101–110 of 352 posts
He wouldn't be speaking like this if he was born on Mars.
I think what you meant to say was that he wouldn't be speaking like this if people were born with 3 fingers.
Earlier quoted context omitted.
Changing units in Electrodynamics for instance comes with unexpected factors in formulas though, indeed containing π. (CGS SI)
Isn't that just the change between rad/s and Hz?
[1] https://phys.libretexts.org/Bookshelves/Electricity_and_Magn...
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…
This is interesting, but I have to quibble with this: > If you express this value in any other units, the magic immediately disappears. So, this is no coincidence Ordinarily, this would be extremely indicative of a coincidence. If you’re looking for a heuristic for non-coincidences, “sticks around when you change units” is the one you want. This is just an unusual case where that heuristic fails.
Doesn't the relationship hold if we change units? It seems like it must. When I worked with electric water pumps I loved that power can be easily calculates from electrical, mechanical, and fluid measurements in the same way if you use the right units. Volts Amps, torque rad/sec, pressure*flow_rate all give watts.
This is interesting, but I have to quibble with this: > If you express this value in any other units, the magic immediately disappears. So, this is no coincidence Ordinarily, this would be extremely indicative of a coincidence. If you’re looking for a heuristic for non-coincidences, “sticks around when you change units” is the one you want. This is just an unusual case where that heuristic fails.
Period = 2π√(length/g)
So the "magic" holds in any units where the unit of time is the period of a pendulum with unit length.
> Sometimes that was even useful. If you needed to buy more cloth, you'd call the tallest person in the village and have them measure the fabric with their cubits. I highly doubt this bit of strategy would have worked with sellers of said fabric. They may have not had formal measurements but they weren't stupid either.
Earlier quoted context omitted.
Actually no, the whole equation boils down to the definition of meter. Or rather, one of the earlier definitions.
Yeah, I read the post. What I’m saying is “this relationship vanishes when you change units, so it must not be a coincidence” is a bad way to check for non-coincidences in general. For example, the speed of sound is almost exactly 3/4 cubits per millisecond. Why is it such a nice fraction? The magic disappears if you change units… (of course, I just spammed units at wolfram alpha until I found something mildly intere…
Or after-atmosphere insolation being somewhat on average 1kw/m2.
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)
On the other hand, 10 e9 = 10 * 10^9.
Earlier quoted context omitted.
Doesn't the relationship hold if we change units? It seems like it must. When I worked with electric water pumps I loved that power can be easily calculates from electrical, mechanical, and fluid measurements in the same way if you use the right units. Volts Amps, torque rad/sec, pressure*flow_rate all give watts.
No, the equality requires the length of a 2 second period pendulum be g / pi^2. Change your definition of length - that no longer holds true. g in imperial units is 32 after all. g has units; pi does not
The pendulum is a device that relates pi to gravity.
This is interesting, but I have to quibble with this: > If you express this value in any other units, the magic immediately disappears. So, this is no coincidence Ordinarily, this would be extremely indicative of a coincidence. If you’re looking for a heuristic for non-coincidences, “sticks around when you change units” is the one you want. This is just an unusual case where that heuristic fails.