Partly Paradoxes, Part 4

Ahh, here we are at last!  We have arrived at the final five memes in our Partly Paradoxes miniseries.  Perhaps you’d like to check out Part 1, Part 2, and Part 3 before proceeding.

As before, we’re still working our way through the Cracked.com article called 20 Paradoxes Most Human Minds Can’t Wrap Themselves Around.  It’s not that the meme-based article is particularly bad; it’s just that the person who compiled the memes doesn’t seem to fully understand what a paradox is.  I’ll admit, it can be difficult to determine whether a proposition is truly paradoxical or not, but that’s why I’m doing this.  I thought it would be an educational and challenging mental exercise to examine each of the article’s memes and determine whether they depict paradoxes or something else.  And you know what?  It has been!  I feel that I’ve learned a lot over the past week, and if you’ve been following along, I hope you did too.  So without further ado, let’s finish this!

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Partly Paradoxes, Part 3

Let’s continue our whirlwind tour of Cracked’s roundup of 20 Paradoxes Most Human Minds Can’t Wrap Themselves Around.  If you haven’t already read them, you might want to check out Part 1 and Part 2.

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Partly Paradoxes, Part 2

Yesterday we examined the first five memes from a Cracked.com article called “20 Paradoxes Most Human Minds Can’t Wrap Themselves Around“.  These memes are not particularly Stupid or Bad, but three of them didn’t fit the definition of paradox.  I know the world won’t end because of this.  I just thought it would be fun and informative to look at each meme individually and discuss the ideas contained therein.  If you’ve come looking for the brain-meltingly heinous memes that are usually my stock-in-trade, I promise: there will be a fresh shipment next week.  Until then…

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Partly Paradoxes, Part 1

Back in May, the Cracked website produced a page called “20 Paradoxes Most Human Minds Can’t Wrap Themselves Around“.  As a subscriber of the Cracked YouTube channel, I am well aware of Cracked’s penchant for misleading clickbaity titles.  (Interestingly, the URL contains the string “insane-thought-experiments-thatll-blow-your-mind”, which is an entirely different concept.).  I knew going into the article that at least some of the examples they presented would not be true paradoxes, nor would they be particularly difficult to comprehend.  I was correct in my suspicion.  This week I thought I’d take a break from the depressingly never-ending slideshow of racist, sexist, privilege-soaked memes to examine a group of memes that stretch the meaning of the word paradox to its very breaking point.

We’ve looked at an alleged paradox before.  Since many people struggle with the definition of paradox, let’s consult our friends at dictionary.com before proceeding:

paradox [paruh-doks]

noun

  1. a statement or proposition that seems self-contradictory or absurd but in reality expresses a possible truth.
  2. a self-contradictory and false proposition.
  3. any person, thing, or situation exhibiting an apparently contradictory nature.
  4. an opinion or statement contrary to commonly accepted opinion.

Consider the Twin Paradox.  In the Twin Paradox, one half of a pair of twins sets off from Earth in a spaceship traveling very close to the speed of light.  Einstein’s Theory of Special Relativity says that if you travel very close to the speed of light, a stationary observer will see your clock running more slowly than his own clock.  Hence, the Earthbound twin, who is stationary for all intents and purposes, witnesses his twin aging slower than he is.  When the traveling twin returns, he ought to be younger than the twin he left behind.

But Relativity also tells us that there is no preferred inertial reference frame; i.e. the traveling twin may reasonably view himself as being stationary while Earth speeds away and then returns to him.  From the traveling twin’s reference frame, the Earthbound twin’s clock is running more slowly, so the traveling twin might expect to return to find that his Earthbound brother has aged less than he has.  If both inertial reference frames are equal, then both twins ought to be correct – a contradictory answer.

Many paradoxes can be resolved with a deeper understanding.  The resolution of the Twin Paradox comes from within Special Relativity.  Since the traveling twin’s reference frame changes between the outward and homeward legs of his trip, it is he that ages less than his twin.  The traveling twin returns to find that his brother (and everybody else on Earth) has experienced more time during his absence than he did.

