Logarithmic
A Celebration of Numbers and Time
by WK Adams
Foreword: this essay-ish thing was inspired by a wonderful (and long) Kurzgesagt video that you should check out if your mind is blown by big numbers.
One thousand.
I want to show you something.
Let's pretend that each word I write here takes us back a thousand years in time.
At the word “something,” we entered a time before written language. If it seemed like it happened fast, allow me to introduce you to the concept of deep time.
We're approaching sixty words. At sixty-four, we'll reached some of the oldest art that we know of.
Seems like it went by quickly, doesn't it?
Therein lies the difficulty in explaining deep time. We're talking about times so long ago that human minds just kind of go fuzzy trying to process them. We're taking steps a thousand years long. If you could take steps this large through time, your first step would see you as a subject of Genghis Khan, witnessing the invention of the saddle stirrup. Another step would put you in the last days of the Roman Empire at its largest, before it would be split in two. One more step, and you may very well be in a place where humans didn't know how to work with iron.
Even this explanation falls short. Maybe this will all become clearer as we go on.
We are now two hundred thousand years in the past. A hundred thousand more remain until we reach the point where we diverged from our most recent common ancestor species, Homo heidelbergensis. Every human who has ever lived at this point was born in - and has never left - Africa. In fact, as we keep going, we're finding ourselves increasingly outnumbered by that ancestor species, as we haven't yet outcompeted the other hominids.
Feel like I'm stretching this out a bit? Well, I am. Don't worry, by the end of this sentence, we'll reach our first landmark in time: the first anatomically modern human.
Of course, that means we have a lot of time to fill at our current pace before the next significant moment in the evolutionary road that led to us. We'd need another four hundred words to reach Homo heigelbergensis's beginning, at which point I'd need another fifteen hundred words to reach the dawn of their ancestor species, Homo erectus. I could, if pressed, fill that many pages with musings on why time is so long, but neither of us would enjoy the wait, so once we get to four hundred thousand years in the past, let's multiply our speed ten-fold.
Ten thousand. 400 thousand years in the past.
We are now moving at ten thousand years per word. A single step this far from the present day would land you in a time when wooly mammoths were still quite plentiful. Going back this far in history presents us with two new problems: margins of error, and obscurity of evidence. The older a thing is, the less likely it survives the passage of more time. Knowing for certain what we're seeing and when it came from becomes harder.
For example: we are now 1.31 million years in the past. Homo erectus will be around for 700,000 more years, having been around for 600,000 already. With every word in this sentence, thirty thousand generations of our hominin ancestors live and die.
We have pieces of a little more than 40 individuals from that entire time period. If spaced evenly from each other, they'd have 32,500 years between themselves.
This presents a unique perspective. Let's say you have a fossil that is 32,500 years old, to a one percent margin of error. How many years off might your estimation be?
325, in either direction. That's the timespan between taking one trip in a sailing ship and another in a star ship.
Oh dear. It seems I got carried away. I meant for us to witness the first Homo erectus, but we overshot our destination in time by about 600,000 years. That's just how tricky it is to ponder deep time. No matter what level of zoom is used on this chronological microscope, the small and the large are never both visible at once.
We are now 2.6 million years in the past. The Australopithecus genus, another set of steps behind on the path that leads to modern humanity, will flourish in Africa for another 1.9 million years.
Here, we've zoomed out on another scale: taxonomy. We've moved one level up, from talking about species to genuses. It is a natural consequence of taking bigger steps. Ten times the time, ten times the number of accumulated changes.
Which means that while Australopithecus lived half again as long as Homo, we have a tenth the time to witness them before they're gone. By the end of the next paragraph, we'll have reached a point beyond their origin.
This is what numbers do for us. We may be no closer to truly interacting with something so vast as 4.5 million years (and everything that existed during those years), but with enough time to sit and think, we can figure out how many steps it would take to cross that vast gulf, if our steps were large enough.
It's been 4.8 million years now. We're far enough back that our ancestors look more like apes than humans. At this pace, we'll reach Sahelanthropus, thought to be the first of our family tree to spend time walking on two legs, in about 100 words.
It's possible that you're getting used to this pace. Humans are insanely adaptable; to wit, when we changed our literary speed, we went from moving at peak human running speed to that of an airliner about to soar into the sky.
