A moment, if you will, for a philosophical reflection.
Once a month or so I do a talk for a local amateur astronomy club about what's available up in the night sky in the coming month. I offered to do the talk a few months ago, just a few months after I joined the club, which was just a month or so after I bought a telescope and for the first time in maybe 25 years looked up at the sky with more than drunken longing. (Astronomy is honestly my first love; I got into Philosophy and math because of the larger considerations explained below, but in all fairness I just married Philosophy of Math, intellectually. Astronomy is the one I'll always love.) The talk is designed to be useful and interesting for kids and adults alike, so we use simple flashy pictures and don't go too much into the science; the point of the talk is more slideshow empiricism than it is deep astronomical science. I want the kids and the adults just starting to go outside into their backyards on a new-moon Wednesday night and take a look around with some binoculars. That will provoke questions, but it helps to have some names on things. In much the same way that people are able to understand the health of their neighborhoods if they can name the trees and shrubs and vegetables growing there as well as the middle schools and coffee chains and the name of the people with the purple fence down the street, people will feel more comfortable looking up if they have some sense of what they're looking at. So to encourage that, we need to show them around a little, so they get a sense of the texture of the night sky and what's visible, and what's just out of visibility.
Some of what they might see is in the sketch of M81 and M82 to the left. There are two galaxies in the sketch, one 11 million light years away, and the other 12 million. (A "light year," for the uninitiated, is the distance unencumbered light will travel in an Earth year, or about 9.5 trillion km. Multiply by .6 for miles.) The person who did the sketch used some very basic binoculars, the kind of thing people keep in the back of the car for trips to the mountains or the ocean, and while they had very dark skies with which to see these two objects, I've seen both galaxies on multiple occasions, including from my light-polluted suburban backyard by the light of a very bright silvery moon.
The sketch doesn't look like much, and you, dear reader, may need to blow up the image to get a good look at the smudges. That's partly because those objects are 11.5 million light years away; the photons are pretty tired out. That's also because the binoculars were 8X26, and the human eye is adapted to quick edge detection and can't pick up the full-on color we know is there. I'll show both images side-by-side and often get quizzical, puzzled looks - why even look at the thing if all you can see is smudges? I'm not sure why it is, but people who see the smudges will still be enthralled, especially kids. Its like seeing the first ultrasound picture of your daughter. Sure its a smudge, but let's be honest: There's a whole lot of meaning packed into that one little smudge. You don't even know what meaning there is, but you know there's lots.
If we use a camera that doesn't blink attached to a bigger telescope and allow the various wavelengths to collect, we get something like the image to the right. Its a very pretty picture and required a lot of technology, but this image isn't the work of a professional or a satellite; this was just someone with about $5000 worth of equipment, a lot of time, and a good clear night. The galaxy on the left is a spiral, like the one we live in, and the one on the right is presumed to be a spiral as well. They've interacted recently, because there are shreds of material in between them, like the bits of fender and smashed taillight you see on the road after a collision between two cars.
Except of course that these aren't cars. They're spiral galaxies. They're part of our neighborhood cluster, which includes our immediate neighbor the Andromeda galaxy, which is larger than our own Milky Way. M81 and M82 may not be as large as our own, which is big by spiral standards, but they probably weigh somewhere in the vicinity of 100 billion solar masses - which is to say, if you added up all the big and small stars, planets, asteroids, black holes, dust clouds of perchlorate and carbon tetrachloride and hydrogen and vaporized iron, as well as whatever consumer goods and garbage you might find cluttering up the inhabited planets, you'd have something like 100 billion of our suns worth of material. So there you are: two sets of 100 billion suns worth of stuff, sitting in the same picture, about 11 million light years from us, in our neighborhood cluster, which includes at least our own large 150-200 billion star galaxy plus the estimated 1 trillion stars in Andromeda. (Plus the 200 billion or so in M33, which appears in the sky close to Andromeda.) Plus the various satellite galaxies of both our own and Andromeda, which might add up to another 100 billion or so suns.
All of which is observable from my backyard. Well not all of them; I haven't seen the greater and lesser Magellanic clouds, which are two of the Milky Way's satellites, visible from the southern hemisphere. But if I were in Melbourne they'd be visible on any clear night.
Now my point here isn't just to say that space is awfully big. Because simple arithmetic tells me that our "local neighborhood" contains something like two trillion stars. Give or take a hundred billion or so. Maybe there's a couple of hundred-billion-solar mass black holes hidden in there somewhere.
No my point is a much more philosophically pointed one. Consider the "powers of ten" video at the top of this post. The smallest know identifiable object - the smallest thing we've seen as a species - is the neutrino, 10^-27 meters smaller than our scale of cars and trucks and dogs and cats. The universe itself, as we currently understand it, is 10^25 meters big. So the difference in scale between the universe and us is a couple of orders of magnitude smaller than the difference between our scale and the smallest known constituents of matter - only about a hundred times smaller than the universe is larger than us.
Know anything 100 times smaller than you? Easy: If you're 60 inches high, then something half an inch long, say a thumbtack, is a hundredth your size. So pretty close.
And none of that makes any sense, does it? You need a particularly adept mind to put those scales into comparison, mentally, and I find the whole conversation to be little more than verbal gymnastics. Once you memorize the grammatical rules its easy to play around with the numbers, but that doesn't mean you know what you're talking about, or even understand it.
