By The Metric Maven

Now and then after I’ve given a lecture on the metric system, someone will invariably ask me about metric time. My standard answer is “The only base unit of time in the metric system is the second. It’s up to you to divide them up.” This may sound a bit flippant, but there is a reason for the statement.

Sven once related an interesting anecdote about measuring time. It is from the book Keeping Watch by Michael O’Malley. In 1826, New Haven Connecticut gave Eli Terry, a celebrated clock-maker, \$200 to install a clock in their town hall. This would be a clock with the utmost accuracy possible. It was to be a symbol of punctuality and reliability. All seemed well with the clock, but after a while it began to diverge from the other standard of civic time, the Yale College clock.  The new clock fell further and further behind until it lagged by about 15 minutes. It then began to catch-up with the Yale clock. There were hopes that the new clock only needed to “break itself in” and that it would, in time, settle down and match the Yale timepiece. To the great concern of the civic authorities, the new clock approached, equaled and then overtook the time displayed by the Yale clock, until it was almost 15 minutes in advance of the college standard. This advancing and retarding of the new clock with respect to the Yale clock continued in a predictable manner. Terry was a competent clock-maker, and the Yale timepiece was also considered to be a good standard, so which clockwork was wrong?

The answer is that each clock represented a different definition of time. Yale’s clock followed the Sun, but Terry’s device was designed to compute mean time, which is an average of the Sun’s daily variation. This difference caused a local controversy about what the proper definition of time should be.

There is still a global brouhaha about the definition of time.[1] 2016 will be one second longer than last an ordinary year. At the end of this year, clocks will read 2016-12-31 23:59:60 before greeting 2017. This is done to keep Coordinated Universal Time (UTC) synchronized with changes in the Earth’s rotation. Since 1972 twenty-six leap-seconds have been added to deal with the slowing rotation of the Earth. Current standard clocks are more stable than the time kept using the Earth’s rotation. There are some who would abolish the leap-second. This  would slowly allow the Sun to drift in its celestial position with respect to time. Those that would abolish the leap-second often cite the difficulties they can create for computer systems.

I recall the concerns that were raised about the dangers of the Y2K bug. Just before the year 2000, there was much concern that because of the abbreviated way time was stored in computers, that 2000 would be the same as 1900. This was a possible error that could affect computer code in an adverse manner it was argued. There were hand-bills posted on trees offering, for a price, to give advice on how to survive the digital Armageddon which was about to visit itself upon us. I went to the most computer knowledgeable and trusted engineer I knew and asked him if there was any reason for concern. He dismissed the idea that a PC would have a problem as its system time is computed from an offset in seconds from January 1, 1980. Wikipedia indicates that the internal clock resolution is 10 milliseconds. Unix time is the number of seconds elapsed since the start of the Unix epoch on 1 January 1970 00:00:00 UT, with exceptions for leap seconds. There are many examples found in the Wikipedia entry for system time, and they are not consistent. System time can be converted to calendar time with months days and include leap seconds.

In his fragmentary, and in my view irrelevant examination of time, John Bemelman’s Marciano (JBM) writes in Whatever Happened to The Metric System?

The correlation of these measures [Earth distance and time] had been a fundamental aim of the metric system, but its creators were inconsistent in their method; they split the earth into 400 degrees and its circumference into 40 million parts but divided the day by ten. A plan to correct this original error was proposed to the American Metrological Society by one of its most fiercely pro-metric members, Fredrick Brooks, who advocated splitting the day into 40 parts. (pg 171)

I’m not sure why time would be included in JBM’s book, other than as a polemic device to impugn the originators of these ideas and then connect them with the modern metric system. JBM claims that the introduction of a ten hour day was an “original error.” What does Wikipedia have to say about metric time?:

When the metric system was introduced in France in 1795, it included units for length, area, dry volume, liquid capacity, weight or mass, and even currency, but not for time. Decimal time of day had been introduced in France two years earlier, but was set aside at the same time the metric system was inaugurated, and did not follow the metric pattern of a base unit and prefixed units.

If you are not comfortable with Wikipedia, Isaac Asimov wrote this in his 1960 book Realm of Measure (pg 100):

The original committee that established the metric system never attempted to do anything with time measurement. They realized that the day and the year were fixed by the rotation of the earth and by its revolution about the sun. Nothing could be done with either. The repetition of day and night, and the seasons was too basic and fundamental to be tampered with, and these simply could not be fitted into the decimal system.

The originators of the metric system did not introduce “metric time” and  JBM’s “original error” is more of a contemporary error on the part of the vacuous author of an anti-metric polemic. In her informative PhD thesis: The Role of Five Eighteenth-Century French Mathematicians in The Development of the Metric System (tip of the hat to Amy Young) Ruth Inez Champagne quotes Lagrange concerning metric time:

I observe that, in the measurement of time, the decimal system is much less important for the needs of everyday life than all the other units of measure; since, with the exception of astronomers, no one ever needs to do long calculations with hours, minutes and seconds, ….

JBM indicates that this “original error,” which is so obvious to him, but does not actually exist, made it past the mind of Joseph Louis Lagrange (1736-1813)? Lagrange contributed to the calculus of variations.  Lagrange also worked on systematizing mechanics (a lot of algebra) and worked out the mathematics of our solar system. Perhaps you’ve heard of Lagrange Points? But poor Lagrange allegedly could not realize the problem with a ten hour day divided into a 400 degree circumference? My mind reels at the juvenile hubris.

But why on Earth, so to speak, would dividing a circle into 400 degrees make any sense? Ken Alder in his book The Measure of All Things has this to say:

A 400-degree circle (with a 100 degree right angle) would not only ease calculation, it would synchronize astronomy and navigation. In a world where the quarter meridian was 10 million meters long, each degree of latitude would then measure 100 kilometers. This would simplify maps and assist sailors.” pp 141-142

Ferdinand Hassler (1770-1843) also realized the utility of the metric system for surveying. Andro Linklater in Measuring America has this to say:

..the exacting standards he set had become a part of the United States Coastal Survey. As a result it took another fifty-five years to survey the entire coastline from Maine to New Orleans, and every yard of it was measured in meters. Later the Coast Survey was extended to cover the entire United States. The words and Geodetic were added to this title, and the whole landmass was mapped in the same careful, metric fashion.

JBM’s chronology is completely askew in my view. He impugns brilliant mathematical scientists like Lagrange and others for an error that never occurred in 1795, yet his fractional titled chapter 11/16 opens in the 1870s? JBM has chapters designated 1/16, 2/16, 3/16 …..16/16 in the table of contents. Chapter 8, as most of us who like integers might call it, is designated 8/16 or One Half on page 115. Sven rightly points out that one is not half-way through the book until one has read all of this chapter (i.e Chapter 8/16, 1/2, or 8), so perhaps the next chapter should be 9/16 or One Half?—to properly divide the book into halves.

How, by the way, does any of this have anything to do with why the US does not have the metric system? As the old beer commercial used to nihilistically inquire: “why ask why?” The “metric time” section of JBM’s work is just one more part of a monograph who’s origin seems to not rest on its merit, and so if it was not written to explain why the US does not enjoy the metric system, one must wonder why and how it was published at all.

[1] “Leap Second Ahead” New Scientist 2016-07-16 pg 6.

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