Thorns, odds, and the impossible

A few years ago I was walking on a disused path in some woods near where I live, when I noticed a small branch that seemed to have attached itself to my foot. When I looked more closely, I saw about an inch of thorn sticking up through my boot just in front of the ball of my foot.

This was a genuine official hiking boot with about an inch and a half to two inches of combined Vibram outsole and orthotic insole, and a Gore-Tex and nylon upper. Needless to say, I was dumbfounded. How had a thorn managed to penetrate all that? More to the point, how had it penetrated my foot without my feeling it?

I pulled out the thorn; it was easily four or five inches long and almost a quarter of an inch thick at its base. A honey locust, I figured, although I hadn’t seen one with thorns quite that big. As I tossed the branch away from the path, it occurred to me that I’d better get a look at my injury before too long. A little way further up the path I found a convenient log, sat down, and gingerly removed the shoe, fully expecting to see a slowly expanding patch of red where the thorn had come through. When I looked, I realized why I hadn’t felt anything.

The damned thing had passed precisely between my big toe and its neighbor as far back as it could without hitting flesh. When I say precisely, I mean there was no evidence of its passage whatsoever — not blood, not broken skin, not so much as a minor scratch.

What, as they say, were the odds of that happening? Well, I maintain that, since it had actually occurred, the odds must have been 100%.

You could calculate the odds as a hypothetical exercise, taking into account such variables as the average number of dead branches small enough to go unnoticed on a disused path, the percentage of those likely to have huge thorns, the probability of such a thorn lying at the precise angle required to use the force of a footfall to penetrate a sturdy shoe. You’d also have to take into account the width of the path, the length of my stride, the size of the shoe, the total area of the sole, and so on. Then you could come up with some number, which would surely be vanishingly small.

And yet, it happened. You might be familiar with the concept of the black swan, popularized in a book of that title by Nassim Nicholas Taleb. I’m not interested in the failings of statistics which do not take all of the significant variables into account; it may be true that probability calculations can be improved by using the proper data. My point is that even when all knowable variables are taken into account, you can still end up on the wrong side of the conclusion.

Why is that? It’s simple. Statistics are descriptive, not predictive. They describe in detail past events in similar contexts to the one you’re interested in. In the end, any conclusion you draw is based on inductive reasoning, which by its nature is vulnerable to data gaps. When an event actually occurs, such as my adventure with the thorn, it becomes data, and statistical inference is irrelevant to it. The question, “What are the odds of that?” is pointless.

Does that mean that judging risk on the basis of probability is useless? Not at all. But it is why the severity of a negative outcome is so important in the decision process.

If I have a 10% chance of spilling wine on my shirt, that’s not going to stop me from drinking some. But if I have a 10% chance of dying if I get Covid-19, that’s a different story.

Congratulations: the incredibly improbable you

You’ve made it this far.  There were never any guarantees, were there?

Take the Big Bang, for instance.  By all accounts, this event should have resulted in equal amounts of matter and anti-matter, and we all know what that means.  Nothing.  A big, fat zero.  You put the two together, and that’s what you get, so for physicists, the old chestnut of why there’s something rather than nothing takes on a whole new significance.  For some reason, after the Big Annihilation, there was this miniscule (comparatively) amount of stuff left over; that’s us, and all we are in and around.

Even so, a lot of different things could have happened from there.  The laws of nature could have been different.  If gravity was just a tiny bit stronger, no sooner would the universe have begun to expand, than it would have collapsed back on itself.  No time for matter to come together slowly, forming stars while waiting for the Great Dissipation of entropy.  Which brings up another thing: if entropy is a law, if everything ends up at the lowest, most uniform possible state of energy, why wasn’t that the case immediately before the Big Bang?  It could have been.  It should have been.  But it wasn’t; big chunk of luck for us!

Even taking all of that ultimate origin stuff as a given, it’s been no cakewalk.  You start with a bunch of protons and electrons whizzing about the fledgeling universe, but because it’s not uniform, some of them clump together due to our friend gravity.  Actually, enormous clumps of them, so huge the pressure pushes them into units composed of two protons and electron each: helium atoms.  It’s fusion, and lumps of it were happening all over.  Altogether disorderly and un-entropic.  Worse yet, all that energy causes flares, explosions, various ways of ripping it all apart, with the result that bits of stars are flung out, kind of like bits of fur in a cosmic cat fight.  More and more atoms are forced together, and eventually you get all the elements we are familiar with, including the ones we are composed of ourselves.  Stars have clouds of gases and debris swirling around them.  Sooner or later, the same thing that brought the original matter together to make the stars begins happening in the debris clouds.  They start clumping up, and some get rather large, at least by our standards.  We call them planets.

