Sorry to ruin the party, but g is a quite random number, on other planets the corresponding acceleration is different. So π^2~g is a pure coincidence and not relevant. The Newtonian gravitational constant G is a real constant btw.
Have you read the article? The point is that the definition of the metre, which is used in g, originates from the length of a pendulum that swings once per second in the gravity field around Paris. So it is a matter of definitions, and the length of the metre originates from the duration of the second and the Earth's gravity field. The definitions of 1/40.000 of the Earth's circumference or ~1/300.000.000 of a light second came later.
My intuitive assumption, then, is that on Mars they would have come up with a different meter such that π² ≈ 10 "mars meters" / s².
Or alternatively stated, that the Mars meter would be much shorter than Earth's meter if they used the same approach to defining it (pendulums and seconds).
A Martian meter defined by martians should relate their average size, the number of fingers they have on their hands and some basic measure of the planet.
I mean, one meter is defined as 1/10^7 of the distance between the equator and the poles which leads to a round number in base 10.
A unit system is not just something that matches objective reality but something that has some cognitive ergonomy.
> A unit system is not just something that matches objective reality but something that has some cognitive ergonomy.
Beautifully stated!
And that's one reason why I like the US units of measurement better than SI. I mean, the divide-by-ten thing is nice and all. But _within a project_ how often are you converting between units of the same measurement (e.g, meters to centimeters)? You pick the right "size" unit for your work and then tend to stay there. So you don't get much benefit from the easy conversion in practice.
But if you're doing real hands-on work, you often need to divide by 2, 3, 4, and so on. So, for example, having a foot easily divisible by those numbers works well. And even the silly fractional stuff make sense when you're subdividing while working and measuring.
Of course it all finally breaks down when you get to super high precision (and that's probably why machinists go back to thousands of an inch and no longer fractions).
I think there's a little bit of academic snobbery with the SI units (though, it is a good idea for cross-country collaboration), but for everyday hand-on work the US system works really well. I always love the meme: There are two kinds of countries in the world, those who use the metric system and those who've gone to the moon.
I'm an AMO physicist by training and my choice of units are the "Atomic Units" where hbar, mass of the electron, charge of the electron, and permittivity are all 1. That makes writing many of the formulae really simple. Which is what you say: it has cognitive ergonomy (and makes all of the floating point calculations around the same magnitude). Then when we're all done we convert back to SI for reporting.
One example where picking units within a project is still not saving you from cognitive load is e.g. when doing woodworking. Ymmv, but I can add decimals way faster than I can add 7 9/16" + 13 23/32" (numbers picked arbitrarily but close to a precision of 1mm so if you are ok w/ that precision, you don't even need fractions in SI).
I have to admit I only read half of the article. Even if there is some historical fact there (but it was not mentioned at the beginning of the article), from a physical standpoint this comparison is already dimensionally wrong and also coincidentally only correct if you choose appropriate units. That was the point I was trying to make. There is not anything "deep" here.
"I only ran the first half of the program, but it didn't seem to give the correct answer, so it's obviously broken."
"I only read the first half of the proof, but the answer wasn't contained there, so I'm forced to conclude the proof is worthless."
You simply gave up before encountering the mathematical reason the relationship exists, why the units are different, and so on. You just ran with your incorrect initial assumption.
It's not about the values, but the units of measurement. g is in units of meter/second^2. The article discusses the dependency of the meter's original definition on the value of pi.
The situation with trains in Germany is appalling. Our kids need to go to school by train. Even though it is the only line using that route, there are constant delays and cancellations. DB (Deutsche Bahn) often does not even care to inform the passengers of such events over the loudspeakers or displays. I routinely take at least one train earlier to increase the probability of reaching my destination in time. Working from home has saved me a good amount of stress over the years.
This is not motivating anyone to switch from cars to trains.
Exactly the same for me :-) Because of the package management I have only been using Arch based distros since 2020. I used Manjaro with xfce for quite some time, but now I have installed EndeavourOS with KDE Plasma on my work and personal laptops. Everything works fine, even the bluetooth connection to my Bose noise cancelling headphones works very reliably. I just needed to deactivate some animations, especially the default one for switching between desktops because I do that about 100 times each day and would get sea sick if I kept that.
