The basic thesis will be that neither the definition of the basic unit, nor division by ten, is particularly scientific. Once stated, the truth of the thesis should be intuitively obvious. But let’s unpack this a bit anyhow.
The standard unit
The first official definition of the meter was “one ten-millionth of the length of a quadrant of the earth’s meridian (i.e., one ten-millionth of the distance between the equator and the North Pole).”
And they dare laugh at us, that a “foot” had some connection to a man’s foot?!
At least you could “calibrate” your foot to the official foot — “a smidgeon more than the length of my dress shoe” — and do useful calculations like measuring the size of a room. To that, our opponent would have had to answer “Dumbkopf! Everyone knows that a meter is 1/10,000,000 of a quarter-meridian! Now measure!”
Note that you can only measure the quarter-meridian using some pre-existing metric. Thus, it was a rather funny way to define the base metric. It really only provides a method for converting from another, existing measure.
Next, they went to a standard stick that rested somewhere in Paris. At least, this had the advantage of making apparent the arbitrariness of the standard. And, it inspired Wittgenstein’s interesting discussion, “how long is that stick?” in which he pointed out that it was confused to say “it is one meter long.” That would be to attach a predicate to the stick, implying we know what a meter is prior to predicating it of the stick. But I digress.
In 1983, the meter was redefined again. “The definition states that the meter is the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second. The speed of light is c = 299,792,458 m/s.”
Two comments. First, there seems to be something circular in this definition. Suppose they discovered that the speed of light was actually only 299,792,457.99 m/s. Well that couldn’t be, could it– think of Wittgenstein’s comment. Yet, if the previous measurements were wrong, then something has changed– either the meter, or the definition of the meter. The same comment applies to the time part of the definition.
Second, how is such a definition useful to anyone but an advanced laboratory? In practice, a meter is still just “the length of this stick here.”
Perhaps I am belaboring the point. Probably everyone agrees that our basic unit has something arbitrary about it.
Some arbitrary is better than other arbitrary
My colleague pointed out:
(4) The traditional units of measurements evolved by slow, natural forces. They do not constitute a pre-packaged â€œsystemâ€ of measurement. In it, much of our past is preserved and passed on to future generations.
(5) The traditional units worked because they were personal, quotidian and humble. Feet, inches, cups, bushels, etc. were based upon objects in the real world. (Want to know how long an inch is, look at the width of your thumb.) Such measurements are easily grasped.
The impulse to use units of measure that are part of common life is not just something medieval; it continues right into our times. How many times have you heard someone say something like “wow, that aircraft carrier is as long as two football fields!”
How about: “Philadelphia is two hours from New York, and two hours from Baltimore.”
“The cafÃ© is only a 10 minute walk from here.”
They still measure the height of a horse in hands. Granted, the length of a “hand” is now defined precisely; but still, there is a “feeling” about what unit is “right,” which no doubt includes both intuition and a sense of continuity with the past.
I like to remember the speed of light as a foot per nanosecond; then I convert this to 30 cm/ns if need be. Technically, it is more like 29.98…. if you need it. Which is better? There is no answer to that.
Which is more intuitive?
It might be helpful to remember that the important numbers in pure math can also only be used in approximation. Trousered apes used to chuckle at the verse in the Bible (I Ki 7:23) where the circumference of a round object is given as three times the diameter.
You would like it better if it had said 3.14 times?
How about 3.1415926536 times?
Still just an approximation!
Scientific pedagogy deals with arguing for relationships between quantities that are discovered empirically. Various constants are used to express a fixed proportionality that is discovered: G, e, mu, epsilon, etc.
All of these constants are crazy numbers that are best looked up, regardless of which system you use. Except, sometimes units are defined to “get rid of” ugly constants, for convenience. In the esu units, Coulomb’s law is F=q1 q2/r^2, where r is in centimeters (note: not meters; remember to convert answer to meters if that’s what you need! Make sure you get the right power of 10!) In that system, q is no longer the Coulomb, but is an “esu unit of charge” that makes the equation work.
The point is, pick a system of representing your forces and fields, and do your deductions. Then, at the end, plug in whatever units you need. There is nothing magic here.
And so far, there is no advantage per se to the notion of “divisibility by 10.” The formulas know nothing about division by 10.
However, most people that favor the metric system, I suspect, do so because of all the factors of 10 lying about. So we need to unpack if and when that is an advantage. However, I have talked long enough for now; the great factor of 10 will be discussed in a future post.