A paradox need not be unsolveable, or even unsolved, to be called a paradox.  But it must lead simultaneously to two contradictory outcomes, even if the contradiction disappears with further study.  Without further ado, then, let’s see how Cracked’s list of paradox-bearing memes measures up.

(To be fair, some of the memes do depict actual paradoxes, and when they do, I’ll say so.)

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The Gravity of the Situation

gravity

Oh Aunty Acid, I hate to be the bearer of bad news, but…there is gravity on the Moon.  There’s gravity everywhere.

I’ve seen this misconception enough that I figure it warrants some discussion.  Take a trip back in time with me to the days of Sir Isaac Newton.  Newton is known for many things, including his Law of Universal Gravitation, which says that any two particles in the Universe will attract each other with a force that is proportional to the product of their masses, and inversely proportional to the square of the distance between them.

In plain English, imagine you have two particles (and particles can mean any two objects, large or small.  They don’t have to be protons or electrons, for example.)  Let one of the particles have a mass of A kilograms, while the other particle has a mass of B kilograms.  As long as the two particles stay the exact same distance apart, then the gravitational pull between them will be proportional to AB.  If you increase the mass of either particle, then you increase the gravitational pull between them by that same ratio.  For example, double the mass of Particle A only, and the gravitational pull between A and B will also double.  If you double both masses, then the gravitational pull between them will quadruple, since 2 x 2 = 4.

The second part of Newton’s L.U.G. tells us that the gravitational attraction between any two “particles” decreases as the particles get farther apart from each other.  You might expect that, but the force doesn’t drop off in a linear way.  Instead, the force decreases with the square of the distance.  So let’s say that you keep the masses of A and B the same, but double the separation between them.  The gravitational force will drop to (1/2)², or 1/4 of its original value.  If you triple the separation between the particles, the gravitational pull drops to (1/3)² = 1/9 of its original value.

As you can see, gravity drops off rapidly with increasing distance.  Perhaps this is what leads some people to conclude that the Moon has no gravity; after all, it is quite far away from Earth by human standards.

But the Moon does have its own mass – quite a lot of it, in fact – and it has its own gravitational pull on nearby objects, separate and distinct from the Earth’s gravitational tug.  In fact, if you fly your spaceship to a point about 66,000 kilometers away from the Moon, the Moon’s gravity will be the dominant force that guides your trajectory.  This is what happened with the Apollo missions (indeed, with any lunar mission, manned or unmanned, that has ever successfully reached its target).

On the surface of the Moon, you experience a gravitational pull that is about 1/6 of what you experience on Earth.  Again, that’s not because you’re so far away from Earth; it’s because the Moon’s mass – albeit large – is still significantly less than the Earth’s mass.  When you stand on the Moon, there is simply less mass beneath your feet pulling you downward.

Contrary to what some people believe, there is even gravity in outer space, between the Earth and Moon, and anywhere else in the Universe that you care to look for it.  Remember, the gravitational influence of a body drops dramatically as you get farther from the body, but it never actually drops to zero.  Plug in any number you want for x, and the expression (1/x)² will never, ever be equal to zero.  So even when a spacecraft is far from Earth, far from the Moon, far even from the Sun, there will be a gravitational influence guiding its path.

(But wait a minute, you might interject, if there’s gravity everywhere, how come the astronauts float around inside the space station?  Check and mate, mister science nerd!)

Strangely enough, astronauts float inside the space station not because they have escaped gravity, but because gravity affects the space station as well as the astronauts.  The entire kit and kaboodle is in a state of free fall, just like on the Drop Zone ride.  The astronauts are indeed falling…and the space station is falling around them.  And they avoid falling to Earth because the station is also moving sideways fast enough that it falls around Earth instead of down to Earth.  But that’s a topic for another day.

