HAS NEVER MADE SENSE: Isaacson recounts what Einstein wrote!

TUESDAY, AUGUST 3, 2021

On its face, it never made sense: Walter Isaacson is a highly experienced journalist and an acclaimed biographer. Unsurprisingly, he's also a very good teller of stories.

In Chapter Six of his biography of Albert Einstein, he describes a "eureka moment"—the "eureka moment" in which Einstein "took one of the most elegant imaginative leaps in the history of physics." 

Isaacson's chapter deals with Einstein's special theory of relativity, which Einstein formulated in 1905, when he was just 26. The eureka moment occurred in early May of that year, on  a beautiful spring day in Bern, as Einstein was walking and talking with Michele Besso, "the brilliant but unfocused engineer" who was his best friend.

By all accounts, Isaacson is describing a key moment in the history of physics—indeed, in the intellectual history of the twentieth century. What "key insight" had suddenly come to Einstein that day? Isaacson starts his account like this:

Only five weeks elapsed between that eureka moment and the day that Einstein sent off his most famous paper, "On the Electrodynamics of Moving Bodies." It contained no citations of other literature, no mention of anyone else's work, and no acknowledgments except for the charming one in the last sentence [to Besso]...

So what was the insight that struck him while talking to Besso? “An analysis of the concept of time was my solution,” Einstein said. “Time cannot be absolutely defined, and there is an inseparable relation between time and signal velocity.”

More specifically, the key insight was that two events that appear to be simultaneous to one observer will not appear to be simultaneous to another observer who is moving rapidly. And there is no way to declare that one of the observers is really correct. In other words, there is no way to declare that the two events are truly simultaneous.

In Isaacson's paraphrase, Einstein's key insight was this:

Two events that appear to be simultaneous to one observer will not appear to be simultaneous to another observer who is moving rapidly. And since there is no way to say that one or the other observer is right, there is no way to declare that the two events are truly simultaneous.

There's no way to declare that two events are truly simultaneous! Remember, this is Isaacson's paraphrase of Einstein's "key insight"—but as we'll see tomorrow, it's a perfectly reasonable account of what Einstein actually said in the source upon which Isaacson is relying.

There's no way to declare that two events are simultaneous! This principle is generally known as "the relativity of simultaneity." According to Isaacson (and many others), it's the key insight—the eureka moment—which suddenly came to Einstein on that spring day in Bern.

Within five weeks, Einstein had sent off his most famous scientific paper, On the Electrodynamics of Moving Bodies. In Isaacson's words, it was that key insight which lay at the heart of "one of the most elegant imaginative leaps in the history of physics." 

As far as we know, no one disagrees with Isaacson's general portrait of this historic event. The problem arises when Isaacson further explains Einstein's "key insight"—though, in fairness to Isaacson, he's working directly from Einstein's own work when he offers his account of this important matter.

On what is Isaacson relying? As he continues, Isaacson doesn't quote from Einstein's work in the famous technical paper he sent off in June of 1905. Instead, he sensibly turns to a different source as he tries to explain Einstein's key insight.

Sensibly, Isaacson turns to the account Einstein offered in Chapter IX of Relativity: The Special and the General Theory, the book he wrote for general readers in 1916. (For the text of that book, click here.)

As he continues, Isaacson presents Einstein's account of the relativity of simultaneity—but he explains it the way Einstein did in that 1916 book, the one Einstein wrote for non-specialists. That said, there is a problem here::

Unfortunately, the account Einstein offered in that book has, at least on its face, never quite seemed to make sense.

Isaacson offers a reasonably faithful rendering of the explanation Einstein presented in Chapter IX of his book. This is what Isaacson writes as he continues from the passage posted above:

Einstein later explained this concept using a thought experiment involving moving trains. Suppose lightning bolts strike the train track’s embankment at two distant places, A and B. If we declare that they struck simultaneously, what does that mean?

Einstein realized that we need an operational definition, one we can actually apply, and that would require taking into account the speed of light. His answer was that we would define the two strikes as simultaneous if we were standing exactly halfway between them and the light from each reached us at the exact same time.

But now let us imagine how the event looks to a train passenger who is moving rapidly along the track. In a 1916 book written to explain this to nonscientists, he used the following drawing, in which the long train is the line on the top.

"Einstein later explained this concept using a thought experiment involving moving trains?" As becomes clear two paragraphs later, Isaacson is referring to the explanation Einstein offered in his 1916 book.

At this point in his exposition, Isaacson reproduces the drawing Einstein used in that book. The drawing appears in Chapter IX, The Relativity of Simultaneity, in Einstein's extremely brief historic text. 

That chapter is only three pages long. You can see the entire chapter, and the drawing Einstein employed, by just clicking here. The rudimentary drawing does purport to show a railroad train and two distant lightning strikes.

From here, Isaacson proceeds to explain this important concept involved in this matter almost exactly as Einstein did. He faithfully describes the thought experiment Einstein employed—a thought experiment involving that fast-moving train and that pair of lightning strikes.

As he proceeds, Isaacson is faithful to Einstein presentation. There's only one problem:

On its face, Einstein's presentation didn't seem to make sense. On its face, it didn't seem to make sense back in 1916, and it still doesn't today. 

Tomorrow, we'll consider the presentation Einstein offered in his 1916 book. Isaacson worked directly from that presentation in his deeply-researched 2007 book. Eight years later, Nova followed suit, in an hour-long PBS program, Inside Einstein's Mind.

Tomorrow, we'll look at what Einstein said in his presentation. Quite reasonably, Isaacson thought that Einstein was saying this:

The key insight was that two events that appear to be simultaneous to one observer will not appear to be simultaneous to another observer who is moving rapidly. 

It's reasonable to think that Einstein was saying that—that he was offering that account of his key insight. That's what Einstein appears to be saying in his 1916 book.

There's only one problem with the explanation Isaacson (and Nova) derived from Einstein's presentation. On its face, their explanation of this key principle had never seemed to make sense.

On its face, Einstein's presentation for general readers didn't seem to make sense in 1916. It still didn't make make sense in 2007, or in 2015, but neither Isaacson nor Nova seemed to notice this fact.

By now, more than a hundred years have passed since Einstein published his 1916 book. On its face, the presentation he made in Chapter IX of his book still doesn't seem to make sense. 

It's one of the most important moments in the history of physics—in the intellectual history of the twentieth century. But more than a hundred years later, on the highest levels, no one seems to have noticed that Einstein's account of this historic moment didn't quite seem to make sense.

Two events which appear to be simultaneous to one observer will not appear to be simultaneous to another observer who is moving rapidly?

In most cases, though not in all, that will surely be true. But that will also be true for most observers who aren't moving rapidly—indeed, for most observers who aren't moving at all!

Isaacson accepted Einstein's presentation at face value. Eight years later, Nova followed suit.

On its face, that presentation had never made sense! Tomorrow, we'll journey back in time to 1916 to see what Einstein wrote.

Tomorrow: On its face, this didn't make sense

Thursday or Friday: As seen on PBS


HAS NEVER MADE SENSE: Einstein offered a key explanation!

MONDAY, AUGUST 2, 2021

On its face, it has never made sense: We hold in our hands a copy of Albert Einstein's 1916 book, Relativity: The Special and the General Theory.

Einstein formulated his special theory of relativity in 1905, when he was just 26. Ten years later, he produced his general theory.

Oner year after that, in 1916, Einstein published the aforementioned rather short book. The  book was intended to explain relativity to non-specialists—to the general reader. 

Einstein's 1916 book remains in print to this day. The edition we hold was published by Bonanza Books / Crown Publishers in 1961, though it was purchased much later.

Our copy of Einstein's book is an instructive artifact. On its cover, beneath the title of the book but above the name of its author, the publisher offered a fanciful claim:

A CLEAR EXPLANATION THAT ANYONE CAN UNDERSTAND

That claim appears in bold, and all caps. On the front flap of the dust jacket, the claim is slightly scaled back:

It has long been a popular misconception that only a handful of people in the world can understand Einstein's theory of Relativity. Here is a book, however, by the originator of the theory himself explaining the theory in simple words that anyone with the equivalent of a high school education can understand.

By now, the reader will need a high school education, or its equivalent, to understand the "simple words" of the historic book. 

