FRIDAY, JULY 23, 2021
In search of clear, cogent speech: Some aspects of Einstein's universe are easy to describe. In that sense, and to that extent, these particular aspects of Einstein's universe are easy to understand.
Can (what we think of as) small amounts of matter be converted into (what we think of as) gigantic amounts of energy?
We may not understand the process by which that comes to pass. But it's easy to understand the claim, and in various ways, we've all come to see that the claim is actually true.
As we noted on Wednesday, it's also easy to understand Brian Greene's counterintuitive statement concerning "time travel." His claim is very clearly stated. However astounding the claim may be, it's easy to understand.
Greene is a high-ranking theoretical physicist. He understands the physics of Einstein's universe. He even knows the math.
The Fabric of the Cosmos was Greene's second book aimed at general readers. However implausible it may seem, it's easy to understand the following presentation from that best-selling book:
When Einstein discovered the nature of special relativistic spacetime, he laid out a blueprint for fast-forwarding to the future. If you want to see what's happening on planet earth 1,000, or 10,000, or 10 million years in the future, the laws of Einsteinian physics tell you how to go about it. You build a vehicle whose speed can reach, say, 99.999999996 percent of [the speed of light]. At full throttle, you head off into deep space for a day, or ten days, or a little over twenty-seven years according to your ship's clock, then abruptly turn around and head back to earth, again at full throttle.
On your return, 1,000, or 10,000, or ten million years of earth time will have elapsed. This is an undisputed and experimentally verified prediction of special relativity; it is an example of the slowing of time with the increasing of time described in Chapter 3 [of Greene's book].
Nothing resembling such high-speed travel is currently possible, not even for Amazon deliveries. But it's easy to understand Greene's presentation, in which he describes what one result of such high-speed travel would be:
The high-speed traveler would return to Earth thousands (or millions) of years in the future!
Planet of the Apes notwithstanding, this may seem like an astonishing claim. But it's easy to understand what Greene has said, and Greene describes it as "an undisputed and experimentally verified prediction."
More specifically, it's "an undisputed and experimentally verified prediction of special relativity," the theory Einstein devised in 1905, when he was just 26. This prediction about "time travel" is part of Einstein's universe.
It's easy to describe the fact that small amounts of matter can be converted into giant amounts of energy. It's easy to describe this puzzling result of high-speed travel into space and back.
It's easy to describe those aspects of Einstein's universe. In that sense, and to that extent, they're easy to understand.
That said, other aspects of Einstein's universe turn out to be extremely hard to report, explain or describe. Despite their honest efforts, writers of "Einstein made easy" books have been proving this point for years, though reviewers have rarely noticed.
It's easy to picture a trip into space, and a return to the Earth. Similarly, real-life events have made it easy to "envision" the fact that small amounts of matter can be converted into enormous amounts of energy.
Elsewhere, the challenges of clear explanation are exponentially greater. As Greene explained in his 2003 interview with PBS, the person who's writing for general readers must then attempt to create "analogies" or metaphors to help the general reader "envision" or understand what the mathematics of modern physics tells the theoretical physicist.
In such instances, high-level academics are trying to translate their high-level knowledge in ways the non-specialist can understand. Quite routinely, such efforts may not go well. This is true even if readers and reviewers fail to notice or acknowledge this fact.
Alas! It may not be easy to translate high-end academic knowledge into the realm of the everyday. Despite their high-level technical knowledge, high-level academics may lack the types of skills which permit such elucidations.
Such attempts at cogent speech may go badly astray. Consider a few striking examples from two high-level attempts to make Einstein (and Gödel) easy.
"Mommy, the trees appear to be moving!"
We'll start with Greene's first general interest book, The Elegant Universe. The book was published in 1999. It formed the basis for a three-part PBS series which aired in 2003.
In his book, Greene describes the full sweep of modern physics, starting with Einstein's work. In Chapter 2 of his well-received book, he presents an overview of Einstein's special theory of relativity, the first of Einstein's two great theories.
With special relativity, Einstein "forever changed our conceptions of space and time," Greene writes near the start of this chapter. For general readers, this claim will remain a mystery until Greene is able to describe these changes in a way they can understand.
What was the essence of special relativity? "The essential concern of special relativity is to understand how the world appears to individuals, often called 'observers,' who are moving relative to one another," Greene writes at this early point.
"In the hands of Einstein," Greene writes, "there are profound implications to grasping fully how even the most mundane situations appear to individuals in relative motion."