So let’s summarize this meme’s misconception: there is gravity on the Moon (and everywhere else) so your saggy parts will continue to sag, albeit less severely.  But instead of trying to figure out how to get to the Moon, Aunty Acid, why don’t you focus on loving yourself the way you are?

Flat Earth Week, Day 7: Water We Going To Do About It?

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All things must come to an end, except for Earth, which does not have ends because it is not flat.  We have reached the final day of Flat Earth week.

And wouldn’t you know it?  I’ve just stumbled across a veritable gold mine of Stupid Bad Flat Earth memes in the form of the Facebook community Flat Earth Matters.  There are enough memes there for a dozen Flat Earth weeks, but alas, I would never write about anything else if I tried to tackle them all.  Perhaps I’ll revisit the topic another time.  Until then, we bid a fond adieu to the looniest of loony conspiracy theories, and what better meme to send us off than this stunning display of Flat Earth “physics”?

Now the obvious answer to this meme is “Yes it does, because gravity.”  But you have to remember that Flat Earthers often don’t believe in gravity.  More specifically, they don’t believe that Earth has gravity, although some of them allow the Sun, Moon, planets, and stars to have gravitational influence because they think that this patches holes in their rapidly sinking model.

I’ll explain how water is able to “stick to a ball spinning 1000 mph”, although I know it won’t convince the average Flat Earther.  That’s okay; this blog has never really been about convincing the other side.  I try to bring logic and evidence to the table while ranting about the stupidity of memes, and the reader may decide for himself or herself whether I have sufficiently made my case.

So let’s start by establishing that Earth does in fact have gravity.  Newton said that anything with mass has a gravitational influence on any other object with mass, and there’s no reason to believe that Earth is any different.  Henry Cavendish showed in 1798 that objects much less massive than Earth have their own gravitational sway, albeit minuscule.

Einstein overhauled Newton’s ideas by showing that gravitation is actually the result of massive bodies curving the fabric of spacetime.  In doing so, Einstein predicted that not only can gravity affect the motion of objects with mass, but it can bend the path of massless light as well.  The famous Eddington experiment of 1919 proved that Einstein was correct.

Although Newton’s and Einstein’s models of gravity vary in important ways, they agree in one important detail: the more massive an object is, the more gravitational influence it wields.  That’s why in the realistic model of the cosmos, the Moon orbits around Earth and Earth orbits around the Sun.

Now the average Flat Earther believes that the Sun and Moon are much smaller – and presumably less massive – than Earth is.  (Well, they’re correct about the Moon, but definitely not about the Sun.)  Let’s pretend that they’re right in both cases.  If the Sun is still massive enough to bend the light from distant stars in exact accordance with Einstein’s General Theory of Relativity (and it is), and if Earth’s mass is much greater than the Sun’s mass (which, according to Flat Earth models, it must be), then surely Earth’s mass is enough to exert a gravitational influence on the objects that rest upon it, right? In fact, Earth’s gravity ought to be enough to squash it into a ball.

Or are Flat Earthers prepared to admit that their model is inconsistent in that it treats Earth as a physically special object, separate from and immune to the laws that govern the heavenly bodies?  No, even the most fact-averse Flat Earther, if he is intellectually honest (he isn’t), must concede that Earth has mass; ergo, it also exerts a gravitational tug.

Earth has gravity, anyway you look at it.  And in the Globe Earth model (i.e. the correct model) Earth is indeed spinning at a seemingly high rate of speed.  However, your speed with respect to the center of Earth diminishes as you move away from the equator.

EarthSpeed

The difference in speed between diverse latitudes gives rise to the Coriolis effect, which causes the rotation of tropical storms and ocean currents (but has no effect on the direction your toilet flushes!)  The easily measurable rotation of wind and water currents is just one more piece of evidence that we live on a spinning, ball-shaped Earth.  But we were talking about gravity.