Below that slightly adjusted claim, the dust jacket of our book offers excerpts from two reviews of the easy-to-understand book. As it turns out, the excerpts were a bit selective, but the dust jacket reads like this:

Some Book Reviews

"The book is intended to give an exact insight into the theory to those who are not conversant with the mathematical apparatus of theoretical physics. In the opinion of this reviewer, in this attempt he has been eminently successful." —The New York Times

"Written in an unpretentious, straightforward style. The trend of his exposition can be followed in the main by any attentive reader." —New York Post

As it turns out, these excerpts tend to misrepresent the overall tone of the reviews from which they were drawn. Also, the first excerpt was attributed to the New York Times, though that's not where the review in question appeared. 

(For a fuller discussion of those excerpts, you can just click here.)

Publishers have tried to sell Einstein's book in such ways ever since it was published. This practice has continued into the present day.

(In our view, the practice has spread to PBS. In our view, PBS has routinely tended to overstate the ease with which its programs about Einstein, and about modern physics more generally, could be understood by  "those who are not conversant with the mathematical apparatus of theoretical physics." More on that in the weeks ahead.)

Einstein's claims about his book were more circumspect. At the start of his short preface, he said his book "presumes a standard of education corresponding to that of a university matriculation examination, and, despite the shortness of the book, a fair amount of patience and force of will on the part of the reader."

For the record, a university matriculation examination is an entrance exam—an entrance exam for the more demanding universities of Einstein's day. 

"I make no pretense of having withheld from the reader difficulties which are inherent to the subject," Einstein said at the end of his preface. In the years which have followed, publishers have tended to make this book sound a good deal easier than it actually is.

In his historic book, Einstein did not present “a clear explanation [of relativity] that anyone can understand.” Nor did he claim to have done such a thing, though he said that he had done the best he could. 

That said:

In the week which follows, we won’t be trying to evaluate the general accessibility of Einstein’s historic text. Instead, we’ll be looking at one presentation from the book—a key presentation which is being repeated right to the present day.

This key presentation is being repeated even though, on its face, it has never seemed to make sense. On its face, it didn't make sense when Einstein offered it, nor does it do so today.

The presentation started with Einstein himself, back in 1916. In 2007, it was accurately repeated, in all particulars, by Walter Isaacson in his well-received biography, Einstein: His Life and Universe.

Eight years later, Nova produced a program for PBS, Inside Einstein's Mind, commemorating the hundredth anniversary of Einstein's general theory. The presentation was accurately repeated there as well. 

On its face, it still didn't seem to make sense.

The presentation of which we speak is offered by Einstein in Chapter IX of his historic book. It comprises the whole of that very short chapter, which is found on pages 24-26 of the rather short book.

The chapter carries this title: The Relativity of Simultaneity; you can read the whole chapter here. The presentation is one of Einstein’s most widely cited—and, at least on its face, it has never seemed to make sense, even though it’s intended to explain one of relativity’s most fundamental principles.

Did Einstein stumble at this point as he tried to make his work intelligible to general readers? Einstein is universally acclaimed as one of history's most brilliant theoretical physicists. There's no obvious reason to assume that he was an infallible popular writer as well.

Did Einstein stumble at this point? Writing as non-experts, we’re not sure how to score it.

That said, the presentation, on its face, has never seemed to make sense—but it has been repeated again and again, and no one has seemed to notice. So it can go as our journalistic and academic elites conduct our society's intellectual work on the highest levels.

Tomorrow, we’ll look at Isaacson’s succinct presentation of this important aspect of Einstein’s special theory of relativity. According to Isaacson, we’re talking about the “eureka moment” in 1905 in which Einstein "took one of the most elegant imaginative leaps in the history of physics."

Isaacson offers a short, essentially accurate account of Einstein's presentation from his Chapter IX. So did Nova, in its 2015 commemorative program.

On the down side, Isaacson didn’t seem to notice the fact that Einstein's presentation has never seemed to make sense. Nova didn't notice that either. So these matters have gone through the years. So they'll continue to go in the future.

More than a hundred years have passed; this puzzle remains unnoticed. When it comes to efforts to make Einstein easy, the salesmanship is often effusive:

The analytical skills, and the cogency, are often instructively weak.

Tomorrow: Isaacson’s (accurate) account


Ethically, you can watch the Olympics!

SATURDAY, JULY 31, 2021

Phantom erudition: We're so old that we attended "the greatest track meet of all time."

The aforementioned "greatest meet" took place in July 1962 at Stanford Stadium. Thanks to the generosity of a friend and his family, we were there both days. 

We were 14 at the time—just over 14 and a half. By the time of our senior year, our friend was a 9.8 sprinter himself, though that was 100 yards.

Back to the greatest meet, which you can also read about here:

Bob Hayes won the men's 100 meters; Wilma Rudolph won the women's 100. Valery Brumel set another world record. On overall points, the Soviet team prevailed.

On overall points, the Soviets won; Tamara and Irina Press won their standard three events (shot put, discus, low hurdles). That said, at the end of the second day, the athletes of the warring nuclear nations circled the track, arm in arm, as the capacity crowd applauded and occasionally wept.

Three months later, the Cuban missile crisis occurred. NAME WITHHELD, our high school's most spirited cheerleader, said this to us on one of those days, and she was completely sincere:

"I'm afraid I won't get the chance to grow up."

We're fairly sure that a tape recoding would have recorded those very words. Three months earlier, we'd watched Bob Hayes win the 100.

Track and field was very big in the California high school world at that point in time. At the 1968 Olympics, four gold medal winners had come out of the California state meet during the years we'd been in high school. 

(The years in question were 1962-1965. In 1968, gold medals in Mexico City went to James Hines in the 100; to Tommie Smith in the 200; to Lee Evans in the 400; and to Bob Seagren in the pole vault. Earl McCullouch would have been favored to make it five, but he'd gone to the NFL.) 

We loved the Olympics back then, to the extent that it was accessible. We don't watch the Olympics today. Over the years, we came to hate the bloated corporatism which came to define the games, along with the increasingly silly way the games were broadcast, at least here in the U.S. 

Also, we've learned something in the years which have passed. We've learned that a whole lot of children, all over the world, don't get a chance to grow up. 

They may die alongside their parents, under bombs or out in the sea. In other circumstances, they may be forced to live in conditions which are an insult to the notion of human dignity.

We've learned about this state of affairs as the years have passed. We've also seen that very few of us—almost no one, in fact—ever commit themselves to doing as much as they possibly can to respond to this state of affairs.

Concerning which, there's this:

In the spring of our senior year in high school, we were suddenly enormously in love. We spoke for hours, every day, to the very wise person by whom we were suddenly overwhelmed. 

From 3-5, we could pretend that we were watching the swimming team work out as we sat there endlessly talking. From 5-6, it was just us and the custodians, plus the occasional tumbleweed.

(We had to be home for dinner at 6; we lived across the street from the school. Her family ate at 9. We hailed from somewhat different cultural frameworks. That was instructive for us.)

We spoke for hours every day, but we can remember only one specific exchange:

We had just learned about Dr. Tom Dooley, the medical missionary who had lost his life in southeast Asia. If you know that people are suffering, you're obligated to address it, we told our new friend one day. We told her that if someone was dying in the street in front of her house, she'd feel obligated to do something about it, and that there was no difference here.

"It just isn't like that," she wisely said. She was wiser and saner than we were, for which we're still grateful today. But in all those hours of conversation, that's the only specific exchange we can recall.

We don't like the bloated monstrosity the Olympics has become. For that reason, we haven't watched any coverage this week.

Others feel differently about these matters, and there's no reason why they shouldn't. Other people are watching the games. Yesterday, thanks to the New York Times, we learned that their conduct is ethically permissible.

We learned that in an op-ed column by an assistant professor. For reasons which go unexplained, she's described in the Times' identity line as "a moral philosopher." 

We have no doubt that the columnist is a thoroughly good, thoroughly decent person. That said, her column appeared beneath this silly headline:

Are You a Bad Person for Watching the Olympics?

That was the headline on the column. In our judgment, the column is a prime example of "phantom erudition," the type most likely to appear in the New York Times.

In our view, the fact that the column was written—much more strikingly, the fact that the column was published—helps us see how limited our human judgment is.

