The Consolation of Big Numbers: The Long View

[Let’s back away a few trillion steps from our world’s tragedies, comedies, inspirations, follies, triumphs, losses, meaningless accidents and meaningful enterprises, to muse upon the otherworldly. It gives me some tranquility at a time when tranquility is hard to come by. To do so, I will have to venture far into Nerdland.  If big numbers leave you cold, stop right here.]

Zillions of Planets Akin to Ours?

While here on our own planet things are lurching from bad to worse, I was comforted to hear the news of nonzero odds for the habitability of  several planets in the “nearby” solar system TRAPPIST-1.  Located a mere 40 light years from us, these planets are rocky, not too big and not too small, not too heavy, not too light, and at a distance from their sun that liquid water could exist on them, and harbor Earthlike life forms. Their distance from their sun is smaller than the orbit of Mercury around ours, but the star is so cool—an “ultra cool dwarf”—that three of them are evidently situated in the “Goldilocks Zone” amenable, with the presence of water, to life as we know it.

[Trivia: the Trappist order of monks are noted for their beer-brewing capabilities. Does this tell us anything about astronomer refreshments?]

TRAPPIST-1 discovery

Enthusiasts of exoplanets, exobiology, and astrobiology are salivating over the prospects for getting more out-of-this-world news about these planets once the James Webb telescope, scheduled for launch in 2018, is up and running its supersensitive instruments.

The probability of life on these particular planets is pretty low, but that’s not the point.  The point is, that if three of the TRAPPIST-1 planets are at all friendly to life at such a “short” distance from us, then we can be pretty sure that there exist tens of thousands, if not hundreds of thousands, of similar systems in our galaxy alone—population 100 billion stars, plus or minus some tens of billions.*

The probabilities for life elsewhere in the observable Universe (population about 2,000 billion galaxies per the latest estimate) just got a whole lot better. It would even seem that the probability for intelligent life elsewhere in the universe is way above zero.

Whole big awesome number of galaxies

The News of Trappist-1 Is  Consoling, Scary, and Sad

It is consoling to think that, very likely, We Are Not Alone. Somewhere out there are/were/will be creatures such as we, who are/were/will be, speculating about the existence of Us. But it is sad to think that, on account of the speed limit of light, the vast distances between stars and galaxies, the fact that space is expanding faster and faster, and the unlikelihood that the existence of other life will overlap with ours in time, even if we could cover the distances instantaneously, the chance of ever communicating with other intelligent life forms is vanishingly small. We as a biological species are almost certainly doomed to extinction in less than half a million years, or less than half a day if Donald Trump has a temper tantrum at a tense moment.

And even if we heard from Them, should we answer? The fate of Native Americans at the hands of their European conquerors should give us pause. (Many descendants of those  conquerors now believe America to be their God-given right. It could be a mistake to assume that the morality of distant aliens would be much kinder.)

A signal from an alien civilization could be the equivalent of a fishing hook they could use to reel us in for a banquet.

Realizing the extreme unlikelihood of communicating with other intelligent life in the Universe, in our or any human lifetime, leaves a gap in the soul which no religion fills.   But that sadness is joined by the sense of wonder that we, or they, even exist. Even can exist.

A Feast of Big Numbers

The discovery of the TRAPPIST-1 system got me to considering not only exo-life, but also the incomprehensible magnitude of the cosmos, and moreover to considering just how extraordinary it is that we even know about the incomprehensible magnitude. That we have any grasp of how huge our universe is (and how huger the multiverse might be)—how can it be? (Einstein: “The most incomprehensible thing about the universe is that it is comprehensible.”) (More cool Einstein quotes  here. )

First off: how come the stars are even visible?  Look up at night and you see a lot of stars, but I went out to view the night sky not long ago and had a Neil de Grasse Tyson moment—for me, a new thought: how amazing it is we can see any objects at such unfathomable distances.  I had come to take it for granted, but . . . We can, with the naked eye, see stars many trillions of miles away—some of them thousands of trillions.

How can they be bright enough that we can see them? OK, they’re big, we know that. Our Sun’s diameter is 106 times that of Earth’s, and the largest stars are more than a thousand times the Sun’s diameter. (Check out UY Scuti .  Where do even the not-so-big ones get so much energy? Fusion, of course, but fusion on a mind-boggling scale.

Which brings us to the big number which has lodged inextricably deep in my memory: 600 million. That is, 600 million tons of hydrogen fused to helium each second in the heart of our Sun. The Sun has been radiating for about five billion years and is slated to go for about five billion more at about this rate. Our Sun, just an ordinary star. Wow. In an old-fashioned sense, awesome.

Paradoxically, many of the most massive, brightest stars—hundreds of times the mass of our sun—burn far more furiously and live shorter lives, meaning some ginormous stars live for less than 10,000 years. But these Live Fast, Party Hard celebrities of stellar evolution get a lot of attention—they are why you can see stars 10,000+ light years away with the naked eye. In between are hosts of dimmer stars we cannot see unaided.

