Moulton Lava

Moultonic Musings

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Location: New England, United States

Friday, October 31, 2014

The Parable of the Egg Man

Moulton's Boarding House has 12 residents. Every Sunday, Moulton serves brunch for the boarders (which includes a fresh egg). Moulton has a standing order with the Egg Man to deliver a dozen fresh eggs a week. The Egg Man employs a neighborhood urchin named Dennis to deliver fresh eggs from the Egg Man's cold storage warehouse.  Dennis gets paid a penny an egg for each one-way trip. So Dennis expects to earn 12¢ for each weekly delivery of a carton of eggs from the cold storage facility to Moulton's boarding house.

About once a month, one of Moulton's boarders misses the regular Sunday brunch to join his girl friend at another boarding house. But the peripatetic boarder also invites the girl friend to join him the following week for brunch at Moulton's table. Thus, most Sundays there are 12 people for brunch, but about once a month there are only 11, and about once a month there are 13 at the table.

Alas Moulton never knows which Sunday there will be an empty chair, and which subsequent Sunday there will be an extra person at the table. When Dennis comes with the standard carton of a dozen eggs, Moulton sometimes says, "I only need 11 eggs this week. Please take one of them back to cold storage.  And next week you can bring me 13 fresh eggs."

The accountant for the Egg Man notices that, at the end of the year, Moulton's Boarding House purchased 52 dozen eggs, as expected. But the delivery charges from Dennis come to $6.42 (for transporting 54 dozen eggs) rather than $6.24 (for delivering 52 dozen eggs). Dennis explains to the accountant that there were twenty-four occasions (twice a month) where he either carried one egg back to the cold storage facility or one extra egg to Moulton. As far as the Egg Man is concerned, Moulton purchased 52 dozen eggs over the course of a year. But as far as Dennis is concerned, he transported 54 dozen eggs — 53 dozen in the usual direction, and one dozen in the alternate direction. So he is owed $6.42 for his labors transporting eggs over the rough cobblestone streets. The Egg Man thus had an extra cost of 24¢, over and above his expected cost of $6.24 for paying Dennis to deliver eggs. The Egg Man ended up paying 3.85% more to Dennis than he would have expected if there had not been any perturbations in the number of boarders at Moulton's table.

Moral:  There's no such thing as a free brunch.

Monday, October 13, 2014

The Sad Case of the Blind Logician

Once upon a time there was a logician who imagined that his ability to reason logically was without error, and that he could reliably identify, diagnose, and report errors in logic by his erstwhile correspondents. He also demanded evidence to support the premises upon which logical arguments were constructed. But curiously enough, this otherwise self-professed logician was blind. Alas, he could not observe and interpret visual evidence with his own faculties; he literally could neither see the evidence nor reliably interpret its meaning. He was obliged to rely on the reports of others as to what was observed, and the meaning or interpretation of those observations.

One day, late in October, a neighbor set out a Jack-O-Lantern — that being a hollowed out pumpkin shell with a small candle inside. The orange skin of the Jack-O-Lantern thus glowed a lovely orange, as if it were luminescent. I asked the blind logician what could be deduced from the luminescent pumpkin. He replied that since the pumpkin shell obeyed the physics of an isothermal black body radiator, it must be glowing because it is at an incandescant temperature, presumably from an interior heat source that was warming up the pumpkin shell to an incandescent temperature. I asked him how he knew that the pumpkin shell was opaque and not translucent. He replied that, according to Wikipedia, pumpkin shells are opaque, and that he could see no evidence to the contrary. So I showed him evidence to the contrary, but he demurred, saying he was blind and thus could not see or interpret the visual evidence before his non-functional eyes.

I was thus reminded of a quote from John Heywood who, in 1546, said, "There are none so blind as those who will not see. The most deluded people are those who choose to ignore what they already know."