Given the major moral quandaries we're currently facing in this nation, it's hard to believe that a major newspaper would think this question was worth exploring in the erudition-rich way this column did.

That said, the assistant professor undertook that task. In her column, she notes a few of the fairly obvious problems with the way the Olympics now operates, then states her column's reason for being:

Of course, viewers aren’t watching the Games to intentionally endorse a corrupt system or the idea of profit over public health. They’re watching to celebrate our common humanity, to be awed by athletic excellence and to witness the drama of Olympic dreams being dashed or realized. But by opting to watch the Olympics, do we give a tacit thumbs-up to the entire spectacle, ethical problems and all?

At the heart of this worry is the idea that merely by choosing to be entertained by something that involves wrongdoing, we become complicit in it. But just how worried should we be? To answer this question, the idea of complicity needs unpacking.

For the record, some viewers are watching the games because nothing else is on. But let's not linger on such side issues. At issue is an ethical question: 

Readers, have you become "complicit in wrongdoing" by choosing to watch the Olympics? That's the question the New York Times ate valuable space to explore.

Have viewers become complicit in wrongdoing? At this point, the assistant professor says the idea of complicity "needs unpacking." 

Very long story short! Powering ahead, she tells us that Olympic watchers aren't guilty of "participation complicity." She then proceeds to the more difficult questions, wondering whether such viewers may be guilty of "tolerance complicity." 

All in all, the erudition was hard to miss.

In the end, the TV viewer gets a pass. "Just because all complicity is bad does not mean that it is always morally criticizable," the assistant professor says. Believe it or not, this is the way her exegesis ended:

[T]he Games are underway, and for most of the world’s population, there is only one moral decision left to make: To watch or not to watch? If you are one of the many who view the actions of the International Olympic Committee, the television stations and sponsors, and the nations competing as morally wrong, is it ethical for you to tune in?

Olympic athletes offer us an ideal of achievement and determination in the face of adversity. Knowledge that we are always, in some measure, complicit offers us a kind of moral adversity that we overcome not through the pursuit of an impossible moral purity, but through renewed efforts to engage in our deeply flawed world. Choosing to watch the Games, for all their faults, is perfectly compatible with these efforts.

Watch away.

There is only one moral decision to make—whether or not to watch. And yes, we're always complicit to some extent, the assistant professor contends. 

But according to the assistant professor, it's "ethical for you to tune in." All complicity is bad—but that doesn't mean that it's always "morally criticizable."

"Watch away," she cheerfully says as the column ends.

Amazingly, yet not amazingly, editors at the New York Times thought this example of "moral philosophy" was worth publishing. They even published it in yesterday's print editions. 

That doesn't make them bad people! The woods are lovely, dark and deep, but even among the elites of Our Town, human judgment is very limited.

Many children, all over the world, don't get the chance to grow up.  They often die beside their parents. Or they may live in conditions which insult any notion of human dignity.

Also this: Very few of us ever make a full commitment to fully addressing such facts in the ways we live our lives. 

It may be that Dr. Tom Dooley did. (His story turned out to be more complicated than was known at the time.) 

Meanwhile, at the Times, they're puzzling over participation complicity versus the tolerance version of same. In our view, they're offering the phantom erudition which largely defines the intellectual way of life in our own self-impressed town.

It's like this on "cable news" every night. And no, we don't mean over on Fox, where the human shortfall can perhaps, to Our Town's delight, seem to be even worse.

Permission to watch the games has been granted. "Watch away," The Voices have said.

Swimming song: Swimming was also big in the California high school world of that time. 

Donna de Varona, a teenage gold medal winner, was right down the road from us at the Santa Clara Swim Club. From 3 to 5, you could pretend that you were just watching the swim team swimming their endless laps.

In 2005, we attended our fortieth reunion. Due to geographic separation, we'd hardly ever been back.

At one point, we listened as the 13-year-old son of a classmate enthused, in some detail, about the water polo team at Bellarmine High, 30 miles to the south.

What a madeleine moment that was. We remembered being that very same kid, right on those same teenaged grounds!

(In 1964, the Associated Press and United Press International voted de Varona the "most outstanding woman athlete in the world." She was 17 years old at the time—an Olympics record-holder.)


A SIMPLE CONCEPT: The science was his Achilles' heel!

FRIDAY, JULY 30, 2021

Also, Krauthammer's conjecture:  Way back in April 2007, Janet Maslin reviewed Walter Isaacson's book for the New York Times. 

Credit where due! According to Maslin, Isaacson hadn't managed to make the science especially easy.

In question was Isaacson's well-received biography, Einstein: His Life and Universe. In Maslin's view, Isaacson had done a very good job with Einstein's life, but Einstein's universe had perhaps been quite a bit harder.

Maslin cushioned her blow with an "if." But she seemed to make it clear that the science hadn't been especially easy to understand:

Mr. Isaacson deals clearly and comfortably with the scope of Einstein’s life. If his highly readable and informative book has an Achilles’ heel, it’s in the area of science. Mr. Isaacson had the best available help (most notably the physicist Brian Greene’s) in explicating the series of revelations Einstein brought forth in his wonder year, 1905, and the subsequent problems with quantum theory and uncertainty that would bedevil him.

But these sections of the book are succinctly abbreviated. Paradoxically that makes them less accessible than they would have been through longer, more patient explication. Still, the cosmic physics would be heavy sledding in any book chiefly devoted to Einstein’s life and times, and Mr. Isaacson acknowledges that. “O.K., it’s not easy,” he writes, “but that’s why we’re no Einstein and he was.”

If the book had a shortcoming, it lay with the science, she said. In this way, Maslin softened her assessment, which otherwise seemed fairly clear,

Maslin cited Isaacson's joke—the sensible joke from the book's page 4 which we mentioned three weeks ago, in the first of our current reports.

(“O.K., it’s not easy,” Isaacson jokes.  But that’s because we aren't Einstein.)

Maslin cited the role of Brian Greene, the theoretical physicist who played the leading role among Isaacson's dozen or so major science advisers. In Maslin's view, the participation of figures like Greene meant that Isaacson had "the best available help" when it came to reporting the science. 

(Once again, we'll suggest a different possibility. Undeniably brilliant physicists may not always be the best guides if we're trying to determine what will be understandable to the general reader.)

In Maslin's view, the sections of the book which dealt with Einstein's revolutionary discoveries were "succinctly abbreviated," perhaps overly so. She suggested that Isaacson could have done a better job if he'd given the science "longer, more patient explication."

Everything is possible, but we're not inclined to agree. Isaacson does do an excellent job with Einstein's remarkable life—but Einstein's revolutionary universe is extremely hard. Just consider a few of the things Greene himself has said.

In The Fabric of the Cosmos, his 2004 book for general readers, Greene describes the remarkable strangeness of the universe which emerges from Einstein's special theory of relativity (1905). (The special theory is the subject of Isaacson's Chapter Six.)

"The relativity of space and of time is a startling conclusion," Greene writes in his book. "I've known about it for more than twenty-five years, but even so, whenever I quietly sit and think about it, I am amazed."

"Special relativity is not in our bones," Greene wrote in his earlier book for general readers, The Elegant Universe (1999). "Its implications are not a central part of our intuition." 

Concerning Einstein's general theory of relativity, which emerged in 1915, Greene has said that the human brain may not be designed to understand its workings. "What I can do," he said in a PBS interview, "is I can make use of mathematics that describe those extra dimensions, and then I can try to translate what the mathematics tells me into lower dimensional analogies that help me gain a picture of what the math has told me." 

So Greene said to PBS. He was describing a difficult struggle—the struggle to explain Einstein's universe.

By all accounts, Einstein's universe is extremely hard to report, describe, explicate, explain or simplify. Those bits of testimony come from a major theoretical physicist—from someone who actually does understand the complex mathematics behind the "startling" physics.

Could Isaacson have done a better job if he'd spent more time on the science? Everything is possible. But in fairness, Isaacson doesn't seem to skimp in his attempts to explore the terrain of this difficult universe. 

His Chapter Six: Special Relativity, 1905 covers a full 33 pages. He does go on at substantial length, but it seems to us that the thread has been lost in its first three or four pages.

