Johns Hopkins Magazine -- February 1999
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What is the most difficult instrument to master? Cosmological conundrum to crack? We asked a half dozen Johns Hopkins experts to share the biggest challenge of their discipline.

S P E C I A L    S E C T I O N

Degrees of Difficulty
Illustration by Wally Neibart

What is the most difficult language to learn?
What is the most difficult math problem to solve?
What is the most difficult cosmological conundrum to crack?
What is the most difficult instrument to master?
Who is the most difficult philosopher to fathom?
What is the most difficult procedure to perform?

What is the most difficult language to learn?
Richard Brecht
Deputy Director,
National Foreign Language Center

Japanese is without question the most daunting language for a native English speaker to tackle, according to Brecht. "I would like to learn Japanese but I don't have enough time in my lifetime. That's very depressing," says the linguist, whose center is based at Hopkins's Nitze School of Advanced International Studies (SAIS). He notes that the State Department allows its students three times as long to learn Japanese as it does languages like Spanish or French.

As Brecht explains it, the challenge with Japanese is threefold. First, there's the fact that the Japanese written code is different from the spoken code. "Therefore, you can't learn to speak the language by learning to read it," and vice versa. What's more, there are three different writing systems to master. The kanji system uses characters borrowed from Chinese. Users need to learn 10,000 to 15,000 of these characters through rote memorization; there are no mnemonic devices to help. Written Japanese also makes use of two syllabary systems: kata-kana for loan words and emphasis, and hira-gana for spelling suffixes and grammatical particles.

Get beyond that and you're faced with a culture that, says Brecht, is "truly foreign for most Americans." With many languages, students start by learning introductions (Comment-allez vous? Tr�s bien, merci, et vous?) "But with Japanese, you can't even begin to do that with lesson one because of the social distinctions involved in making introductions," says Brecht. Age, social status, gender--"all these sociological factors make it so complicated that introductions can't be the first lesson," he notes.

Finally, there's the issue of grammar. In English syntax, grammar is right branching. We set a topic and then comment upon it: "I saw the man who was sitting on the red chair, which was sitting beside the door." Japanese syntax is left branching-- "totally contrary to our approach," says Brecht. Thus, the sentence above becomes something along the lines of: "I saw the red, which was the chair, which was....." You get the idea.

While exceedingly difficult, mastering Japanese is not impossible for English speakers, Brecht concedes. "There are thousands of students in our classes at SAIS who learn to function in Japan. It takes really good students and a lot of devotion."
--Sue De Pasquale

What is the most difficult math problem to solve?
Ed Scheinerman
Mathematical Sciences

The ancient Greeks began stewing over the following problem: Using only a compass and unmarked straightedge, divide a 60� angle into three equal parts. In other words, construct a 20� angle. No protractors allowed.

It is a deceivingly simple problem, says Scheinerman. But it was not until 1837, after generations of mathematicians had attempted in vain to solve it, that a French bridge and highway engineer named Pierre Louis Wantzel finally cracked the angle trisection problem. The answer: It cannot be done.

"It is impossible," declares Scheinerman. "But the hard part is understanding why you cannot do it."

Would he demonstrate why?

"No," responds Scheinerman. "It would take a semester."

But the friendly professor agrees to attempt a general explanation. "It boils down to taking a cube root," he says. A compass and straightedge can be used to add, subtract, multiply, divide, and calculate a square root of a given length. But angle dissection ultimately requires taking a cube root. "And that cannot be done with these tools. It is no more possible than adding together two even numbers to get an odd number."

Wantzel's proof involves showing that the algebraic powers of a compass and straightedge--adding, subtracting, multiplying, etc.- -cannot be used to produce cube roots. (There are many hard math problems, notes Scheinerman. Angle trisection may not be the most difficult, but it certainly took the longest.)

"In some sense, the Greeks never had a chance," says Scheinerman. The abstract algebra required to prove that the angle trisection problem cannot be solved was not developed until Wantzel's time. "It took a lot of understanding of the interplay between numbers and geometry."

