In the bustling Cairo markets of 3,000 years ago, when the earliest Egyptian pyramids were well into their second millennium, eggs were being sold pretty much as they are today, i.e. in dozens and half-dozens. The reason for this, then as now, is that fresh market produce can generally only be sold in units, of which eggs are a prime example, or quantities once the units become too small to be sold separately. Grains of salt, for example, but also sprouts. Exactly where the dividing line falls may vary within each market, and across the ages, but we can all agree that the market for half a raw egg will always be small, as it is for half an apple, a third of a lemon, and so on.
The reason for this is that the Earth’s atmosphere, fond though we are, is highly corrosive. It can destroy and corrupt anything from bridges to blueberries, once they are exposed to it. As a result, everything is contained and protected within a skin or shell of some sort, bringing the concept of peiron1to the market stall. One early and natural effect was a special interest in numbers that could most easily and effectively be divided by integers. One of these was the number 6, which is both a perfect number, i.e. one which is the sum of its positive divisors (1, 2, 3), and a superior highly composite number, a category of which the first six are 2, 6, 12, 60, 120, 360. The divisors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30, while those of 6 times 60 (360) are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120 and 180.
The Egyptians adopted all this from the Babylonians, who can only be described as six-mad. They used a sexagesimal (base-60) number system that they adapted from the Sumerians and Akkadians before them. This system must have had significant advantages, presumably derived from the wide range of divisors available, because we know they chose it deliberately. However, it’s incredibly complicated, and seems to have defeated most Babylonians; they needed a huge number of look-up tables just to perform relatively simple calculations. We know it was a deliberate choice, though, because, like the Romans, the Babylonians counted in tens, but unlike the Romans, they used recognisable numerals in a decimal system identical to ours, albeit only up to sixty, with digits up to nine in the right hand column, and tens in the column to the left. They also left a space to denote zero, just as the Romans would. The Babylonians arranged abacus columns from right to left as well, except increasing by 60 each time. For us, however, the lasting legacy of the Babylonians, apart from the 360º circle, is the 60 minute hour and the 60 second2minute3.
The hours themselves, on the other hand, have enjoyed a varied existence, taking minutes and seconds with them. In our Egyptian marketplace, for instance, for at least a millennium before and up to almost the present day, day and night were divided, naturally enough, into twelve hours each, regardless of how long they actually were4. You can see these ‘unequal’ hours marked out on the face of the 15th Century Orloj5in the Old Town Square in Prague, proving that they had the technology at that point, but truthfully, nobody cared. The clock was just a showpiece to impress other countries.
For most people, their interest in the time of day was limited to “Can I see well enough to get started?” through to “Will I be able to see well enough to get finished?”6It didn’t bother anybody that the hours were different lengths. In fact, in northern Europe it was regarded as a sign of the Almighty’s beneficence that he had arranged for the days to be longer when most of the work (ploughing, sewing, reaping) had to be done, and shorter when all you had to do was repair and maintenance7.
These twin ideas of “How long have I got?” and “How long does it take?” dominated all timekeeping for millennia. Clepsydrae, the water clocks that Galileo was still using in the 17th century, would have been perfectly familiar to our Egyptian barrow boys. The Roman army used them to time their watches8, law courts used them to keep testimony to the point, students were examined according to them. Sometimes the water9would flow in, sometimes out, or there might be a flame on a notched candle. In the East, incense sticks were used, which were more consistent, and safer, being flameless. Sometimes the incense would change at fixed intervals, so one would be aware of time’s passing, but not distracted by it10.
None of these was measured against any standard unit of time. Even the first mechanical clocks simply chimed. They had no faces or hands. They were used just to call the monks to prayer during the night, starting with Vespers in the evening, which marked the end of the monks’ working day11, followed by Compline at bedtime, Midnight prayers at midnight, as you might have supposed, and then Matins to take you through to dawn and the start of another day12.
There’s an old proverb: “A man with one clock knows what time it is; a man with two clocks is never sure.” These early mechanical clocks, whether powered by weights or spring-driven, were notoriously inaccurate, losing up to fifteen minutes a day, but for most people they were the only clock, so no one could tell. Besides, they could always be reset at noon, and none the wiser. However, astronomers and other, generally military, professionals went on developing more and more accurate timekeeping mechanisms. Outside a very few professions, the task/process dichotomy that has so dominated and transformed modern organisations and society itself simply did not exist. Each individual’s place within the hierarchy of the community was largely determined at birth, and his or her role in any work to be done was defined by custom and apprenticeship. The timing of any specific step in any sequence of steps depended solely on completion of the preceding step. Even the military, who could be expected to make battlefield decisions on the hoof, so to speak, required only a limited number of calls and signals to initiate and coordinate major troop movements without the need for pre-planning. In short, everybody in all fields knew what to do, and when it needed to be done, without reference to any independent timing mechanism. For those rare instances when an external reference was needed, there was always the Sun itself, or a sundial if greater precision were necessary.
