Dr. Dobb's Journal February 2000
M y Cousin Corbett and I were building a wooden scaffold to stand on outside Stately Swaine Manor II while installing a window on the second floor. "I have a new venture," Corbett told me as we clambered up onto the first plank platform, laden with 2×4s to start building the second level of the scaffold.
"Huh," I commented. One reason that I have trouble getting a word in edgewise with Corbett is that he can talk while doing things like climbing a scaffold carrying an armload of 2×4s, or eating my food.
"It's a comparison shopping service comparison service."
"Huh?" I expostulated, laying down my load and taking several deep breaths. He proceeded to describe comparison shopping services while I did deep-breathing exercises. "There are different models," he said, "Some can tell you while you're examining a book at Amazon.com what it'll cost you at Borders, some watch your shopping habits and make personalized recommendations. Some accept money from sellers, and those you have to suspect of bias in favor of those sellers. So how does the poor consumer judge what shopping comparison service is the best?"
"Your service?" I guessed, hammering 2×4s together like a mad thing.
"That's right; we compare the comparison services and rate them." He had run out of 2×4s and reached down to pry one loose from the structure we were standing on.
"By what criteria?" I asked, as he yanked loose another strut and handed it to me.
"That's proprietary."
"Ah, but who judges the judges?"
I thought I had him with that pithy quote from Plato's Republic, if that's what it was a pithy quote from, but he surprised me. "We do, actually. We have a secondary service in which we rate comparison shopping service comparison services."
"Like yours."
"Like ours." I watched with concern as he pried several more 2×4s out of level one.
"So that would be a comparison shopping service comparison service comparison service?" I asked.
"That's right," he said. "We compare all the comparison shopping service comparison services."
"Are there any others?"
"No, we're alone in the field."
"The comparison isn't worth much, then, I'd think."
"You would be wrong," he said. "It's all explained by Peano's truth convergence theorem. Under optimal circumstances, if a set S1 of sources assigns probabilities to a set S0 of assertions, and a set S2 of sources assigns probabilities to the accuracies of the S1 judgments and so forth, these probabilities of probabilities will converge to a vector of values that is a monotonic function of the truth values of the S0 assertions. And Bretano's corollary states that from this convergent vector of values the original truth values can be derived."
I thought about it. "So what you're saying is that as judges make judgments about judges' judgments, they get closer and closer to the truth."
"Exactly."
"Under 'optimal circumstances.'"
"Of course."
"Sounds like something for nothing to me." I looked nervously at the nearly empty space beneath our platform where he had removed almost all the supporting 2×4s.
"It's just gainy communication. You know, there's lossless and lossy compression. Gainy is the best. That's where more information comes out of a transmission than went in."
"Is that possible?"
"Sure. Like when I talk in my inept French to my French CFO and he tells me what I meant to say. He gets more out of the transmission than I put in. Here, grab the other end of the window."
We set the window in place. North to south it fit like Joshua, but there was a gap of about an inch-and-a-half above the frame. What it needed, I saw, was a 2×4 to plug the hole.
As Corbett bent down and removed the last 2×4 from the first level of the scaffold, I shook my head. "Now how are we going to get down from here?" I asked, pointing out the shortsightedness of his policy of robbing level one to pay level two, as it were. There was nothing but six feet of air under the scaffolding on which we stood.
He sighed, opened the window, stepped through, and disappeared into the house.
Michael Swaine
editor-at-large
mswaine@swaine.com