Fred Hoyle was once quoted as saying that space is close: if your car went straight up you could drive there in an hour. This thin envelope of oxygen, nitrogen and carbon dioxide we walk around under is so unbelievably small, even in comparison to the Earth itself, that its a rather fascinating study in ignorance to listen to people argue that we as a species couldn't possibly have bounced the carbon dioxide levels in the Earth's atmosphere in only 200 years. Well of course we could, because the bulk of that atmosphere is located within ten miles of here. I can run ten miles in a couple of hours; I can see ten miles pretty easily. The top of Everest is only 6 miles from here, if the base of Everest were outside my door. While it may be a challenge to drive your car straight up, don't mistake your challenge as an insurmountable barrier for the billions of the rest of us. The volume of air in the atmosphere is finite, doesn't go much higher than the highest mountains, and is vastly overmatched by the actual size of the Earth itself. Given enough people lighters and fireplaces and they'll happily fill up their local envelope with soot and carbon dioxide. There's 1500 miles of border between Canada and the US, which is 30 times the distance from where I sit to space. And while that covers a bunch of time zones, its only a small portion of the circumference of the planet. The atmosphere is small and thin.
In actual fact Space starts at the surface of the Earth. From the standpoint of other planets in our solar system with an atmosphere, we have very little. Less than Venus, more than Mars, and significantly less than Jupiter, Saturn, Uranus and Neptune. We're just this side of a barren rock. We're lucky we're in the habitable zone, so the water doesn't boil off or freeze solid all the time.
And yet it strikes me, more and more often since I started doing this talk, that our perspective is limited. We can see out 10^25m and in 10^25 meters reliably; that's the width of our perspective. Even from that limited perspective we can easily see, from down here in my light-polluted backyard, at least two trillion possible sites for life besides the one we ourselves live on; and if we look at reasonable probability maybe its just 100 billion houses - only one in 20 - in our neighborhood. We know, from here on high, that there are four fundamental ways things interact: gravity, energy, decay and unity. We've only really been doing this for about four hundred spins around our star, the lifespans of four Japanese centenarians; but even with unaided eyes, before Galileo built a telescope and was able to make out his Earth-shattering details on Saturn, Jupiter and the moon, we can see our immediate neighbor galaxies. We see this immense vastness in either direction. Going inward, we know most of matter is empty space, and going out we also see most of the universe is empty. And even then the number of things in that empty space is enormous.
So this switch in perspective is what's so spectacular. I can see the top of Mount Umunhum from my employer: A short 25 mile drive from here out on the edge of the Bay to the top of the Santa Cruz mountains, less than half the distance from here to the halfway point of the atmosphere. On a clear night I can see out over top of the mountain to the moon, at ~240,000 miles, and next to it Venus and Mars (at least tonight), which are on opposite sides of the Earth's orbit. Next to them but still in view, like housing developments crawling up the edge of the mountains, are a bunch of local stars between 10-40 light years away, like Sirius. And because of the orientation of the Earth at this time of year we're starting to shift from our view in toward the Orion arm of the Milky Way galaxy outward to the north pole of our galaxy and the deep space beyond, into our local galactic cluster, visible as galaxies in Virgo, Ursa Major and Leo (including M81 and M82), which extends outward from Andromeda to the edge of the Virgo supercluster 100 million light years away. In geographic terms we're looking at downtown from tall building somewhere just at the edge of the urban density, slowly turning east toward the country, where we can see much much further, where we can see other cities out there in the countryside. And in geographic terms, while we know there's a whole bunch of other local territory we can see - we can see into the Central Valley, or the tops of the Sierras on a clear day, but not into Nevada, which we know is there because we've gotten postcards - there is so much locally to get your mind around that a lot of people never think about a world any bigger than northern California. A lot of people think northern California is all there is.
And so when I consider the vastness of that space, both up and down, both to the neutrino and out to the quasars dying at the edge of our vision 13 billion light years - and at least that many years old - from us, and the number of years we've been contemplating this space, I marvel at the arrogance. Many of the people I grew up with in small town Alberta used to ask me why I would want to move to San Francisco; they also had coffee houses in their small town, for example, and shopping centers and art galleries and jazz clubs too, just like California. Well yes, and much else in common, including a similar view of M81 and the same scope of efficiency of gravity, electromagnetism, the weak and strong forces. There are neutrinos in both locations. Both of them are made of quarks. They are the same distance to the Andromeda galaxy. But the trees are different; the flora and fauna, the microbes and geology, the weather and architecture and civil society are also very different. So different that many days I wondered at how they could be made of the same quarks.
What we've done here in our short time on this planet is describe the immediate composition of the stuff around us, and named what we can see looking over Mount Umunhum. We've cataloged a few of the flowers and plants and bugs crawling around with us on this space rock underneath our small humid dome. We should remember that. Our little space rock looks big from down here but it doesn't take long to get to the edge of it, and we have barely scratched the surface on our own rock, never mind the rest of it. In the grand scheme we're small-town people proudly asserting we've got everything figured out, that all trees are cottonwood trees and all spiders are black widows, while larger and more fundamental forces pass over unseen and unbidden. Perhaps its time we grew up a little.