But I don't want you to get used to anything, so let's set our sights on something far more distant in the past: the last dinosaur that ever lived. We're 6 million years along (hello Sahelanthropus), and the dinosaurs went extinct 66 million years ago. Which means at our current pace, we only need…
6000 more words.
Hmm.
Well, I could keep talking about our protohuman ancestors until we get there. We'd reach the first hominid, the common ancestor of chimps, gorillas, orangutans and humans at 17 million years in the past, so, about…
1000 more words.
This will take too long. Mind if we hit the gas again?
One hundred thousand. 6.7 million years in the past.
With humanity’s ancestors now walking on all fours, we increase our speed ten times again, and we're moving at a hundred thousand years per word.
Analogies are beginning to break down. Our last acceleration moved us from the fastest runner ever to a Lamborghini at top speed; this one transforms the Lamborghini into an SR-71. And just so you don’t forget: our metaphorical Usain Bolt’s first step took us back to a time when the hot European fashion was crusading the holy land. When we accelerate again, we’ll be transforming our SR-71 into a Space Shuttle. Still, we’re already going so fast already that these numbers are starting to lose their meaning.
For instance: yes, I just did it again. While I was blabbing on about planes and rockets, we passed the earliest hominid. We’re now in the realm of hominoids, which means our distant cousins, the monkeys come into the picture.
Still, even at this rate, I have another 400 words to fill before we get to the dinosaurs, and I have a serious problem on my hands.
100,000 years is just too big a time for me to summarize. So many things can happen in a hundred thousand years; how do I pick just one? It’s not like the…
…let me check…
It’s not like there was nothing that happened in the Rupelian Age, which we entered at the beginning of this sentence. It went from about 28 to 34 million years ago, roughly six million years, but it took me 400 words to describe the steps through the Homo genus. There’s no way I can-
What’s that? We’re about to pass the Rupelian Age?
What do you mean I passed it two sentences ago?
Time is weird. It’s too big and too small. When you’re really trying to get a picture of what 13.8 billion years of existence have been like for everything that…exists, you can take in big stretches of time, or you can take in enormous stretches of time. While you were reading, the Priabonian Age passed; the first time I mentioned it to you, we’d already passed it.
And while I was telling you about the age you missed, another one came and went. Even still, by the end of this sentence, we’ll still be 192 words away from dinosaurs. If I spend all those words telling you about massive amounts of time that I have very little information on, you’re going to get used to those big time scales. You’ll start and stop thinking about ages - which span millions of years - at the end of the sentence.
And we can’t have that, so let’s hit the gas again.
One million. 51.7 million years in the past.
I’ve been resisting “going pro” up until now, but I suppose I should mention that scientists have already divided time up into relatively neat chunks like I’m doing right now, except…you know, better. Each of their timescales, which they’ve handily named (age, epoch, period, era, and eon) also roughly multiply the number of years they contain by ten with each step.
Ah crap, got carried away again. I missed the Cretaceous asteroid by 61 million years. At the rate I’m going, by the end of this sentence, the entire Cretaceous Period will be over. You know, the time that has all the dinosaurs everyone knows: T-Rex, Triceratops, Velociraptors…you know, Jurassic Park-type stuff. Except we’re not in the Jurassic Period.
We skipped right over it. We’re in the Triassic Period, when everything that lived was immensely strange. You’d swear some of what you see are dinosaurs, but we’re 200 million years in the past. All of Earth’s continents are smooshed together, and most of it is way too dry for dinosaurs to exist yet.
So, full disclosure, this has been more of a stream of consciousness than a scientific exercise. If anything, I’m demonstrating math more than I am science. To me, the concept of numbers themselves is astounding.
We’re pattern-matching creatures. We noticed the sun goes up and down in a rhythm, and we called it a day. We started hunting and foraging, figured out that some days were better for that than others, and we came up with years, which had both those kinds of days. We didn’t know what caused the passing of days and years, but when we figured that out, we matched the doings of the universe to the concepts we invented.
Those concepts are helpful, sure, but the universe isn’t obliged to be convenient to us, and that extends to the understanding of time. I’m not even talking about relativity here; that’s a whole other ballgame.
I love thinking about timescales this way. I wanted to share this love with you, dear readers, but I don’t know that I can really do it justice, and I don’t think that’s entirely my fault. This whole concept is just too big. To be able to truly understand the mind-boggling reality of time, one must shed the idea of days, years, centuries, millennia, or even megayears.