Would a more detailed treatment have helped? This new universe is extremely hard. We know of no reason to think so.

Isaacson is an extremely capable writer and a very smart person. He's a highly experienced mainstream journalist. He's an acclaimed biographer.

Still and all, when he tries to explain special relativity, he starts with a presentation which seems almost Onionesque. With apologies, we'll quote it one more time. Isaacson starts with this:

CHAPTER SIX Special Relativity, 1905

Relativity is a simple concept. It asserts that the fundamental laws of physics are the same whatever your state of motion.

Relativity "asserts that the fundamental laws of physics are the same whatever your state of motion?" 

That formulation strikes us as almost Onionesque. Nor do matters get any better as Isaacson meanders ahead. He's an acclaimed biographer and a very smart person, but his treatment of Einstein's universe strikes us as pretty much incomprehensible pretty much all the way down.

Despite this fact, his book is blurbed by major figures saying the science is clear as a bell. Maslin could see that that wasn't the case, but she seemed to pull her punch.

Isaacson's treatment of special relativity starts in a way which seems almost Onionesque. Things don't get a whole lot clearer as Isaacson proceeds from there.

That said, no one seems to be willing or able to notice or mention this fact. In our view, this state of affairs can be seen as instructive.

DESPITE HIS OUTSTANDING TREATMENT of Einstein's life, did Isaacson fail to make Einstein's universe understandable? 

Inevitably, that's a subjective assessment. We'll offer a road map to such assessment below.

Next week, we'll be moving to a part of Isaacson's Chapter Six which is taken straight from Einstein's 1916 book for general readers, Relativity: The Special and General Theory.

In Isaacson's perfectly sensible framing, the passage in question involves the "eureka moment" in which Einstein "took one of the most elegant imaginative leaps in the history of physics." At issue is "the relativity of simultaneity," a central element of the special theory. Indeed, that's the title of Chapter IX in Einstein's short 1916 book.

Midway through his own Chapter Six, Isaacson discusses the logic of this major leap. His treatment of this eureka moment is taken directly from Einstein's own book. That said, the problem is this:

On its face, this presentation has never made sense. On its face, it didn't make sense in 1916. On its face, it didn't make sense when it appeared  in Isaacson's book, in 2007.

On its face, the presentation still didn't make sense when Nova folded it into a hundredth anniversary program on Einstein in 2015. We'll review that presentation next week—but on its face, it's fairly clear that it has never made sense.

Sometimes, presentations fail to make sense in clear, straightforward ways. That doesn't mean that anyone will notice or mention such a fact, especially if the presentation carries the imprimatur of high academic authority.

Other times, presentations are hopelessly murky and jumbled. It's harder to explain what's wrong with such presentations, even though they may make little or no clear sense.

At such times, how can we say that a presentation isn't understandable? Suppose a reader has read the passage and has said that he does understand?

Let's apply that sensible question to the first four pages of Isaacson's Chapter Six. As we do, we'll formulate a pair of challenges for the careful general reader.

THE START OF ISAACSON'S CHAPTER SIX strikes us as almost Onionesque. We say that because it asserts a claim which seems to be comically obvious.

Relativity "asserts that the fundamental laws of physics are the same whatever your state of motion?" That assertion has struck us as puzzlingly obvious ever since we first encountered it, way back in '08.

Why wouldn't the fundamental laws of physics remain the same in the circumstance described? Why wouldn't those "fundamental laws" remain the same, even if I rose from my chair and walked across the room? 

Isaacson's sentences are perfectly formed as his chapter begins.  There's (almost) no technical language; there isn't any math. It's easy for readers to blow past the oddity of such a presentation and move to paragraph 2.

It's very easy for readers to do that, especially when their book jacket is covered with blurbs saying that the science has been made easy. It maybe easy for general readers to fail to notice that they don't understand.

At such junctures, we can ask them to answer some questions. With respect to Isaacson's first six paragraphs, we might as such questions as these:

1) What fundamental laws of physics is Isaacson referring to here?  

2) How many such laws can you name? How many such laws exist?

3) Why wouldn't these fundamental laws of physics remain in effect? How "fundamental" would such laws be if they changed on so flimsy a basis?

If the reader can't answer such questions, he or she has been put on notice—at this point, he or she may not fully understand what is being said. Meanwhile, as Isaacson's first four pages proceed, it's easy to think of other basic questions which might be hard for the general reader to answer.

By the third page of Chapter Six, Isaacson has moved from his description of this "simple concept" to a somewhat similar statement—to the claim that "there is no better description of relativity" than a certain presentation by Galileo in 1632.

The presentation is quoted at length. On its face, it seems to make easy-to-understand sense. But we would bet that the general reader would have a hard time with such questions as these:

4) In what way is that presentation a brilliant description of relativity? 

5) Indeed, in what way is it a description of relativity at all?

Thirteen years later, we can't exactly answer those questions ourselves. No matter how smoothly Isaacson's language sails along from page to page, we'll guess that other general readers would crash on the shoals of incomprehension when faced with such questions too.

A passage isn't understandable just because it avoids technical language and formulas and features good sentence structure. A presentation is understandable if the general reader can discuss it in certain basic ways. 

This returns us to something Charles Krauthammer said. Way back in the winter of '88, he described the way we sometimes repeat and recite the things experts say, even though we may not know what our recitations mean.

Also, he had said that it couldn't be done! Krauthammer had read, or had tried to read, Stephen Hawking's reportedly easy-to-understand book, A Brief History of Time.  

Like Richard Cohen before him, Krauthammer said he didn't understand the book. He even suggested that, in the case of modern physics, such things could no longer be done:

I understand, and if asked can readily repeat, the current notion of superstring theory that the universe has 10 (or 26) dimensions, all but four of which are curled up into tiny little balls. But what can that possibly mean?

I can also recite Hawking's solution to the age-old question: Did the universe have a beginning, or has it existed through an infinity of time? Hawking proposes a finesse: space-time is finite in extent but has no boundary or edge. Meaning: space-time is like the surface of the earth, which also is finite (197 million square miles) but round and enclosed, so that you can go around forever without reaching a beginning or an end. A universe of no beginning and no end, but no infinity. I understand. But what does it mean?

The Hawking book may be proof that physics has reached the limits of metaphor...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. Compare physics to biology, for example. Biology is very complicated, but in principle it is comprehensible. Give the man on the Clapham omnibus an hour, and he can gain a reasonable grasp of, say, immunology. Thirteen hours of Hawking have convinced me that you can no longer do that with physics. 

Krauthammer had struggled with Hawking's "inscrutable" book. He offered a simple but instructive assessment:

He could "recite" and "repeat" the things he had read in Hawking's book.  But he didn't know what those statements meant, and he didn't think anyone could make modern physics understandable to the general reader.

We're all inclined to read the nice sentences in some approved text, then to repeat what we've read. Depending on the circumstances, we may decide to take a pass on admitting that we don't understand some part of what we've read.

In our current series of reports, we're focusing on books which attempt to make Einstein understandable, even easy. When someone attempts to compose such a book, he's entered the World Series of explanation. Almost surely, these are the hardest possible explanations we can choose to pursue.

As we'll see in the weeks and months ahead, our remarkable failures in these areas may tend to trickle on down. In the end, it doesn't matter if we can't explain or understand Einstein's universe. In other arenas, our inability to explain and understand may matter a very great deal.

That said, our skill sets are quite unimpressive. Routinely, the spirit isn't especially willing, and the flesh is remarkably weak.

In each of our society's warring tribes, our analytical skills are persistently overrun by our passions. Have we been failed by our useless logicians? In the end, that's what we'll claim.

Next week: On its face, this has never made sense


A SIMPLE CONCEPT: There's "no better description of relativity!"

WEDNESDAY, JULY 28, 2021

What Galileo said:  As we noted last week, several parts of Einstein's universe are easy to describe. In that sense, and to that extent, those parts of Einstein's universe are easy to understand.

As we noted last week, Walter Isaacson describes one such part of Einstein's universe at the end of Chapter Six in his 2007 biography, Einstein: His Life and Universe. Below, we show you that passage again:

The result was an elegant conclusion: mass and energy are different manifestations of the same thing. There is a fundamental interchangeability between the two. As he put it in his paper, "The mass of a body is a measure of its energy content."

