"(So space is measured by time.)"

Using the SI units of metres and seconds applies a coordinate system on spacetime. One can take a coordinate interval using that, but careful observation shows that the coordinate system cannot be applied at all scales or agreed upon by all users.

In SI terms, the rate of the cycles of hyperfine structure transition frequency of Cs-133 atoms is strictly local to the atoms themselves, and non-local observers will see that rate only if their local Lorentz frame has the same velocity as the atom's, and they are on the same gravitational potential.

As we are not massless inhabitants of a Minkowski vacuum, errors accumulate with coordinate distance from the atom used as a source of frequency, and are observable with laboratory equipment at ranges of metres, and are already wholly non-negligible for practical applications (e.g. GNSS) at ranges comparable to the radius of the Earth and velocities comparable to the speed of sound at STP.

Sadly, SI predates modern conceptions of 3+1 spacetime and has not really adapted to what we know of our physical spacetime's properties.

I think that's more parochial than the base ten issue, personally. :-)

The critical feature of SI is that it directly and explicitly incorporates a single positional numbering system used in scaling all quantities. Exact definition of quantities, while an important feature, has almost always been subordinate to that goal.

Arguendo, let's assume that you are right that the decimal numeral system arose because of the typical number of human fingers. Note, we do not have to agree for the sake of argument that the place-value system is intimately tied to decimal (and indeed in our history, the latter predates the former by several millennia).

That there are ten values per position is therefore parochial, but not as parochial as you think: almost every vertebrate has five digits per extremity (and essentially all of them embryologically[1]), and there are huge numbers of decapod arthropods extant and in the fossil record, and superorder Decapodiformes is an important group of cephalopods.

So if we use base ten because of the number of our fingers (this is far from proven, unfortunately; there are many examples of very different ways of counting and doing arithmetic on human fingers), it is reasonable to think that many plausible civilization-building non-primates would be liable to use similar representational systems. Unfortunately that conflicts with human history, in which there has been a wide variety of number representation...

[1] even in non-tetrapods: https://images.sciencedaily.com/2016/08/160817142550_1_540x3...

Some harder-core evodevo: http://www.scientificamerican.com/article/why-do-most-specie...

It makes no sense that our base has only 2 and 5 as factors. It is a stupid decision that can't be explained by rationality.

The base 12 system is way better. It has 2 3 4 6 as factors. It's so good we use it everywhere. 2x12 hours, 12 eggs, 12 doughnuts, 12 months, 60 minutes, 12 inches.

A base to be good needs many factors without being unwieldy. 10 is stupid as it skip the most useful ones 3 and 4. Nobody ever need to divide anything by 5.

The perfect measurement system would be SI with base 12.

Why 12 and not 2, 1 or 1890? The choice of the number of values per position is entirely arbitrary, and almost the entire reason why you prefer twelve over ten is that twelve has more prime factors AND is close to ten. Six has the same number of prime factors as twelve; so does twenty-four.

"Nobody ever need to divide anything by 5"

So, what is left after you remove your "2 3 4 6 as factors" from your example up there of 60? If you work 35 or 40 hours in a week, how many hours should you expect to work on a work day?

Multiples of primes can be handy. 12 = 2 * 2 * 3, which gives subdivisions of 1/2, 1/3, 1/4, and 1/6.

Other possibly useful values might be 30 (235) or 210 (2357), which has factors of all the primes lower than 10.

The Babylonian system, based on 12, 30, 60, 120, 180, and 360 (223, 235, 2235, 2^3 * 3 * 5, and 2^3 * 3^2 * 5 respectively) have multiple useful subdivisions.

Base-ten decimal is fun, but produces non-finite values when fractional values are considered: 1/3 = 0.333..., 2/3 = 0.666..., etc. Systems in which those fractions are inherently supported, and for which by Benford's law you're likely to see the divisors 2 - 9 fairly frequently (https://en.m.wikipedia.org/wiki/Benford%27s_law), this can be convenient.

Particularly in an age of rulers, protractors, compases, and no digital electronic computors.

Isn't one of the main benefits of metric the ability to quick convert between the various scales? Converting between say 1.4m to mm is a lot easier than 4.5ft to inches. Or answering questions like how many square metres are in 5.2 hectares (vs square feet in acres). Arbitrary measurements of eggs and doughnuts (don't forget gallons) are not great examples - no one buys them for that precise amount, they buy them because that is what they are available in.

I've never understood why some Americans are so stubborn about the metric system. The rest of the world has essentially made the switch for various reasons but arguably the most advanced nation on earth can't?

Using order-of-magnitude prefixes to scale up and down units is orthogonal to base. Things just look strange if you refer to other bases in base 10.

Consider base-2 prefixes (now being known as kibi, mebi, gibi, etc)

    1 kibibyte = 1024 bytes

    1 mebibyte = 1048576 bytes

These don't look like nice round numbers because I am representing scaling of a base 2 number in base 10. It's more clear if I say:

    1 kibibyte = 10000000000

    1 mebibyte = 100000000000000000000

    1 gibibyte = 1000000000000000000000000000000

Each further prefix just adds 10 zeros to the binary value. Just like metric prefixes add zeros.

