1.9. Round numbers 15 1.9. Round numbers It is a convention in popular culture to use round numbers as milestones in order to reflect on the progress of some statistic, such as when a major stock index passes, say, the 10,000 level. People often celebrate their birth- days each year, and also use the new year to make resolutions institutions similarly observe centenaries and other round number milestones. Of course, thanks to the artificial nature of both our system of units, and also our decimal system to express numbers, such milestones have no particular intrinsic significance a day in which the Dow Jones Industrial Average, for instance, crosses 10,000 is not intrinsically much different from a day in which the Dow Jones crosses 10764, or 213, or any other number. However, there is some value in selecting some set of milestones of a given spacing (or log-spacing) in order to set up a periodic schedule in which to focus occasional attention on a topic. For instance, it is certainly useful to spend some time occasionally reflecting on one’s past and making resolutions for one’s future, but one should not spend every day of one’s life doing so. Instead, the optimal fraction of time that one should invest in this is probably closer to 1/365 than to 1/1. As such, the convention to use the first of January of each year to devote to this is not such a bad one, though, of course it is ultimately a somewhat arbitrary choice. Similarly, for the majority of people who are not professional stock traders, the daily fluctuations of an index such as the Dow Jones are too noisy to be of much informational value but if one only pays attention to this index when it crosses a multiple4 of 1000, then this already gives a crude picture of the direction of the market that is suﬃcient for a first approxima- tion, without requiring too much of one’s time to be spent looking at this index. At a somewhat less frivolous level, one advantage of selecting a conven- tional set of preferred numbers is that it allows for easier comparison and interchangeability between people, objects, and institutions. For instance, companies who report their financial results on a quarterly basis can be eas- ily compared to each other, as opposed to companies who report at irregular or idiosyncratic schedules. In order to have interchangeability between re- sistors made by different manufacturers, the resistance is by convention set to lie in a discrete set of preferred numbers that are roughly equally spaced in log-scale (and which are famously colour-coded to indicate this number). 4Note though that if this index changed value by an order of magnitude or more, then one should presumably replace multiples of 1000 with an appropriately rescaled multiple. Ideally one should use milestones that are equally spaced in log-scale rather than in absolute scale, but with the decimal system the round numbers that do this (i.e., the powers of 10) are too far apart to be suﬃciently useful.

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