For all practical purposes, we humans have very very limited horizons. We like to play a little cognitive misdirection on ourselves and believe that we can do a lot, think a lot, be a lot but it isn't really so. True, we can face infinity (night sky), and even face it down. We can check out the eco-damage we've done and the mighty works we have wrought and feel a certain guilty pride that could stoke the conscienceless ego. Perched on a hilltop we can maybe believe that we can take in the whole of the world, encircle it, view it all with one sweep of the eyes from horizon to horizon[13]. This kind of arrogance hasn't hurt us in the past, is probably partly responsible for where we are today (good or bad). But we are fooling ourselves (others agree with this statement).

Elbow room, for squillions of elbows

I've been thinking about this since first playing with Celestia, a rather cool "simulator of the known universe" found via Dave Shea. In Celestia, you begin looking down on a gently spinning planet Earth against a backdrop of stars. You can point yourself at, say, Mars (or, say, Betelgeuse) and zoom there. And the perspective (though not the g forces you'd undergo) is all true to scale, so you experience just how far it is and just how spread out everything is. It turns out to be quite disturbing to experience the true scale. For example, start at Earth and pick another planet, go there and, without using the Home button, attempt to find your way back to the Earth again -- it's a daunting (microscopic-)needle-in-a-(humungous-)haystack task. Or take a vastly accelerated ride on Halley's comet and experience an inner system flyby from the comet's point of view: contracting Halley's 76 year cycle into five minutes results in a flicker of planets and Sun then an awful lot of outer darkness. Or park yourself beside Cassini, aim for the sun, accelerate to ten times the speed of light, and wait…three quarters of an hour before you pass Earth. You constantly find yourself expecting the stars to stream past like they do when TV sci-fi spaceships go into hyperdrive but Celestia is prosaically accurate about the real size and scale so you have to watch for a minute or so to see the nearest suns parallax sideways one pixel at a time.

Lesson: Celestia conveys just how unnervingly huge and empty it all is. How do I convey this to the kids? Celestia itself is fun for them but they don't relate it to their own experience; why should they? The question is, could anyone?

Putting aside the rest of the known universe for a bit, there have been numerous attempts to present the solar system at a comprehensible scale. I remember one from a book I read as a kid (based on the Jodrell Bank scale model I think), where the sun was represented by a small beachball and the Earth, it turned out, was a dried pea fifty paces away. But--let's be honest--who can make sense of that? You can't see a pea that far away! One suggestion is to stick it to a piece of card, which sort of removes the one-to-one correspondence with reality:

Dad, is the piece of card a million miles high?

Even if you equip yourself with cards and binoculars, you are still at least one metaphor or conceptual model away from anything that is real for you. This is because relating the pea you are squinting at to your personal experience (i.e. a mostly flat earth, yourself at the centre of horizons 5km away) is impossible. You have to build another scale model:

Kids, imagine a pea a mile across with a little house from the Monopoly set stuck on it to represent our home.

What, dad?

There really isn't any scale model that can incorporate items from your daily life (yourself, your house, the Great Wall of China) and interplanetary distances, let alone interstellar or intergalactic distances.

Size doesn't matter, but maybe speed does

If human distance scales are inadequate to the task, how about time? What sort of time periods can we grasp? If we can intuit "three score and ten", can we come up with some sort of comparison that squeezes the megadistances into a parsable, think-about-able story?

How about a speeding car? The speed limit hereabouts is 100 km/h. So, to explain to the kids how really really big the Earth is, I remind them that, as per their personal experience, it takes 15 minutes to get to the city centre on clear roads. They know this. Now, I said,

if we travelled at the same speed, not stopping for sleep or food or toilet or fuel, and let's assume there's a handy motorway going where we want to go, it would take us 9 days to drive around the Equator.

That seemed parsable. It's a comprehensible span of time, I think. I'm not too sure (and they were doubtful) because I think it is still far from truly intuitable, grokkable time; can anyone really hold in their head the period of time that can accommodate 150,000 breaths? [Aside: and notice the unavoidable use of a distance metaphor built in to the language - "far from truly intuitable" - yet another conceptual model helping us along (and those last three words are another such metaphor…)]

Nevertheless, at this point I'm doing okay. However, we've got some way to go. I want to communicate to them the point that the Earth is really huge, space is really big, the universe is really enormous. Earth, we've done: 9 days of driving. But it rapidly gets out of imaginable numbers, as, in truth, the Earth is hugely huge, space bigly big, the universe enormously enormous to an enormous degree. With the equator now (probably, temporarily) fitted into their heads, what next? Why, a motorway to the moon!

Kids, if we had a motorway to the moon, plus the inclination and ability to avoid sleep and food and fuel and all that, and we stuck to the speed limit the whole time -- how long?

