The Meaning of Measure (Origins of The Metre and The Kilogram)

Where were you when I laid the earth's foundation?
    Tell me, if you understand.
Who marked off its dimensions? Surely you know!
    Who stretched a measuring line across it?
On what were its footings set,
    or who laid its cornerstone —
while the morning stars sang-together
    and all the angels shouted for joy?

- God

[Book of Job 38:4-7 (NIV Version) - Italics mine]

The nature of measurement is as old as the foundations of this earth, as God told Job in so many words, "Where were you when I sculpted the fabric of timespace? When I stretched a measuring line across it?"

Because of its arbitrary nature, measurement has always had idiosyncracy about it. Humans seem to historically speaking, prefer to measure things after their own bodies, as the body itself, measurements based on the hand or arm, were used throughout ancient cultures to represent what later were considered "standard measurements". The Cubit of Egypt and the Hebrew Bible [אטה (am-mah′) in Hebrew] [πήχυς (pay′-kus) in Greek] was the distance from the from the elbow to the tip of the of middle finger, The Greeks used the Lick, and this was the distance from the outstretched thumb to the top of the index finger.  although alternate variations included to the wrist, or the space between the outstretched pinky and thumb; hang ten dude.

The English inch was initially the width of a thumb, the foot (approximately 11 1/42 Inches), you guessed it, the size of an average foot. A yard was the size of an "average" man's belt, or girdle. The Roman span was about five feet, and this was the length of a Roman soldier's stride (they took doubly sized strides, probably how they seized so much land). All of these measurements are based on anthropomorphic phenomena. 

The Metric System (The Measure System) is the key to many shared systems of measurement in standardization today, for instance, length, velocity, and volume are all extrapolated from the measurement of a meter. It is formally referred to as SI, which stands for the Système International d'Unités, (International System of Units). The metric system is decadic, and in this fashion, continues the anthropomorphic proportions of the body, but unlike the others which were solely based on the body, the meter has the fraction of the distance of an arc of the earth as its origin,  and as such, is an impressive geocentric extrapolation of measure. 

The French metre, (English Meter), is calculated by dividing the distance from the N. Pole to the Equator along an arc that passes through Paris, France by ten million. In other words, one meter is 1/10,000,000 of the distance from the North Pole to the Equator. How the heck did they figure that out? 

The standard Meter bar, an early iteration of the definition of the distance of one meter. 

The standard Meter bar, an early iteration of the definition of the distance of one meter. 

Well, the story goes like this: French Astronomers Joseph Delambre and Pierre Méchain were charged with the task of measuring the distance from a bell tower in Dunkirk to a Castle due south in Barcelona from 1792-1799 , in order to extrapolate an approximate distance of the meridian of the earth. At the time, the primary competing method in contention for standardization in measure was a pendular method initially proposed by Sir Christopher Michael Wren (a founding member of the The Royal Society), but ultimately championed by John Wilkins (another RS Founder) who promoted the notion that the measure be a pendulum whose half period was equal to that of one second (A length of what is today known as 997 mm). The French Academy of Sciences considered both options and then opted for the meridional method over the pendular method, citing the fact that forces of gravity change over various faces of the earth which could influence the pendular motion, making it potentially less constant than the distance from north pole to the equator. The selection of geometers Delambre and Mechain, by The Academy of Sciences, was sanctioned in a proclamation by King Louis XVI dated June 10th, 1792, "to undertake the geometric measure of the meridian, in order to establish a standard length for the measurement of the meter."

Delambre and Mechain's measurement consistedspecifically the distance of the meridian from the north pole to the equator as it ran through Paris. There, of course, remains the punctilious question of the type of measurement Delambre and Mechain originally used if meters were not yet defined. 

Perhaps unbeknownst to them, Delambre and Mechain had set in motion a method of the measurement in relation to the meridian of the earth, that would be forever ingrained into our sense of time and space in this world. Their work was stellar, unprecedented, and quite literally "earth changing", for in 1793 France adopted this equation as the standard formula for the unit of measurement, the meter. Also, at this time, the other fundamental measurements, other than distance, which was in need of standardization, were both volume and weight, and the methods for measuring volume and weight were derived from the measurements of distance.

