As a result the universe seems impressively and awe-inspiringly huge.
But size can be deceptive.
Notice that the word "huge" that I used there was preceded by the descriptive terms "impressively" and "awe-inspiringly".
This is because although we're not particularly proficient at judging sizes accurately we are certainly obsessed with using size as a yardstick for gauging the significance of things. Essentially, the bigger something is, the more important it is. You very rarely hear of anything being described as pathetically huge.
In our normal everyday world, especially in the past when everything was simpler, there was some justification for this approach, which is probably why our brains think that way.
In stone-age times the biggest sabre-toothed tiger was the most dangerous (unless it was twenty miles away of course), while the biggest woolly mammoth would feed more people.
The consequences of our attitude to size can be seen all around us at a day-to-day level. For instance, on a summer's afternoon in the garden, imagine that you're sitting relaxing with a glass of wine or fruit juice. You notice that a very small fly, perhaps a couple of millimetres long, and of indeterminate species, has rather annoyingly drowned itself in the drink. What do you do? If you're like most people, you'll fish the fly out with a finger and you'll then continue to drink your drink. However, if a large fly were to drown in your drink, what would you do? You'd throw the drink away. Is the small fly really less disease-laden than the large one? It's just as likely to have flown in straight from the same unmentionable object that's festering under the hedge.
To prehistoric people size mattered on the personal side too. The biggest man in a nomadic group was probably the strongest and was therefore most likely to be the leader of his group. Things were much more straightforward and unsophisticated back then. A small man in the group might have been the cleverest and wisest, but so what? In those days the big guy could win any argument just by caving the little guy's head in with his fist.
The world is different now of course, and intelligence is generally more useful than physical size, but we still have that fossilized imprint in our heads that big is better, messing everything up for the short guys.
The attitude that big is better isn't just a human obsession. It's relatively ubiquitous in the whole of the animal kingdom. In the world of insects there are species where the males measure up the size of potential rivals by standing head to head and checking who's got the longest antennae. Needless to say the one with the longer ones wins and the short-antennaed insect scurries away (usually without a blow being exchanged).
In the world of mammals similar things happen. Take the Irish elk, megaloceros giganteus (which is Latin for gigantic bighorn - these Latin names are rarely as fancy as they sound), shown in Figure 46. This was a form of giant deer that's now extinct, in which the males had unfeasibly large antlers, probably largely for the purpose of impressing the females (The antlers stuck out sideways, for maximum visual effect, and thus were probably as much ornaments for display as armaments for fighting - although their visual effect could aid rival males in the task of sizing each other up too, a little like those insects with their antennae).
The extinction of the elk used to be attributed to the fact that it was endowed with these overwhelmingly cumbersome appendages, and that the beast had therefore ceased to be able to function properly. It was thought that it probably fell victim to such silly misfortunes as becoming trapped in the middle of forests because it couldn't walk between the trees.
If you ever see an Irish elk skeleton in a museum you'll observe that the total span of the antlers is truly awesome (in fact they are so wide that it's hard to guess their span without taking a tape measure to them), and you'll think that the idea that the elk's extinction was due to these inappropriately proportioned protrusions seems entirely appropriate - it is in fact the theory that will pop into your head almost entirely unbidden when you gaze upon the creature.
Not only does the theory look right, but you really want it to be right too. The idea that a species could be undone by its acquisition of a feature that's a combination of ostentatious ornamentation and grossly excessive armamentation seems so much like poetic justice, and to so much parallel our own dubious grip on the priorities of life, that it's almost irresistible.
But it's wrong.
The Irish elk died out for the same reasons that most things die out, due to such causes as changes in the environment (resulting in diminished food supply and so on).
The "hoist on its own petard" theory of the elk's extinction falls neatly into the category of theories that you have to be suspicious of because of their appeal.
Even if you weren't swayed by the desire to think that the elks were the victims of their own arms race, it would still seem reasonable to assume that the huge antlers were at least a contributing factor in the elk's downfall. Jumping to this conclusion is similar to reaching the wrong conclusion in the Wason card test (on page 64). It's a good example of a case in which what seems to be the obvious answer is in fact wrong - a recurrent theme of this book.
Let's explore the subject of size further by moving away from its significance in the natural world and by having a look at it in the world of our own making - specifically in the world of electronic machines. A world in which size most definitely isn't everything.
Here, in Figure 47, are drawings of computers from different ages: an ancient one, from around 1960, and a new one, from 2009. Which one do you suppose is the better computer? Which one can do more and faster computing? Which one is the more intricate in terms of its electronics? Which one is the more complicated?
The drawing above shows the difference in physical size between the two computers reasonably accurately. In contrast, in Figure 48 below I've drawn the same computers in a different way. Instead of drawing them in terms of their physical dimensions I've made their sizes reflect their relative complexity. The more modern computer is thousands of times more powerful and complicated than the older computer, so I've drawn it thousands of times bigger. (Please don't check the drawing for accuracy of scale though - it's purely illustrative.)
Below, in Figure 49, I've used the same representational principle to compare a modern laptop computer with a pre-electronic mechanical typewriter. Physically they are about the same size, as shown in the top half of the illustration, but in terms of internal complexity they are separated by many orders of magnitude.
