Can we do the same with 432Hz please
432: yes it's a super fun and interesting number 432 cycles per second: seconds are not in fact special
A wonderful coincidence or an expected connection: why π² ≈ g
231–240 of 352 posts
Re: A wonderful coincidence or an expected connection: why π² ≈ g
#232Earlier quoted context omitted.
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…
Alpha brainwaves are almost exactly 10hz, in humans and mice. The typical walking frequency (for humans) is almost exactly 2hz (2 steps per second). And the best selling popular music rhythm is 2hz (120bpm) [1]. Perhaps seconds were originally defined by the duration of a human pace (i.e. 2 steps). These are determined by the oscillations of central pattern generators in the spinal cord. One might suspect that these…
Well, a second is also a pretty good approximate resting heart rate (60 bpm)
Re: A wonderful coincidence or an expected connection: why π² ≈ g
#233Earlier quoted context omitted.
Another bad way to check for non-coincidences is to use a value like g which changes depending on your location. Pi is the same everywhere in the universe. g on Earth: 9.8 m/s² g on Earth's moon: 1.62 m/s² g on Mars: 3.71 m/s² g on Jupiter: 24.79 m/s² g on Pluto: 0.62 m/s² g on the Sun: 274 m/s² (Jupiter's estimate for g is at the cloud tops, and the Sun's is for the photosphere, as neither body has a solid surface.)
My physics prof said g is actually a vector field. Because the acceleration has a direction and both magnitude and direction vary from point to point.
Your physics Prof is correct of course, and so is GP. "Standard" values for g exist for these bodies, but it also varies everywhere.
Re: A wonderful coincidence or an expected connection: why π² ≈ g
#234Earlier quoted context omitted.
Another bad way to check for non-coincidences is to use a value like g which changes depending on your location. Pi is the same everywhere in the universe. g on Earth: 9.8 m/s² g on Earth's moon: 1.62 m/s² g on Mars: 3.71 m/s² g on Jupiter: 24.79 m/s² g on Pluto: 0.62 m/s² g on the Sun: 274 m/s² (Jupiter's estimate for g is at the cloud tops, and the Sun's is for the photosphere, as neither body has a solid surface.)
I volunteer for the Mars mission as a weight loss tool.
Surviving on Mars will probably involve some mass loss, too.
Re: A wonderful coincidence or an expected connection: why π² ≈ g
#235Earlier quoted context omitted.
I don't agree, I thought what he said was very interesting. It never occurred to me that pi might vary, and over a non-flat space I can see what they're saying. I think it's intrinsically interesting simply because it breaks one of my preconceptions, that pi is a constant. Talking about it being 'not very useful' just seems far too casually dismissive.
Pi doesn't vary. The ratio of circumference to diameter of a circle may vary depending on the geometry. Clearly everyone means euclidean space unless specified otherwise. Any other interpretation will only lead to problems, which is why it's not useful. There is really no ambiguity about this in mathematics. Mathematicians still use the pi symbol as a constant when they compute the circumference of a circle in a give…
There is no "clearly" in Math. The fact that pi is a constant while at the same time not being "the same constant" in all spaces, and not even being "a single value, even if we alias it as the symbol pi" is what makes it a fun fact.
Heaven forbid people learn something about math that extends beyond the obvious, how dare they!
Re: A wonderful coincidence or an expected connection: why π² ≈ g
#236Earlier quoted context omitted.
In non-euclidean spaces, your definition of pi wouldn't even be a value. It's not well defined because the ratio of circumference to diameter of a circle is dependent on the size of the circle and the curvature inside the circle. It's probably true that it's only well defined in euclidean space. Your relaxed definition, which I have never seen before, is not very useful.
This whole conversation is painful to read: 1. Your parent was talking about projections from one space to another and getting it confused. 2. Pi is pi and their non-Euclidean pi is still pi (unless you want to argue that a circle drawn on the earth’s surface has a different value of pi). The problem comes down to projections, then all bets are off.