Nevertheless, some stubborn souls continue to attempt a solution. Every year several amateur mathematicians submit a new "solution." Mathematician Underwood Dudley has compiled a collection of these "proofs," called A Budget of Trisections (Springer-Verlag, 1987). The only problem, says Scheinerman, is that they are all erroneous.
--Melissa Hendricks

What is the most difficult cosmological conundrum to crack?
Rosemary Wyse
Physics and Astronomy

The universe's deepest, darkest secret, which so far has defied cosmologists' probing, is the nature of dark matter, Wyse replies. "Dark matter is extremely important," she says. "It is the dominant component of the universe." In fact, astronomers estimate that there is about 10 times more dark matter than luminous matter (matter that can be seen).

What makes dark matter so puzzling is that it is invisible to telescopes and other instruments that espy the photons of stars and galaxies. So rather than observe the stuff directly, astronomers infer its existence through indirect means, essentially by measuring its gravitational tug.

"But essentially everything has gravity," notes Wyse. "So how you would detect dark matter is extremely difficult."

Astronomers have posited many candidates for the nature of the dark matter. Perhaps it is made up of strange particles not included in the Standard Model of physics. Another theory: Very faint, barely luminous stars might account for some or all of the dark matter.

Wyse recently tested the second theory. Using the Hubble Space Telescope, she probed deeply into a galaxy that contains an especially immense amount of dark matter (about 10 times the normal ratio of dark/luminous matter). If dark matter were composed of very faint stars, then this galaxy ought to contain an abundance of them. The number of stars ought to increase the deeper (i.e., fainter) Wyse probed. But such was not the case. "We went down to a few tenths of a solar mass and we didn't see any difference in the number of stars," she says. "So it argues against the dark matter being very faint stars."

The universe's most puzzling problem has yet to be solved.

What is the most difficult instrument to master?
Robert Sirota
Peabody Conservatory

The amiable Sirota won't bite. "You could argue that strings are more difficult to play than keyboards because you need to adjust the [tuning] by ear," he says. "But a pianist needs a very fine ear for color dynamics, to hear various qualities of the timbre. And on the piano, you may be playing four or five melodies at the same time, which requires multitasking."

What about the French horn, a notoriously treacherous instrument? The horn's conical bore does make finding pitches very challenging; it's all in the lip, and the potential for cracking a note looms ominously for even the most seasoned player, he concedes. "But is it more difficult to play the Strauss tone poem "Heldenleben" than Rachmaninoff's Third Piano Concerto? I couldn't say."

One thing Sirota is certain about: "There is not necessarily a correlation between how difficult something sounds and how difficult it is to play."

He bristles at the adulation given the showiest musical performers. "This isn't a Las Vegas show, P.T. Barnum," he says. "For many of us, playing a Bach fugue is the most difficult thing to [play well], even though it doesn't sound difficult."

Hastily pushing back his chair, he dashes to a Steinway in the corner of his peacock blue office. "I could play something like this," he says, and tosses off a Debussy prelude, a loud, lush melody with many flourishes. "Or like this," and the director this time launches into a Bach Sarabande at a fraction of the volume and tempo. "The Bach piece, with its mastery of counterpoint, is actually much more difficult," Sirota says. "With any instrument, the subtle gradations of sound, the slight nuances that distinguish one expressive moment from another, are more difficult than the noise and flash of one virtuoso movement."

And that, he says, is what is wrong with today's notion of "the prodigy."

"We have a romantic myth about the prodigy, that he or she can do all kinds of pyrotechnics on an instrument," Sirota says. "But there is a difference between athletic ability and true artistic expression." Usually a prodigy is good at the first, he says. "But it takes maturity to accomplish the second."

Who is the most difficult philosopher to fathom?
Jerome Schneewind
Philosophy Department

"Kant," replies Schneewind, without a second's hesitation. "I've spent 40 years trying to figure out what Kant meant in [Groundwork]," the little book considered among those central to the history of modern moral philosophy. "Now I think I have some idea of at least two parts of it."

