Dr. Dobb's Journal June 1997
My cousin Corbett had dropped by the farm and was telling me some story he'd read online. Something about an oddball Church of Science Allergy founded by some L. somethingorother. L. Moe Fudder, I think. Big on liturgy. Except I think Corbett called it liturgation. He'd read about it on some online news site called Murky Center or something like that. I was only half listening.
"You seem a little preoccupied, Michael."
I looked up from the soil I was working. "Oh, I had a little problem while writing my next OOs column "
"Ooze?"
"OOs. Acronyms with a pair of Os in them. I find some, I invent some. JOOP, SCOOP, HOOPS, OOPSLA, OODBMS, OOBABY, YAHOO, JUDOO, WAZOO."
"Oh yeah, I like that column. You do it, what, like once a year?"
"I beg your pardon! I guess I did do something similar once before."
"Whatever. So what's the problem? Need my help digging up some better ooze?"
"No thanks. The problem is, I let the column distract me from my farm work."
"Usually the other way around, isn't it? What happened? Forget to bring in the sheaves?"
"Oh, I forgot to do the temperature readings yesterday, so I've now lost two days' data."
"You mean one day's data."
"No, it's really two. You're aware that I've been reading the daily high and low temperatures every day for a year and a half now?"
"Vaguely." He wrinkled his nose as he watched me work.
"Well, after I record the data, I reset the high-low thermometer. Only if I don't do the readings, I don't reset the thermometer either. Yesterday I forgot to do the readings and to reset the thermometer, so yesterday's data is lost, and so is today's."
"Hold on a minute. You haven't lost two days' data. You've still got a day's worth."
"Huh? How do you figure that?" I scooped up a big handful of prime specimens and dropped them into the soil patch in front of Corbett, who jumped a foot.
"Okay, look," he said. "You've got a high and a low reading on the thermometer, right?"
"Right, but -- "
"Representing the high and low temperatures for this two-day period, right?"
"I guess so, but -- "
"So you've got a day's worth of data. Record it." He backed away, watching them wriggle.
"Record it where? Under today or yesterday? I mean, those values could be yesterday's high and today's low, or yesterday's low and today's high, or -- "
"Yeah, yeah. I get the idea. But the information content is identical to what you'd have if you collected the data for one day and threw it away for the other. It's still exactly one day's worth of data."
"Oh, well, if you're going to talk information content, maybe. But I need to know where to write it down. Yesterday or today?"
"Flip a coin. Statistically, it won't make any difference."
"And beside that, you're wrong. It's something less than a day's worth of data, because you've got a daily high and a daily low, but you can't match either one to a particular day. That's less information than if you just had a single day's readings."
"Hmm. I think I am wrong."
"Aha." I dropped another bunch in front of Corbett, and he jumped again.
"No, I think you've got more than a day's data."
"Corbett!"
"No, really. A two-day high contains more information than a one-day high, and a two-day low -- "
"Is too low for me. Corbett, I'm just a simple worm farmer. I'm OOMD here."
"OOMD. That would be -- ?"
"Out of my depth."
But you're not, right? So who's correct here, in a strict information-theoretic sense? Do I have more than a day's worth of data, or less, or what? E-mail me at mswaine@cruzio.com with your answer and justification. The usual no prizes will be awarded, but the worms will thank you.
--Michael Swaine