Astronomers had a different motivation, not least John Flamsteed13, the first Astronomer Royal. He was a young man, only 29, when he was appointed in 1675, and the Royal Greenwich Observatory had not even been begun. It was just half a century since Kepler had modelled the solar system as we know it, and Newton had not yet confirmed Kepler’s calculations. He was already a boy of nine when Christiaan Huygens, also an astronomer, invented and built the first accurate pendulum clock. Both Huygens and Flamsteed were interested in what is called the ‘equation of time’, the question of whether or not sundials and mechanical clocks would keep the same time14. Flamsteed was convinced that the rotation of the Earth on its axis was constant, and therefore that the passage of the Sun across the sky must be regular, thus the shadow cast upon a sundial would keep correct time15. Even in 1677, he was still confident enough to write:
“… our clocks kept so good a correspondence with the Heavens that I doubt it not but they would prove the revolutions of the Earth to be isochronical… “
Sadly, he was wrong. The Sun does not go smoothly around the Earth. At the beginning of the year it appears to go slower, so sundials lag behind clocks, but they catch up, and indeed overtake them towards the end of the year. It’s an effect of two things: the fact that the Earth’s axis is tilted slightly16as it orbits the Sun, and that its orbit is very slightly eccentric17. Even without clocks, the Babylonians were aware of this, and Ptolemy also devoted much of Book III of the Almagest to it. He needed to correct for it when getting a reading for noon. The apparent time of the Sun is called, conveniently, the Apparent Solar Time, and this has to be converted to the Mean Solar Time, i.e. the average of the total annual solar time18. Four times a year, in April, June, September and December, ‘apparent’ and ‘mean’ solar time coincide, but they can be out by as much as a quarter of an hour19at other times.
This wasn’t the only problem. Not only did you have to adjust for the Sun being in the wrong place, you also had to worry about where the sundial was, and take that into account. The Sun goes around the Earth at a ground speed of a little over a thousand miles, i.e. one time zone, per hour at the equator, which equates to around six hundred or so miles per hour in the UK, lying, as it does, between 50º and 55º N20. At its widest point, the UK is about three hundred miles across, so getting on for half an hour in terms of possible noon readings. Noon in Bristol, for example, at 2.5º west of London, is ten minutes behind Greenwich as the Sun flies.
This is where the “man with two clocks” problem raises its ugly, or beautiful, head, depending on what you are trying to do. If you want to know where Bristol is in relation to London, or more practically, if you want to know where the ship that recently left Bristol is in relation to London, then the discrepancy between their respective noon readings can tell you. As I’m sure you know, the Yorkshireman John Harrison based his ultimately successful attempt at winning the Longitude Prize21on just this principle. However, the solution to the longitude problem didn’t just depend on having an accurate clock on the ship; there had to be an agreed time and an accurate clock in an agreed place on the shore for use as a reference. This took longer than you might think to organise. The Longitude Act was passed in 1714. It was nearly sixty years22, 1772, before Harrison finally produced H5, the world’s first marine chronometer, making it possible to take an accurate copy of the time on shore with you on the boat. Now for the clock on shore.
Henry VIII always had a soft spot for Greenwich. He was born there, for a start, and it was where he used to go for a little rest and recreation, keeping a park well-stocked with deer, and his mistresses in the old Castle. It was handy for the Palace23. He founded the Navy Royal24there, and moved the Royal Dockyards from Portsmouth to Deptford, next door to Greenwich, and Woolwich further towards the mouth of the Thames. Sir Christopher Wren demolished the old Castle to build the first Royal Observatory, known for a long time as Flamsteed House, after John. Sir Jonas Moore, the driving force behind the establishment of an observatory25, originally wanted it to be built on the site of Chelsea College26, but Wren had other plans for that. The King, Charles II, commissioned it specifically “to find out the so much desired longitude of places for the perfecting of the art of navigation”, which at the time was thought most likely to be achieved by an astronomer, not a carpenter from Yorkshire27.
