by Pepper White
Step 2. Go to Barker Engineering Library and look through every book on thermodynamics to see whether the example has been worked out in print before. Notice that tables of contents are almost identical for all the thermo books. Fail to find worked-out solution of balloon-filling problem. Quit working on the problem for the time being.
One week later
7:00 A.M. Shave. Brush teeth. Rinse. Spit. Step 3. Flash of inspiration. Redraw picture on paper towel ...
The old picture is intractably complex because the geometry of the balloon's expanding is three-dimensional and I'm not a mathematician, I'm an engineer. If I convert to the new picture, I can clearly see the stretchiness of the balloon lumped into a spring that can expand and contract, and I can see the expanded volume aspect as a movable balloon skin wall with very little mass, moving in only one direction. If the equations for the simplified approach are similar to the equations for the real balloon, I can predict the behavior of the real balloon with my simplified, one-dimensional equations. This is what they mean by a model.
Step 4. Redraw new picture, showing the motion of the balloon skin.
As air enters the balloon from the tank, the balloon skin moves (A2) and the spring stretches. Now to remember the problem. Find how the balloon volume varies with time. The volume of the imaginary, one-dimensional cylindrical balloon is just its length times the constant area of its circular movable skin. The problem reduces to finding how the balloon length varies with time. I'm making progress.
February 27
Professor Heywood's Internal Combustion Engine class was on the third floor of Building 38, in another interior room with dimmers.
Heywood favored the handouts and slides approach to lecturing. He distributed copies of what would be on the screen and pointed to the diagram and made notes on the transparencies with different colored pens. This was efficient both for him and for us. We would not waste time trying to redraw what would be easier for him to photocopy, and Professor Heywood would not get chalk dust on his beige corduroy jacket.
Heywood was trim and looked younger than his forty-five years. Maybe the bicycle ride to and from his house in Newton every day helped. He was one of the many mechanical engineering professors who cycled to work even though funded by oil and car companies-he valued efficiency.
He'd received tenure young, and although smarter than most of the faculty, he hadn't started a company. He preferred to write his book, to consult when asked to, to be a distinguished scholar. One day I saw him eating his lunch and looking out onto the trees of Killian Court, perhaps thinking about how MIT wasn't quite as pleasant an environment as Cambridge or London's Imperial College, but the pay and the taxes were better here, and America's auto industry wasn't dead yet. Perhaps one day the Sloan Lab would be the Heywood Laboratory, and labbratory would be pronounced the British way.
The day's lecture concerned volumetric efficiency, or how much air you can push into a can. If the bottom of the can moves up and down, you have something like the heart of an internal combustion engine, a.k.a. the cylinder. If you can figure out how to push more air into the can, you can put more fuel in and then use the more air to burn the more fuel. It's sort of like blowing up a balloon.
Toward the end of the lecture, Professor Heywood mentioned that the volumetric efficiency of an engine decreases markedly as elevation above sea level increases and air becomes thinner.
The fellow sitting next to me in the front row just right of center raised his hand and was recognized by Professor Heywood. "Yes, Ari."
"You are absolutely right, Professor. Thees phenomenon was a great problem for my tank batallion on the Golan Heights. Fortunately, it was also a problem for the Russian-made Syrian tanks."
"Thank you for mentioning that," Professor Heywood said. "That's a good example of how important an issue volumetric efficiency is."
Professor Heywood finished his lecture and I introduced myself to An. He looked as if he was in his late thirties or early forties and his hair, parted on the side, was graying and thinning a lot. He wore glasses, a plaid shirt, and jeans and had a bit of a paunch.
"How do you do, Meestair Pepper White," he said. "Would you like to join me for a cup of coffee at the student center?"
"Sure," I said. As we walked and talked he told me a bit about his background. Presently a major in the Israeli army, he'd been born to Romanian Holocaust survivors just after World War II and then raised in Israel from the birth of the nation. He had graduated from the Technion in Haifa with degrees in both mechanical engineering and industrial management and was on the second of three years of leave from the army to get a Ph.D. at MIT. A general had done precisely that, and the degree to end all degrees had helped that general advance from major and colonel. Ari hoped the same would happen for him.
After coffee, Ari said, "Come, my friend. I want to show you something in the room next door here." We entered the video game room, in general occupied by the geekiest of the geeks, the ugliest acne-ridden prototypes of what people expect of MIT nerds. Instead of thinking about how to have a life, how to maybe go out on a date, they while away their leisure minutes looking at a cathode ray tube and make rapid gestures with the buttons below the screen. If I ever felt ugly or fat or like I had a bad complexion, I'd go to the video game room and come out feeling ready for a modeling career.
(Some of the video geeks had a major advantage on the games; they knew where the hacks were. A hack is a trick encoded by the programmer who designs the machine so that he can play the game forever at whatever bar he happens to be in. Since half the people who program the video games are from MIT, and many of the programmers from MIT worked for video game developers during high school or during their summer jobs, there is a fair amount of insider video hack trading. It's a constant source of annoyance to the people who control the video game industry.