Now let's be a bit bolder and attempt to use the same technique to create a model that somehow represents the complexity not of typewriters or computers, but of the whole universe.
The complexity of the universe is essentially the sum of the complexities of all of the objects within it, so let's have a look at a few of these objects to see what we've let ourselves in for.
What do you see when you look up at the rest of the universe on a dark night? Usually clouds if you reside in the part of the world where I live, but just occasionally, stars. Millions of them.
The universe is full of stars.
Stars: massive balls of incandescent gas heated to incredible temperatures by the energy of hydrogen atoms fusing together under the force of the stars' own gravity, creating heavier atoms in the process.
Stars are very impressive it's true, but in that last paragraph I've actually managed to describe what they are and how they function in just one sentence (I've simplified things a little of course).
There's not actually much complexity in a star when you really get down to it.
What's more, there may be untold millions of stars in the universe, but they're all doing more or less the same thing. Millions of stars all doing the same thing doesn't make those millions of stars acting together millions of times more complex. If anything it makes them more boring.
I wouldn't want to belittle the nature of stars, but you have to guard against being seduced by their seeming incredibleness. Bear in mind that just because the temperatures within stars are amazingly high doesn't make the temperatures within stars amazing in themselves - they are only incredible to us on earth because such temperatures are unusual here (and are in general inadvisable).
One more thing. Just a few paragraphs ago I said "The universe is full of stars." That needs slightly amending. The universe is actually full of empty space, with stars popping up as ridiculously infrequent pinpoints of matter in the almost endless void. I think that it's safe to say that this endless void isn't complex (even if it turns out to be full of clouds of invisible "dark matter") and that it contributes very little to the complexity of the universe.
In fact, amazingly, there's more complexity in the short distance between your head and the words that you are reading now than there is in the space between the Earth and Proxima Centauri, the closest star to our solar system. And that's an understatement. For one thing, you've just breathed out a lung-full of viruses and bacteria, and I'm prepared to wager that there aren't many of them floating around in interstellar space.
Having done my best to deflate the importance of stars, let's move on now and look at the galaxies that contain the stars. It has to be said that galaxies look incredibly spectacular, with their swirling spiral arms spinning in space. But the underlying mechanism that generates those spirals is relatively straight-forward: in fact it's no more complex than the mechanism that makes bath water spiral down the plug-hole. Indeed the two phenomena are quite comparable (right down to the fact that in both cases the material in the spiral rotates around a black hole at the centre).
This has an interesting implication. It means that if you were to create images of a galaxy and of water going down your bath plug-hole based not on their physical size but scaled by complexity (as with the computers and typewriters above) the spiralling water in your bathtub would be the same size as a whole galaxy, at least as far as the physics behind the spiralling effect goes. Here is the result, in Figure 50.
Again, I'm oversimplifying here, for effect - but you get the idea.
It seems as though the universe, which is essentially made up of stars and galaxies swirling around, expanding, contracting, collapsing and so on, is actually quite a simple place, contrary to what you'd think from a cursory inspection.
However, there's one thing that's floating in this vast sea of cosmic uniformity that's very, very interesting indeed. What's more, despite the fact that the universe is untold billions of light years across, you don't have to look very far to find this thing.
It's right here on Earth.
What are the chances of that! This thing is life.
Life is the single most complicated phenomenon in the entire universe, by a long chalk (as far as we know).
Incredibly, the life on our planet is so varied that the complexity of the surface of the earth is greater than that of the rest of the entire universe put together.
(Of course there could easily be life elsewhere in the universe, which would instantly confuse matters, but to keep things simple and to keep the effect dramatic, I'll only deal with the universe "as we know it". The existence of life elsewhere wouldn't significantly alter the gist of my argument anyway.) To better appreciate the incredible complexity of life on earth let's look at a typical representative of the phenomenon. Let's look at a mouse.
A mouse is made up of chemicals that are so complicated that they don't exist anywhere else in the known universe beyond earth. These chemicals are arranged into structures that are themselves immensely complicated - legs, eyes, ears, mouth, stomach, heart, liver, lungs, tail, fur and so on. These complicated structures made out of complicated chemicals are performing incredibly complicated tasks, such as running around and eating cheese - although we often don't give them a second thought because we're so familiar with them (unlike the processes that go on inside stars for instance, which as a result we think of as being incredibly exotic).
A mouse's brain is composed of about 16 million neurons. Neurons are cells that process information. They transmit information to each other by using pathways or connections known as synapses. On average there are about 8,000 synapses per neuron. That results in approximately 136 billion (that's 136,000,000,000) synapses in total. In the brain of a mouse.
This all makes a mouse a creature of awesome complexity.
Now let's look at a galaxy by way of comparison.
Galaxies tend to contain somewhere between 10 million and a trillion stars. Our own galaxy, the Milky Way, which is actually larger than the average galaxy, has an estimated 200-400 billion stars in it. Stars are relatively simple structures, as I mentioned, collapsing in on themselves and producing a lot of heat and light in the process. That's about it.
