FRIDAY, JULY 16, 2021
And the wisdom of Isaacson's joke: "The world is too much with us," Wordsworth famously said.
Arguably, the same can be said for Einstein's universe. Has anyone been able to explain that realm in a way the general reader—the average Jenny or Joe—can hope to understand?
Is Einstein's universe comprehensible, even to the "educated person?" More to the point, has anyone ever been able to explain that realm in a way that makes it so?
As far back as 1988, Richard Cohen and Charles Krauthammer suggested, in columns for the Washington Post, that however devoutly it may be wished, such a thing can no longer be done.
At issue was a best-selling book, A Brief History of Time, written by Stephen Hawking, one of the world's greatest physicists.
Reviewers swore that Hawking's book was lucid, accessible, comprehensible—even easy to read. In a pair of highly unusual columns, the columnists rose in dissent.
Hawking's massively best-selling book was "utterly incomprehensible," Krauthammer even declared. In defense of his unconventional view, he adumbrated a theory:
The Hawking book may be proof that physics has reached the limits of metaphor. Sir Arthur Eddington was once told by a journalist that only three people in the world understood Einstein's general theory of relativity. "I am trying to think who the third person is," replied Eddington. There are more than three now. Thousands of graduate students understand the equations whose meaning Hawking has set out to communicate. But physics is becoming the province of a small cadre of cognoscenti who occasionally send out emissaries like Hawking to speak to the rest of us in parables.
Inscrutable parables...Physics has become a kind of fiction, an excursion into a mathematical universe so esoteric and so remote from ordinary experience as to be literally incredible.
In the beginning, Eddington had joked about the difficulty of Einstein's universe. He and Einstein understood it, he seemed to say, but he couldn't name anyone else.
According to Krauthammer, thousands of graduate students understood that world as of 1988. But they understand it mathematically—as a mathematical realm.
There are no homely metaphors which illuminate this world for everyone else, Krauthammer said in his column. We've reached the limits of metaphor for regular people like us.
Thus spake Krauthammer in December 1988. A medical doctor and thus a scientist himself, Krauthammer suggested the possibility that the world had reached "the limits of metaphor" when it came to efforts to explain or describe Albert Einstein's universe.
It's all parables now, the columnist said—inscrutable ones at that.
Thus theorized the columnist. For the record, Cohen's earlier column had cited one reviewer who had stated a different view. In her review of Hawking's book for the New York Times, Michiko Kakutani had seemed to say that the physicist's metaphors were in fact pretty darn good:
Though it contains several dense passages dealing with ''imaginary time,'' ''string theories'' and ''inflationary'' models of the universe, which this reader (who never got beyond trigonometry in school) found impossible to follow, ''A Brief History of Time'' is, on the whole, a lively and provocative book...Mr. Hawking clearly possesses a natural teacher's gifts—easy, good-natured humor and an ability to illustrate highly complex propositions with analogies plucked from daily life.
Hawking was skilled "with analogies plucked from daily life," Kakutani said. Several passages were too hard. But not so with the rest!
In this way, a debate had been formed. More than thirty years later, our question would be this:
Have analogies plucked from daily life actually worked in the past thirty years, as writers have tried, again and again, to make Einstein's universe comprehensible?
Krauthammer's thesis notwithstanding, have Einstein whisperers come up with the metaphors which let his universe swim into view? With this question on the table, let's consider a major example.
Let's return to the highly familiar metaphor which appears at the very start of Walter Isaacson's 2007 biography, Einstein: His Life and Universe.
Indeed, this highly familiar metaphor appears on page 3 of Isaacson's well-received book, as Isaacson sketches his initial overview of Einstein's revolutionary work. As we review this metaphor, we'll also return to "Isaacson's joke," the sensible quip which we discussed in Monday's report.
Isaacson offers his well-considered joke as soon as his resort to metaphor is done. This sensible joke can also be scored as Isaacson's (sensible) warning.