Using Newton’s Law of Universal Gravitation (which will do in a pinch, although it is not as complete or exact as General Relativity), we can calculate that gravity exerts a “force” of about 9.8 newtons (about 2.2 pounds-force) on every kilogram of mass near Earth’s surface.  Is that enough force to keep Earth’s water from flying off into space, especially near the equator where it is moving the fastest?  Let’s find out.

The force required to keep something moving in a circular path is called centripetal force.  The faster an object is moving, or the more mass it has, or the tighter the circle you want to keep it moving in, the more force is required.  For example, imagine swinging a bowling ball in a horizontal circle on the end of a chain.  (No, I don’t know where one might find a bowling ball attached to a chain…just go with me on this one.)  It would take more force to swing a 12-pound ball then it would to swing an 8-pound ball.  It would also take more force to keep a ball swinging in a circle  5 feet across, compared to a circle 10 feet across.

Using the centripetal force formula, we can show that at the equator, it only takes 0.034 newtons (0.0076 pounds-force) of force to keep a kilogram of water moving in a circle with the same radius as Earth.  But remember, Earth’s gravity provides about 9.8 newtons of force per kilogram of matter, which means that each kilogram of water experiences way more than enough force from gravity to prevent it from flying off into space, even at the equator where it is spinning the fastest.  Q.E.D.

Now you might reasonably ask: if Earth’s rotation is causing me to move at hundreds of miles per hour, why don’t I feel like I’m moving that fast?  The answer to that question is two-fold:

  1. Compared to the size of Earth, even 1000 mph is not a very high speed, and
  2. Everything around you, including the air, is moving with you at the same speed.

See, it’s all relative.  We live on a ball-shaped Earth that spins once a day, moving around the Sun at more than 67,000 miles per hour (30 kilometers per second).  The Sun itself is whizzing through space at hundreds of kilometers per second, depending on which reference frame you choose.  But to us tiny humans held fast to Earth by gravity, none of this is readily apparent.  It’s only when we take the time to study the universe that we see the truth.  Humans have been studying the Universe and our place in it for centuries; its only the Flat Earthers, Creationists, and other reality-denying ideologues who seek to turn back the clock of scientific progress.

Flat Earth Week, Day 6: A Fort of Ignorance

fes_fort

Oh Lord.

I would say that this meme was created to troll the Flat Earth Society rather than support it, except that this meme comes directly from the Flat Earth Society’s online forum, where it was posted by John Davis, one of the site’s administrators.  If John Davis is a troll, he’s undercover, and he’s in deep.

Charles Hoy Fort is the author of The Book of the Damned, a dense tome that is right up Flat Earthers’ alley.  The first three sentences of Fort’s non-fiction work are:

A PROCESSION of the damned.

By the damned, I mean the excluded.

We shall have a procession of data that Science has excluded.

Fort’s book is all about the stuff that science supposedly ignores because it doesn’t fit into the mainstream.  Damned delves deep into the paranormal and pseudoscience, tackling such varied topics as UFOs, strangely glowing skies and the weird things that fall from them, mysterious locations, fairies, poltergeists, and vanishings.

The quote in question comes from Chapter 3 of Damned.  Although Fort’s writing style is quite difficult to decrypt, his major thrust in this chapter seems to be documenting numerous cases of strangely-colored detritus falling from the sky.  He also laments the fact that science refuses to recognize the extraterrestrial origins of this peculiar precipitation (or even that it exists).

Early in the chapter, and seemingly apropos of nothing, Fort makes two confusing detours, first into Darwinism, then into the shape of Earth.  I’ll not spend much time discussing Fort’s position vis-à-vis Darwinism, except to say that he mischaracterizes it as a tautology in danger of being abandoned by the scientists that once supported it.  (In reality, Darwinism was being strengthened in 1919, when Damned was published, by the developing field of genetics.)

In his second digression, Fort says:

Or that Columbus never proved that the earth is round.

Shadow of the earth on the moon?

No one has ever seen it in its entirety. The earth’s shadow is much larger than the moon. If the periphery of the shadow is curved — but the convex moon — a straight-edged object will cast a curved shadow upon a surface that is convex.