In 1675, the year that Flamsteed laid the foundation stone for the observatory, Christiaan Huygens developed the world’s first practical clockwork clock. These two approaches – astronomical, eventually focusing on a method involving lunar distances invented and developed by Tobias Mayer28of Göttingen; and clockwork, culminating in John Harrison’s marine chronometer – were both used into the second half of the 19th century to determine the time in Greenwich29. Accuracy was crucial. A clock being ten minutes fast or slow was of little significance in the life of a landlubber, but once at sea, each minute in error was equivalent to ten miles on the map, and the slightest inaccuracy could put you on the rocks in seconds30. With lives at stake, it’s no wonder that chronometry should have advanced during this period. Fortunately, the need arose in England, at that time the world’s leading horologist nation, which had recently welcomed its largest ever31flood of immigrants, Huguenots fleeing persecution in France, predominantly skilled craftsmen in many trades, among them watchmaking32.
The original observatory was equipped with two extraordinary clocks by Thomas Tompion, installed in the Octagon Room, again a gift of Sir Jonas Moore. They needed the room’s 20’ high ceilings, as Tompion had adopted Robert Hooke’s idea of a very long pendulum with a very small arc33, thus minimising Galileo’s error. Each pendulum was over 13’ long, and mounted above the clock face. They were accurate to within seven seconds per day, remarkable for the time, but nothing compared to Harrison’s H5 just a hundred years later, tested by King George III himself to be within one-third of a second per day. Since then, driven, and largely supplied, by advances in science, the accuracy of clocks has continued to improve, until now they are controlled according to the vibration of caesium atoms34. However, it is only recently that such precision has come within reach of the ordinary man or woman. In Harrison’s time, one of his marine chronometers could account for over a quarter of the cost of a ship. A far cheaper, although less precise, option was to use Professor Mayer’s lunar distance method.
Unfortunately, the calculations involved were highly complex and time-consuming. Fortunately, however, Nevil Maskelyne, the fifth Astronomer Royal, had the brilliant idea to do them all ahead of time and publish them annually as tables, along with other useful information, in The Nautical Almanac and Astronomical Ephemeris, starting in 1766 with the tables for 1767. This had two, possibly unintended, consequences. One was that the time in Greenwich suddenly became more important than the time anywhere else. The Almanac tables calculated Apparent Solar Time at Greenwich, on the grounds that the sailors would be doing the same at sea, but the clocks themselves showed Mean Solar Time, or Greenwich Mean Time, for short. Now, however useful it may be to have two clocks for determining longitude, that’s no way to run a railroad. Not knowing precisely when the train was due was one thing; not knowing precisely when the express was coming at you down the same track was quite another. In 1840, the Great Western Railway company was the first to standardise on GMT for its timetables, followed in 1847 by the Railway Clearing House, the coordinating organisation for the industry in Great Britain, making a National Railway Timetable possible. Clocks at the stations would show both what was known as Railway Time and the local time. Given that missing your train because you had Railway Time wrong could ruin your whole day, while being ten local minutes late wouldn’t even affect lunch, people who had clocks or watches started to set them to GMT, especially in business. In 1880, it became the official time across the country, and eventually the international reference time.
The other consequence of Maskelyne’s idea was even greater. Now, not only was the chronometer method of determining longitude more precise, it could determine the longitude from anywhere. Until the 18th century, sailors just wanted to know how far they were from home, so their own port or capital city could be zero on their map. The French were particularly fond of the Paris Meridian35, for instance, but there were others, usually at some westernmost point of something, so that the cartographers could get complete countries on the page. But Maskelyne’s tables only worked from Greenwich. On the other hand, they were cheap, unlike chronometers. Pretty soon the world was full of sailors and traders who knew where places were in absolute terms, in degrees of longitude from Greenwich. By the 19th century, 72% of global shipping was using Greenwich as the meridian. In 1851, Sir George Airy established the Airy Transit Circle in Greenwich through which passed his Prime Meridian. In 1884, at the request of US President Chester A. Arthur, the aptly yclept36International Meridian Conference was assembled in Washington D.C. to agree on an International Prime Meridian. Forty-one delegates from twenty-five countries met there, and various options were put to them. In the end, they settled on Greenwich. The French abstained. For almost thirty years. They finally got on board in 191137.
While we’re on the subject of the Paris Meridian, although going back a bit, it was also involved in another international standard.