Overview, metaphor, joke:
In the first part of this week's report, we quoted Isaacson as he offers his initial thumbnail description of Einstein's remarkable work. The basic history goes like this:
In 1905, Einstein produced his special theory of relativity. During this, his "miracle year," Einstein was still 26 years old.
Ten years later, Einstein produced the general theory of relativity. In the process, he'd reconfigured existing ideas about the way "gravity" works.
Searching for a way to make Einstein comprehensible, Isaacson brings out the trampoline and the bowling ball, as many others have done. He's still on page 3 of his widely-praised book as his work with this metaphor starts.
As he finishes with this analogy, he offers his sensible joke. In doing so, he offers some much-needed comic relief, but he also offers a bit of a warning—Albert Einstein's universe may turn out to be hard:
A decade after that, in 1915, [Einstein] wrested from nature his crowning glory, one of the most beautiful theories in all of science, the general theory of relativity. As with the special theory, his thinking had evolved through thought experiments. Imagine being in an enclosed elevator accelerating up through space, he conjectured in one of them. The effects you'd feel would be indistinguishable from the experience of gravity.
Gravity, he figured, was a warping of space and time, and he came up with the equations that describe how the dynamics of this curvature result from the interplay between matter, motion, and energy. It can be described by using another thought experiment. Picture what it would be like to roll a bowling ball onto the two-dimensional surface of a trampoline. Then roll some billiard balls. They move toward the bowling ball not because it exerts some mysterious attraction but because of the way it curves the trampoline fabric. Now imagine this happening in the four-dimensional fabric of space and time. Okay, it's not easy, but that's why we're no Einstein and he was.
"Okay, it's not easy," Isaacson says, "but that's why we're no Einstein and [Albert Einstein] was."
That last sentence is Walter Isaacson's well-considered joke. Quite appropriately, he seemed to acknowledge a basic fact:
The metaphor of the trampoline and the bowling ball may not be all that easy for shlubs like us to follow.
Einstein understood his theory, but it may not be easy for us! That's what Isaacson seemed to be saying, though he was stating his warning in the form of a joke.
The bowling ball on the trampoline is employed, with great regularity, in attempts to make Einstein easy (or at least understandable). But to what extent does that metaphor actually help?
"Okay, it's not easy," Isaacson quips. But what makes that metaphor "not easy?" Let's start counting the ways:
In Isaacson's rendering, we're instantly told that gravity is "a warping of space and time." We can all learn to repeat those words. But do we really have any idea what those words mean in this context?
Presumably, we all can picture a warping of some object made of wood. But what does it mean to picture a warping of space? To picture a warping of time?
What does it mean to picture a warping of "space and time?"
As Krauthammer stated in his column, we can always recite those words. But it we choose to recite and repeat, will we know what we're talking about? Will we understand what a "warping" might be in this unfamiliar context?
As Isaacson continues, this "warping of space and time" is quickly described as a "curvature."
We all know how to apply that word in an array of everyday contexts. But what is a curvature of space and time?
Does the general reader have any idea what that word might refer to, describe or mean in this new, unfamiliar context? And where would she go to find out?
Already, we're general readers in a strange land as Isaacson tries to explain. Now we're asked to picture ourselves placing a bowling ball "onto the two-dimensional surface of a trampoline."
Presumably, we can all picture ourselves doing that. We can also easily picture what would happen next:
The trampoline's surface, which had been flat, would now sag toward the center under the weight of the bowling ball. Similarly, we can picture what would happen when a couple of billiard balls were introduced into this mix.
It's easy to picture the trampoline—to picture its "two-dimensional surface." Everyone knows what we're talking about when we refer to its "fabric."
But now we're asked to imagine this happening "in the four-dimensional fabric of space and time." For us, the average Jeremiahs, how well will that effort work out?
We all know what it means to talk about the fabric of a trampoline—but in what sense do space and time form something we'd call a "fabric," let alone a four-dimensional fabric? We can always repeat the words, but do we have any idea what they mean?
There's at least one more problem with this metaphor as offered by Isaacson. We refer to the part of the passage which says this:
[The billiard balls] move toward the bowling ball not because it exerts some mysterious attraction but because of the way it curves the trampoline fabric.
