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…
Is this a paradox? Yes, although it may not be obvious from this retelling. The paradox of thrift is a problem in economics first popularized by economist extraordinaire John Maynard Keynes (not by some fellow named John Robertson). The paradox works on the assumption that people are either saving money or spending money. If they save money, then they’re not spending, which means that demand for goods and services will plummet. Consequently, the businesses that provide goods and services will be unable to pay their employees, and income will decrease, which will have the adverse effect of decreasing savings overall.
The logical contradiction is that thrift is generally regarded as good for an individual, but collective thrift is bad for the economy as a whole. Since consumers are part of the economy, what’s bad for the economy is bad for consumers. Ergo, saving is simultaneously good and bad.
Is there a resolution? Critics of Keynes’s paradox of thrift point out that when demand falls, prices follow. Lower prices for goods and services might help offset the potential loss of savings caused by lower income. Also, a thrifty individual could save his money in a bank. Increased savings in banks might lead to banks lowering their interest rates for loans. Lower interest rates would encourage people to borrow from banks, which in turn stimulates spending and investment.
Furthermore, the paradox assumes a closed system. Of course the global economy is a closed system, but a nation’s economy is not. Even if, say, every American decides to start pinching pennies, American companies can still earn money from exports to nations more willing to spend. Consequently, a company surrounded by spendthrifts may nevertheless experience economic growth, and pay its workers accordingly.
Is this a paradox? I honestly don’t know how to call this one.
This isn’t the original form of Epimenides’s paradox. Allegedly, Epimenides, who was from Crete, said “All Cretans are liars.” How should we evaluate his claim?
Realistically, a paradox only arises if you answer true. If the statement is true, then Epimenides himself must be a liar, since he is from Crete. But if Epimenides is lying, then the statement is false and not all Cretans are liars. Answering true leads to a logical contradiction.
(We’re assuming that liars always lie, and that honest people are always truthful. I don’t know anybody who meets either criterion, but for the purpose of this discussion, we’ll run with it.)
If you say false, however, the paradox vanishes. The word all assures you of this: if you decline to believe Epimenides’s claim, then not all Cretans are liars. There is at least one truthful Cretan, although it obviously isn’t Epimenides.
The same logic applies to the altered version presented in this meme. If you say that the man is telling the truth, then you reach a logical contradiction, since in order for the man to be telling the truth, he must be lying. But if you assume the man is currently lying, there is no contradiction. The man doesn’t always lie, although he is lying right now.
Is there a resolution? Yes. Just say false and move on with your life.
Wait…how did a pole and a barn become a hot dog and…a toilet paper tube? What is that thing on the right?
Also, does this paradox strike anybody else as vaguely sexual?
Is this a paradox? Yes, this is a paradox in the same vein as the Twin Paradox, which I mentioned yesterday. And like the Twin Paradox, it can be resolved by a deeper understanding of Special Relativity. But first things first…
Length contraction is a real effect of traveling close to the speed of light. Suppose there is a train – or…ahem, a hot dog – traveling close to the speed of light. A stationary observer will measure the train to be shorter than it is at rest. If the train is one kilometer long when standing still, it will only be 136 meters long when it travels at 99% of the speed of light, as measured by a stationary observer.
Of course, there is no preferred inertial reference frame; i.e. a passenger on the train would be just as valid to claim that he is sitting still while the world whooshes past him at 99% of the speed of light. From his perspective, then, the entire Universe has become foreshortened along the direction of travel, to about 14% of its original length.
Now suppose there’s a tunnel ahead whose rest length happens to be one kilometer. The train could park inside the tunnel and it would just fit. From the perspective of a stationary observer, however, the relativistic train is now considerably shorter than the tunnel. It will fit inside the tunnel with plenty of room to spare (although it will spend the briefest instant passing through the tunnel, on account of the fact that it’s moving fast!)
A train passenger, on the other hand, will see the tunnel as being shorter than the train. From the passenger’s perspective, the front of the train will emerge from the tunnel before the last car has entered. The tunnel will be too short for the train, in much the same way that a regular-sized hot dog bun is too short for a jumbo-sized hot dog.
