The reason why there are 12 inches in a foot, 16 ounces in a pound, 360 degrees in a circle, or 5280 feet in a mile are not random.
5280 has 48 factors, which allows you to use pure geometry for a significant amount of needs. Base 10 can only be divided in half to maintain an int result.
You can divide a meter-long object into halves, thirds, fourths, sixths, or twelfths just as easily as you can divide a yard-long object.
What’s the need to maintain an integer amount in some other unit? You don’t measure a third of a mile and then nod to yourself in satisfaction that it’s exactly 1760 feet. Either start measuring in feet and do your whole calculation in feet, or measure in miles and do your whole calculation in miles.
12 and 16 have a solution in pure geometry to find the distance the distance between the value of 1.
Base 10 doesn’t have the same option, so it is harder to find the base interval and create accurate graduations. This is less of a problem in the modern world obviously.
Are you claiming that it’s ever useful to be able to find 1/11 of a mile?
A more useful list of factors is the prime factors of a number. 5280 = 2^5 * 3 * 5 * 11. The 2s, 3, and 5 make sense, but is that 11 really useful for anything? It seems to me that it’d be more convenient to make it 4800 feet: That lets you do another halving, if that’s your thing, or to divide it into 100 integer parts.
As for temperature being a property of the average behavior of molecules, that’s true, but it’s typically 10^20something molecules. With that many, the error due to random variation from molecule to molecule is going to be quite small, smaller in fact than many other sources of error in measurements of both temperature and of other quantities.
None of those land on the integer units, and all except 10/4 will result in a loss of precision if used in cumulative divisions if you try to correct for that.
The problem is with how you come to a value of exactly 1 with geometry.
I assume you mean that it’s possible to use a compass and straightedge to divide a line segment into 12 or 16 equal parts? It’s possible to do that for any other number, 7 or 10 or 97 or whatever. Euclid, book VI, proposition 9, also known as the Thales theorem.
Do you have an example of prop 9 that isn’t n=3, like n=10?
In reference to Thales theorem how do you construct equal perpendiculars in real life with accuracy? It is a lot harder.
I as mostly referencing dividing a line using little more than a compass.
Why do you have to convert from fractions to decimals before your calculation is complete? You don’t. You don’t have to divide 10 meters in 3 and write it 3.333333, you can just write it 10/3. You never lose precision.
And you can’t divide 10 feet into 3 parts, and get integer values, can you? OK, you can write it 3 feet 4 inches, but that’s just another way of writing 3 and 4/12 feet, isn’t it?
Having smaller units that are fractional values of larger units doesn’t produce any mathematical precision, it’s just a way of writing fractions that doesn’t look like you’re writing fractions. If precision is important, just keep writing fractions and don’t convert to decimal until the very end, if then. Just like it’s better to keep pi and e and square roots of 2 as separate units and not multiply them out until the very end.
The point is not to produce rational segments, but to mark your units. You need marks that = your unit.
To try and explain this position, and because the IPK is one of the few physical object standards in SI.
We both get a balance scale and some sand and some containers. You get a perfect copy of the IPK which has the mass of 1KG. I get a perfect object that weighs 1 Pound. Or job is to derive the sub units accurately.
You can choose hecto grams, deka grams or just grams, I will derive ounces.
Here is my solution.
Create a pile of sand that equals the pound prototype.
Separate that to pile into equal portions.
Separate one of the piles from step 2 into two equal parts.
Separate one of the piles from step 3 into two equal parts.
Separate one of the piles from step 4 into two equal parts.
Each pile from Step 5 ~= 1oz
For the base 16 and base 12 for length or graduation you can derive your single divisions by just folding a piece of paper of a known length in reliable ways that is way too simple to look anything like origami.
For base 16 you only have to fold it ~4 times to be fairly close but is a bit more complicated for 12.
How are you separating your sand into equal parts? You realize that is not a simple process right?
But here’s my method for hectograms.
Create a pile of sand that equals the kg prototype.
Separate that pile into five roughly equal parts.
Weigh piles against each other.
Transfer small amounts of sand from the heaviest to the lightest.
Repeat 3 and 4 until desired accuracy is achieved.
Each pile after Step 5 ~= 1 hg
No reason to believe it would be less accurate than your production of 1 oz references.
For dividing a meter into decimeters I take ten rulers of equal width less than 1 dm, lay them next to each other, put my meter on top and turn it until it exactly spans my ten rulers and mark where the lines separating the rulers hit the edge of the meter.
So your contention is that you can derive 1/16th of a pound fairly easy, and since you have a name for this unit–“the ounce”–the traditional system is superior?
Dude, how often you you have to derive your standard for the ounce? Once every few weeks? And when you do derive your ounce standard, are you just limited to a scale balance and bags of sand?
And why is it so great that you have a special name for “1/16th of a pound”? I could name 1/16th of a kilogram with some name, so what? I guess it satisfies you somehow to imagine measuring something as 1 pound 5 ounces, and seeing those integer values soothes the existential dread within. But you’re just measuring 1 and 5/16th pounds. I can measure 1 and 5/16th kilograms just as easily. The fact that the metric system has official names for decimal multiples of fundamental units doesn’t mean that fractions of those units don’t exist. They exist, they just don’t have traditional names.
If you like, we could invent them. So we could call 500 grams “a pound”. We could call 30 grams “an ounce”. We could call 5 milliliters “a teaspoon”. And so on. Then we’d have all sorts of traditional names for fractions or multiples of metric units, and we could talk about “one liter and three teaspoons” and have lovely integer values for all our units instead of gawdawful decimals like 1.15 liters.