The formula he used to describe this relationship was also strikingly simple...

E = mc2.

Energy equals mass times the square of light. The speed of light, of course, is huge. Squared it is almost inconceivably bigger. That is why a tiny amount of matter, if converted into energy, has an enormous punch. A kilogram of mass would convert into approximately 25 billion kilowatt hours of electricity. More vividly: the energy in the mass of one raisin could supply most of New York City's energy needs for a day.

It's easy to understand what's being said in that passage. Tiny amounts of matter can be converted into enormous amounts of energy. 

The raisin which could fuel New York makes this presentation memorable. It may be hard to understand how any such thing could actually happen. But it's easy to understand what is being said.

That easy-to-understand presentation comes at the very end of Isaacson's Chapter Six. Once again, this is his full chapter title:

CHAPTER SIX Special Relativity, 1905

According to Isaacson, the raisin which could fuel New York emerges from Einstein's special theory of relativity. Chapter Six is devoted to that theory. It ends with a presentation which is easy to understand.

As we noted yesterday, the chapter doesn't start that way; in our view, it starts in a highly murky fashion. Today, we'll see the lack of clarity grow—or at least, so it says here—as Isaacson's presentation continues.

Yesterday, we looked at the first six paragraphs in Isaacson's Chapter Six. The chapter opens with a counterintuitive claim—"Relativity is a simple concept"—then wanders forward from there.

The first six paragraphs of the chapter form a fairly obvious unit. We've struggled to make clear sense of that unit ever since we first encountered Isaacson's book thirteen years ago. 

As noted yesterday, Isaacson starts Chapter Six by saying what relativity "asserts." (At this point, he's speaking about the general concept of relativity, not about Einstein's "special theory.")

"Relativity asserts that the fundamental laws of physics are the same whatever your state of motion," Isaacson says in his opening paragraph. But he fails to explain why anyone should be surprised, or should feel informed in some way, by any such assertion. 

From there, he meanders through a set of somewhat fuzzy claims concerning a rapidly-changing set of topics whose interconnections are poorly explained. Thirteen years into our search, we still can't master this wandering presentation.

At the end of this opening unit, Isaacson signals that he is moving ahead to a new point of focus. As we noted yesterday, the transition from paragraphs 5 and 6 to paragraph 7 reads like this:

The special theory of relativity that Einstein developed in 1905 applies only to this special case (hence the name): a situation in which the observers are moving at a constant velocity relative to one another—uniformly in a straight line at a steady speed—referred to as an “inertial reference system.”

It’s harder to make the more general case that a person who is accelerating or turning or rotating or slamming on the brakes or moving in an arbitrary manner is not in some form of absolute motion, because coffee sloshes and balls roll away in a different manner than for people on a smoothly gliding train, plane, or planet. It would take Einstein a decade more, as we shall see, to come up with what he called a general theory of relativity, which incorporated accelerated motion into a theory of gravity and attempted to apply the concept of relativity to it.

The story of relativity best begins in 1632, when Galileo articulated the principle that the laws of motion and mechanics  (the laws of electromagnetism had not yet been discovered) were the same in all constant-velocity reference frames. ...

There you see paragraphs 5 and 6, plus the first sentence in paragraph 7. At this point, we'll be moving back to the year 1632, when "the story of relativity" can best be said to have gotten its start.

We're moving back to something Galileo said in 1632. In our view, the initial murkiness of this chapter only continues as Isaacson explores this early part of "the story of relativity."

AT THIS POINT IN HIS PRESENTATION, Isaacson transitions to a question Galileo addressed in 1632. Copernicus had advanced a revolutionary idea—the idea that the earth doesn't rest motionless at the center of the universe, with everything else revolving around it. 

Traditionalists made the following claim: if the earth was moving, as Copernicus said, we would be able to feel it. In his Dialogue Concerning the Two Chief World Systems, Galileo offered an argument in support of Copernicus’s view.

By modern reckoning, of course, Galileo was right and the traditionalists were wrong. By modern reckoning, the earth is moving at a very high speed around the sun, as are the other planets in the solar system.

As he discusses this historical episode, Isaacson gives a perfectly coherent account of Galileo's response to the traditionalists in support of Copernicus. And sure enough:

 As Isaacson proceeds, it's fairly easy to understand what Galileo is said to have said. 

This new discussion makes fairly clear sense—but does it help the general reader understand what has gone before it in Chapter Six? We would be inclined to say no, but this is the way Isaacson starts this new discussion:

The story of relativity best begins in 1632, when Galileo articulated the principle that the laws of motion and mechanics (the laws of electromagnetism had not yet been discovered) were the same in all constant-velocity reference frames. In his Dialogue Concerning the Two Chief World Systems, Galileo wanted to defend Copernicus’s idea that the earth does not rest motionless at the center of the universe with everything else revolving around it. Skeptics contended that if the earth was moving, as Copernicus said, we’d feel it. Galileo refuted this with a brilliantly clear thought experiment about being inside the cabin of a smoothly sailing ship:

If the earth was really moving, we would be able to feel it! According to Isaacson, Galileo refuted this claim with a thought experiment about a smoothly sailing ship.

At this point, we offer a warning. The first part of that paragraph may be challenging for general readers. The notion that the laws of motion and mechanics "are the same in all constant-velocity reference frames" may be about as clear as Venetian mud for such non-specialist readers.

(Possibly adding to the problem: As we noted yesterday, the use of such technical language shifts about in various ways in this chapter's opening pages.)

That said, Isaacson's treatment of Galileo's thought experiment seems fairly easy to follow. Below, you see the way Chapter Six proceeds through paragraphs 8 and 9, with Galileo quoted at length:

The story of relativity best begins in 1632, when Galileo articulated the principle that the laws of motion and mechanics (the laws of electromagnetism had not yet been discovered) were the same in all constant-velocity reference frames. In his Dialogue Concerning the Two Chief World Systems, Galileo wanted to defend Copernicus’s idea that the earth does not rest motionless at the center of the universe with everything else revolving around it. Skeptics contended that if the earth was moving, as Copernicus said, we’d feel it. Galileo refuted this with a brilliantly clear thought experiment about being inside the cabin of a smoothly sailing ship:

"Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath; and, in throwing something to your friend, you need throw it no more strongly in one direction than another, the distances being equal; jumping with your feet together, you pass equal spaces in every direction. When you have observed all these things carefully, have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still."

There is no better description of relativity, or at least of how that principle applies to systems that are moving at a constant velocity relative to each other.

That's the full text of paragraphs 7-9. Question:

Back in 1632, would that presentation by Galileo have convinced the skeptics that their argument was flawed? Maybe yes and maybe no. But we'll guess that today's general reader would find it reasonably easy to follow the presentation, in which Galileo was apparently saying this:

You can be inside a moving ship without having any idea that the ship is moving. Similarly, you can be riding on a fast-moving planet without experiencing any effects of that motion.

So far, so understandable! But while this may help us understand what Galileo said to the skeptics, does it help us understand what "relativity" holds, asserts or maintains? Does it help us understand the "simple concept" described by Isaacson at the start of this chapter?

At this point, Isaacson proceeds to offer a set of full-length paragraphs fleshing out the physics behind Galileo's presentation. To give you a sense of where this goes, the next four grafs say this:

Inside Galileo’s ship, it is easy to have a conversation, because the air that carries the sound waves is moving smoothly along with the people in the chamber. Likewise, if one of Galileo’s passengers dropped a pebble into a bowl of water, the ripples would emanate the same way they would if the bowl were resting on shore; that’s because the water propagating the ripples is moving smoothly along with the bowl and everything else in the chamber.

Sound waves and water waves are easily explained by classical mechanics. They are simply a traveling disturbance in some medium. That is why sound cannot travel through a vacuum. But it can travel through such things as air or water or metal. For example, sound waves move through room temperature air, as a vibrating disturbance that compresses and rarefies the air, at about 770 miles per hour.

Deep inside Galileo’s ship, sound and water waves behave as they do on land, because the air in the chamber and the water in the bowls are moving at the same velocity as the passengers. But now imagine that you go up on deck and look at the waves out in the ocean, or that you measure the speed of the sound waves from the horn of another boat. The speed at which these waves come toward you depends on your motion relative to the medium (the water or air) propagating them.