It's only fair that there should be some mastery of these machines by MIT students. The first video game, PONG, the little black and white bars that I moved back and forth with a joystick when I was a freshman at Hopkins, was invented as a semester project by two students in course six one eleven, MIT's Digital Electronics lab.)
Ari put a quarter on the ledge below the Tank Commander screen to establish our place in line. When our time came, he said, "You go first. I will pay."
"Thanks. Could you give me a little briefing on how to work this thing?"
"Certainly. You need to put one hand on each joystick. If you want to go forward, you push both joysticks forward, and you pull both back if you want to go backward. Each joystick controls one of the treads of the tank, just like in a real tank. If you want to turn right, push the left one forward and pull the right one back, and you do it the other way to go left. When you've lined up on the target, press both buttons on top of the joysticks."
He put the quarter in and I gave it a shot. It was fun to see the barrel of the tank move up and down with the simulated noise of the tank corresponding to whichever way I was turning to avoid the enemy fire and shoot on the pillboxes. Ari's coaching helped"Right ... back ... forward ... left ... now fire!"-and in my thirty seconds I knocked out three of the pillboxes. I could get good at this after a few hundred quarters.
Then it was Ari's turn. He stood farther from the machine than I did and bent over so his torso was almost horizontal. "I get a better feeling for the machine this way," he said.
Boom, pow, left- right- forward-back-Ari was a master. He jerked the joysticks quickly, decisively, grunting as if all his nervous energy were channeled into reflexes and fast response. Three minutes and 97 pillboxes later one finally got him.
"You must play this a lot," I said.
"Not this one, actually," he answered. "I developed my abilities with the real thing during the Six Day War and the October War. And this one is much easier because I am not afraid for my life when I play it. I find it very relaxing."
February 28
Back to the balloon. Step 5. Refer to picture from Step 4. Think a
bout problem again. Remember fluid mechanics study session with Mary et al. and Bernoulli looking over the bridge on the Arno at the two rocks. If the pressure in the tank is not a whole lot higher than atmospheric pressure, and the air is therefore not compressible, I can call it incompressible flow and use Bernoulli's equation. That will tell me how fast the air will flow from the tank into the balloon, depending on how much pressure there is in the tank compared to how much is in the balloon.
I can also say that everything that goes into the balloon results in enlargement of the balloon. That's another equation, called the continuity of mass equation.
And finally, I can balance the forces on the skin of the balloon-the stretchiness of the balloon has to be balanced by the air pressure inside and outside the balloon. That gives me three equations and five unknowns.
Now all I have to do is show how x varies with time, so I can graph the position of the balloon and Greene will think I'm a hero.
Step 6. Dust off differential equations book from sophomore year at Hopkins. A differential equation deals with things that move in time, like the piston of an engine, the earth, and the moonor the skin of a balloon being blown up.
Everything in the differential equations book deals with "linear" differential equations. That means that the second term, the x-dot-squared term, means I can't solve this using any methods in that book. I'm multiplying the velocity by the velocity, and that makes it "nonlinear."
Step 7: Punt. This is what you do at MIT when the institute or the problem set has painted you into a corner.
March 2
Greene looked quickly through my steam system solution, checking off the steps with his Cross pen. Then he asked me to go to the blackboard to present my solution to the balloon problem.
"Now that is a good idea," he said of my making the balloon expand in only one direction. "You know, in my years as a manager, I've found that there are people who are creative and can invent things and then there are people who can analyze things that the creative people have invented. Not many people can do both, but this solution shows me you might be one of them."
Kvel city. This guy's bound to give me an A. They won't be able to kick me out, after all.
I went through the steps for him and showed him my insoluble set of equations. "This is my answer," I said. "Unfortunately, I don't know how to solve it, to be able to graph the position of the skin of the balloon as a function of time. I thought you might have some suggestions."
"Well, if you brought that problem to me at Union Carbide, I'd get the head of the applied mathematics department in here and one of his people would solve it on the computer," he said. "But you want to know at least enough to talk knowledgeably with the applied math types and prevent them from billing too many hours to the project. Let's go down the hall to the Apple and I'll show you how to boot it up."
The computer room was a corner office the size of a large closet, with windows on both walls and a desk and the Apple. The windows looked out onto a seven-story courtyard; since the room was on the second floor it never received direct sunlight, but the soft diffuse light and the tree just outside the window made me feel I was in a cloister's cloister.
Greene put a diskette into the machine and turned on the on switch. I presumed that's what he meant by "booting it up."
"I'll just write a three-line program that will add two numbers for you to show you how to get started," he said.
His fingers blurred around the keyboard, like a concert pianist's. Unlike speech or writing by hand, which have natural speed limits on how fast information can be transfered, the computer could receive information almost as quickly as he thought. He must have done well in touch typing class in high school.
When he was done, the screen said "Input A," and I typed 3. "Input B," it said, and I typed 5. "A + B = 8," it said.
"You've programmed before, haven't you?" he said.
"Well, just a little in college, but that was always on a teletype terminal with the yellow paper that was connected to a big computer in an air-conditioned room down the hall. This looks a little different."
