This is from The Sense of Style by Stephen Pinker. He is explaining the Classic Style of writing with reference to the astrophysicist, Brian Greene’s, explanation of the theory of multiverses. Both are eloquently explained at the same time.
Greene begins with the observation by astronomers in the 1920s that galaxies were moving away from each other:
“If space is now expanding, then at ever earlier times the universe must have been ever smaller. At some moment in the distant past, everything we now see—the ingredients responsible for every planet, every star, every galaxy, even space itself—must have been compressed to an infinitesimal speck that then swelled outward, evolving into the universe as we know it. The big-bang theory was born. … Yet scientists were aware that the big-bang theory suffered from a significant shortcoming. Of all things, it leaves out the bang. Einstein’s equations do a wonderful job of describing how the universe evolved from a split second after the bang, but the equations break down (similar to the error message returned by a calculator when you try to divide 1 by 0) when applied to the extreme environment of the universe’s earliest moment. The big bang thus provides no insight into what might have powered the bang itself.”
Greene does not tut-tut over the fact that this reasoning depends on complex mathematics. Instead he shows us, with images and everyday examples, what the math reveals. We accept the theory of the big bang by watching a movie of expanding space running backwards. We appreciate the abstruse concept of equations breaking down through an example, division by zero, which we can understand for ourselves in either of two ways. We can think it through: What could dividing a number into zero parts actually mean? Or we can punch the numbers into our calculators and see the error message ourselves. Greene then tells us that astronomers recently made a surprising discovery, which he illustrates with an analogy:
“Just as the pull of earth’s gravity slows the ascent of a ball tossed upward, the gravitational pull of each galaxy on every other must be slowing the expansion of space. … [But] far from slowing down, the expansion of space went into overdrive about 7 billion years ago and has been speeding up ever since. That’s like gently tossing a ball upward, having it slow down initially, but then rocket upward ever more quickly.”
But soon they found an explanation, which he illustrates with a looser simile:
“We’re all used to gravity being a force that does only one thing: pull objects toward each other. But in Einstein’s … theory of relativity, gravity can also … push things apart. … If space contains … an invisible energy, sort of like an invisible mist that’s uniformly spread through space, then the gravity exerted by the energy mist would be repulsive.”
The dark energy hypothesis, however, led to yet another mystery:
“When the astronomers deduced how much dark energy would have to permeate every nook and cranny of space to account for the observed cosmic speedup, they found a number that no one has been able to explain … : .00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000138.”
By displaying this number in all its multi-zeroed glory, Greene impresses upon us the fact that it is very small yet oddly precise. He then points out that it is hard to explain that value because it seems to be fine-tuned to allow life on earth to come into being:
“In universes with larger amounts of dark energy, whenever matter tries to clump into galaxies, the repulsive push of the dark energy is so strong that the clump gets blown apart, thwarting galactic formation.
“In universes whose dark-energy value is much smaller, the repulsive push changes to an attractive pull, causing those universes to collapse back on themselves so quickly that again galaxies wouldn’t form. And without galaxies, there are no stars, no planets, and so in those universes there’s no chance for our form of life to exist.”
To the rescue comes an idea which (Greene showed us earlier) explained the bang in the big bang.
“According to the theory of inflationary cosmology, empty space can spawn other big bangs, creating a vast number of other universes: a multiverse. This makes the precise value of dark energy in our universe less surprising:
“We find ourselves in this universe and not another for much the same reason we find ourselves on earth and not on Neptune—we find ourselves where conditions are ripe for our form of life.”
Of course! As long as there are many planets, one of them is likely to be at a hospitable distance from the sun, and no one thinks it’s sensible to ask why we find ourselves on that planet rather than on Neptune. So it would be if there are many universes. But scientists still faced a problem, which Greene illustrates with an analogy:
“Just as it takes a well-stocked shoe store to guarantee you’ll find your size, only a well-stocked multiverse can guarantee that our universe, with its peculiar amount of dark energy, will be represented. On its own, inflationary cosmology falls short of the mark. While its never-ending series of big bangs would yield an immense collection of universes, many would have similar features, like a shoe store with stacks and stacks of sizes 5 and 13, but nothing in the size you seek.”
The piece that completes the puzzle is string theory, according to which “the tally of possible universes stands at the almost incomprehensible 10 500 , a number so large it defies analogy.
“By combining inflationary cosmology and string theory, … the stock room of universes overflows: in the hands of inflation, string theory’s enormously diverse collection of possible universes become actual universes, brought to life by one big bang after another. Our universe is then virtually guaranteed to be among them. And because of the special features necessary for our form of life, that’s the universe we inhabit.”
In just three thousand words, Greene has caused us to understand a mind-boggling idea, with no apology that the physics and math behind the theory might be hard for him to explain or for readers to understand. He narrates a series of events with the confidence that anyone looking at them will know what they imply, because the examples he has chosen are exact. Division by zero is a perfect example of “equations breaking down”; gravity tugs at a tossed ball in exactly the way it slows cosmic expansion; the improbability of finding a precisely specified item in a small pool of possibilities applies to both the sizes of shoes in a store and the values of physical constants in a multiverse. The examples are not so much metaphors or analogies as they are actual instances of the phenomena he is explaining, and they are instances that readers can see with their own eyes. This is classic style.
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