Beware Of “Fools Gold” Logic

You’ve seen the memes. You’ve heard the soundbites. You’ve read the talking points. The gun culture’s arguments inevitably boil down to the premises that “the only way to stop a bad guy with a gun is a good guy with a gun” and “bad guys don’t obey gun laws”. Those are tenets that, on the the surface, seem to make sense — at least to those who put great stock in firearms. But reality is quite a different matter.

When you look at the statistics, you see that stricter gun laws correlate with lower crime; and conversely, looser gun laws correlate with higher crime. The gun culture mantra of “more guns, less crime” is a prime example of what I call fools gold logic. Like iron pyrite, such premises appear to be the real thing at first glance; but when you subject them to closer scrutiny, they turn out to be worthless.

Killing criminals will prevent crime? Sex education encourages kids to have sex and results in higher teen pregnancy rates? Being a military bully will cause other nations to be peaceful? Teaching people religion will necessarily make them more moral? Spanking kids will make them disciplined? These all sound like perfectly logical conclusions — at least to some people. You’ll even hear them referred to as “common sense”. But common sense only works when you have the facts. And the facts don’t support any of these beliefs. At best, they are untested theories; and even scientists often find that their theories were mistaken.

More often, however, fools gold beliefs don’t even qualify as theories. They’re simply presumptions rooted in prejudice and narrow worldview. It was once considered “common sense” that the earth was the center of the universe. And that the white race was superior to everyone else, and the black race was created to be slaves. And that women were incapable of having careers or making wise decisions at the voting booth. And that air travel or travel faster than 15 mph were impossible. It might appear to be “common sense” that a starving person should be given lots of food and a frostbitten person should be administered lots of heat. Both actions, in fact, would be quite harmful and possibly fatal.

No doubt you’ve seen optical illusions showing that our eyes can play tricks on us. In this one, for example, we’d swear just from looking that in each image, one line is shorter than the other.

But when we actually measure we see that all the lines are the same length. Not only do our eyes play tricks on us, but also our minds play tricks on us — which in fact is why our eyes play tricks on us. And we may end up drawing a false conclusion if we don’t take the “measurement” — whatever that may entail.

Whenever a politician gets caught philandering, there is always a great deal of pearl clutching and demands that the politician resign. Provided, of course, that the individual in question is a Democrat; if he/ she is a Republican, they pretty much get a pass — even if the target of their affection is a teenage boy. But if a Democrat cheats on his wife, the ubiquitous claim is that if he is unfaithful to his spouse, then he can’t be trusted to honor his commitments in general. And hey, you must admit that seems to have a certain logic to it. But in real life, it often doesn’t pan out that way at all. Some of the most notorious marital cheaters to hold office have also been among the most honorable in performing their official duties. Conversely, some who were unswervingly loyal to their spouses have been among the biggest liars and crooks. Sometimes, the truth is simply counterintuitive.

A classic case in point is the so-called Monty Hall Problem, which was originally posed, and resolved, in The American Statistician in 1975:

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?

Most people — in fact, probably just about everyone at first glance — would insist that, no, it doesn’t make any difference. The chances of picking a car were one out of three in the beginning; and now that one door has been opened, those odds have been changed to one in two — for either door. So what difference could it possibly make whether you switch?

Upon investigation, however, it turns out that, strangely enough, it would indeed be to your advantage to switch. Because doing so would not change your odds to one out of two, but to two out of three. Conversely, sticking with your original choice leaves your chances at one out of three. Seriously. Here’s the chart of possible outcomes to prove it.

This problem gained widespread public attention when it appeared in a Parade magazine column written by Marilyn vos Savant, known as the “world’s smartest person” because she supposedly has the highest IQ ever recorded. (In fact, her IQ scores were questionable estimates, and IQ is not a direct measure of intelligence. But there’s no denying her brilliance.) Many readers challenged her answer, and insisted that she was wrong. Some even insulted her. Among them were scientists and PhDs. Which just goes to show that sometimes even highly intelligent individuals fall prey to fools gold logic.

Indeed, Marilyn herself is no exception. During her decades at Parade, she’s provided enough bad answers (both demonstrably wrong and subjectively off-base) to fill a book. She initially declared that she found modern art to be pointless; it was only after a number of readers wrote urging her to reconsider that she changed her tune, and announced that she was taking a tour of major art museums to study these works in more depth. She defended the Electoral College by resurrecting the infamous World Series analogy. (We’ve previously explained why this is a terrible analogy, and why the Electoral College is bad for many reasons.) And despite her facility in performing complex math, she’s been known to stumble over very simple problems. Like this one, which you may have heard before:

If a hen and a half lays an egg and a half in a day and a half, how many hens will it take to lay 6 eggs in 6 days?

This one has been around for ages, though sometimes the exact number of fowl in the henhouse may vary, and the question may be reversed to ask how many eggs will 6 hens (or whatever) lay in 6 days (or whatever). Traditionally, the “correct” answer to the problem as stated is one hen — because a hen and a half laying an egg and a half is the same as one hen laying one egg. And this is the response that Marilyn gave.

But it’s wrong. Because it overlooks a crucial piece of information: it takes each hen a day and a half to lay one egg. Thus, the hens are laying at the rate of two-thirds of an egg per day. Therefore, it actually would take a hen and half to lay an egg in a day, or 6 eggs in 6 days. (Accordingly, 6 hens laying for 6 days would lay 4 eggs.) Marilyn corrected her answer when several readers, including myself, pointed out the mistake. But she has not always been so willing to acknowledge mistakes. Which unfortunately means that, for all the good her column has done, it also occasionally may have led the public astray with fools gold logic.

