On Arbitrary Measurements | Vol. 4 / No 12.2

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The Grand K, or 10/87 of a Badger | Image: Greg L., CC BY-SA 3.0

Measuring things in Badgers might seem ludicrous, but if you defined a Badger (unit) according to something relatively constant in the universe? Well it wouldn’t be the most ridiculous thing I’ve heard.

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This week, friend of the blog @GladiatorGirl sent me in the direction of this tweet by @HistoryGems:

If it’s not coming through, it reads that “the Lindisfarne Gospels weigh 8.7kg, which is as much as an adult badger.”

And I started to think — what if we measured everything in badgers? What if we measured everything in completely arbitrary units of measurement? And then I thought: what if we already do?

So here’s the thing: the US uses more arbitrary units than most. A mile is 5280 feet, or 8 furlongs (each furlong consisting of 660 feet, or 40 rods, or 10 surveyors’ chains). A degree Fahrenheit is 1/100th of the temperature difference between what Fahrenheit (the man) thought was the coldest liquid temperature which he set at zero (it’s not) and human body temperature which he set at a hundred (it’s not).  A degree Fahrenheit is, well, a quarter of a slightly adjusted Rømer degree (which was a scale that put freezing at 7.5 and boiling at 60, because “degrees” should be divisible by 60, right?).  A pound is 16 ounces, all of which are based originally on an arbitrary prototype weight.

But if you live in the US, don’t think you’ve escaped metric. Since 1959 a foot’s length has been determined by international agreement to be precisely 0.3048 metres. Same goes for the pound, which is legally 0.45359237 kilograms. A degree Fahrenheit, being defined now by the freezing and boiling points of water at 32 and 212 degrees respectively (so much for Fahrenheit’s original plans) is precisely 5/9 of a degree Celsius — the metric standard for temperature used by every country on the Earth that isn’t America.

But what about metric? Is that any less arbitrary? Well, yes and no.

Take Celsius (or Centigrade): originally defined as 1/100 the distance between the freezing and boiling points of water at 1 atmosphere of pressure, it seems pretty accurate. The metre was designed as 1/10,000,000 the distance from the equator to the north pole. And the kilogram was intended to be the mass of 1000 grams, with a gram being equal to the mass of a cubic centimeter of ice at just below the freezing point. These were intended to be units of measurement relative to the physical laws of the Earth, something we all had in common.

But they aren’t — not really. They’re not accurate enough. Boiling and freezing are physical processes that take place over time. The Earth isn’t a sphere. And a kilogram is legally the weight of a specific cylinder of 90% platinum and 10% iridium sitting in a vault on the outskirts of Paris (the International Prototype Kilogram, or IPK).

So we’ve made them relative to laws of the universe instead.

Now, a degree Celsius is set such that 0.01°C is the “triple point” of water (where it can be gas, liquid, or solid — by definition at the lowest pressure water can exist in a liquid form), and -273.15°C is absolute zero, at which all atomic motion supposedly stops (or at least weird quantum-physical phenomenon start happening).1 A meter is the distance travelled by light in a vacuum in 1/299 792 458
seconds. A kilogram is still the weight of a lump of metal on the outskirts of Paris, but we’re getting close to a solution (or three).

That said, all of these units of measurement — that is, the size of those units, not just where their scales begin and end — are very specifically calibrated to make sense to humans. Because we’re from Earth. Because we’re roughly two thirds water. Because we live in one atmosphere of pressure, which is called “one atmosphere” because it’s one of our atmospheres. Our units of measurement, even if we do eventually relate them all to physical laws of the universe (and not just lumps of metal on the outskirts of Paris), will just be awkward mathematical definitions of arbitrary numbers, chosen for their importance to us, not to the universe.

Even making things “round numbers” is arbitrary — we only think of 10 as a round number because we have ten fingers and therefore use base ten math. If we had twelve we’d be counting 12 as 10 — something like 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ɔ, ǝ, 10 — and 10 would be base-ten 12, and base-ten 10 would be the as-yet-unpronouncable ɔ. Our 100, seeming like a nice round number to us, would be written 86.

This, of course, has major implications for how we might talk to extra-terrestrial intelligences, even in the so-called “universal language” of math. Thankfully, prime numbers are prime numbers regardless of the base you’re using (so long as you’re counting pulses) so that might be a good start. But that’s beyond the scope of today’s post, which I’ll sum up by saying this:

Measuring things in Badgers might seem ludicrous, but if you defined a Badger (unit) according to something relatively constant in the universe — like the charge used to lift a single, prototype stable metal badger replica in precisely 1g – well, it might not be the best unit of measurement, but it would at least make as much sense as the pound.

And for the record, if we define a Badger as precisely 8.7 kg, I weigh 7.82056321839 Badgers.

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Notes
1. A degree Kelvin, if you’re wondering, is precisely the same size as a degree Celsius, it just starts at absolute zero and counts up. 0°C is 273.15°K.
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Also: as reader Dan Silverio points out, Veritasium did a great video on Fahrenheit which clears up some misconceptions, but still doesn’t really make it make all that much sense. You can watch that here:

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Richard Ford Burley is a human, writer, and doctoral candidate at Boston College, as well as Deputy Managing Editor at Ledger, the first academic journal devoted to Bitcoin and other cryptocurrencies. In his spare time he writes about science, skepticism, feminism, and futurism here at This Week In Tomorrow.