In 1789, with the stirring example of the American colonists firmly before them, the French embarked on a revolution of their own. They, too, were imbued with the same Enlightenment ideals as Jefferson, Adams, Paine, Franklin, et al., one major difference being that, while George III38was an ocean away in England, the French monarch was in Versailles, just outside Paris where the mob lived. The War of Independence had been a relatively civilised affair. The Americans were revolting on principle39, and when John Adams was sent to England as the American Minister to London a mere two years after the war ended, King George was able to tell him sincerely that, although he was the last to consent to the loss of America, once done, he had always meant to be “the first to meet the friendship of the United States as an independent power.”[i] The French crown would be given no such opportunity.
Everything about the ancien régime had to go. Not just the monarchy, but the entire apparatus of government. The Church could stay, but not the saints. The untidy Gregorian calendar was replaced by twelve months of thirty days apiece40, named not after saints, but the fruits, vegetables, tools and animals of the farm. The months themselves were named after the weather, Brumaire, Frimaire (foggy, frosty), or the farming year, Germinal, Floréal, Messidor (sowing, flowering, harvesting41). As to years, the birth of Jesus was replaced by the birth of the Republic, with 1792 becoming the year 1.
Early on, they decided to be rid of the wildly varying system of weights and measures that was the French marketplace, and the Académie des sciences appointed a commission to do it. They could, of course, have simply decided to standardise the existing system, but that was based on royal body parts – the forearm, the foot, the thumb – and clearly would have to go. Still, given their propensity for the bucolic, you would expect them to retain some version of the Babylonian market arrangement, and indeed, Pierre-Simon Laplace, who was on the commission, did suggest adopting a duodecimal scheme, but it was rejected in favour of decimals. This was, after all, the age of reason, and the decimal system did have one extraordinary advantage: for so long as people have been counting, they’ve been counting in tens42. All you have to do is add a decimal point, and you can go on for as long as you want in either direction.
It was Simon Stevins again who, in 1585, taking some time off from one-upping Galileo, had first proposed extending decimals43to include fractions44. In 1614, John Napier used decimal fractions in his logarithmic tables, and that was that. Perhaps more to the point, the commission was chaired by Jean-Charles, chevalier de Borda45, author of Tables of Logarithms of sines, secants, and tangents, co-secants, co-sines, and co-tangents for the Quarter of the Circle divided into 100 degrees, the degree into 100 minutes, and the minute into 100 seconds. I leave you to guess where he stood on decimalisation.
The commissioners themselves were in no doubt as to what they were setting out to achieve. In the words of the Marquis de Condorcet, it was to be “for all people for all time”[ii], and ultimately, with the Système international d’unités (SI), that is what it has become. At the beginning, though, they were given just five measures to define:
- The mètre for length
- The are (100 m2) for area [of land]
- The stère (1 m3) for dry volumes (stacked firewood, in their case)
- The litre (1 dm3) for liquid volumes
- The gramme for mass.
Of these, only the first presented any problem. The others could easily be defined and measured without leaving Paris, or indeed, the office. The metre, however, was to be defined in relation to the planet itself. According to John Tabak (2004), Stevin thought that coinage, weights and measures would all eventually be decimalised. However, the first actual proposal came over a century later from John Wilkins in An Essay towards a Real Character, and a Philosophical Language, in which he laid out a system of weights and measures that closely resembles the metric system, while a couple of years after him, in 1670, Abbot Gabriel Mouton proposed a measure of length he called the Virga, which would be equal to a thousandth of the distance along the Earth’s meridian equal to one minute46of angle. The Virga would thus be around six feet long, and more or less equivalent to a Toise47, which itself was about a fathom. In 1673, Leibniz came up with a similar plan, all three of them – Wilkins, Mouton and Leibniz – suggesting the actual length be based on a seconds pendulum48in some form.
A century and a quarter later, de Borda rejected the whole seconds pendulum approach for the very sensible reason that the second was one of the very measures they were supposed to be redefining. He – and the commission agreed with him – thought the length should be based on the planet itself, and fixed it at one ten millionth of a quarter arc of the Paris Meridian. It was not just that he was the poster boy for decimals; he was looking for a measurement that would be handier and more practical than the Toise, something more along the lines of the yard. The yard, based on a single pace49, was a useful standard in everything from weaving to carpentry. Ever since Columbus’s lucky escape in 1492, everybody in Europe was acutely aware of the circumference of the Earth – a little less than 25,000 miles, and the meridian would be approximately the same. 25,000 times 1,760 equals 44,000,000 yards, making a quarter arc 11,000,000, so his desired measure would be about 10 per cent over a yard. This suited him well. The only problem was that they would have to leave Paris to measure it.