What makes the prospect of studying the 18th-century German philosopher so daunting? First, there's the issue of style. A single Kantian sentence can run on for more than a page. Many German scholars turn to English translations--which break Kant's convoluted sentences into shorter ones--to better figure out what he first said in German, Schneewind says.

Another cause for vexation: Kant's "examples don't usually clearly exemplify what he has in mind. Students have a terrible time getting it straight--so do professionals and commentators," Schneewind says.

Those who can get beyond how Kant makes his points frequently find themselves stymied by what he has to say. "He has something difficult to convey; something that, in itself, was quite revolutionary." Plato thought of morality as requiring conformity to eternal Forms of the Good and the True, Schneewind explains. Christian Europe thought of morality as essentially involving obedience to God. Kant's revolutionary thought is that morality is obedience to a law we impose upon ourselves. "In being self-legislative in this manner, we are God's equals, not his subordinates," says Schneewind. "It is a view that still shocks orthodox Christians."

Schneewind, author of The Invention of Autonomy (Cambridge University Press, 1998), covers the philosopher in both his graduate ethics seminars and in an intro course for freshmen and sophomores--most of whom have never taken a philosophy course before. His teaching strategy: Start with Aristotle and Hume, so that students have a basis for contrast. "In order to understand a philosopher, you need to understand what he or she is not saying," says Schneewind. The bearded professor is also up front with his students: "I tell them, 'This is very badly written, but you'll have to live with it.'

"If you have any luck, you will leave them convinced that Kant had hold of something very important indeed." He stops, then smiles. "And then, if they have the unfortunate tendency to like philosophy, they'll spend the rest of their life worried about it. That's what happened to me. My first teacher of Kant didn't explain it very well. He kept me puzzled."

What is the most difficult surgical procedure to perform?
John Cameron
Surgeon in Chief, Johns Hopkins Hospital

"For decades the Whipple procedure has been considered the most technically challenging," says Cameron. Formally known as a "pancreaticoduodenectomy," the Whipple is used to remove cancers of the pancreas. It is named for a Columbia University surgeon who demonstrated the technique in the 1930s.

Pancreatic cancers often do not cause any symptoms, and many patients do not learn they have the illness until the cancer is advanced and inoperable. Only a minority of patients are candidates for surgery, and until about 20 years ago, even those patients had a 25 percent chance of dying during or soon after surgery, mainly from blood loss.

But in recent years, Cameron and a handful of other surgeons have honed their skill at the Whipple procedure almost to perfection. At Hopkins, fewer than 2 percent of patients who undergo the procedure now die from its complications.

One reason that the Whipple is so difficult is that the pancreas is about as deep inside the body as an organ can possibly be. The 10-inch long yellowish organ is wedged between the stomach and backbone. To get to it, surgeons painstakingly remove one organ system after another.

"We take out the duodenum (the upper small intestine), bile duct, gallbladder, part of the stomach, and about one-third of the pancreas," says Cameron. Surgeons tie off and sever the blood vessels leading to each organ system. They then cut out the tumor, which can be as tiny as a pea or as large as a golf ball, and cut around the diseased area, ultimately removing about a third of the pancreas. They then reconstruct what remains of the pancreas and the gastrointestinal tract. The whole procedure takes about six hours.

"There are so many structures that come together there; lots of large blood vessels are in the vicinity," says Cameron. "There are lots of opportunities for blood loss."

Cameron, who has spent his entire career at Hopkins, has performed more than 500 Whipple operations. The secret to improving the outcome for the procedure has been pure and simple practice, he says. At Hopkins, about 150 to 200 patients undergo the Whipple procedure each year, more than at any other hospital in the United States. "It is done well at only a few hospitals. Unless it's done in great numbers, surgeons don't get good enough at it to do it well," says Cameron.