computing , he thought. Sure, no problem.
“NP means Non-Polynomial time,” Kevin said, speaking quickly now. “But never mind that. It’s just a way of describing a type of problem that computers can’t solve.”
“And why not?”
Kevin shrugged. “Some puzzles just have too many possible outcomes. No matter how fast the computer, it would take millions of years to work out one of these things by brute force. Speed doesn’t matter. You have to be smart .”
Danny shook his head. “Example, please.”
“Let’s say you’re a Fed-Ex truck driver in Manhattan, and you’ve got ten deliveries to make today. You want to go as quickly as you can, and drive the shortest distance possible.”
“Good so far.”
“Well, that’s no big task for you – just get out a map and eyeball the thing, and you can probably work out the quickest route. Maybe not the absolute best route, but something pretty close.”
Danny nodded. “Yup, I could handle that.”
“Okay, but you’re actually doing something incredibly sophisticated. From a computer’s point of view, you’re a drop-dead genius. Because with ten destinations, there are 10-factorial possible routes.”
“Which means?”
Kevin smiled. “There are over 3.5 million different possible routes to deliver those packages. And even a fast computer will have to work for a bit to go through all those possibilities.”
Danny’s mouth dropped open. “3.5 million. Son of a – ”
“Exactly,” Kevin said. “And remember that having just 10 drop-offs would be unrealistically low. A real Fed-Ex guy probably has to deal with something like 30 or 40 deliveries on a busy day.”
Danny was still nodding. “That sounds right. And how many possible routes are there for a 40-delivery day?”
“It’s a number we don’t even have a name for. It’s an 8 with 47 zeros after it.”
Danny threw his hands up. “I’m an English teacher,” he protested. “I don’t work with numbers like that.”
“Neither do I. Put it this way: if the Fed Ex guy has to make 60 deliveries, then the number of possible routes is roughly the same as the number of atoms we think are in the universe.”
Danny let out a little laugh. “All right,” he said. “That seems like a lot.”
“I agree. And the larger point is that NP problems are all like this one. The complexity goes up too fast for any computer to handle it with raw speed. Only a human can solve – or even try to solve – problems of this kind. Computers have power, but they don’t have any real intelligence. They can’t see the big picture.”
Danny was silent for a minute. “So the kid’s dad, Billaud. He might be close to solving the Fed Ex problem?”
“Not the Fed Ex one in particular, but it doesn’t matter. All the NP problems are related. If you can solve one, you can solve them all.”
“How’s he going to do it?”
Kevin shrugged. “No idea. I don’t know how close he is. But even the possibility is huge. Because if you get a computer to solve an NP problem, all bets are off. Past NP, there’s theoretically no limit to what a computer could do. And then we hit the singularity, which would be absolutely incredible.”
Danny put his head down. He was getting tired. “Are you going to explain that last bit?”
Kevin frowned. “No way. I can’t squeeze the singularity into a two-minute lesson. I need to get to class.”
Danny nodded. “Fair enough. Talk to you later.”
They let in a few last straggling students, and then they let the door close behind them. They headed up the stairs.
Out on the street, the men in the blue painting jumpsuits climbed back into their van. They seemed to have left most of their painting supplies somewhere.
In the other van, perhaps.
Blood Began To Spill
Kevin was back in the classroom, and the teaching was
“NP means Non-Polynomial time,” Kevin said, speaking quickly now. “But never mind that. It’s just a way of describing a type of problem that computers can’t solve.”
“And why not?”
Kevin shrugged. “Some puzzles just have too many possible outcomes. No matter how fast the computer, it would take millions of years to work out one of these things by brute force. Speed doesn’t matter. You have to be smart .”
Danny shook his head. “Example, please.”
“Let’s say you’re a Fed-Ex truck driver in Manhattan, and you’ve got ten deliveries to make today. You want to go as quickly as you can, and drive the shortest distance possible.”
“Good so far.”
“Well, that’s no big task for you – just get out a map and eyeball the thing, and you can probably work out the quickest route. Maybe not the absolute best route, but something pretty close.”
Danny nodded. “Yup, I could handle that.”
“Okay, but you’re actually doing something incredibly sophisticated. From a computer’s point of view, you’re a drop-dead genius. Because with ten destinations, there are 10-factorial possible routes.”
“Which means?”
Kevin smiled. “There are over 3.5 million different possible routes to deliver those packages. And even a fast computer will have to work for a bit to go through all those possibilities.”
Danny’s mouth dropped open. “3.5 million. Son of a – ”
“Exactly,” Kevin said. “And remember that having just 10 drop-offs would be unrealistically low. A real Fed-Ex guy probably has to deal with something like 30 or 40 deliveries on a busy day.”
Danny was still nodding. “That sounds right. And how many possible routes are there for a 40-delivery day?”
“It’s a number we don’t even have a name for. It’s an 8 with 47 zeros after it.”
Danny threw his hands up. “I’m an English teacher,” he protested. “I don’t work with numbers like that.”
“Neither do I. Put it this way: if the Fed Ex guy has to make 60 deliveries, then the number of possible routes is roughly the same as the number of atoms we think are in the universe.”
Danny let out a little laugh. “All right,” he said. “That seems like a lot.”
“I agree. And the larger point is that NP problems are all like this one. The complexity goes up too fast for any computer to handle it with raw speed. Only a human can solve – or even try to solve – problems of this kind. Computers have power, but they don’t have any real intelligence. They can’t see the big picture.”
Danny was silent for a minute. “So the kid’s dad, Billaud. He might be close to solving the Fed Ex problem?”
“Not the Fed Ex one in particular, but it doesn’t matter. All the NP problems are related. If you can solve one, you can solve them all.”
“How’s he going to do it?”
Kevin shrugged. “No idea. I don’t know how close he is. But even the possibility is huge. Because if you get a computer to solve an NP problem, all bets are off. Past NP, there’s theoretically no limit to what a computer could do. And then we hit the singularity, which would be absolutely incredible.”
Danny put his head down. He was getting tired. “Are you going to explain that last bit?”
Kevin frowned. “No way. I can’t squeeze the singularity into a two-minute lesson. I need to get to class.”
Danny nodded. “Fair enough. Talk to you later.”
They let in a few last straggling students, and then they let the door close behind them. They headed up the stairs.
Out on the street, the men in the blue painting jumpsuits climbed back into their van. They seemed to have left most of their painting supplies somewhere.
In the other van, perhaps.
Blood Began To Spill
Kevin was back in the classroom, and the teaching was
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