In any other year but 1792, this would not have been an issue, but the project was unfortunately timed to coincide with the outbreak of the French Revolutionary Wars50. It outlasted the entire war against the first coalition of European states, France against the combined might of Austria, Spain, Belgium, the Netherlands, Germany and Great Britain, together with Portugal and much of Italy. France won51, although Great Britain did not accept this and went on fighting. Throw in the Reign of Terror, which only lasted 11 months, from September 1793 to July 1794, but accounted for over 40,000 executions throughout France, and the whole idea of doing the survey in France because it would be safer starts to look a bit weak; however, there was nowhere else in Europe they could go, so the Paris Meridian it was.
The hapless crew sent out to do the work was to have been led by Pierre Méchain, an astronomer and member of the Académie, as well as a Fellow of the Royal Society, and Jean-Dominique, Comte de Cassini. However, Cassini was a royalist, and refused to work for the National Assembly once they arrested52the king in August of that year. He was replaced by Jean-Baptiste Delambre, a newly, but unanimously, elected member of the Académie des sciences, who took charge of the northern section to be surveyed, while Méchain took the southern part. The whole route, from Dunkirk to Barcelona, was 242 leagues; the northern part, from Dunkirk to Rodez in the south of France, was 167 leagues, while the shorter part, from Rodez to Barcelona, was only 75 leagues. However, that part contained the Pyrenees, while the north was largely flat, so it seemed a fair division. As a baseline, Delambre used a six mile stretch of straight road, between Melun and Lieusaint, as it happens, which he measured using platinum rods, each two toises in length. Méchain found a similar stretch between Vernet and Salces, and did the same.
At this point you may justifiably be wondering precisely what a toise might be, and if so, how long is a league? Good point. As if to prove that the whole exercise was justified, in 1792 Paris alone had four, count ‘em four, definitions of a league (lieue in French). The oldest was the one used by the Public Works department, originally called just the lieue de Paris, but from 1737 on known as the lieue de ponts et chaussées (bridges and roads). It was 2,000 toises long. There was also one for the Post Office at 2,200 toises, and another for calculating tariffs at 2,400 toises. The fourth, and the one I am using here, was defined by Jean Picard in 1669. It was to be one twenty-fifth of a degree of the polar circumference of the Earth, and called simply the Twenty-five to a degree league. Picard calculated it to be exactly 2,282 toises.
“So what about the toise?” I hear you cry. Well, the toise changed very little, except in name, between Picard’s definition and the 1792 survey. In Picard’s time it was called the Toise du Châtelet, and the one that replaced it, known as the Toise du Pérou, was almost identical. So far, so good. However, the year before Picard did his measuring, somebody decided to check on the original reference toise which went back to Charlemagne’s day, and found it had shrunk by nearly half an inch, or about five lignes. Désastre! But no; just time for a swift, collective Gallic shrug, and they go with the new short version, so that’s what Picard used.
I want you to be impressed by Picard. If you take his 2,282 toises, multiply them by 25 to give you a degree, then by 360 for the polar circumference, you get 20,538,000 toises. Divide that by 40,000,000, as the metre was intended to be, and that gives you 0.51345 of a toise. There are 864 lignes to a toise, so a ‘real’ metre, one that corresponds to the original specs, is 443.6208 lignes according to Picard, and according to World Geodetic System 84 it should be 443.38308 lignes (or at least it would be if anyone had known what a ligne was). Anyway, the difference between Picard and the WGS is less than a quarter of a ligne, otherwise known as 20 thousandths of an inch, or half a millimetre in metric. Respect.
Méchain and Delambre did better of course, but even they weren’t perfect. It may not have been their fault. Cassini’s father had already done a survey in 1744, and Delambre reused a lot of his triangulation points, for instance, while Méchain had the opposite problem; large parts of Northern Spain had never been surveyed at all. On top of all this, they were constantly being arrested and slung in gaol as spies for one side or the other in either the war or the revolution. Méchain ultimately gave his life for the survey, dying in 1804 of the yellow fever he contracted in Spain while trying to improve on his work there53.
