The Thing about the Arrow of Time

The odds are that you have a reasonable grasp of basic statistics. It seems like it’s practically a requirement these days; so many things are communicated in terms of percentages, chances, likelihoods, probabilities, and averages (not to mention medians) that you kind of just absorb it naturally. At least I think you do, on the average.

The whole universe can be described statistically. The whole second law of thermodynamics (aka entropy) is the one that says when you have a cup of hot coffee in a normal-temperature room, the coffee will cool off so you can drink it — and eventually reach the same temperature as the rest of the room. My friend Dan sometimes points out that this is a statistical law, and once in a great while (“great” meaning probably much longer than the age of the universe itself), the coffee might get hotter while the room gets cooler. Statistics allows for anything to happen, even if it’s unlikely.

People act on the basis of statistics all the time, and they feel things on the basis of statistics too. How many people are more comfortable riding airplanes because it’s well-known that travel by air is much safer — statistically — than by car? I don’t know precisely what the answer is, but I’d estimate it’s somewhere around 75% at least. I mean, go ahead, prove me wrong!

That’s another thing about statistics, though; that provability thing. I suspect the more you know about statistics, the more removed you think the real world is from the world of logic and geometry, where things can be proven. Even basic scientific experiments — things we base important actions on, like the design of bridges and how we’re going to cure illnesses — aren’t really “proven,” they simply indicate that statistically, the chances that the conclusion is wrong are less than some limit. Sometimes it’s 5%; sometimes it’s much less. Theoretically that means that some of the time, everything is going to turn out differently.

But we mostly don’t act that way. We act like a statistically significant result is about the same as proof, and we move on from there. But here’s the thing; if you string together a set of probabilities, you get a different probability about the overall end result. Don’t worry, I’m not going to go all mathy here. But it’s fun to speculate about what could happen within the realm of statistics.

There’s a cosmological theory that’s a corollary to the “black hole” that Stephen Hawking theorized — it’s called a “white hole.” This one wasn’t Hawking’s idea; Igor Novikov first came up with it in the mid-1960s. The key thing about a black hole is that stuff can go in, but nothing can come out. A white hole is the reverse; nothing can go in, but stuff can come out. What kind of stuff, you ask? Where does it come from if nothing goes in? Well, the physicists have one answer, but statistically, there are more storytellers than physicists (I’m 85% sure of it). And to a storyteller, it’s obvious what comes out of a white hole. Absolutely anything. It could be a giant unicorn, or it could be an ordinary cup of coffee in an ordinary room. One that gets hotter while the room cools.

There’s another odd thing about entropy. It has to do with the arrow of time, an idea from Arthur Eddington about a century ago in his book The Nature of the Physical World. He pointed out that things he studied in physics could generally work in either “direction” with regard to time. He visualized time as an arrow that could point either to the future or the past, arbitrarily. If you filmed a ball bouncing, you could play the film forward or in reverse, and you couldn’t tell which was which. But if you kept going, and the ball’s bounce was lower each time (because of entropy), then you’d see which direction the arrow of time was pointing. But he couldn’t find anything except entropy — statistics! — that was an actual, physical manifestation of time. In a way, the only way we know the difference between past and future is that entropy adds randomness over time.

We can remember the past, but not the future — we desperately want to know more about the future, though. We forecast, predict, plot trend lines, estimate, and foretell. Statistically, some of our predictions come true, even in a future that’s — again statistically — more random than the past. And maybe that’s the thing about statistics; they’re in part an attempt to make sense of what looks at first like randomness.

That’s a poignant thing about life. If we’re lucky enough to begin childhood in a stable and safe environment, we traverse the arrow of time coping with more and more randomness. Chaos. The people and things we love slowly fall away, becoming undetectable parts of an undifferentiated whole. The melancholy of the autumn time always lies ahead. As we age, the differences we perceive stand out more brightly, more vivid in the fog of life. We can see, eventually, how statistically unlikely the gleanings of life are. We know the alternative better, so we value them more. Ninety-three percent more, on the average.

Tales from the Forest

Magpie was puzzled; she’d been swooping over the river for quite some time, but hadn’t seen any trace of either Otter or Muskrat. They were usually romping around in the water or sliding down Otter’s mudslide, but today they were nowhere to be seen. Beaver’s house was closest, so Magpie flew over there to see if anybody knew what was up.

Beaver wasn’t home either. “Hmm,” said Magpie to herself, “very strange coincidence. Squirrel probably knows what’s going on.”

But Squirrel wasn’t home either. Neither was Fox, Raccoon, Owl, or Hare.

By this time, Magpie was getting considerably vexed. “This is ridiculous,” she muttered, “the chances of everyone being away from home at the same time — especially at this time of day — is at least…let me see…four hundred and twenty-seven thousand, nine hundred and three to one. That’s if they’re just acting at random, of course. If they’re acting together, it’s much more likely — but then the chances that they’d be acting together, well, those are even higher.”

“Nonsense,” said a voice from overhead. It was Coriolus the goose, flying even higher.

“What do you mean, ‘nonsense’?” asked Magpie. “It’s perfectly obvious that to have that many individuals suddenly act in concert is quite unlikely, and the chances…”

“Not if they’re already connected,” honked Coriolus. “If they can be represented as nodes in an existing communication network, then acting together is simply a function of the…”

“Oh, you’re right,” said Magpie. “I hadn’t thought about that.”

