Comment by mistercow

In the example case, the earth's rotation is producing the apparent observation: it's the cause, not a separate phenomenon that happens to coincide, or that might be indicative of a deeper relationship. For something to be a coincidence, it must be otherwise unconnected causally, which is not the case if the reason you found a ~24 hour period is that you forgot to account for the earth's rotation.

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/...

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.)

Or the speed of light being almost a sweet 300 million m/s.

Or after-atmosphere insolation being somewhat on average 1kw/m2.

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.

    palm : 7,64 cm
    span : 12,36 cm
    handspan : 20 cm
    foot : 32,36 cm
    cubit: 52,36 cm

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 ?

Reminds me of https://xkcd.com/687/

X^2 is a lot more interesting than x*0.0000743 or whatever it is

> 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

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."

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.

It does, and the formula in the post explains the connection

> since reality is definable as that which is independent of measurement.

In terms of quantum mechanics, would that mean the wave function is real until it collapses due to measurement? Or am I misunderstanding your use of measurement there?

Something about that is sticking in my mind in an odd way, but I can't put my finger on exactly what it is - which is intriguing.

The comma differentiates. The comma indicates a short pause and a certain intonation in speech (the period means a longer pause and a different intonation). If you say that sentence with and without a pause/comma, you'll see (hear) that the sentence is correct. Reading unambiguously is also hard.

Only because you're using metric seconds instead of "imperial seconds" (the time it takes for a 1 foot long pendulum to complete a full oscillation).

A more natural way to say it is that equality requires that the unit of length is the length of an arbitrary pendulum and the unit of time is the half-period of the same pendulum.

The pendulum is a device that relates pi to gravity.

The equation holds in imperial units as well. The length of the 2 second pendulum needs to be in feet AND the value of g in ft/sec2.

It’s more precisely the difference between “rationalized” and “unrationalized” units.

You need a factor 4pi in either Gauss’ law or Coulomb’s law (because they are related by the area 4pi*r^2 of a sphere), and different unit systems picked different ones.

It’s more akin to how you need a factor 2pi in either the forward or backward Fourier transform and different fields picked different conventions.

It is more involving [1]

[1] https://phys.libretexts.org/Bookshelves/Electricity_and_Magn...

I initially had an objection due to a misconception I was carrying.

I see now that the pendulum formula is a pure relation between time and distance/length. It will apply regardless of the units used. For example if we measure time in fortnite and length and furlongs the formula will be the same. The gravitational acceleration of course will be in those units: furlongs per fortnights squared. Needless to say that will not be 9.81.

Now the meter unit was chosen in relation to the second unit by the length of a pendulum that produced an integer period. So that choice/relation caused the gravitational acceleration g to take on such a value that its square root cancels out the π on the outside of the root.

I was confused for a moment thinking that the definition of the kilogram would somehow be mixed up in this but of course it isn't. g doesn't incorporate mass; and of course pendulum swings are dependent only on length and not mass.

There are all sorts of situations in which certain units either give us a nice constant inside the formula or eliminate it is entirely.

For instance Ohm's law, V = IR. It's no coincidence that the constant there is 1. If we change resistance to some other unit without changing how we measure voltage and current we get V = cIR.

Truth feels like a coincidence when 1 small thing can make anything wrong.