“… a basic misunderstanding of how we make successive approximations. Unless you get this basic point, you’ll never get any further. Brian — will you do this correctly so we can move on. And, Kim, I want to see you after class.”

The Italian verbs vanished as Brian pushed the calculator aside. He looked at the screen and tracked her first error. “The misconception begins here,” he said, moving the cursor and highlighting the equation. “After you find the first-order solution, you have to remove it — subtract it from the original equation — before you can apply the same method to find the next term. If you forget to do that, you’ll keep getting the same term again. And then you have to divide out the independent variable, or you will just get zero the next time. And finally, you have to go backward again, adding the terms back in and multiplying back the variable again. I think the trouble is that everyone in the class believes that there are a lot of different ideas here, derivatives, approximations, second-order approximations, and so on. But there’s only one idea, used over and over. I don’t see why they make it out to be so complicated…”

An hour later Brian was eating his cheese and tomato sandwich and reading Galaxy Warhounds of Procyon when someone sat down heavily on the bench beside him. This was unusual enough since he was left strictly alone by the other students. More unusual were the tanned fingers that pulled the book from him and slammed it onto the table.

“Juvenile science fiction space crap that only kids read,” Kim snapped at him.

He had had this argument often enough before. “Science fiction utilizes a vocabulary twice as large as that of all other popular fiction. While SF readers are in the top percentile…”

“Space balls! You made me look pretty dumb today.”

“Well you were pretty dumb! I’m sorry.”

Brian’s worried expression got to her; she could never stay angry very long in any case. She laughed aloud and pushed his book back to him. Pushing it through a slice of tomato on the table. He smiled and wiped the cover with his napkin.

“In fact it wasn’t even your fault anyway,” he said. “Old Betser may be a wizard programming mathematician but he doesn’t know a gnat’s fart about explaining it to anyone.”

“What do you mean?” She was interested now, reached out and broke off a corner of his sandwich. He noticed that her teeth were very white and neat, her lips red — and that was without lipstick. He pushed the remains of the sandwich over to her.

“He’s always going off on tangents, getting sidetracked into explanations that have nothing to do with the material he should be teaching, things like that. I always stay a chapter ahead of him in the text so he won’t confuse me when he starts to explain something.”

“Amazing!” Kim said, meaning the thought of reading a text you didn’t have to when there were so many other wonderful things to do. “Can you do better than him, Mr. Smartass?”

“Run circles around him, Miss Birdbrain. Using the heretofore totally secret Brian Delaney lightning instruction system all will be made clear! In the first place, it’s not really so important to know exactly how to solve each problem.”

“That sounds stupid. How can you solve a problem if you don’t know how to solve it?”

“By doing just the opposite. You can learn a lot of ways not to solve it. A lot of wrong methods not to try. Then, once you find the most common mistakes, you can hardly help doing the right thing without even trying.”

He remembered exactly where she had gone wrong and knew at once what her misunderstanding was. He explained it patiently, two or three ways, until she finally caught on.

“Is that what my trouble was! Why didn’t Beastly Betser explain it like that? It’s obvious.”

“Everything is obvious once you understand it. Why don’t you work through the rest of those examples while this is clear in your head?”

“Maybe tomorrow. Got things to do, gotta run.”

Run she did, or at least trotted out of the dining room, and he shook his head as he watched her go. Girls! They were a strange breed. He opened his book and winced at the red tomato stains. Sloppy. Sloppy thinking too, she should have worked this thing out while it was fresh in her head. Five will get you ten she would forget the whole thing by tomorrow.

She did. “You were right! It was gone, zip. I thought I remembered, but not exactly.”

He sighed dramatically and rolled his eyes heavenward. Kim giggled.

“Look,” he said, “there’s really not much use spending the time to learn something unless you spend a little more time making sure that it stays learnt. First, you can’t really understand anything if you only understand it one way. You have to think a little about each new idea — which old ones it is like, and which are really different. If you don’t connect it to a few other things, it will evaporate the moment anything changes. That’s what I meant yesterday, about the solution not being important. It’s the differences and similarities.” He could see that this was having no effect, so he played his ace. “Anyway, I worked out an auto-tutor program that simplifies the subject of successive approximations. I’ll give you a copy. Then you can run it whenever the curtain starts to fall in your brain and all will be made instantly clear. At least it will get you through this part of the course.”

“You really have a program like that?”

“Would I lie to you?”

“I don’t know. I really don’t know anything about you at all, Mister I.Q. Kid.”

“Why did you call me that?” He was angry, hurt, both feelings mixed together. He had overheard the other students calling him that behind his back. Laughing.

“I’m sorry — I didn’t mean it, I just never thought. Any moron that calls you that must be a moron. I apologized so you can’t be angry.”

“I’m not,” he said, and realized mat he meant it. “Give me your log-on ID and I’ll zap a copy of that program to your modem.”

“I always forget the ID, but I’ve written it down someplace.”

Brian groaned. “You simply can’t forget your ID. That’s like forgetting your blood type.”

“But I don’t know my blood type!”

They both laughed at that and he found the only solution. “You better come over to my place and I’ll give you a copy.”

“You will? You’re a great guy, Brian Delaney.”

She shook his hand in gratitude. Her fingers were very, very warm.

8

March 25, 2023

There were muttered complaints from people waiting in the line, but not from Benicoff. Not only didn’t he mind — he enjoyed the security. When he finally reached the two M.P.s they coldly asked him for his ID — although they knew him very well. They examined this closely, then his hospital pass, before they let him approach the front door of the hospital. Another guard inside unlocked it for him.

“Any troubles, Sergeant?”

“None other than the usual with you-know-who.”

Benicoff nodded in understanding. He had been present when General Schorcht had chewed the Sergeant out, him with hash marks up to his elbows, a Master Sergeant, not that the General cared. “I got my troubles with him too — which is why I’m here.”

“It’s a tough life,” the Sergeant said with marked lack of sympathy. Benicoff found the internal phone and called Snaresbrook’s secretary, discovered that the surgeon was in the library, got instructions how to find it.

Leather-bound medical books lined the walls; but all of them were years out of date and just there for decoration. The library was completely computerized, since all technical books were published in digital form. This had only become possible when conventions and standards were set for illustrations and graphics which were animated most of the time. So any medical book or journal was entered into the library’s data base the instant that it was published. Erin Snaresbrook sat in front of a terminal speaking instructions.