Of course most planets, even the ones in our own little star system, with the notable exception of Earth, are places completely inhospitable for life.  The bulk of them are like Jupiter, Saturn and Neptune, great gassy blobs with no place to even stand on, let alone survive.  Even most that are solid enough to stand on are inhospitable, like Mercury, or Venus.  Just our little Earth is perfect, and it causes us huge headaches on occasion.  True, in the incomprehensible vastness of the universe, there are doubtless others like it, maybe even some better equipped for life.  But they are in a minority.  Just our luck we’re here.

Although, to be honest, even Earth was no picnic for much of its history.  Our lump of clay is a little more than 4.5 billion years old, and for almost the first half of that, its atmosphere was largely nitrogen and methane.  Don’t get me wrong; it was buzzing with life, little anaerobic  specs happily bathed in the major component of our modern farts.  How they came to be is a matter still hotly debated, but we’ll leave that, and the odds of it happening, aside.  Earth was a very warm place, indeed.  Then, catastrophe!

Evil, wicked, cyanobacteria arose, making energy directly from the sun via photosynthesis, and giving off as a waste product — oxygen.  It was a deadly poison, and the tiny microscopic newspapers of the day were full of dire predictions.  Just kidding.  Had they been, though, their predictions would have been all too true.  It’s said that this was by far the greatest extinction event the world has ever witnessed, killing off almost all of the existing life, leaving only the new photosynthesizers and a smattering of the older bits near ocean vents and the like.  Even they had it rough, though, because the sudden burst of oxygen turned almost all the methane into carbon dioxide.  The Earth cooled, and remained encased in ice – snowball Earth – for millions of years.

Well, there it is.  They’re still with us; they’ve become all the rich and glorious diversity of plants.  From our perverse point of view, or course.  We are essentially what’s become of alien invaders wallowing about in their own waste products.

I can’t begin to tell you all the trials and tribulations that followed.  For the next couple of billion years, the Earth vacillated between toasty warm and crippling cold, and all the range between, each shift engendering a new catastrophe for whatever life had grown accustomed to the previous conditions, and a marvelous opportunity for those few misfits who had managed to survive in spite of it.  You really should check out some of the incredible trials and errors along the way: hard-shelled predators with razor like appendages; floating masses of jello; tiny diatoms whose gazillions of weeny skeletons form the vast limestone deposits of Earth.  But let’s cut to the chase.

What with one thing and another, bilaterally symmetrical soft-bodied creatures with internal structures of calcium carbonate evolved: the vertebrates.  I mean, anyone care to calculate the odds?  One major theory of the evolution of skeletons is that organisms found a way to sequester the deadly calcium in their environment, and that that eventually was pressed into service as the internal skeleton, providing rigidity and support for locomotion and other kinetic activities.  Talk about making lemonade from the lemons you’ve been given.

You may think that by this point, we are well on the way to the obvious: us and all the clever world about us.  Not so fast.

Although you could make a case that in such a changeable, unreliable world as Earth, it was just a matter of time before an intelligent, generalized creature like the primates would evolve, we’re still a long way from ourselves here.  Even today, there are hundreds of primate species, with hundreds more having gone extinct.  It is said that at one point, about 60-50,000 years ago, Homo sapiens was down to a breeding population of fewer than a couple of hundred individuals.  We’ve all been squeezed through a very narrow funnel, my friends, which explains why we’re so damned alike.

Think of it.  A species comprised of many thousands, culled to a couple hundred.  Most humans died back then.

But not your ancestors, or mine.  The odds against any one of us being here are astronomical.  Since then, of course, we’ve burgeoned to a population of something over 7 billion.  All the same, countless ancestral lines have gone extinct since the big crunch of 60-50k alone.

But not yours, and not mine.  At any point along the vast expanse of time, from the first flicker of life to now, your personal ancestor organism might have been one of the countless gazillions that died without issue.  Congratulations.

Now, about those horrendous odds you say you’re up against…