Specifically, in in 1793, volume, termed a pinte (later a litre) was defined as "the volume of a cube having a side equal to 1/10 of a meter), and mass, called the grave (later termed the kilogram), was defined as "the mass of one pint of distilled water at the temperature of melting ice". Since we can see the "one pint" derived from "the volume of a cube with size 1/10 of a meter", it is easy to see how the grave (now called the kilogram), which is defined by the mass of a pint, is also derivative of a the original unit of measurement, the meter (or 1/10,000,000 of the distance from the N. Pole to the Equator through Paris). The metric system was officially adopted on April 7th, 1795, and in 1799 platinum objects were made to represent the meter and the kilogram based on a new survey from Delambrey and Mechain. These objects of the metric bar and and metric kilogram were accepted as official by an act on December 10th, 1799.

This of course was near the conclusion of The French Revolution which lasted between 1789-1799, when the pre-existing method of measurement was thrown out, in favor of this decimal based metric system. Just to give you an idea of what went out the window, prior to this time period, there were over seven hundred different types of terms of measurement in use in France, the majority of which were passed down from Roman influence, and many of which varied from town to town.

So began the standard measurements for "size" (length, volume & weight), with standardized objects made for both one meter and one kilogram, thanks France! It is quite important to underscore here that the pint, the origin of both volume and mass, was calculated by using space defined by a particular fraction of length of meters (which are of course 1/10,000,000 of the distance from the equator to the N. Pole through Paris as extrapolated by Delambre and Mechain). By seeing clearly how the weight and volume of an amount of water at freezing level came out of the specific lengths of the container (1/10th of a meter) the water is held in, we can begin to grasp how apropos the name meter (measure), truly is.

The Meter is nothing less than the building block and source code of all standardized forms of modern measurement.

Finally it was discovered that the meter as measured by Delambre and Mechain was ultimately off by .2 mm (an infinitesimally small amount considering the techniques and crudeness of the originally extrapolated measurement attesting to the brilliance of both Delambre and Mechain), because it didn't account for the earth's spin, which makes it slightly fatter at the sides, and shorter at the top and bottom, and thus the earth's shape geo-spatially is closest to what in geometry (literally geo=earth metry= measure) is considered an oblate spheroid (think Mr. Potato Head). Although, it is not an oblate spheroid either because even this isn't specific enough for the contours of a uniquely-shaped planet at sea level along a meridian from equator to the north pole when passing through Paris. I mean, honestly, how can we truly measure such specificity?

In order to improve these calculations the earth is currently considered a, geoid, which ironically means 'earth shaped', though does not correspond to the actual shape of the earth but instead is mathematical model that approximates this shape. As we will see, the relationship between space and math as a form of "measurement" in the real world was originally and still is now (albeit with ever narrowing margins) an elusive, shifty, and rather un-pin-pointable phenomenon. And I might add, rather poetically so, as if nothing were meant to be static in this world. But for now, back to this chronological tale of the telling of measure.

So Delambre Mechain meter was off by a couple milimeters, so what? Well the meter took a while to take hold, and wasn't compulsory as a unit of measure in France until the 1840's. Once in circulation, these calculations stood as the basis for the Metre for nearly a century until in the 1870's, when the BIPM (Bureau International des Poids et Mesure - International Bureau of Weights and Measures), decided to get together to build a new set of metric standards. These scientists, geometers, astronomers, and mathematicians, rubbed their heads together and realized it would be best to build another object which could better represent the unit of the meter, (which don't forget, simply means measure, and which at this point in time still is meant to indicate 1/10,000,000 of the distance from the equator to the N. Pole on a meridian running through Paris). So in 1873, the BIPM gathered at the headquarters in Sèvres, France, and built a better one. The next physical object to represent the meter, was termed, "The 1874 Alloy, and consisted of Platinum-Iridium." This object was intended to diminish the .2 mm margin of error due to the earth's spin.

The casting of the "1874 Alloy" consisting of Platinum-Iridium to be a more accurate physicalization of 1/10,000,000 of a quadrant of the Earth (more specifically 1/4 of the meridian from the N. Pole to the Equator, through Paris, France).

The casting of the "1874 Alloy" consisting of Platinum-Iridium to be a more accurate physicalization of 1/10,000,000 of a quadrant of the Earth (more specifically 1/4 of the meridian from the N. Pole to the Equator, through Paris, France).