In other words, the speed at which an ocean wave reaches you will depend on how fast you are moving through the water toward or away from the source of the wave. The speed of a sound wave relative to you will likewise depend on your motion relative to the air that’s propagating the sound wave.

The first three paragraphs help us understand the physics which prevails inside a smoothly moving ship. Presumably, the same principle obtains on our fast-moving planet, which carries its atmosphere along with it as it travels through space.

This is all well and good for those who want to understand this historical dispute. By now, though, we're on the fourth page of Chapter Six, and we still may lack a clear idea of the way this succession of ruminations is meant to illuminate the "simple concept" which appeared at the start of the chapter. 

Does this presentation about Galileo help the general reader explain the puzzling description of relativity which appears at the start of the chapter? We can't really see why it would.

Meanwhile, how about this statement by Isaacson: "There is no better description of relativity" than the quoted passage from Galileo.

Will the general reader be able to explain that ringing endorsement? You'd have to question the general reader, but we'll guess that he or she would have a hard time expounding on that statement.

In what way does Galileo's presentation qualify as a "description of relativity" which can't be surpassed? Indeed, in what way can it be described as a "description of relativity" at all?  We'll guess that many general readers will have a hard time with such basic questions.

Alas, this Chapter Six! The chapter starts with a somewhat peculiar statement concerning what relativity asserts. At this point, four pages in, to what extent would the general reader be able to speak to that basic topic in an intelligent way?

Has relativity emerged as "a simple concept" in the mind of the general reader? Again, consider the contrast with the presentation with which we began today:

The general reader will have no problem understanding the claim that a small amount of matter can be transformed into a huge amount of energy. Similarly, the general reader will probably have little trouble understanding Galileo's defense of Copernicus' revolutionary claim.

The statement about the production of energy is easy to understand. But at this point, can we expect the general reader to be able to explain what relativity has been said to assert? 

The general reader may be able to repeat or recite the words in that opening paragraph. ("Relativity asserts that the fundamental laws of physics are the same whatever your state of motion.") 

The general reader may be able to repeat those words. But how well will the general reader do if he or she is questioned about that somewhat puzzling statement? Even after the passage from Galileo, we'll guess that he or she wouldn't do especially well.

By the point we've reached today, the general reader is on the fourth page of Isaacson's Chapter Six. Isaacson is making a transition to yet another basic topic, to a discussion of the nature of light.

That next discussion may or may not seem to make sense to the general reader. But how well do these brief discussions of various topics form a coherent larger discussion? How well do these short, successive discussions illuminate some major point?

On a periodic basis, we've been reading Isaacson's book for the past thirteen years. We still can't make  clear sense of these opening pages of Chapter Six. We still can't answer those questions. 

Unlike the brief presentation about the raisin which fueled New York, this part of Isaacson's book has always seemed remarkably murky to us. After thirteen years of parsing his text, that impression hasn't changed.

Next week, we'll be moving to a part of Chapter Six which is taken straight out of Einstein's own book for general readers. At issue is an important part of Einstein's special theory of relativity, the subject of Chapter Six.

In Isaacson's words, the passage concerns the "eureka moment" in which Einstein "took one of the most elegant imaginative leaps in the history of physics." Isaacson's presentation concerning that leap comes right out of Einstein's 1916 text—the book whose lucidity was vouched for by Einstein's awestruck teen-aged niece.

On its face, the presentation in question has never seemed to make sense. Indeed, the passage doesn't seem to make sense in a remarkably straightforward way. More than a hundred years later, it seems that no one has noticed.

Next week, we'll look at that fascinating, straightforward part of Isaacson's Chapter Six. For now, we're still struggling with the meandering way the chapter begins as Isaacson attempts to explain what relativity asserts.

Is the general reader likely to understand the opening pages of Chapter Six? Despite the blurbs by major experts on the jacket of Isaacson's book, it seems to us that the answer is no. 

Tomorrow, we'll offer more thoughts on that possible state of affairs. The science was going to be hard, Isaacson says he was told.

Tomorrow (or Friday): What Brian Greene (and Charles Krauthammer) said


A SIMPLE CONCEPT: It's "a simple concept," he said!

TUESDAY, JULY 27, 2021

Then came his next six grafs:  As we noted last week, several parts of Einstein's universe are easy to report or describe. In that sense, and to that extent, those parts of Einstein's universe are easy to understand.

(Can small amounts of matter be transformed into enormous amounts of energy? We may not understand how such a thing can possibly happen, but it's easy to report and understand that claim, especially since observable events in the real world have shown us that it's true.)

By way of contrast, most parts of Einstein's universe are extremely hard to explain. For that reason, these parts of Einstein's universe are extremely hard for non-specialists to understand. 

Einstein's universe is deeply puzzling—hard! As he worked on Einstein: His Life and Universe, Walter Isaacson was duly warned about this fact, as he noted near the end of his lengthy list of acknowledgements:

Ashton Carter, professor of science and international affairs at Harvard, kindly read and checked an early draft. Columbia University’s Fritz Stern, author of Einstein’s German World, provided encouragement and advice at the outset. Robert Schulmann, one of the original editors at the Einstein Papers Project, did likewise. And Jeremy Bernstein, who has written many fine books on Einstein, warned me how difficult the science would be. He was right, and I am grateful for that as well.

Bernstein delivered a warning to Isaacson—the science would prove to be hard. We'll willing to offer a very safe guess:

Isaacson, being a very smart person, understood that fact coming in. We feel quite sure that Walter Isaacson didn't need to be warned.

Isaacson's 2007 book is a full biography. It covers the events of Einstein's remarkable life as well as the shape of his physics.

Einstein delivered his special theory of relativity in 1905, when he was just 26. His general theory of relativity would emerge ten years later.

Isaacson starts to tackle relativity in his Chapter Six. The bulk of the science is very hard, but, including his chapter title, Isaacson starts with this:

CHAPTER SIX Special Relativity, 1905

Relativity is a simple concept. ...

Relativity is a simple concept? Given the radical nature of Einstein's discoveries, that's an arresting opening statement, one which may capture the reader's attention.

The statement may fly in the face of the reader's preconceptions, but that doesn't mean that it's wrong. That said, is Isaacson able to back his statement up as he proceeds from there? 

In our view, the answer is no. 

For today, we'll look at the first six paragraphs of Isaacson's Chapter Six. (Tomorrow, we'll move on from there.) Those opening paragraphs form a unified discussion. In our view, that discussion is murky, confusing and unclear pretty much all the way down.

We'll also try to establish some criteria for forming a few basic judgments. On what basis can we say that some presentation is unclear? Also, on what basis can we say that a reader hasn't actually "understood" some given passage or presentation?

If a reader feels that he has understood, how can we say that he hasn't? We'll offer one obvious basis for forming such a judgment.

IN FAIRNESS, ISAACSON isn't talking about Einstein's theory of relativity in that surprising first statement, At this point, he's talking about a general principle or concept, a general concept he'll soon trace back to Galileo in 1632.

Isaacson is saying that this general principle is "a simple concept." He isn't saying that Einstein's later theory (or theories) was or were.

That distinction isn't clear as Chapter Six starts, but little else is going to be made especially clear either. As we proceed down this murky road, we'll float a basic question:

How many questions go unanswered as Isaacson discusses this "simple concept" at the start of this important chapter? How many basic questions about this "simple concept" will the general reader still be unable to answer after reading these first six grafs—even after reading the section which follows?

For ourselves, we've struggled with this opening passage—with these initial six paragraphs—ever since we first encountered it back in 2008. We've never been able to puzzle it out. We find it very unclear.

BY ALL ACCOUNTS, Einstein's universe is hard to explain to the general reader. Isaacson takes note of this unavoidable fact right there in his acknowledgments, and then again in the joke he offers on page 3 of his text.

As he starts his Chapter Six, he isn't yet talking about Einstein's special theory. Below, you see his opening paragraph, the first in a group of six:

CHAPTER SIX Special Relativity, 1905

Relativity is a simple concept. It asserts that the fundamental laws of physics are the same whatever your state of motion.

We've got our simple concept right there! "Relativity...asserts that the fundamental laws of physics are the same whatever your state of motion." 

