The Incomplete Theory of Watches [4/98]
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The Incomplete Theory of Watches…
Posted by bryan goh on April 06, 1998 at 21:08:57: An almost complete and inconsistent set of axioms regarding horology. 1.There exist a watch. 2. For every watch, there exists a watch such that the satisfaction gained from the latter exceeds the satisfaction gained from the former. 2a. The set of watches is not bounded above. Corollary: There is no best watch. 3. The satisfaction gained from a watch is a decreasing function in time. 3a. New equivalent models introduce discontinuities in the satisfaction function. 3b. Nobody can agree whether these discontinuities are up or down. 4. The preferences over the set of watches are not transitive. 5. Two watches in hand are worth one in the showcase. 6. Under the assumption of public preferences, the watch one possesses is superior to anyone else’s watch. This is true even if they are the same model. 6a. Under the assumption of private preferences, the watch one possesses is inferior to someone else’s watch. This is not true if they are the same model. 7. The chronograph seconds hand is faster than the constant seconds hand. 7a. The chronograph and constant seconds hand agree at all points. 7b. In a complex watch ( see Q3. below ) if the two hands agree on a dense set then they are equivalent. 8. The seconds hand is usually at rest. It only begins moving when observed. Sometimes there is a lag. 9. The probability of having the date change at exactly 0000hrs is almost always zero. 10. The probability that the minute hand lies on the mark as the seconds is at 12 is almost always zero. 11. There are eleven instances in [ 0000, 1200) where the minute and hour hands coincide. The positions and proof are left to the reader. 12. A more massive watch requires a faster balance wheel. 13. A complicated watch is one that simply will not run. 13a. Franck Muller is Master of Complications. (apologies Franck, just kidding around) 14. A 2 dimensional axis tourbillon where the angular velocities of the tourbillon in the 2 axes are not a rational ratio takes the balance wheel through in infinite number of positions in 3 dimensions. 14a. A tourbillon is a device for turning your pocket inside out. 14b. A the rate of a tourbillon is never constant. 15. There are no shock proof watches above 2000 usd. 16. Rolexes were made to be bashed. Physically not verbally. 16a. Rolex bashers (verbal) own a Rolex. 17. The greater the care, the greater the damage. ( also applies to automobiles, cameras, pens, clothes, Ö) 18. Perpetual Calendars were built for people who are very happy and 19. In hand wind watches, power reserve indicators were built for compulsive winders. 20. In automatics, power reserve indicators were built for compulsive ****ers. (British joke. Rated R. Under 18s apologies) 21. A prospective buyer of watch A is likely to change his mind and buy watch B when informed that watch C is unavailable. This violates axiom of irrelevant alternatives. 22. The purpose of a chronograph is to time ones own attention span. 22a. The purpose of the split second chronograph is to time ones attention span having forgotten to stop the first hand. 23. A squelette that looks beautiful in the showcase only shows off the warts on the back of one wrist. Q1. A quartz watch is not a real watch. Q2. A quartz watch is a more efficient time keeper. Q3. A quartz watch and a mechanical watch together form a complex watch. bryan I can now prove that Ironman > AP Royal Oak O. S. (more) Posted by Marc Rochkind on April 06, 1998 at 22:04:23: In Reply to: The incomplete theory of watches…….. posted by bryan goh on April 06, 1998 at 21:08:57: Great theory. Actually, these are axioms, not theorems, which is why you omitted the proof, I’m sure. I am enjoying proving various recreational theorems using your axiomatic system of watches. From your Axiom 2a (there is no best watch), I have proven that an Ironman is better than an AP Royal Oak Off Shore, but my approach is very general and can easily be extended to any pair of watches. (Exercise left to the reader.) Proof follows: 1. There are a finite number of watches in the world. (Proof is too complicated to go into here.) 2. From Axiom 2a, for every watch there is a watch that is better. 3. If we order all the watches in the world according to their “better” value, in an increasing sequence, we will eventually be forced to choose a watch that already appears in the sequence, thus in effect repositioning it. 4. Since that watch already appeared in the sequence (e.g., in the sequence Ironman was much earlier than AP R. O. O. S), we must reposition it to follow the watch at the top of the sequence. It is now better than the watch that formerly was better than it. That’s not all–it’s better than ALL the watches that appear earlier in the sequence. QED (To summarize this proof, it follows directly from Axioms 2 and 2a that the “better” relation on the finite set of watches forces the sequence into a circle.) Many of us on this forum have experienced this phenomenon anecdotally, although it usually baffled us. (Example: When cleaning out my crawl space, which I have decided to do for a maximum of 1 hr., I wear my Ironman rather than my AP R. O. O. S. because I momentarily believe the Ironman to be “better.”) But, Bryan, you were the first to provide a mathematical foundation for this wellknown effect, and for this I, and I trust the entire watchwearing world, will be eternally grateful. (On second thought, we will be grateful for 75 years. None of my watches can measure eternity.)