Meanwhile, back at the ranch, de Borda54and the commission had jumped the gun somewhat, and calculated a provisional value for the metre based on earlier surveys. This was put into law in 1795 as 443.44 lignes, so within a couse55of Picard’s value. Based on this, they had a bunch of platinum bars made up so that when Méchain and Delambre got back they could just pick the nearest one to their measurement, and get on with things. The survey duly came back with a length of 443.296, the appropriate bar was chosen and went on record in 1799 as the mètre des Archives. Unfortunately, 443.296 fell short of meeting the 10 million to the arc requirement, a fact which quickly became apparent. Désastre! But no; another swift shrug, and life carried on56.
The mètre des Archives may have fixed the length of the metre itself, but work still went on into improving the reference bar. In the 1870s, the International Metre Commission, comprising some thirty countries, met to discuss, and eventually, in 1875, sign, the Metre Convention which set up the Bureau international des poids et mesures in Sèvres, just outside Paris, although not actually in France57. As a reference, they used the distance between two marks on a longer bar, which reduced the wear and tear problems associated with earlier metre-long “end standards”, what Wikipedia wittily calls their “shortcomings”58. The new international prototype metre was made of an alloy of 90% platinum and 10% iridium, and copies in the same alloy were distributed to all the signatories, along with precisely calibrated notes as to each bar’s variation from the prototype59. However, this only pointed up the difficulties inherent in having a physical artefact as a reference, and in the early 1890s, Michelson (of Michelson and Morley), together with one Jean-René Benoît, using interferometry, managed to measure the prototype to within a tenth of the wavelength of the red line of cadmium.
Nonetheless, it was not until 1960 that the 11e Conférence générale des poids et mesures would agree a wavelength-based standard for the metre:
“The metre is the length equal to 1,650,763.73 wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p10 and 5d5 of the krypton 86 atom.”
At that same conference, which, incidentally, formally established Le Système international d’unités, the definition of the second was officially ratified as:
“1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time60”
It had been redefined four years earlier because the daily rotation of the Earth was not uniform enough to measure accurately, but the point about this definition is that it was not measured at all; it was calculated based on Newcomb’s Tables of the Sun, and Brown’s Tables of the Moon. However, even as this definition was being ratified, Louis Essen at the National Physics Laboratory in England and William Markowitz at the US Naval Observatory were collaborating on a new definition of the ephemeris second in terms of the “hyperfine transition frequency of the caesium atom”, which turned out to be
“the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom”
as ratified in 1967 at the 13e Conférence générale des poids et mesures. The Earth herself may wobble and slow, as indeed she does, but the second would henceforth be divorced from all that. When this new definition was compared to the observed ephemeris second, it agreed to within a tenth of a nanosecond, the time it takes light in vacuum to go three centimetres, or a little over an inch.
Talking of light, in 1975 the 15e Conférence générale des poids et mesures recommended that c, the speed of light in vacuum, should be set at 299,792,45861metres per second, based on a number of experiments and using the above definition of the second; the 17e Conférence générale des poids et mesures agreed in 1983. This allowed the metre, too, to let slip the bonds of Earth, and take its value from c, which thereby became the universe’s first quasi-dimensionless62physical constant. I say ‘quasi-‘ because any speed is described by two factors, one of which is invariably a unity – mph, fps, etc. This inversion of the usual definition – in which any uncertainty is seen in the value of a factor – leaves the actual metre with the task of reconciling the definition with reality, and absorbing any disparity, should there be one (Famously, the speed of light used to vary somewhat, which was embarrassing. Now the metre varies somewhat but, with the speed of light fixed, we have no way of measuring it. Sneaky, no?).
And they’re going to do it again. This November, 2018, in Versailles, France, representatives from 57 countries plan to revise the SI, finishing the job of creating a complete system that does not depend on physical objects. Instead, everything will be based entirely on the speed of light and other “constants” of physical science, resulting in a measurement system that might truly and finally be “for all people for all time”, as the Marquis de Condorcet had hoped.
When implemented on May 20th, 2019, the kilogram, based on the definition of Planck’s constant, which has recently been defined as having a value of 6.626 069 83*10-34 Kg M2/Sec, in combination with existing definitions of the metre and the second, will also cease to depend on a material artefact, and be based on a physical constant that would be universal in its scope and application. The work begun by the Babylonians 4,000 years ago, and carried on by the French revolutionaries, will culminate in a system that will work “for all beings, human and alien, for all time and throughout the universe”, based entirely and uniquely on this planet.
Not so insignificant now, eh, Carl?