Presumably, this statement by Greene is accurate. But as he continues, Greene offers an extremely puzzling account of one such mundane situation. An explication which starts this way may not be destined to end especially well:
Common experience highlights certain ways in which observations by such individuals differ. Trees alongside a highway, for example, appear to be moving from the viewpoint of a driver but appear stationary to a hitchhiker sitting on a guardrail. Similarly, the dashboard of the automobile does not appear to be moving from the viewpoint of the driver (one hopes!), but like the rest of the car, it does appear to be moving from the viewpoint of the hitchhiker. These are such basic and intuitive properties of how the world works that we hardly take note of them.
Brian Greene is a highly accomplished theoretical physicist. He knows more math and physics than all the kids in your high school trigonometry class combined.
That said, as he starts on a road designed to let us envision this first part of Einstein's universe, he pens an other-worldly account of a simple car ride. We'll only repeat our earlier warning:
Explications which start this way may not end especially well.
On what planet does Greene's peculiar account actually make sense? If someone drives past a clump of trees alongside a highway, would that person ever be inclined to say that the trees "appear to be moving?"
Do the trees "appear to be moving?" Would anyone, even the driver's young children, ever make any such claim?
"Mommy, the trees appear to be moving!" Has any child ever said any such thing? We're going to say they have not.
According to Greene, the trees "appear [to be] stationary" to a hitchhiker sitting on a guardrail as the car goes past. That said, the trees "appear to be stationary" to the people in the car as well—not that any of them would ever make such an odd observation, one that's roughly equivalent to saying that the sky appears to be up.
Meanwhile, does the dashboard of the car "appear to be moving from the viewpoint of the hitchhiker?" Actually, as Greene notes, the whole car "appears to be moving," to which we must add an obvious point:
The whole car "appears to be moving" because, as a matter of common parlance, it actually is! In that peculiar sense, the car "appears to be moving" to its occupants as well, though no one would put it that way.
The indulgent reviewer will likely say that we understand what Greene is trying to say in this peculiar passage. We may be inclined to say that we understand his point.
That said, readers shouldn't have to work to understand what Greene is trying to say. Especially at the start of a difficult explanation, it's the writer's job to find a clear, cogent way to say it.
In his books for general readers, Greene is claiming that he can turn the astonishing world of special relativity into everyday analogies—analogies the average person can "envision" and understand. That early paragraph has long stuck in our heads as one of the most poorly fashioned paragraphs we have ever read.
It's the first link in a chain which is supposed to make Einstein easy. At this point in our own ruminations, we'll simply repeat our warning:
Brian Greene is a brilliant physicist. But such other-worldly opening gambits may not turn out well.
A catastrophe of reason which causes the mind to crash
For our second example, we turn to the most remarkable paragraph we've read in the past twenty years. It's drawn from Rebecca Goldstein's 2005 book, Incompleteness: The Proof and Paradox of Kurt Gödel.
Goldstein has had an admirable career as a high-ranking philosophy professor. (She's also a well-regarded novelist.) Her attempt to explain Gödel's incompleteness theorem was praised for its lucidity and accessibility by an astounding array of high-end academics.
Goldstein is a philosophy professor. One would assume that she's familiar with the basic tools of everyday logical analysis.
Despite these qualifications, she offered this remarkable passage fairly early in her book. In this passage, she's sketching the basis upon which Gödel's incompleteness theorem is based:
Paradoxes, in the technical sense, are those catastrophes of reason whereby the mind is compelled by logic itself to draw contradictory conclusions. Many are of the self-referential variety; troubles arise because some linguistic term—a description, a sentence—potentially refers to itself. The most ancient of these paradoxes is known as the "liar's paradox," its lineage going back to the ancient Greeks. It is centered on the self-referential sentence: "This very sentence is false." This sentence must be, like all sentences, either true or false. But if it is true, then it is false, since that is what it says; and if it false, well then, it is true, since, again, that is what it says. It must, therefore, be both true and false, and that is a severe problem. The mind crashes.
Paradoxes like the liar's play a technical role in the proof that Gödel devised for his extraordinary first completeness theorem...
Do such "paradoxes" really play a technical role in Gödel's work? We'll let the experts assess that claim, but Goldstein's presentation of "the liar's paradox" is the most memorable writing we've encountered in the past twenty years.
The notion that the liar's paradox causes the mind to crash—constitutes "a catastrophe of reason"—is just utterly daft. It's stunning to think that that passage was crafted by a high-ranking philosophy prof.
The liar's paradox is, at best, a bit of a carnival trick. It's astounding to see a philosophy professor treat it with such reverence. If Gödel's theorem is really built upon such a house of cards, we can only suggest the possibility that something is wrong with Gödel's extremely hard-to-explain theorem.