"It's the same in principle," he said. "There's a programming manual in the drawer here, so you can refer to that if you need help. What I want you to do for our next meeting is to set up the equations you showed me in such a way that you can step through little increments of time and see what happens to the skin of the balloon as the spring in your model stretches and the pressure in your balloon rises. Try to organize the equations so the information will flow from one equation to the next, so that at each step in the program, the computer has all the data it needs to go on to the next step. Oh, and read up on'subroutines' in the programming guide. You can use them to break up a big, complex problem into several smaller, simple problems. It'll make debugging much easier. For now, let's go back to my office and go over the examples of entropy you've come up with."
Landfills, overeating, smoking, drug addiction-all the ills of modern life had come to mind during the past two weeks, but I knew he'd want something more specific.
"Well, the other day I was at the crosswalk at Mass. Ave. and I saw somebody trying to parallel park in a space that was about 6 inches too short for the car. For the length of the block there were 2 or 3 feet between the other cars, sometimes as much as 4 feet. So if you added up the little pieces of space you'd probably be able to fit three or four more cars into the block comfortably. But the little pieces of space by themselves were useless. That's the best I could come up with."
"That's a good one," he said. "You could make the analogy that space is the equivalent of energy, and the shortness of the space is the equivalent of entropy. The longer the space is, the more ordered a system it represents and the more useful it is. That's good. I like that. I think you're making progress."
C H A P T E R
9
Spring
March 15
The Ides of March. The first day above freezing, and time to blast the mental cobwebs out. Time to go on a bicycle ride. My escape route was out Trapelo Road through Belmont.
The pressure was still constant, but with only two exams scheduled for the term, there was more relaxing time. Up the first major hill, Belmont Hill, I remembered my old cycling coach's telling me to sit back in the saddle and pull on the upstroke. He said that would allow the muscles in the front of my legs to relax and let the used blood flow out and the new blood flow in. If I always pushed on the front of my legs the tension would build up and my legs would feel tired and I'd be dropped from the pack.
It was sort of like Heywood's description of an internal combustion engine. Fuel goes into the cylinder, gets burned, then pushed out and exhausted. If you kept the exhaust in the cylinder, there wouldn't be room for the fresh, unburned fuel and air, and your car would stall.
At the Route 128 overpass, I looked both ways up and down the eight-lane highway. On both sides were continuous lines of two-story buildings. The sign on the side said, "Route 128: Amer ica's Technology Highway." I rode on, past Honeywell's ElectroOptic Division, past Raytheon's Bedford Missile Systems Division, past Digital, past E.G.& G.
All these places were either founded by or heavily populated by MIT grads. The Harveys have most of their power in New York, but the most powerful Techies live and work within twenty miles of Building 7. I wondered what it would be like to work in a lowrise building with cubicles and very few windows.
On through Concord Center and past Ken Olsen's house. Ken Olsen graduated from MIT in '50, went on to work with Professor Jay Forrester on computer memory technology in Project Whirlwind, and from there spun off a company-Digital Equipment Corporation. Ken is worth a billion or two and still lives in a modest home.
Farther on, I saw the fruit of Gyftopoulos's industry. Well, not the whole fruit, because you can't see the whole house from the street because the driveway's so long. Next door was the house of the other Thermo Electron founder, George Hatsopoulos. George showed that you don't have to be a professor
at MIT to make a million bucks. In his case, a Ph.D. in mechanical engineering and a good idea for how to measure the concentration of nitrogen oxide in automobile exhaust were sufficient.
Back toward town Thermo Electron was less than a fiveminute drive from their houses. Maybe, if I worked hard, I could emulate all of them.
The ride felt good, and after my shower, it was Apple time. Greene had given me a key to the computer room and a floppy disk.
It was two o'clock, and sunny, and if I'd had my druthers I would have happily continued cycling on to Concord or Carlisle or Acton or Harvard, but that's not why I was in Cambridge.
The cloister, facing inward, shielded from the street, with the tree just outside the window and the diffuse sunlight brightening the upper part of the pink limestone walls, was a peaceful sanctuary. Here it was just my thoughts, and the wit of the manual written by two guys who hadn't gone to college, Wozniak and Jobs.
Okay Apple. I'm a user. Be friendly.
Apple taught by example. The language was BASIC, the language in which most people learn to program. In BASIC, it's fairly easy to follow the logic of the sample programs. I typed in the sample programs, and they worked. This began to establish a cause-and-effect relationship for me; if you type in the right thing and don't misplace parentheses and don't misspell anything and do it absolutely, perfectly, uniformly right, it works.
By six o'clock I'd finished the manual. It was sort of like listening to a Paul Desmond record and trying to pick out the improvisational riffs and play them by ear on my clarinet. I'd pick it up a phrase at a time, and once I knew what Paul Desmond was doing, what chords he was working from, what scales he was embellishing, I could experiment on my own, maybe change the order a little bit, try different permutations of the notes. Before I knew it I was a programmer. You imitate the patterns, and by accident you discover new combinations and develop your own style. The time disappeared and I became lost in it and it became almost fun, not work.