A Sense of Proportion: What is a Trillion, Anyway?

Forget TRAPPIST-1, there is a still nearer system around Proxima Centauri, the closest stellar neighbor to our solar system, that includes a candidate planet with a chance, albeit slim, for supporting life.

How close is close? Proxima Centauri is about 3.5 light years away. A light year is about 6 trillion miles, or 10 trillion kilometers (I’m using very round numbers here to simplify the calculations, but when it comes to cosmic dimensions a variation of 10-15% is a trifle, and an order of magnitude is not far off from reality). So, Proxima Centauri is about 3.5 x 6 trillion = 21 trillion miles, or 34 trillion kilometers, away.

A trillion is a big number. It’s hard to convey just how big without using an analogy from the physical world. From the haystack of all the other analogies that have ever been proposed, I now draw one: the human hair.

A human hair is about .1 millimeters in diameter, depending on race. (Actually, globally .07-.08 mm is closer, but we’re doing ballpark numbers. . . . )

So how wide is a trillion human hairs laid side by side, with no gaps in between?

10 miles? 100 miles? 1,000 miles? 10,000?

Try 60,000 miles, or 100,000 kilometers.  You’d be close. Twice around the earth, and then some. The width of a trillion human hairs. (Ronald Reagan did much the same thing with a stack of dollar bills, but I like human hair as more organic.)

Walking to Proxima Centauri: Out of the Question?

How long would it take to walk the distance of a light year (6 trillion miles) at a rate of 3 miles per hour, walking without interruption 24/7? That’s a typical walking speed, although difficult to maintain for more than a few hours at a stretch.

There are 8,760 (plus a small fraction) hours in a year, so at three miles per hour you walk 3 x 8,760 = 26, 280 miles in a year. About once around the Earth, less than half the width of a trillion human hairs. Divide 6 trillion miles by 26,280 miles/year and you get roughly 228 million (228,000,00o) years.** You would have had to start walking before the Age of Reptiles to cover six trillion miles: one light year.

With the nearest star, Proxima Centauri, 3.5 light years away, to reach it would take 3.5 x 228 million years, or only 798 million years walking—less than a billon years! Doesn’t seem that farfetched, does it?

Pragmatic Obstacles

However, you would have an engineering problem: the building of a pedestrian bridge to Proxima Centauri.  Even if you had the technology, you would have no laborers to implement it, since animals did not come out on land, much less the air, even much less outer space, until about 375 million years ago. If you waited around for them to arrive and get them cracking on the bridge project*** and then wait for completion (another 200 million years; it would have to be built on Earth, spooling around the planet, then launched toward Proxima Centauri), you would end up having to sprint the distance to Proxima Centauri at a pace faster than Usain Bolt’s top speed, without rest, in order to arrive there by 2017.

If you took the return trip at a more leisurely pace, taking naps and breaks to suck up bits of space dust every so often, by the time you got back (say two billion years) there would be no one around to congratulate you, because by then the Sun would have gotten hot enough to kill off all life on the surface of the Earth (BTW, don’t blame the Sun heating up for present-day climate change; it’s far too slow to account for more than a tiny fraction of what we are doing to ourselves in a matter of decades). Heat-tolerant robots might still be hanging around, telling each other extinction jokes (year 2,000,000,000 A.D. robot humor: what’s more extinct than a cockroach? Mount Kill a Man Jaro), but I think they would present a very awkward reception.

Beyond Proxima Centauri: the TRAPPIST-1 system that has exo-biologists dancing in the observatories, is more than ten times further away, and the other side of the Milky Way galaxy is more than 2,500 times further than that.  Multiplying the latter distance by another 100,000 gets you to the most distant observable galaxies. . . whoa! Now we’re talking  a Very Long Walk.

Thinking at cosmic scales calls for a sense of Absurdity as well as a sense of Humility

If the Proxima Centauri thought experiment above is absurd, then it’s in keeping with the vastness of the Universe in both space and time. Even the “closest” stellar neighbors are almost inconceivably distant, absurdly so.  Humbling enough to make politics somewhat irrelevant in the grand scheme of things. I count that as a good.

——————-finis——————-

 

*The great majority of stars are either too big or too small, or bound within a binary or multi-star system, or too close to other stars (as in the center of galaxies) to have much chance of boasting life-friendly planets. Still, there are a LOT of candidates: a feast of big numbers.

** This number is actually smaller than I was expecting, but I computed it three times over in three different ways and came up with about the same answer. If I missed by an order of magnitude, please correct me ASAP.

*** If Jurassic Park is any guide, getting cooperation from the smartest dinosaurs—velociraptors—to build your bridge, could be very touch-and-go.

 

 

 

 

 

 

 

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