By the end of that summer of 1983, Richard had completed his analysis of the behavior of the router, and much to our surprise and amusement, he presented his answer in the form of a set of partial differential equations. To a physicist this may seem natural, but to a computer designer, treating a set of boolean circuits as a continuous, differentiable system is a bit strange. Feynman’s router equations were in terms of variables representing continuous quantities such as “the average number of 1 bits in a message address.” I was much more accustomed to seeing analysis in terms of inductive proof and case analysis than taking the derivative of “the number of 1’s” with respect to time. Our discrete analysis said we needed seven buffers per chip; Feynman’s equations suggested that we only needed five. We decided to play it safe and ignore Feynman.
The decision to ignore Feynman’s analysis was made in September, but by next spring we were up against a wall. The chips that we had designed were slightly too big to manufacture and the only way to solve the problem was to cut the number of buffers per chip back to five. Since Feynman’s equations claimed we could do this safely, his unconventional methods of analysis started looking better and better to us. We decided to go ahead and make the chips with the smaller number of buffers.
Fortunately, he was right. When we put together the chips the machine worked. The first program run on the machine in April of 1985 was Conway’s game of Life.
If you remember nothing else from this blog post, remember this chart. The Y axis is time spent collecting garbage. The X axis is “relative memory footprint”. Relative to what? Relative to the minimum amount of memory required.
What this chart says is “As long as you have about 6 times as much memory as you really need, you’re fine. But woe betide you if you have less than 4x the required memory.”
As a psychology major, Grant always hoped to do a study on the “Let’s Go” staff, in which the books’ editors and writers would meet with or read letters by people whose travels had been enhanced by their work. Would knowing how the books benefited others inspire them to work harder? Now, at the call center, Grant proposed a simple, low-cost experiment: given that one of the center’s primary purposes was funding scholarships, Grant brought in a student who had benefited from that fund-raising. The callers took a 10-minute break as the young man told them how much the scholarship had changed his life and how excited he now was to work as a teacher with Teach for America.
The results were surprising even to Grant. A month after the testimonial, the workers were spending 142 percent more time on the phone and bringing in 171 percent more revenue, even though they were using the same script. In a subsequent study, the revenues soared by more than 400 percent. Even simply showing the callers letters from grateful recipients was found to increase their fund-raising draws.
When Grant went back and talked to the callers about their improvement, many actively discounted the possibility that the brief encounter with a scholarship student helped. “Several of them were stunned,” Grant said. “Their response was, ‘Yeah, I knew I was more effective, but that was because I had more practice,’ or, ‘That was because I had a better alumni pool in that period — I got lucky.’ ” Eventually, having replicated the test five times, Grant was confident that he had eliminated other explanations. It was almost as if the good feelings had bypassed the callers’ conscious cognitive processes and gone straight to a more subconscious source of motivation. They were more driven to succeed, even if they could not pinpoint the trigger for that drive.