As presented, what makes the liar's paradox a house of cards, a carnival trick? Consider normal procedures:
Stating the obvious, it makes no sense to say that a sentence (more accurately, a statement) is false until a statement has actually been made. The standard progression is this:
Someone makes an actual statement. After someone has made an actual statement, others can proceed to decide if the statement is true or false.
As offered by Goldstein, the liar's paradox turns on this locution: "This very sentence is false." Unfortunately, this creates no pre-existing statement which can be judged to be true or false. The first link in the chain has gone AWOL.
Goldstein refers to that collection of words as being "self-referential." Unfortunately, it includes no pre-existing statement which can be judged to be false.
No one will ever come up to you in real life and say, "This very sentence is false." The whole thing is a parlor trick—but in Goldstein's account, this silly pseudo-assessment ranks as a catastrophe of reason which causes the mind to crash!
Our suggestion to you would be this: Even ranking academics can offer remarkable twaddle. We don't know why Goldstein, a philosophy professor, wasn't more helpful with this.
The mathematician's apology
A brilliant center fielder might be a terrible shortstop. Just because a person can sing, that doesn't mean that he or she knows how to play the trombone.
Similarly, brilliant physicists and mathematicians may stumble when they play out of position—when they move outside their realm of expertise. Consider G. H. Hardy, "an English mathematician of great distinction," whose "Platonist convictions" are described by Goldstein in that same book.
What, if anything, does it mean to be a modern-day "Platonist?" Goldstein offers this jumbled account before quoting from Hardy's famous book, A Mathematician's Apology:
Platonism is the view that the truths of mathematics are independent of any human activities, such as the construction of formal systems—with their axioms, definitions, rules of inference and proofs. The truths of mathematics are determined, according to Platonism, by the reality of mathematics, by the nature of the real, though abstract entities (numbers, sets, etc.) that make up that reality. The structure of, say, the natural numbers (which are the regular old counting numbers: 1, 2, 3, etc.) exists independent of us, according to the [Platonist]...and the properties of the numbers 4 and 25—that, for example, one is even, the other is odd and both are perfect squares—are as objective as are, according to the physical realist, the physical properties of light and gravity.
According to Platonists, "the truths of mathematics are determined by the reality of mathematics!" The murkiness continues from there, with Goldstein reporting that the fact that number 4 is an even number "exists independent of us," whatever that may mean.
This particular truths of mathematics—for example, the truth that 4 is an even number—is independent of any human activities, we're further told. From there, Goldstein quotes a passage from Hardy's iconic text, in which, among other things, Hardy offered these murky claims:
I believe that mathematical reality lies outside of us...317 is a prime, not because we think so, or because our minds are shaped in one way or another, but because it is so, because mathematical reality is shaped that way.
Most simply, 317 is a prime because it can't be evenly divided by any other number. The rest of this is mumbo-jumbo—the sort of thing which may result when a brilliant mathematician ventures beyond his field of expertise, into a whole different realm.
People of high academic attainment may venture beyond the limits of their (substantial) skill sets when they start to ruminate in such ways. Similar problems may occur when people try to take their enormous knowledge of mathematics and physics and create the kinds of analogies which are designed to make Einstein understandable, even easy.
Some aspects of Einstein's universe actually are easy to understand. Most parts of Einstein's universe are not.
Brian Greene is a brilliant physicist and a high-ranking media figure. Reviewers tend to defer to such people when they publish books which claim to make modern physics understandable.
Reviewers tend to stand in line to say that they understand what has been said in such books. Presentations which are actually very murky are said to make perfect sense. Leading logicians may not step forward to help.
We learn about the human project when we encounter such patterns of behavior. We learn how easily we may fail to see that certain types of presentations may not make actual sense. We learn how reluctant we may be to admit that we don't understand.
In the old joke from the Soviet Union the Soviet worker said this:
We pretend to work, and they pretend to pay us.
We have no doubt that Brian Greene and Walter Isaacson have been fully well-intentioned in their attempts to make Einstein understandable. If we didn't feel certain of that, we'd characterize their efforts this way:
They pretend to make Einstein easy, and we pretend to get it.
Next week, we'll look at the start to Isaacson's CHAPTER SIX: Special Relativity, 1905. Isaacson is a superb biographer. He does a wonderful job describing Einstein's life.
That said, Einstein's universe tends to be extremely hard. The skills of cogent, clear explanation will often be in short supply when we try to enter a space ship and transport ourselves to such realms.
Coming next: "Relativity is a simple concept."