothetical questions which are then used to govern the universe, solving the problem of people wanting to be politicians being kept away from the business of actual decision making (see above). A paradox is solved in the process.

There are many other paradoxical examples in Adams’s work. Ships that hang in the air the way that bricks don’t. The man who proclaims nothing is true, but is later found to be lying (shades of Epimenides’s Cretan). The golden age of the galaxy where everyone was rich and no one was poor; at least no one worth speaking of.

Adams’s work is filled with logical inconsistencies from which his comedy arises. But beneath the surface there is to be found much depth. For my money, he was one of the most important philosophers of the 20th century.

Douglas Adams