So, after the "1874 Alloy" was cast the physical meter was put into motion in the world. However, the 1/10,000,000 of the distance from the equator to the n. pole, to whatever degree of hyper-specificity, we will see, has continued to prove elusive to pin down, which will and does, beg a question about the exact nature of "measure", and it's ability to be a specific "measurement."  The prototype of the kilogram was developed shortly after, in 1875.

CPGM, 1875 pose for photo in front of Pavillon de Breteuil, Paris. Photo Cred:

CPGM, 1875 pose for photo in front of Pavillon de Breteuil, Paris. Photo Cred:

In 1875, the International Prototype of the Kilogram (SI Unit Kg), is built and The Kilogram is defined as being equal to the mass of the International Prototype of the Kilogram (IPK, also known as "La Grande K" or "Big K")

In 1875, the International Prototype of the Kilogram (SI Unit Kg), is built and The Kilogram is defined as being equal to the mass of the International Prototype of the Kilogram (IPK, also known as "La Grande K" or "Big K")

So, by the end of the 19th century, we have the meter defined as 1/10,000,000 of the meridian from the N. Pole to the Equator as passing through Paris, and the Kilogram defined as a physical thing [pictured above] built to represent the mass of "one pint of distilled water at the temperature of melting ice" (Initially said to be 0 Centigrade, later redefined at Waters temperature of maximum density said to be 4 degrees Centigrade). Due to chemical processes and atmospheric imbalance, the prototype for the meter was proposed by Albert Michelson to be calculated in relation to the speed of a wave length of light, as measured by a machine he invented called a interferometer.

Calculations derived from an amount of wavelengths began to be popular, slowly dematerializing the need for a physical prototype of the meter. However, it didn't officially vanish as the prototype of the meter until, 1960, at the 11th CPGM (Conférence générale des poids et mesures - General Conference on Weights and Measures), when it was redefined (now derived by calculations involving the interferometer) as a specific number of wavelengths of the red-orange emission line of the Krypton-86 atom. In this higher degree of specificity, the meter became defined "as equal to 1,650,763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum", which was found to be a more stable representation of the length, and which now relied on believed to be fixed "law of nature", namely, the speed of light or C.

By 1983 at the 17th CPGM, the meter was pegged solely to the speed of light and fixed by the number of intervals of seconds. This is how we arrived at the number we are familiar with today, for the speed of light, which is 299,792,458 meters per second.

In simpler terms, the meter is how much distance light covers in 1/299,792,458 of a second. In 1983, the meter officially became pegged to the speed of light. This brings to light an interesting and alleged anomaly discovered by Rupert Sheldrake wherein he found that the speed of light dropped ever so slightly, (by about 20 kilometers per second) between 1928 and 1945, and then in 1948, it suddenly popped back up again, and metrologists began getting the same increased speeds from different pieces of equipment around the globe.

This brought Sheldrake on a journey to question the fundamental constants presumed by science namely Big G (Newton's Universal Gravitational Constant) and The Speed of Light (Referred to as C, as in E=MC2). The first which expands the conditions surrounding the mass of a Kilogram, the second which expands the conditions surround the distance of a Meter. These two enquiries brought Sheldrake into a conversation with a Metrologist (metrology is the science of measuring constants) about whether or not these anomalies with respect to The Speed of Light could be occurring today.

Yes, but we’d never know it because we’ve defined the meter in terms of the speed of light. So the units would change with it.
— Metrologist, Teddington

Learn the whole story about that encounter and his finding in his Ted Talk on my other post, Rupert Sheldrake on The Speed of Light & Big G . To put the issue as simply as I can. The measurements for the speed of light from the leading laboratories of metrology around the world are done in meters. While meters are defined by the speed at which light travels. This becomes what is referred to as a closed loop. Any alterations in the speed of light would be hidden in the fixed amount of meter and any alteration to the exact distance of a meter would be hidden in the speed of light which it is defined by. 

Another way of putting this is that the "timing of a second", which is to say, "of the speed of light", is self-adjusted in this equation by the fact that the meter is pegged in terms of the distance light travels during 1/299,492,458 of a second, to the speed it is attempting to define. The way we put this in English Lit class was you can't use the same word to define that word. Well this is exactly what is going on with The Meter and The Speed of Light. It is also what may end up going on with The Kilogram and Big G. Both of these raise questions about the constancy of measure, and thus everything we extrapolate from measure including but not limited to "the light barrier" the "weight of precious metals" and the "volume of a pint". 