Their guesses are (naturally) all over the place, itself a clue that we are into the ungrokkable. The real answer: a day less than 23 weeks. That's a harder timespan to grasp, but we can have a go: it's the time between their birthdays, or between Easter (when we get eggs) and Dad's birthday (when he gets socks). You can do an unimaginable amount of breathing in that time, but perhaps we can believe that 23 weeks fits in our heads. So: 23 weeks to the moon; what if we drove on past to the sun?

Kids, that would be 170 years.

That's harder. 170 years is too long to imagine. Of course, it isn't too long to write down, or to talk about as though we understand it, or to come up with some significant historical events that far apart:

Kids, if you set off for the sun the day Queen Victoria first sat on the throne of England, you'd be getting there round about now.

Kids, if you set off for the sun on the day your great, great, great grandmother was born…

Kids, if you set off the day Melbourne, Australia was founded…

No, that's not a true comprehension of the timespan, not grokking it in fullness. After all, assuming you feel you can hold a representation of your life up until now in your head, that makes for probably only thirty or forty years of memories -- for 170 years you need four or five heads, each one just as full of incident and accident and love and death and fights fought and hearts broken and books read and games played and conversations had and visits to relatives and doctors and friends and foes and public toilets. So, unless you are 170 years old, I contest that you can't truly intuit that period.

But it is a comprehensible sort of number, isn't it? I can't feel it as a personally experienced continuous span but I can sort of imagine it as a period in which half a dozen generations can be born and die, in which dozens of wars and peaces can take turns, in which cars and televisions and telephones and the internet can be invented. The kids can't, no question. But let's press on anyway, for my satisfaction and their mystification.

Pretend we've crammed 170 years into our head. That's how long to drive to the sun, right? Okay, got that. How long to drive to the next nearest star, to Proxima Centauri?

Give in? Well, er, that would be 45 million years.

Nope, lost it: too big, doesn't fit. Forget the car -- doesn't work. The speeding car allows us to comprehend the size of the Earth (just), the distance to the moon (perhaps) and the distance to the sun (academically, historically, theoretically). But now we're going interstellar it is as much use as peas and beachballs.

A plane, Dad!

No, that's only four or five times faster, and 9 million years travel time to Proxima Centauri is an equally ungrokkable timespan. 9 million years ago the orang-utans speciated off the ape family tree though hominids were not going to follow suit for some time yet, and there are plenty of people who can't grasp that! Let's up the pace a bit. What is the very fastest that any human being has travelled? The Apollo 10 return trip to Earth reached 24,791 mph at one point apparently, a shade less than 40,000 km/h. Wow! That's more like it. If our car went that fast (constantly), how long to get to the moon? A paltry 9 hours, start early from your home crater and you can be on Earth in time for children's TV. To the sun? Only 22 weeks (the inter-birthday period). Proxima Centauri? Proxima Centauri?!?

112,000 years.

Gah! Better than the car, but still well off the Imaginability Scale. There was a scientific speculation recently that this is roughly how long our species has been wearing clothes (on the basis that head and pubic lice genomes indicate speciation around then, which may be due to reproductive isolation between these areas as humans became less hairy). However distracting, this fact doesn't help us fit the distance to Proxima Centauri in our heads.

Kids, how about if you set off at that fastest-ever-human speed (Apollo 10) the very day that the Earth was created (scientific timescale), guess how far would you get? Go on, guess. That's 4,600,000,000 years at a constant 40,000km/h…? How long? Eh?

It's a meaningless question to them. (In fact they've stopped listening now.) The answer, by the way, is, " all the way to the Magellanic Clouds".

Not only is this utterly incomprehensible but it is, cosmically speaking, still in our neighbourhood. It depends on your definitions but I'd call it an interstellar distance. In other words, intra- (not inter-) galactic. Our nearest galaxy, Andromeda, is 12 times further (in another direction).

Lost cause, lost in the universe

So, to recap:

• Travelling at a speed which you can comfortably recognize from your personal experience, and doing so for a period of time which you can more or less recognize from your personal continuous experience, will just about get you to the moon. That's it. You'll still be within radio receiver distance and you still won't have become the furthest-travelled human.
• Stretching instead to record-breaking extremes, by travelling at the very top speed which humans have so far experienced and by doing so for a truly awesome amount of time which humans struggle to conceive, you still won't get out of our galaxy. (Bear in what is left of your mind that there are perhaps 100 billion other galaxies, this number also being unimaginable. In fact, this particular number is structurally unimaginable because it is the total number of neurons in your brain).

The illusion that we can comprehend the size of the universe? That, not the universe, is all in your head.