Brief for the Flat Earth Society
Most people have come to the conclusion that the Earth is actually round, and they probably think they have pretty good reasons for thinking so.
But of course it’s no such thing. On a sufficiently small scale it’s highly irregular–hills, valleys, and mountains, and on a smaller scale still there is the roughness of the trees and the dirt and the gravel; and on a calm ocean, negative curvature, as apparent from the disappearance below the horizon of a distant ship’s sail, and on a smaller scale still, ripples and tides and waves.
Hypothesizing a round Earth does not immediately explain why we are not hurled off the big rock, if the Earth is indeed rotating on its axis to give us night and day. And why the atmosphere swirls as it does. For that explanation, we have to thank Newton and the law of universal gravitation, and gas dyanicists, and systems modellers; even then the answer is not trivial and is of potential momentous consequence concerning the question of anthropogenic (human-induced) global warming.
But back to the flat-Earth question: Everything is kind of linear or kind of irregular on the smaller scales. Linear like the broad sweep of the ocean or the atmosphere, or with a lower-order fractal irregularity if you follow the altitude variations of the hills and valleys and oceanic trenches on our planet.
But on the big picture, let’s hypothesize, for purposes of discussion, that the Earth is round. We’ll do this only as a basis for discussion without actually conceding the point.
The curvature scale of the Earth is on the order of the radius r of the Earth.
French scientists tell us that, by convention, the distance d from the Equator to the Pole on a perfectly round (fictional) Earth is d = 10,000 km, i.e., 109 cm. Therefore 4d=2πr or r = (2/π)d = 0.64 d = 6,370 km (there lurks in the region between 3/5 and 2/3 an irrational creature called 2/π).
They couldn't decide between the meringue pie and the apple pie, which led to the fight. They were 2/π. #badsciencepuns (2/π = 0.6366…)
— Charles Dermer (@chuckdermer) February 9, 2017
The radius of the Earth is 6,370 km = 3800 miles = 4 or 5 day drive. Mount Everest is about (~)30,000 feet tall (precisely, 29,029′), that is, ~10 km (precisely, 8,848 m) high, which also corresponds to the scale height of the atmosphere. So our Earth is round on the scale of 10 km/10,000 km, that is, 0.1%. Pretty smooth. Smoother than smooth jazz by a long shot, considering amplitude variations in sound.
Compare that to the scale height of a Long Playing record album, for those vinyl freaks out there like me. An LP* (if you’re lucky you’ll get 30 min on one side) has a radius of 17.1 cm/(2.54 cm/in) = 6.7″. Its thickness can’t be more than 2 mm, so the relative half-thickness to radius is 0.1/17.1 = 0.6% (or less). Our planet is smooth by comparison with an LP.
At this point I would like to entertain how smooth our planet is with respect to a “baby’s bottom,” which relates to an expression that I have unfortunately used concerning the monotonically decaying γ-ray emission from an extraordinary Gamma Ray Burst that took place in 2013: “smooth as a baby’s bottom.” I would only note that a “baby’s bottom” is neither topologically congruent with a sphere, nor is it conventionally smooth in a way that we associate with a mathematical function or a planet.
I elect we move on.
So if an LP is smooth to about 0.5%, and our planet to ~0.1%, what about our Galaxy, the Milky Way?
Depends on which gaseous matter you’re talking: molecular gas, atomic Hydrogen, ionized H, old stars, young stars, new stars, dead stars, tracers of dark matter,….
Being optimistic, and since we live in a blue galaxy that’s still making young stars (which are, after all, as they say, to be honest, while youth must be served, in due course, are in any case, our future), we’ll consider the thick mollie disk and young star scale height, which is ~90 parsecs.** The radius of the Galaxy is ~10 kpc (we live some 8 kpc from the massive 4 million Solar mass black hole at the center of our Galaxy), so the relative thickness to width of the Milky Way is ≈ 90 pc/10,000 pc ≈ 1%, similar to an LP.
The Milky Way just looks thick from a Southern sky because we’re stuck in the disk. We can’t see the stars for the belt.
Everything’s smooth until it’s not, and on the sub-atomic level the nuclei carry just about all the mass. This is at heart a failure of conventional (pre-chaos theory) mathematics to describe the world as it is using simple algebraic or mathematical functions. A function like y = x2 must always and forever live in a Platonic cave housing the logical ideals to which we must contemplate and from which we must be forever separate. [Cue existential angst.]
But speed looks like a pretty smooth function, right? Well, not exactly. Small scale turbulence in a quiet atmosphere can produce fluctuations in speed, which can get quite large and even catastrophic for high speed transients in turbulent or cyclonic atmospheric conditions.
The speed of light is 300,000 km/s. The circumference of the Earth is 2πr = 4d = 40,000 km. It takes light about 3.3 ms to go around the Earth. Latency effects are detectable by the human ear to a few milliseconds. This just shows how slow the speed of light really is. The Earth-Moon distance is 384,402 km (238,856 mi) or 1.28 light-seconds away. As you get farther away, the news recedes into the distance.
Speaking of smoothness, we return to the “baby’s bottom” question translated to the human sphere. Tactile sensation is associated with a calming, and fingerprints can induce the sort of low frequency purring found in ASMR. So fingerprints have a Darwinian functionality, and represent a sort of limit on smoothness of a human. Fingerprint depth is maybe 0.1 mm = 0.01 cm, so that the relative smoothness is ~15 cm, so 0.01/15 ~ 0.1 %.
Lot of interesting things take place at the 0.1% level.
Everything's logarithmic, time, space, thought; we just sit on such a small piece of it that we think it's linear. Or chaotic.
— Charles Dermer (@chuckdermer) February 6, 2017
Let’s close by trying to unpack this tweet. There is nothing linear about the world when human cognition enters. If the input ramps up, the output can crash, or go postal. Time may run linearly, but when I look back on my life, the last hour is equal to the last week is equal to the last year is equal to the last decade is equal to my lifetime (which allows us to glimpse our entire life as we lay dying).
MIT Professor Philip Morrison showed how the scale of the universe, from the sub-atomic to the cosmological, can be grasped using powers of 10, that is, a linear logarithmic scaling of distance d = 10x m, x =0, ±1, ±2, ±3, etc., with a meter (m) fiducial so apposite the human body (“man is the measure of all things”).
Boring units mention: Rather than meter-kilogram-second human-scale MKS system (also systeme international), I prefer the centimeter-gram-second spider-scale cgs system. It just works better for people my size.
Within our cognition, something like a logarithmic scaling also reigns: that which is within my arms’ width occupy me about the same as something within a hundred arms’ widths, and the same for a hundred hundred arms widths, until it reaches a periphery of apathy to which I attend not a whit.
Back to our starting point, the question of the roundness or flatness of the Earth. We conclude that it’s a question that needs more study. [Geez, where have I heard that before?]
*I grabbed the one on the turntable for these measurements, which turned out to be Rolling Stones’ Dirty Work.
**A parsec is 3.26 light years (ly) = 3.086×1018 cm. For reference, classic paper by Bacall & Soniera; see Binney & Merrifield 1998
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