The fundamental paradox persists into mass. But less so, as mass is still defined by a physical hunk of metal. To this day the Kilogram is defined as the weight of the International Prototype of the Kilogram.

The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.
— 3rd CPGM (1901)

According to the BIPM website, "It follows that the mass of the international prototype of the kilogram is always 1 kilogram exactly, m() = 1 kg. However, due to the inevitable accumulation of contaminants on surfaces, the international prototype is subject to reversible surface contamination that approaches 1 µg per year in mass. For this reason, the CIPM declared that, pending further research, the reference mass of the international prototype is that immediately after cleaning and washing by a specified method (PV, 1989, 57, 104-105 and PV, 1990, 58, 95-97). The reference mass thus defined is used to calibrate national standards of platinum-iridium alloy (Metrologia, 1994, 31, 317-336)."


So basically, the kilogram is defined right after the kilogram is washed in a ritualistic fashion, and then these measurements are sent out to be used as national standards. Meanwhile, The Kilogram sits in a room in an atmospheric vacuum near Paris, France, and everyone tip toes around it hoping it won't change. But it keeps changing, recent evidence indicates its getting fatter.

Also, it is of note to point out that the standard Kilogram, just like the original meter, is near the geographic location of Paris. The Kilogram is how much the Kilogram weighs near Paris. The Meter is the length of the meridian from the N. Pole to the Equator through Paris. This, though expected since the origin of the meter comes from France, is still a geographic oddity of sorts, worth pointing out with respect to the origin of standard measurements.

The Kilogram is the last method of measurement in all of SI (International System of Units) to be based on a physical thing and not a Universal Constant. Considering Sheldrakes forecast, it may behoove us to revert back to a standard model for the meter once again, as well. However, according to a metrologist from the International Bureau of Weights and Measures in Paris, who was quoted in an article on, "Long-term, however, most scientists want to get away from defining the kilogram based on a hunk of metal. Instead, it should somehow be based on a fundamental law of nature, Davis said. [He added,] "I think the definition will be changed in the next five to 10 years," Davis told LiveScience.

The International Prototype of the Kilogram (IPK) is of cylindrical form, with diameter and height of about 39 mm, and is made of an alloy of 90 % platinum and 10 % iridium.

What is interesting about this intention from the Bureau of Weights and Measures is that changing to a "fundamental constant" could evoke the same "closed-loop" phenomenon which Sheldrake encountered with the Speed of Light and Meters. If Big G were defined in terms of Kilograms, and Kilograms in terms became defined on a "fixed amount" of Big G, then any fluctuation of the gravitational force of the earth within the electromagnetic spectrum would be folded into the black box Schrodinger's cat never got out of, change in either The Gravitational Constant or The Weight of the Kilogram would be so inextricably linked that no change in either could be detected.

If fluctuation of The Universal Constants of Gravity and The Speed of Light do change, as Sheldrake suspects, then it is not so surprising that just like in 1972, when metrologists pegged the speed of light to meters, that within the next 10 years, Davis predicted they would do the same for mass. After all, if you run the system that sets the standardization of measurement across all nations the notion that your constants weren't constant would certainly undermine the authority of your profession. Further more, defining your measurements in relation to constants that are pegged to a specific amount of your measurements would ensure you wouldn't lose a foothold on what weighs how much and who says so, and how fast and according to whom.

Measure has been pursued since time immemorial, and man will continue to pursue it. So what is the meaning of measure? In my estimation, it is no less than a Godly pursuit. It is our pathway into the key codes of our reality. Yet perhaps, at its most basic level, it is the desire to seek grounding in a world of constant flux. But may we remain ever aware that this universe has always been in flux, and new science is indicating this may be the only constant. Let's not let our desire to feel safe and secure by "Laws" that may blind us to evidence of the contrary. I'd be remiss not to say that if in the pursuit of measure, we forget that Science has often upended itself, and shown greater fundamental truths than heretofore believed, then we have lost what makes Science innovative, and worth our valuable time. I can almost hear an elementary school science teacher in the distant future, "That's was back when we thought the speed of light was fixed, and all measurements remained constant. Once we realized that wasn't true. Everything changed. Everything."