81–90 of 352 posts
Earlier quoted context omitted.
It does not? Pi has nothing to do with our arbitrary unit system.
pi is always just pi, but g may be defined in terms of the meter.
heck, g is not even a constant, it just happens to measure to roughly 9.8 m/s² at most places around here.
Earlier quoted context omitted.
Actually no, the whole equation boils down to the definition of meter. Or rather, one of the earlier definitions.
It does not? Pi has nothing to do with our arbitrary unit system.
"The meter was originally defined as one ten-millionth of the distance between the North Pole and the equator, along a line that passes through Paris."
> was actually proposed back in the 17th century Pretty sure it was done back in Sumer first.
>“It was contended," says Dr. Peacock, " by Paucton, in his Mẻtrologie, that the side of the Great Pyramid was the exact 1/500th part of a degree of the meridian, and that the founders of that mighty monument designed it as an imperishable standard of measures of length.
https://www.theguardian.com/science/2020/dec/06/revealed-isa...
>Newton was trying to uncover the unit of measurement used by those constructing the pyramids. He thought it was likely that the ancient Egyptians had been able to measure the Earth and that, by unlocking the cubit of the Great Pyramid, he too would be able to measure the circumference of the Earth.
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Universal isn't a way we describe numbers. You meant to say dimensionless. Pi is dimensionless constant because it describes a relationship between two measurements of a dimensionless unit circle.
Pi is expressed as a pure ratio between two other dependent numbers. Dimensionless values are special because they don't rely on any particular measurement in any particular location, lending to your misconception of "universal" constant.
This article explains how a particular dimensionful constant (g, the strength of gravity on earth's surface) is related to pi.
They are related because the dimensions in question are both derived from dependent properties of our planet. These dependent properties will be found on any other sphere floating in space if they are derived in the same fashion.
It's good to thoroughly or even marginally understand a topic before adopting a dismissive and authoritative argument against it.
As a physicist, this makes sense. Pi = 3, pi^2 = 10, which is g Not sure why everyone is surprised. Ah, and a year is pi*10e9 seconds (IIRC)
I assumed the pi / g connection was because cows that accelerate in a vacuum are spherical .
As a physicist, this makes sense. Pi = 3, pi^2 = 10, which is g Not sure why everyone is surprised. Ah, and a year is pi*10e9 seconds (IIRC)
I've got a related one I like. Why are the Avogadro's number and Boltzmann's constant inverses of each other N ~ 1/k? The statement doesn't make sense because the units don't work out, but it is true in mks. It's because they multiply to the gas constant which is ~1. They both are numbers to transfer from the microscopic to human scale units and they cancel for the gas constant, which is about human scale experience…
But it's a coincidence, right? N*k=8.31 is pressure*volume/temperature for a mole of gas. Temperature has a relatively small range (100-1000) and there's no reason why the range of P*V couldn't be far from that range, for example 0.01–0.1, with a different definition of meter, second or kilogram.
g is related to the radius of the earth; the meter is related to the circumference of the earth; and pi is the relationship between the radius and the circumference.
Earlier quoted context omitted.
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.
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.