Stated that way, it may well seem that we're being acquainted with a simple concept. It may seem that this opening statement is easy to understand.

There is no obvious technical language. No formulas or mathematical symbols appear.

The sentences are relatively short, and they're perfectly crafted. In that superficial sense, that passage is easy-to-read—but unless we simply want to recite or repeat the various things we've been told, it leaves many things unexplained.

(See Charles Krauthammer's claim about modern physics. In 1988, he said modern physics had become so complex that we can only repeat and recite the things we're told about it. We can repeat and recite the things we're told, but we won't understand them.)

Simple though it may seem on its face, the opening paragraph of Chapter Six has struck us as puzzling right from the first time we read it. A basic question lies at the heart of our puzzlement:

Why would "the fundamental laws of physics" change on the basis of on my state of motion? How "fundamental" could such laws be if they suddenly decided to change because I've risen from my chair and walked across the room?

Why would the fundamental laws change on a basis like that? Why would anyone be inclined to think that they would?

The basic laws of physics don't change because I get up from a nap? If that is the heart of "relativity," the concept seems to pass beyond the realm of the simple to the land of the simple-minded. 

Meanwhile, for the general reader, this secondary question might arise at this point in time:

What are the fundamental laws of physics? How many such laws are there? Can the general reader name as many as one? 

At this point, the general reader is something of a stranger in a somewhat strange land. Almost surely, the general reader has no idea what Isaacson's talking about at this point. In theory, that state of affairs can be set right—but here's what we're told next:

CHAPTER SIX Special Relativity, 1905

Relativity is a simple concept. It asserts that the fundamental laws of physics are the same whatever your state of motion.

For the special case of observers moving at a constant velocity, this concept is pretty easy to accept. Imagine a man in an armchair at home and a woman in an airplane gliding very smoothly above. Each can pour a cup of coffee, bounce a ball, shine a flashlight, or heat a muffin in a microwave and have the same laws of physics apply.

We're told that this concept is "easy to accept" in a special type of case—in the special case in which observers are moving at a constant velocity. 

In our view, the concept seemed "easy to accept" as a general matter, right from the jump. But we're told it's very easy to accept the concept in this special case—a special case which now seems to involve two different people.

We're now talking about two observers, not just the original one. One is sitting in an armchair. The other is gliding smoothly in an airplane.

We're told that each can pour a cup of coffee and have "the same laws of  physics" apply. It's still hard to know why that should be surprising, but another source of potential confusion has now entered the field.

We're told that these two observers are "moving at a constant velocity"—but in what way is that true of the man in the chair? In common parlance, he isn't moving at any velocity at all. Have we been exposed to some technical language without an attempt to explain it?

Just for the record, we still don't know what laws of physics apply to these people as they pour their cups of coffee. We still don't know why anyone should be surprised to learn that "the [same] fundamental laws of physics" prevail in these two circumstances—and we certainly don't know why anything which seems so mundane should or could actually matter.

To this point, Isaacson's language is gliding along just as smoothly as the woman's ride in that airplane. But now, he suddenly seems to change course and head in a new direction:

CHAPTER SIX Special Relativity, 1905

Relativity is a simple concept. It asserts that the fundamental laws of physics are the same whatever your state of motion.

For the special case of observers moving at a constant velocity, this concept is pretty easy to accept. Imagine a man in an armchair at home and a woman in an airplane gliding very smoothly above. Each can pour a cup of coffee, bounce a ball, shine a flashlight, or heat a muffin in a microwave and have the same laws of physics apply.

In fact, there is no way to determine which of them is “in motion” and which is “at rest.” The man in the armchair could consider himself at rest and the plane in motion. And the woman in the plane could consider herself at rest and the earth as gliding past. There is no experiment that can prove who is right.

Indeed, there is no absolute right. All that can be said is that each is moving relative to the other. And of course, both are moving very rapidly relative to other planets, stars, and galaxies.

At this point, Isaacson seems to begin discussing a different, somewhat abstruse point. It isn't that anything he says here is "wrong," but he makes no attempt to explain why he has suddenly seemed to shift his field. 

Meanwhile, consider this sentence:

"Indeed, there is no absolute right."

A supple reader can perhaps imagine what Isaacson must have meant by that oddly constructed statement. We'll guess he meant something like this: 

There's no ultimate way to say that one of these people is moving and the other person isn't.

A great deal more could be said about the principle involved in that statement, but we'll guess he meant something like that. (Spoiler alert: Writers of Einstein-made-easy books, not excluding Brian Greene himself, often seem to reverse themselves on this basic point, as we'll see below.)

We'll guess that Isaacson meant something like that. But already, at the start of paragraph 4, Isaacson's perfectly formed sentences have given way to a construction which seems to have emerged from a land which lies beyond the realm of everyday, easy-to-understand speech.

How do paragraphs 3 and 4 connect to paragraphs 1 and 2? To this day, we can't say that point is clear as we read this presentation.

Nor can we say that we understand the "simple concept" with which we began—a simple concept which still seems to be oddly simple-minded.

Isaacson continues as shown below. Einstein's special theory is now specifically mentioned, but along the way, has a certain reversal occurred?

The special theory of relativity that Einstein developed in 1905 applies only to this special case (hence the name): a situation in which the observers are moving at a constant velocity relative to one another—uniformly in a straight line at a steady speed—referred to as an “inertial reference system.”

It’s harder to make the more general case that a person who is accelerating or turning or rotating or slamming on the brakes or moving in an arbitrary manner is not in some form of absolute motion, because coffee sloshes and balls roll away in a different manner than for people on a smoothly gliding train, plane, or planet. It would take Einstein a decade more, as we shall see, to come up with what he called a general theory of relativity, which incorporated accelerated motion into a theory of gravity and attempted to apply the concept of relativity to it.

We're told that Einstein's special theory applies only to this special type of case. We still aren't told what the theory maintains, but we're told told that it only applies to situations involving a pair of "observers."

Meanwhile, notice this: Has Isaacson perhaps reversed himself on the question of what he now calls "absolute motion?" 

In paragraph 4, we were told that "there is no absolute right" concerning the question of which observer, the man or the woman, was in motion. Now we're told that it's harder to say that certain types of people actually aren't "in some form of absolute motion." 

Is a contradiction lurking there? Is it only harder to make the case, even though the previous principle holds? For our money, this is one more element of confusion which appears in this opening in passage—an opening passage which began with a statement about "a simple concept" which seems to be simple-minded.

In fairness to Isaacson, he has only offered six paragraphs in Chapter Six at this point. If some lack of clarity exists in those opening paragraphs, he could proceed to resolve it.

Instead, he shifts his focus to Galileo in 1632. Tomorrow, we'll look at what he says, but his new passage starts like this:

The story of relativity best begins in 1632, when Galileo articulated the principle that the laws of motion and mechanics...were the same in all constant-velocity reference frames. 

The laws of motion and mechanics are the same in all "constant-velocity reference frames," we're now told. Our question for the general reader is this:

Is a "constant-velocity reference frame" the same thing as an “inertial reference system?" (See paragraph 3, where that technical term is introduced.)

Is the reference frame the same thing as the reference system? To this day, some thirteen years later, we still can't say that we're totally sure.

For our money, Isaacson's opening passage is extremely murky. For our money, it may have the feel of a passage which was "written by committee"—imaginably with too many high-ranking physicist cooks throwing pinches of language, and an array of concepts, into the teeming broth.

This opening passage strikes us as very jumbled. At the heart of our puzzlement lies the question with which we started: 

Why would anyone be surprised to learn that the fundamental laws of physics (whatever they may be) apply in a wide array of cases? Why wouldn't that simple statement be something like a tautology? Why wouldn't that statement be obvious pretty much just on its face?

"RELATIVITY IS A SIMPLE CONCEPT." That's what the general reader is told as Isaacson's Chapter Six starts. 

We're even told what the concept asserts. Relativity "asserts that the fundamental laws of physics are the same whatever your state of motion." 

We're then exposed to a jumble of concepts, in a progression which doesn't seem to make clear sense. Nor do things get any clearer as Isaacson proceeds to explain what Galileo once said.

The general reader can always recite and repeat Isaacson's words. He can read every word on every page. He can then say, and even believe, that he understands what he's read. 