The number of synaptic connections in a mouse's brain is up there with the number of stars in an average galaxy. If I were to include an illustration in this book comparing the complexity of a mouse with that of a galaxy the mouse would be much bigger than the whole galaxy. In fact you can easily argue that a single mouse is much more complex than a whole cluster of galaxies. Bear this in mind next time you catch one in a trap.
A mouse is indeed a very impressively complex thing compared to a galaxy. In fact, we know of few things in the universe that are more complex than a mouse. We do know of some things that are though - and all of them are different life-forms living right here on our planet.
And what's the most complex life-form that's living on our incredibly complex planet? We are.
We humans.
Where a mouse has 16 million neurons in its brain it's estimated that we have a staggering 100 billion. That's about 6,000 times more.
Not only are we more complex than mice in terms of the physical makeup of our brains, but the consequences of what we do with our brains generates further complexity still: by devising languages, composing music, building things, destroying things.
If a single mouse is more complex than a whole cluster of galaxies, just try to think how complex a single human is.
It's actually been calculated that, incredibly, the possible number of brain states, or permutations of possible activity in the human brain, is greater than the number of elementary particles in the known universe..
Just let that sink into your unbelievably complex brain for a second before you move on. (And stop thinking "That can't be true!" I don't actually know quite what that statistic means to be honest, so I can't comment on it - but even if it's wildly in-accurate the general principle of the sheer stupendousness of the human brain is nicely expressed by it.) Next time that you're feeling like an insignificant speck of dust in the vastness of space call to mind the fact that you yourself are more complex than the whole of the known universe that extends beyond the earth's atmosphere.
A single human brain is as complex as the rest of the cosmos - and there are six billion humans on earth, each thinking different thoughts and doing different things (up to a point). That means that the collective complexity of the human population of our planet is possibly greater than that of several million universes.
If you add together all of the life-forms on earth the complexity of our tiny planet would put the combined forces of who knows how many universes in the shade.
As a result of this, if we were to make models of the universe and the earth scaled to complexity rather than to size we end up not with a huge universe alongside an earth that's the size of a grain of sand, as is usually envisaged, but with an unbelievably immense earth compared to the rest of the universe which is the size of the grain of sand. Everything flips round.
This way of measuring things based on their complexity is not simply a mathematical diversion or meaningless but interesting exercise. It's as valid a method of measuring things as is to take a ruler to them.
(Physical) size isn't everything.
I know that earlier I said that our insignificance in the vastness of things could be thought of as a bit of a comfort. Now I'm saying that we're the biggest thing that there is, by a very very long way. You may also like to draw comfort from this fact too.
That may sound contradictory: drawing comfort from both the fact that we're insignificant and that we're hugely significant. But personally I think that it's very healthy to hold seemingly contradictory views. It shows that you're a complex person (if you want to feel even more complex than you obviously already are, with your brain that's bigger than the universe).
You can then choose whichever status you prefer - insignificant or significant - to suit the mood that you're in at any particular moment.
If you feel the need to throw off responsibility, maybe because you've had a hard day at the office, adopt the "The universe is vast and we're tiny specks of dust" stance. On the other hand, if you need to feel more important, perhaps because you've had a hard day at the office, opt for the "We are the biggest thing in all of creation" approach.
Whatever's right for you at the time.
As you read this you may be feeling a little unsettled because you're not too keen on the idea that, measured in terms of complexity, people are the biggest thing in the known universe.
Your objection to this concept may be along the lines that it elevates the significance of we humans to what you think is a totally unacceptable level. You may be worried that if we start thinking in that way we may become too big for our boots (as if we weren't already). You may think that the whole thing smacks of supremacism on a megalomaniacal scale.
If, as a result, we indeed ended up as a species of obnoxious supremacists it would be unpalatable in the extreme. However, the inverse view of our place in the universe - that we're tiny insignificant dots - is also fraught with danger in itself. Amongst other things, it breeds insecurity. This insecurity may in turn foster aggressive overcompensation as manifested in psychological states such as the Napoleon complex. (Named after the theory that Napoleon was driven to conquer half of the known world as overcompensation for his allegedly short stature. The fact that Napoleon's height is not known precisely and may indeed have been the average height for his time is conveniently ignored. Perhaps Napoleon's real complex was that he was so average.) Feeling that we're insignificant has another down side. It encourages us to think that because we are small and inconsequential then whatever we do to our planet is inconsequential too, allowing us to delude ourselves as to our actual significance - a sort of inversion of the Napoleon complex in fact.
If, having weighed up these considerations, you're still feeling unsettled by the whole idea of having a brain bigger than the universe, don't fret.
I have personally conducted a psychological test, selflessly using myself as the guinea pig. In the test I had a shot at wandering round thinking that my brain was bigger than the cosmos, to see how it felt, and to my surprise it didn't actually make an iota of difference. I kept forgetting the fact. Even if it is a fact it seems to be something that we're not psychologically equipped to hold in our heads - possibly because, amongst other things, we're all painfully aware that our brain is only a heartbeat away from being nothing more than a three pound lump of inert mush.