One kilometer would still equal 1000 meters. But that 1000 is now in base 12, not in base 10. So rather than 10^3 it's now 12^3. But that just seems strange because you grew up with base 10.

Eggs and doughnuts and many other things are measured in 12 because of its historical utility. It allows you to say things like "I'd like a quarter of dozen" and "a third of a dozen" which are not possible with 10.

Extending a bit further, if you want division by 2, 3, 4, and 5 you can go up to base 60. The Babylonians (among others) did this and nowadays we have 60 seconds in a minute, 60 minutes in an hour, 6 * 60 degrees in a circle, etc:

https://en.wikipedia.org/wiki/Sexagesimal

If our number system had 12 digits, then you could apply powers of 12 by just moving the decimal point in exactly the same way.

Yes, but base 10 is the common language we use today. And mm to m, is a lot easier than in to ft...

In base 10 that's all true. The comment you replied to proposed using base 12 instead. If your arguments are based on the assumption that we can only use base 10, then you can't really make an argument against base 12. It seems your arguments are constructed on the assumptions that contradict the proposal.

Use a calculator.

Specifically: use a units-aware calculator.

I've been doing a lot of calculations based on energy and related terms, and am finding GNU Units (and yes, distinctly specified as an alternative to, say, BSD Units, which has a small subset of features) a phenomenally useful tool.

It turns out that even SI units get confusing and non-base-ten-rational pretty quickly -- pretty much the moment you go from watts to watt-hours (and yes, there's an alternate unit of energy: Joules, but watt-hours turn out to be a really useful concept).

It turns out that units-based measurements are complicated, and keeping tabs manually is a PITA, and using a units-aware calculator is all kinds of awesome. I wrote a little paen to it a couple of years ago here: https://www.reddit.com/r/dredmorbius/comments/1x9u0f/gnu_uni...

What's powerful is that GNU Units doesn't just do straightforward converstions (e.g., what's 180 cm in inches), but can do calcuations of multiple quantities: energy per unit area times area to give energy for a given size of land, etc. Since you can specify the units of the result, there's also a built-in sanity check that your units correspond (a common source of error in physics calculations).

Where GNU Units really shines is in being extensible. You can define constants, values, or units that you want to have readily available. I've plugged in "hiroshima" (the equivalent energy content of the ~15 kt atomic bomb dropped over Hiroshima, Japan), as well as values for the land areas of earth, the various continents, and several nations and states, as well as other area and other metrics for planets and moons within the Solar System. This makes a few relative comparisons fairly straightforward.

I'm aware that metric is "more logical" by certain ways of thinking, but old-school units had their own logic:

Units of length were based off of body parts or could be rapidly assessed. An inch is roughly a thumb's width. A foot, obvious. A yard is roughly a man's pace. A cubit, the length from elbow to fingertips. A fathom, that width of a man's arms, outstretched, as you'd find them whilst measuring out a sounding line shipboard. An acre is the amount of land a man could plough in a day (the German for this recognises the origin explicitly: tagwerk, or "days work"). An acre-foot seems silly until you realise that knowing the area of a reservoir, you can calculate its capacity quickly by simply noting water depth in feet. A british thermal unit is handy if you're sourcing coal for a steam engine -- how much water are you going to heat and boil each day? A mile ("mille") was one thousand double paces, from a slightly shorter-than-typical-today Roman soldier. A furlong was, literally, "one furrow long".

Volume measures: "bushel" derives from "bosta", a handful. Cup is obvious, from a typical drinking vessel. "Gallon" originates from "galleta", latin for bucket or pail.

Measures of weight are ancient -- "pound" comes nearly directly from latin, "libra pondo", with the same meaning. Ton is derived from volume -- the weight of a tun cask. Grain is another obvious one.

What these have in common is that for a quick and dirty in-the-field (often literally) assessment, these measures offered an immediate and sensible-in-context quantification. Measuring land area in acres gave a sense of how much work was required for that land -- how much one man might farm in a year, or how many men and horses you'd need to work it. Egyptian stonemasons could measure out their work by arm, sailors water depths, soldiers distance, farmers grain, hydraulic engineers stored water, without any significant calculations. There's something to be said for that.

I'm not saying the units make more sense now. I am saying that failing to recognise the logic by which the units were derived misses some highly salient points.

> I'm not saying the units make more sense now. I am saying that failing to recognise the logic by which the units were derived misses some highly salient points.

I can recognise the logic in historical units of measurements, but I do think some of them are forced - "I want a third of a dozen" - wouldn't you just say you wanted four?.

Base 10 can be explained rationally. Look at your hands. See those pointed bits? Count them. Now do you understand why use base 10?

Look at your knuckles. You have 8 knuckles. Therefore, use base 8.

You can put each finger in an up, down, or medial state, except the two thumbs which give only up or down. That gives base 28.

You can count binary on your fingers as a positional number system. That's base 2.

Base 10 is not the only base that's usable on our dexterous digits.

> Look at your knuckles. You have 8 knuckles.

If you have all fingers on one hand, the thumb of the other hand, and the last joint of each of the remaining fingers removed, sure.

But 28 is the usual number of knuckles.