“Moreover,” said Coriolus, in the ‘I’m smarter than you’ way he sometimes talked. It annoyed everyone, and Magpie wasn’t any different. “Moreover,” he said, repeating himself with an angry glance at the narrator, who had taken so much time explaining that Coriolus felt the continuity of his extremely erudite analysis had been disrupted. This was too much for Coriolus, who had by this time lost his train of thought. “Will you shut up!” he honked.

“I wasn’t saying anything,” said Magpie.

“Not you,” said Coriolus.

“Coriolus,” said Magpie “there isn’t anybody else here.”

“That’s not necessarily the case,” said Coriolus. “If you accept the conjecture that a given universe can be completely simulated in a computer, or something like a computer, and that we are all aspects of that simulation, then you have to agree that it’s more likely than not that we are exactly that; simulations. And if we are, then there must be someone else here — the simulator, so to speak.”

“What are you talking about?” asked Magpie.

“It’s simple,” said Coriolus, smiling with that little half-grin that told everyone who knew him well enough that he was just about to launch into a long technical explanation that was anything but simple. “Cut that out” he honked.

“Are you sure you’re feeling okay”? asked Magpie, who didn’t really care so much, but thought that feigning empathy would be an effective gambit for redirecting the conversation to anything else besides whatever nonsense Coriolus had been about to start. “Hey,” said Magpie, “maybe I do know what you’re talking about.”

“You mean about the Bayesian statistics behind the probability calculation about everyone in the forest — except for you, of course — acting together?”

“No,” said Magpie, “I mean about talking to the narrator. I think I get it now.”

“Good,” said Coriolus, taking care not to affect the air of superiority he normally would after convincing someone about one of his theories. “Oh great,” he said, rolling his eyes (which is, as I’ve mentioned before, a pretty good trick if you’re a goose), “no it’s not.” he finished.

“Narrator again?” asked Magpie. Coriolus nodded (which is a very simple trick if you’re a goose).

“Well sure, physically it’s simple,” said Coriolus, “but doing it at just the right time, with the precise angle of nod to communicate the nuances of your position, that’s a product of a superior mind.”

“You know,” said Magpie, “all I really want is to find out where everybody is. This has gotten a lot more complicated than I really counted on.”

“Well just look what we’re flying over right now,” said Coriolus, looking down. Magpie looked down too. They were over the farm, and there was everyone, sitting or standing around long tables set up in the barnyard. “It looks like they’re all there. Let’s go down and find out why.”

“Good idea, said Magpie. They swooped down and landed in the barnyard; Coriolus on the ground; Magpie on a fence just right for roosting.

“What’s everybody doing here?” said Magpie to everyone. To her surprise, everyone started talking at once. Everybody was explaining a different reason why they happened to be in the barnyard all at the same time, especially at this time of day.

“Well what do you know,” said Magpie to Coriolus. “Sounds like everybody just got here at random after all. What are the odds of that?”

“Elementary,” said Coriolus. “Four hundred and twenty-seven thousand, nine hundred and three to one, of course.”

Eighty-five percent of all statistics are made up on the spot.

“Cut that out,” honked Coriolus.

Words like words alike

Similaries, similarities.

The words compose and comprise are easy to get mixed up. Or maybe it isn’t? If you go by the “first” definitions of both of these, then you’d be careful to use “compose” to mean a whole that’s made up of parts. “The jury was composed of twelve local people” — and you’d use “comprise” to mean the parts that make up the whole. “Twelve local people comprised the jury.”

In practice, “comprise” is often used to mean “compose”, as in “the jury was comprised of twelve local people”. Now, this is a very popular pet peeve, and it’s not unusual to see or hear “comprised of” criticized as a mistake. But it really isn’t! “Comprise” has been commonly used to ALSO mean “compose” since at least the 1700s. Seems to me that’s long enough to make it qualify as “usage.”

Then there are words that get mixed up because (I bet) their spellings are very similar and it’s hard to remember which spelling is the right one. I think most people understand the difference between a “roll” — either something rotated around a central axis or a hunk of bread you get with dinner — and a “role” — a part you play in a drama or even at work (which is often sort of the same thing. But you see “role” spelled “roll” all the time. Just a spelling thing, not confusion between the two meanings, I think.

“Their” and “they’re” is the same as “roll/role” — it’s a spelling error. After all, those contractions like “they’re“ and “it’s” can be elusive, especially when you were more interested in what was going on outside the window than the lesson back in fifth grade.

But then there’s “farther” versus “further”. “Farther” means physical distance, and “further” means more progress in anything BUT physical distance — when you go farther into a cave, you’re exploring it further. These are often confused, and I don’t think it’s just the spelling. In this case too many people were looking out the window, not in fifth grade, but probably in about seventh or so.

Then there are word confusions that might be spelling, but also might be lack of understanding of the words. I’m not sure which problem it is when “principle” (which is a rule or idea) is confused with “principal” (which is a person in charge). And this one seems an obvious one to internalize in school — every school seems to have a “principal” who is a person — and as a person, the principal could be (but seldom is) your pal.

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