Comment by karmakurtisaani
1 year ago
Actually no, the whole equation boils down to the definition of meter. Or rather, one of the earlier definitions.
1 year ago
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 interesting).
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 are further harmonically linked to alpha wave generators. In any case, 120bpm music would resonate and entrain intrinsic walking pattern generators—this resonance appears to make us more likely to move and dance.
Or it’s just a coincidence.
[1] https://www.frontiersin.org/journals/neurorobotics/articles/...
Well, a second is also a pretty good approximate resting heart rate (60 bpm)
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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.
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I volunteer for the Mars mission as a weight loss tool.
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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 mathematical constant so it's only constant given some very particular preconditions. In this case, it's only our trusty 3.1415etc given the precondition that we're working in Euclidean space. If someone is doing math based on non-Euclidean spaces they're probably not working with the same pi. In fact, rather than merely being a different value, the pi they're working with might not even be constant, even if in formulae it cancels out as if it were.
As one of those "I got called by the principal because my kid talked back to the teacher, except my kid was right": draw a circle on a sphere. That circle has a curved diameter that is bigger than if you drew it on a flat sheet of paper. The ratio of the circle circumference to its diameter is less than 3.1415etc, so is that a different pi? You bet it is: that's the pi associated with that particular non-Euclidean, closed 2D plane.
So is pi the same everywhere in the universe? Ehhhhhhhh it depends entirely on who's using it =D
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Or the speed of light being almost a sweet 300 million m/s.
Or after-atmosphere insolation being somewhat on average 1kw/m2.
I always find insolation and insulation to be such an interesting pair of words
I guess the equivelent of "change the units" is "change the language".
French: insolation et isolation
German: Sonneneinstrahlung / Isolierung
Spanish: insolación / aislamiento
Chinese: 日照 / 绝缘
I guess coincidence
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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.
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> Or after-atmosphere insolation being somewhat on average 1kw/m2.
I’m kind of inclined to say that this one isn’t so much of a coincidence as it is another implicit “unit” in the form of a rule of thumb. Peak insolation is so variable that giving a precise value isn’t really useful; you’re going to be using that in rough calculations anyway, so we might as well have a “unit” which cancels nicely. The only thing that’s missing is a catchy name for the derived unit. I propose “solatrons”.
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There is relationship between the metric system and the French royal system. The units used in this system have a fibonacci-like relationship where unit n = unit n-1 + unit n-2.
cubit/foot =~ 1,618 =~ phi, el famoso Golden ratio. foot/handspan =~ phi too. And so on.
From this it turns out that 1 meter = 1/5 of one handspan = 1/5 x cubit/phi^2
Another way to get at it is to define the cubit as π/6 meters (= 0.52359877559). From this we can tell that
1cbt = π/6m
π meters = 6 cubits
Source: https://martouf.ch/crac/index.php?title=Quine_des_b%C3%A2tis...
32 meters is 35 yards, to within about an eighth of an inch. How's that grab you ?
I wonder if this is related, but imperial measurements with a 5 in the numerator (and a power of two in the denominator) are generally just under a power of two number of millimeters.
The reason is fun, and as far as I know, historically unintentional. To convert from 5/(2^n) inches to mm, we multiply by 25.4 mm/in. So we get 5*25.4/(2^n) mm, or 127/(2^n) mm. This is just under (2^7)/(2^n) mm, which simplifies to 2^(7 - n) mm.
This is actually super handy if you're a maker in North America, and you want to use metric in CAD, but source local hardware. Stock up on 5/16" and 5/8" bolts, and just slap 8 mm and 16 mm holes in your designs, and your bolts will fit with just a little bit of slop.
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My favorite is 1 mile = phi kilometers with <1% error
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Reminds me of https://xkcd.com/687/
X^2 is a lot more interesting than x*0.0000743 or whatever it is
Ok, then by that thinking, you should find it really interesting that Earth escape velocity is almost exactly ϕ^4 miles per second.
In fact, adding exponents here objectively makes it less interesting, because it increases the search space for coincidences.
What makes the case in the post most interesting to me is that it looks at first glance like it must be a coincidence, and then it turns out not to be.
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Why is it more interesting? Is it just more interesting because we use such bases, or can it be interesting inherently? That is the question that is being asked, and why some say it's merely a coincidence.
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> 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.
Yeah, it was a strange claim, which makes me think that the author may have had his conclusion in mind when writing this. I.e. what he meant to say may have been something more like:
"The relationship vanishes when you change units, which suggests the possibility that the relationship is a function of the unit definitions... and therefore not a coincidence."
Because the cubit is a measure of what a body can reach
I never thought of the cubit this way. It's an interesting idea, but the cubit is the length of a forearm, whereas you can reach around yourself in a circle the length of your extended arm, from finger tip to shoulder.
That would be somewhere between 1.5 to 2 cubits for people whose forearm is about a cubit long.
I think the cubit is mainly a measure of one winding of rope around your forearm. That way you can count the number of windings as you're taking rope from the spool. This is the natural way a lot of us wind up electrical cables, and I'm sure it was natural back in the day when builders didn't have access to precise cubit sticks.
I don't see the connection with the units and sound that you're making. But it is kind of interesting to know that sound travels about 3/4 of a forearm length per millisecond. That's something that's easy to estimate in a physical space.
How does that explain the relationship to the speed of sound?
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Im wondering is there connection or not? We use distance unit to get to π number, whatever the distance unit is right? We get π from circumference to diameter ratio, so however long the meter is the π in your distance unit is same ratio
It does not? Pi has nothing to do with our arbitrary unit system.
Pi is related to the circumference of a circle; the meter was originally defined as a portion of the circumference of the Earth, which can be approximated as a circle.
"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."
But that connection actually is a coincidence. From what I can tell, when they standardized the meter, they were specifically going for something close to half of a toise, which was the unit defined as two pendulum seconds. So they searched about for something that could be measured repeatably and land on something close to a power of ten multiple of their target unit. The relationship to a circle there doesn’t have anything to do with the pi^2 thing.
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Can you explain what you’re taking issue with in the post, then? Because it specifically lays out how the historical relationship between the meter and the second does in fact involve pi^2 and the force of gravity on earth.
(Granted, from what I can tell, it’s waving away a few details. It was the toise which was based on the seconds pendulum, and then the meter was later defined to roughly fit half a toise.)
pi is always just pi, but g may be defined in terms of the meter.
sure, that's the entire point.
heck, g is not even a constant, it just happens to measure to roughly 9.8 m/s² at most places around here.
It does, and the formula in the post explains the connection