Technically, nothing is "wrong" with that passage. We can defend it as technically accurate all the way down.
But would anyone ever have said that the billiard balls would behave in the way we know they will—would roll down the slope of the trampoline, eventually joining the bowling ball—"because [the bowling ball] exerts some mysterious attraction" on them?
That wouldn't be a common explanation of the billiard balls' movement. Somewhat ironically, the average sixth grader would probably say something like this:
The billiard balls roll down the slope of the trampoline because of the force of gravity! That's why balls of all descriptions roll down slopes or hills!
As presented, this metaphor is a multi-faceted jumble. We can agree to recite the words, but the words aren't likely to make a mountain of sense.
Isaacson seems to acknowledge as much when he provides some comic relief in the form of his sensible joke.
"Okay, it's not easy!" That's what he sensibly says.
As Isaacson proceeds in his book, he explains Einstein's universe, or at least attempts to do so, at much greater length.
He does a beautiful job with Einstein's life. Einstein's universe is much harder.
Intermittently, Isaacson tries to explain. Two chapters in question are these:
CHAPTER SIX: Special Relativity, 1905
CHAPTER NINE: General Relativity, 1911-1915
Isaacson does a superlative job recounting Einstein's life. As our ruminations proceed in the next few weeks, we'll explore some of the ways he explains Einstein's universe in such chapters as these.
Our view? We think he has a very hard time explaining Einstein's universe. He does a superlative job with Einstein's life—but in our view, Einstein's universe puts up a successful fight.
We'll look at those chapters in future weeks. For today, we're left with Krauthammer's riddle.
One reviewer after another said that Hawking's best-selling book was lucid, accessible, comprehensible—even easy to read. Nineteen years later, the same things were said about Isaacson's book, by a long list of reviewers and academics.
Similar praise was showered on Rebecca Goldstein's 2007 book, Incompleteness: The Proof and Paradox of Kurt Gödel, her attempt to explain the work of the 20th-century figure who is routinely called "the greatest logician since Aristotle," including by Einstein himself.
Goldstein's book was aimed at general readers. Was she able to make Gödel easy? Was Stephen Budiansky able to do so in the book he published this year, Journey to the Edge of Reason: The Life of Kurt Gödel?
Those books were aimed at general readers. Was Budiansky able to explain Gödel's theorem? Or would a reader simply be forced to recite a string of words?
When writers try to make Einstein easy, they've entered the World Series of explanation. Dating all the way back to Einstein's own book for general readers, they've tried and they've tried and they've tried and they've tried, and then they've tried again.
They've tried and they've tried to make Einstein understandable. According to Cohen and Krauthammer's witness, they've tried and they've massively failed.
This leaves us with Krauthammer's riddle—perhaps with Krauthammer's paradox. Dating back to Einstein's own general interest book, these writers have constantly tried and failed, but reviewers have persistently sworn that they've succeeded mightily.
What might this tell us about ourselves, about our own human race? Have we perhaps been "seeing ourselves from afar" dating back to the dawn of the west?
We'll explore such questions in the weeks ahead, focusing on various attempts to make Einstein easy. Along the way, we'll also drift over to "Russell's paradox," and to the 700 pages he devoted to proving 1 + 1.
We'll discuss Wittgenstein's indictment, but also Horwich's hypothesis. We may even drop by the cold, dark waters of the Aegean, looking in on the dawn of the west—on Plato, Aristotle and them.
Lurking always will be a question:
How skillful have we the humans ever been at explaining anything at all?
We can always recite the words! We'll call that Krauthammer's thesis.
Is it possible that this is what our self-impressed species has all too typically done? How often have we simply repeated the words, then claimed that we understood?
How often has Homey played it that way? Why would Homey do that? Why do we defer to failed explanations in this familiar way?
How often has Homey played it that way? We'd call that a very good question. When it comes to Einstein's universe—even to Gödel—we can't seem to stop doing it now!