So who is correct? Einstein tells us that both observers are correct, which leads to an obvious contradiction.
Is there a resolution? Yes, but you’re not going to like it. According to Special Relativity, it is perfectly acceptable for observers in two different reference frames to disagree on when events are happening, including when the train enters and exits the tunnel. As long as both observers agree on the overall outcome – that the train passed through the tunnel completely – it doesn’t matter that they don’t agree on the sequencing of the events. Weird.
This video does a pretty good job of explaining the train/hot dog paradox in greater detail.
Is this a paradox? No. This is an ethical dilemma, as it says at the top. (At least this one is correctly attributed.) An ethical dilemma is not the same as a paradox. There is no logical contradiction. There is merely the horrible choice of being an active killer of one or a passive killer of five.
So what’s the best answer? That depends on whom you ask. The utilitarian approach is that of course you should throw the switch: one death is objectively less bad than five. On the other hand, some argue that throwing the switch makes you personally at fault for the loss of life; inaction means no one is at fault. Others counter that if you are present and able to influence the outcome, you are morally obligated to do so.
If your skin is not already crawling from the moral queasiness caused by this grim scenario, consider this one:
A doctor has five patients, each in desperate need of a different organ. Without a transplant, all five patients will die. The doctor has no matching donors available, and the situation is dire. Then one day, a healthy tourist from a foreign land, who just happens to be passing through, stops into the doctor’s office for a routine checkup. The doctor discovers that the tourist is a perfect match for all five patients, and he knows that if the tourist were to “go missing”, nobody would suspect the doctor…
Objectively this scenario isn’t much different from the original trolley problem, but it’s starting to sound like a horror movie, so let’s move on.
Is this a paradox? Yes. Although this meme refers to it as a Bootstrap Paradox, the more general term is causal loop. A causal loop is a paradoxical problem arising from backwards time travel in which Event A causes Event B, which causes Event A, and so on.
This paradox is closely related to the Grandfather Paradox. Suppose a man goes back in time to kill his own grandfather before his grandfather met his grandmother – for reasons known only to the time traveler. Since his grandfather didn’t live long enough to have kids, the time traveler himself was never born. But if the time traveler was never born, then the grandfather was never killed, which means the time traveler was born. Boom. Paradox.
In this less gruesome situation, a time traveler is not deleting something from history but rather, adding something to it. One can imagine a million possible variations: a time traveler gives a solid-body guitar to a young Les Paul; another one gives the Internet to Al Gore; another teaches Braille to that French guy whose name escapes me.
Come to think of it, if humanity ever invents the flux capacitor, then our technological capability will explode immediately (and mysteriously) thereafter. Think about it: all you have to do is take modern science and technology back to the Victorian Era, and let human ingenuity take care of the rest. Return to the present, and bingo! Technology will have progressed about a hundred years beyond what you took back. Round up the resulting new technology and take that back, and now you’ve advanced human understanding by another century. Lather, rinse, repeat until you pick your son and your daughter too from the bottom of a long glass tube. On second though, don’t do that.
Is there a resolution? Maybe. Some people think that if you travel back in time at all, you create an alternate timeline that branches off from the Universe you started in. It is in this alternate timeline that, say, Beethoven’s sonatas suddenly appear. In that case, you are effectively the author of the sonatas, although you might choose to let Beethoven have all the credit. In the timeline you left, Beethoven remains the true composer.
Others suggest that since the past has already occurred, you are physically incapable of changing it, even if you can travel to it. In other words, your actions in the past must be predestined. If you travel back in time with the goal of creating a causal loop – say, by giving Beethoven his sonatas before he writes them – something will prevent you from doing so. Maybe your time machine will malfunction and send you to a time period one hundred years too late. Or maybe, just maybe…
Maybe a resolution is unnecessary because backwards time travel is utterly impossible. That’s an option too.
Two days in, ten alleged paradoxes covered. Today’s tally of actual paradoxes: 3.5 / 5. Running tally: 5.5/10. See you tomorrow!