Yes, that’s a thing. We’re going so fast, we have to use the metric system, because we’re running out of words made up by old English guys. (fellow Americans: adding the mega- prefix to a word multiplies it by a million).
And it’s still not fast enough to see everything. If you’re a science fan like me (and not a real scientist), now that we’ve left the dinosaurs in the dust (and passed all five mass extinction events), the next most logical place is the origin of life itself. And as you might have guessed, I have some bad news. Yes, you guessed it: this is going to take forever.
It’s possible that the first life on Earth originated 3700 million years ago, a point we wouldn’t reach, even at the godlike speed of a thousand thousand years per word, for another 3100 words. That’s actually the best-case scenario: it’s possible that life started five hundred thousand thousand years before that. At that speed, we’re not even halfway through this stream of consciousness.
Ten million. 621 million years in the past.
I’m going to take another cue from the real scientists and not use the word “billion.” Writing this has helped me to understand why they refrain from it when talking about these massive timescales.
Numbers are wonderful. Think about the ones you grapple with on a daily basis: 24 hours in a day, 10 dollars for a decent meal at a restaurant, 71 inches in height, 85-year average lifespan. All of them take concepts that should be too complex for a three pound, wrinkled collection of proteins to even grasp - much less quantify - and bring them into relation with each other.
But they can’t put everything into human perspective. Not fully.
It’s been a minute since I came up with a metaphor to explain our acceleration, but what could I possibly say to communicate that? If I tell you we’re at 0.002 percent the speed of light (the speed of light really is the only comparison that makes sense at this scale), what will that even mean? It doesn’t illustrate the immensity. If I explain to you just how much faster we’re going than we were when we started, we’ll almost certainly lose sight of just how vast those smaller steps already were.
If I had forgotten to count the first six words of this essay, at the speed we were going, I’d have passed over all of recorded history. But if we had started at our current speed, forgetting to count a single word could bypass everything that could be mistaken for an early, hairy human.
But paradoxically, this far in the past, that kind of mistake would hardly matter. We’re still fifty to a hundred words away from the origin of life. Probably. Maybe. The evidence we have to work with is beyond obscure. There are no fossils of 3500 million year old single-celled organisms; we only know how many of them there are by the concentration of gasses they left in the rocks when they died.
If I pull the brakes on this rhetorical time machine now, at 3900 million years in the past…
Or now, at 4100 million years…
Or now, at 4200 million years, I could still be missing the origin of life by tens of millions of years in either direction…if I’m lucky enough to be that accurate.
Maybe that’s the best, most awesome, most terrifying way to sum up what it means to contemplate eons: that doing so requires you to say that getting things wrong by a thousand thousand thousand times as long as your planet takes to go around your star 365 times is only a minor error, all things considered.
Stop. 4991 million years in the past.
I was too slow on the brakes. I not only passed the beginning of life; I passed the beginning of Earth.
I’m not going to accelerate again. Our scale is broken. At a hundred million years per word, we'd reach the beginning of everything in 100 more words, and then we'd have the unknowable, infinite time before everything - including time - ever existed.
What would I be communicating at this point? Who could tell at a glance the difference between a million and a hundred million years, when all you can see of Earth is a ball of lava in a fiery dust cloud?
Not that this should detract from the incredible achievement that is the number. The humble digit has given us the beginning of a grasp on our history and our future. It is the most concrete concept humans have ever put to stone, papyrus, page and pixel. Add enough of them together as you reach for understanding, and all of existence becomes trivialized, compressed into one’s brain like a plastic bag somehow filled with a warehouse full of clothing.
When I started writing this, I wanted it to be a fluid, digestible glimpse at the history of our world. That obviously didn’t work out, but I think I prefer how it turned out. I love being reminded how much depth there is in everything, how much knowledge can still be gained, even about subjects that seem so self-evident like numbers and time. Asking what they are so easily leads to me asking what we are, and if the rest of the universe is as obsessed with knowing how much.
Does the universe “see” everything within itself? Does it count along with us?
Maybe it doesn’t. Maybe these rhythms, these patterns, these repetitions are nothing special to the rest of existence. Take in enough of them together in one glance, and even we fail to notice the difference between one set of a hundred million years and the one that came before it.
But that’s beautiful, knowing that we, these tiny little hairless apes, managed to take in the infinite and the boundless, then looked at our fingers, and found the connection.
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