Yes. That's what makes it a fun fact. Most people never even learn about non-euclidean math, and this is the kind of "wow I never even thought about this" that people should be able to learn about in a comment thread.
Calling it painful to read is downright weird. Pi, the constant, has one value, everywhere. So now let's learn about what pi can also be and how that value is not universal.
Re: A wonderful coincidence or an expected connection: why π² ≈ g
#237Regarding "Catholic meter": its definition depends on time measurement. How did they ensure that "seconds" of different clocks were equal?
The traditional definition of the second before modern timekeeping was 1/86400 of a day. I’m guessing that was precise enough for their purposes.
Re: A wonderful coincidence or an expected connection: why π² ≈ g
#238Earlier quoted context omitted.
Fun fact: pi is both the same, and not the same, in all of those places, too. Because geometry. If you consider pi to just be a convenient name for a fixed numerical constant based on a particular identity found in Euclidean space, then yes: by definition it's the same everywhere because pi is just an alias for a very specific number. And that sentence already tells us it's not really a "universal" constant: it's a m…
Just sounds like you’ve confused yourself. It’s like spinning in circles and acting like no one else knows which way is up. That isn’t a different pi. That’s a different ratio. Your hint is that there are ways to calculate pi besides the ratio of a circle’s circumference to its diameter. This constant folks have named pi shows up in situations besides Euclidean space.
Good job, you completely missed the point where I explain that pi, the constant, is a constant. And that "pi, if considered a ratio" (you know, that thing we did to originally discover pi) is not the same as "pi, the constant".
Language skills matter in Math just as much as they do in regular discourse. Arguably moreso: how you define something determines what you can then do with it, and that applies to everything from whether "parallel lines can cross" (what?) to whether divergent series can be mapped to a single number (what??) to what value the circle circumference ratio is and whether you can call that pi (you can) and whether that makes sense (less so, but still yes in some cases).
Re: A wonderful coincidence or an expected connection: why π² ≈ g
#239Earlier quoted context omitted.
Usefully, the speed of light is extremely close to one foot per nanosecond. This makes reasoning about things like light propagation delays in circuits much easier.
I really wish we had known this back before it was way too late to seriously change our units around. It would mean that our SI length units wouldn't have to have some absolutely ridiculous denominator to derive them from physical constants, and also the term "metric foot" is pretty fun.
See, the issue with "foot" is that different people use different body parts to measure length. Germany used the "Elle", which is the distance between wrist and elbow, or roughly one foot. Other regions used the foot or the cubit instead.
The primary advantage of the SI system is that it has only ONE length unit that you add prefixes to.
Re: A wonderful coincidence or an expected connection: why π² ≈ g
#240Earlier quoted context omitted.
I really wish we had known this back before it was way too late to seriously change our units around. It would mean that our SI length units wouldn't have to have some absolutely ridiculous denominator to derive them from physical constants, and also the term "metric foot" is pretty fun.
See, the issue with "foot" is that different people use different body parts to measure length. Germany used the "Elle", which is the distance between wrist and elbow, or roughly one foot. Other regions used the foot or the cubit instead. The primary advantage of the SI system is that it has only ONE length unit that you add prefixes to.
I’m saying that the single SI length unit could have been defined precisely as the light nanosecond, or “metric foot”, had people known that that length fit closely to an existing unit back around 1790.
There would still be one unit with prefixes added, but that unit would have a really clean correspondence to physics rather than a hacky conversion factor.
But you have to go back that far in time for it to work, because it’s a fraction of a percent off of the current standard foot. They were happy to make those kinds of changes (as in the case of defining the meter to be ~0.51 toises) back when all of the existing measurements were pretty imprecise to begin with.
Of course, that’s why it could never have worked out this way. By the time we could measure a light nanosecond, we were already committed to defining units very closely to their existing usage.