All the other so-called proofs may be taken up in the same way. It was impossible for Columbus to prove that the earth is round. It was not required: only that with a higher seeming of positiveness than that of his opponents, he should attempt. The thing to do, in 1492, was nevertheless to accept that beyond Europe, to the west, were other lands.

I offer for acceptance, as something concordant with the spirit of this first quarter of the 20th century, the expression that beyond this earth are — other lands — from which come things as, from America, float things to Europe.

It was not required for Columbus to prove that Earth is round because everybody in 1492 already knew that Earth is round.  Remember, Erastosthenes not only knew about the shape of Earth, but made a somewhat accurate measurement of its circumference seventeen centuries prior to Columbus’s voyage.  The story that Columbus alone believed in Earth’s rotundity was invented from whole cloth by Washington Irving for his 1828 book A History of the Life and Voyages of Christopher Columbus.  Irving was a writer of fiction who highly romanticized (and in many cases fabricated) the story of Columbus’s life in order to instill his American audience with nationalist pride.  Unfortunately, Irving’s myth-making talents worked too well: Many people swallowed the Irving story hook, line, and sinker, without a hint of skepticism.

Is Fort parroting the Irving-inspired Columbus myth?  To be honest, it’s hard to tell.  Reading Fort’s prose is similar to learning calculus from somebody with a severe concussion.  For that matter, I’m not even sure what Fort thinks about the shape of Earth.  He does offer a half-hearted explanation for the seemingly curved shadow of Earth as an optical illusion caused by the concave surface of the Moon, but maybe Fort is just playing devil’s advocate.  It’s possible that Fort does not really believe Earth is flat, but enjoys pointing out how it could be flat, if you really wanted to prove that.

For what it’s worth, though, the Moon is not concave.  If you need convincing, simply ask any of the surviving Apollo astronauts that landed on its surface and orbited around it.  Of course, if you don’t believe Earth is round, you’re not likely to accept the word of Apollo astronauts.  Is there a way to prove the Moon’s convexity for yourself?

Yes, but it’s difficult.  You need a camera and a lot of patience.  The trick involves taking photographs of the Moon over the course of a month, during which you’ll witness the phenomenon called lunar libration.

See, the Moon’s orbit around Earth is not perfectly circular; it is slightly eccentric.  In other words, as the Moon orbits around Earth, it gets closer to and then further away from our planet.  According to Kepler’s laws of orbital motion (which you probably also dismiss as false if you’re a Flat Earther), an object in an elliptical orbit moves faster when it is closer to its primary, and slower when it is further away.  So as the Moon moves around Earth over the course of a month, it speeds up and slows down.

The Moon is tidally locked with Earth, which means it rotates once on its axis in the same amount of time that it orbits around Earth.  A consequence of tidal locking is that the Moon always keeps the same hemisphere facing Earth.  Well…nearly the same hemisphere.  As the Moon speeds up in its orbit, it moves a little bit faster than its rotation can keep up, and when it does, we see just a little extra sliver of the Moon’s trailing hemisphere.  When the Moon slows down, we see a little extra sliver of its leading hemisphere.  Due to libration, we can actually see about 59 percent of the Moon’s surface over the course of a month, rather than the 50 percent you would expect if libration did not occur.

You can also witness a small amount of libration over the course of a day.  As Earth rotates you beneath the Moon, you see the Moon from slightly different perspectives.  Compare a highly-detailed picture of the Moon taken shortly after moonrise with a picture taken just before moonset, and you might be able to spot the tiny difference.

Even if the Moon were concave, we would be able to distinguish the difference between a round shadow and a curved shadow.  There are many, many concave surfaces on Earth, and artists have spent generations studying the subtle interplay of light and shadow upon various geometries.  If the Moon were concave, we’d have known long ago.  If Earth were flat, we’d have figured it out by now.  Neither premise is true.