For ourselves, we've never been able to extract clear sense from this opening passage—and we've been trying for years.

Is anything "wrong" in that opening passage—in those first six paragraphs? We can't say that anything's "wrong." But we also can't say that anything much in that passage has been made especially clear. 

Is relativity a simple concept? Many questions may stump the general reader after this strangely simplistic concept has allegedly been unpacked.

Einstein's universe is very hard. Must it be as opaque as this? Our light-speed journey will continue tomorrow, and in the weeks ahead.

Tomorrow or Thursday: What Galileo said


A SIMPLE CONCEPT: "A simple concept," Isaacson says!

MONDAY, JULY 26, 2021

After that, conceptual chaos:  Has anyone ever been able to make Einstein's universe understandable for the general reader—for the non-specialist? Has anyone ever been able to make Einstein easy?

In the first two weeks of our rumination on this topic, we've mentioned five books by four different writers who tried to accomplish that task. Our list includes Einstein's own early attempt to explain his universe to the general reader. 

We've mentioned the following writers and the following books:

Albert Einstein: Relativity: The Special and the General Theory (1916)

Stephen Hawking: A Brief History of Time (1988)

Brian Greene: The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory (1999)

Brian Greene: The Fabric of the Cosmos: Space, Time, and the Texture of Reality (2004)

Walter Isaacson: Einstein: His Life and Universe (2007)

These are hardly the only books which have tried to make Einstein easy. For now, though, they'll have to do. We offer a quick overview:

Einstein's 1916 book stands out for the obvious reason. The book was Einstein's own attempt to make his theories of relativity understandable for the general reader.

As of 1988, Hawking was considered to be one of the last century's most accomplished theoretical physicists. Surprisingly, his book became a massive best-seller. It was widely praised for the way it made modern physics understandable.

Greene is also a major theoretical physicist. Each of the books by Greene was turned into a multi-part series on PBS. 

This leaves Walter Isaacson as the outlier on this list. Isaacson isn't a physicist, and his book, alone on this list, is structured as a full biography of Einstein, not just as an account of the science.

Isaacson isn't a physicist, but he is a highly experienced major journalist and a widely acclaimed biographer. Beyond that, he had access to a wide range of major physicists as he assembled the parts of his book which detailed Einstein's universe rather than Einstein's life.

No one could think that Isaacson shirked as he tried to get the science right—or in his effort to make the science understandable. In his Acknowledgments, he thanks a long list of major physicists who helped with those tasks.

His list starts—repeat, starts—like this:

Brian Greene, the Columbia University physicist and author of The Fabric of the Cosmos, was an indispensable friend and editor. He talked me through numerous revisions, honed the wording of the science passages, and read the final manuscript. He is a master of both science and language...

Lawrence Krauss, professor of physics at Case Western Reserve and author of Hiding in the Mirror, also read my manuscript, vetted the sections on special relativity, general relativity, and cosmology, and offered many good suggestions and corrections. He, too, has an infectious enthusiasm for physics.

Krauss helped me enlist a protégé of his at Case, Craig J. Copi, who teaches relativity there. I hired him to do a thorough checking of the science and math, and I am grateful for his diligent edits.

Douglas Stone, professor of physics at Yale, also vetted the science in the book. A condensed matter theorist, he is writing what will be an important book on Einstein’s contributions to quantum mechanics. In addition to checking my science sections, he helped me write the chapters on the 1905 light quanta paper, quantum theory, Bose-Einstein statistics, and kinetic theory.

The acknowledgements start with Greene himself. From there, they proceed through an extensive list of highly qualified physicists who served as editors and, in some cases, as virtual co-writers. 

In addition to the scholars named above, Isaacson describes the contributions of a dozen more highly qualified academics. No one could think that Isaacson shirked in his attempt to get the science right, and to make it understandable.

Isaacson was diligent—and Isaacson is smart. From the jump, he understood that it wouldn't be easy to make Einstein's universe accessible to the general reader. Near the end of his lengthy list of acknowledgements, he offers these well-chosen words:

Ashton Carter, professor of science and international affairs at Harvard, kindly read and checked an early draft. Columbia University’s Fritz Stern, author of Einstein’s German World, provided encouragement and advice at the outset. Robert Schulmann, one of the original editors at the Einstein Papers Project, did likewise. And Jeremy Bernstein, who has written many fine books on Einstein, warned me how difficult the science would be. He was right, and I am grateful for that as well.

In addition, I asked two teachers of high school physics to give the book a careful reading to make sure the science was correct, and also comprehensible to those whose last physics course was in high school. Nancy Stravinsky Isaacson taught physics in New Orleans until, alas, Hurricane Katrina gave her more free time. David Derbes teaches physics at the University of Chicago Lab School. Their comments were very incisive and also aimed at the lay reader.

Isaacson was warned that the science would be hard. Presumably, he knew that coming in. 

Beyond that, he even checked with two high school teachers to make sure that his accounts of this (very difficult) science would be comprehensible for general readers. We're forced to make a whimsical point:

Based upon her name, one of these teachers may have been related to Isaacson. In a brief but instructive part of his book, Isaacson describes the way Einstein, a giant of world intellectual history, tried to check the lucidity of his own 1916 text.

Einstein asked his awestruck teenaged niece to  review his 1916 text as a way to assess its lucidity. This seems to have been a flawed decision, for reasons Isaacson whimsically describes in his book.

Walter Isaacson isn't a physicist, but he had plenty of help from such experts. Imaginably, he may have received too much help from too many such experts. 

Some of these scholars, Greene included, blurbed the book with words of high praise. In quite a few cases, they praised the book for the way it made the science accessible for the general reader. 

"Isaacson's treatment of Einstein's scientific work is excellent: accurate, complete," Yale's Professor Stone wrote in his editorial review of the book. Also, Isaacson's treatment included "just the right level of detail for the general reader." 

In his acknowledgements, Isaacson thanked Harvard professor Gerald Holton for being willing "to read my book, make comments and offer generous encouragement." Holton joined Stone in his assessment of Isaacson's book. 

"It is excellently readable," Holton wrote in his own review of Isaacson's book. As a general matter, we'd strongly disagree with that assessment. 

We'd strongly disagree. We're general readers ourselves, and it seems to us that Isaacson's attempts to explain the science are almost wholly incoherent almost every step of the way. In fairness, the same has been true of the many writers who tackled this daunting project before him. 

Professors Greene, Stone and Holton are high-ranking academics. They actually do understand the mathematics and the physics of Einstein's astonishing universe. 

They know the mathematics, and they know the physics! But perhaps for those very reasons, they may not always be the best judges of what will be understandable to the general reader, who very much does not. 

Next week, we'll examine one highly significant, puzzling passage from Isaacson's book—a passage which comes straight from Einstein's 1916 text. On its face, the presentation has never seemed to make sense, and no one has ever noticed.

That said, it seems to us that Isaacson's treatment of relativity is basically incoherent, right from the first few paragraphs he offers on the subject. 

To our eye and ear, his presentation has the feel of a text written by committee—of a text which may have been edited and reviewed by too many qualified experts. 

Beyond that, these highly qualified theoretical physicists understand the mathematics which underlie Einstein's deeply challenging universe. But do they understand the warp and woof of clear, cogent explanation—the kind of cogent explanation which would have a chance of making sense to general readers?

We know of no reason to assume that they do. But at any rate, Isaacson's treatment of relativity strikes us as almost wholly incoherent right from his opening passages.

Einstein devised his special theory of relativity in 1905, when he was just 26. Isaacson starts to tackle that topic in Chapter Six: Special Relativity, 1905.

(Einstein's general theory of relativity came along ten years later.)

Chapter Six starts with five fateful words: "Relativity is a simple concept." What follows, though, is extremely unclear.  In our view, there's a great deal to learn from that fact.

For all we know, it may be true that relativity is "a simple concept" in its broadest outlines. It may also be true that Einstein's special theory of relativity can be made understandable for general readers. 

But has anyone ever delivered on any such claims? As far as we know, the answer is no.

In our view, a great deal about our world can be learned from that fact.

Tomorrow: Six puzzling paragraphs


PITFALLS: "Mommy, the trees appear to be moving!"

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.

To peruse the full chapter, click here.

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."