This is not meant as an attack on Marilyn vos Savant. The point is that even the “world’s smartest person” can be bamboozled by fools gold, so you shouldn’t feel bad if it happens to you as well. Still, it’s certainly a good idea to try to avoid it. Unfortunately, I don’t know any simple magic formula to prevent it. But these pointers might help: (1.) Make sure you have all the essential information. (2.) Try to exclude extraneous and irrelevant information. (3.) Make certain you define the question accurately. (4.) Don’t trust your eyes, your instincts or your biases to provide the final word — though they certainly may point you in the right direction. (5.) Avoid believing something without verification. Whenever possible, make the appropriate measurement or experiment — which is often simply a matter of charting the possible outcomes and/or applying some simple grade school arithmetic.

We all are subject to being fooled by fools gold. But that doesn’t mean we have to be fools.


  1. Considering how many eggs are laid by a hen and a half in six days etc. is confusing to me, because after all, there is no such thing as a half a hen, and if there were, it would likely not have the physical equipment to lay eggs. You may just as well ask yourself how many people do one and a half goblins scare in six days? And of course, the answer would be none, because there is no such thing as a “goblin” to begin with.I understand that your point is about things that may sometimes even seem mathematically correct, may only appear to make sense. But those kinds of brain teasers are not even necessary to invoke if one wants to discuss the issues they are epitomize.

    The rest of your suggestions, (like making sure you have all the right information, are not making decisions based on extraneous information, and that you are making sure that the question is being defined accurately) are points that make a great deal of sense, because believing anything without verification contributes more to one’s own gullibility quotient.

    One issue I find very hard to communicate to conservative people is the fact that “critical race theory,” is not really being taught in k-12 and that most grade school teachers have very little, if absolutely no, idea what CRT is. The moment one brings up the fact that this issue has been created by Republicans in order to demonize liberal democrats, they assume that I am not aware of the facts, and this is complicated by the fact that many conservative people take the idea that teaching that systemic racial bias exists in America as an accusation against anyone who differs with perceived liberal policies? The case in fact, is that Biden struck down policies associated with CRT because their very unclear definition, might have allowed conservative Trump supporters, (for instance), to ban virtually anything about our racial history from being taught. And they could also insist that the implication that any racial bias in America exists, is a direct cut on their own character.

    Likewise, when it comes to the idea of white privilage, most conservatives insist that anyone who has such bias must be trying to vilify conservatives and teach their children that all white men are all evil. So, to explain, I use myself as an example of how white privilage comes with the territory merely because of one’s race as at birth–not because all white people insist on rejecting black Americans as inferior, or because the issue of race is simply attributable to the ignorance of black malcontents who want to make sure that all white people are held responsible for the brunt of all racial bias. Instead, I tell them it’s not something one makes a conscious decision to accept. Rather it’s the result of never having been required to use a “whites only” restroom, or of, being stopped and frisked inordinately, no matter if one is driving an expensive car and is dressed in expensive clothes, So I ask them to consider how they would react if a black cop stood on the neck of a white guy for 9 minutes, until the white man died? But they persistently confuse the issue as one that impugns all white people whom (liberals think) must voluntarily choose to adopt an attitude held by those who talk about having white privalage, and therefore must choose to be evil. So, I explain further that I know I suffer from white privilage simply because I was born white and have never experienced the many ways in which black Americans have been oppressed and vilified in a society that is still recovering from the massive ill will caused by slavery. I tell them that I have never owned slaves, that my parents have never owned slaves, and that I have never had to recite the entire preamble to the constitution in order to vote (just because white guys were not held to the same standards), and thus, because my ancestors were Finnish Immigrants, and I am from the third generation of Americans in my family tree, I just do not have the historical background that most black most Americans have. But the realization that white privilege exists itself, is only common sense– because I have no basis on which to understand the ways that many black Americans feel.

    The problem is that despite my honest intentions to use myself as an example, conservatives think that I must be trying to cloud the issue in order to make them think like liberals? But in fact, the existence of white privilage is not often a consciously adopted mind set, so we who know we have it, should not think that all southern conservatives are evil or immoral people? However, in reality, the existence of white privalage makes simple common sense. Another way of putting it might be that no one without a commonly shared social experience can truly understand another’s social background and their views of racial history. Still, on a lot of social media forums I have seen many liberal commenter’s attack anyone on the right as being evil incarnate, (unless they admit that they are racially biased)? But If you want to open the minds of yourself and others, it does little good to stage a screaming match in which one side or the other rudely insists that the other side is completely wrong, and that vilifying those who think differently, is morally justified. One feeling I do get, is that using the word “privilage,” often polarizes many conservatives, since many of them (correctly) do not consider themselves as being privilaged at all. In fact, many of them have worked hard to provide food, shelter, and love to their children as the primary focal point of their lives. So, it’s understandable that using the word “Privilege,” immediately turns them off.

    • Next time I will fwrite out my comment using my word program first, where I can keep checking for errors until the cows come home. I am becoming more adelpated than usual due the incredible and despicable barrage of falsehoods that Trump provides to his supporters each day, until we are all forced kiss our democracy goodbye,

  2. Lots of good points here, and I appreciate your articles whenever they appear.

    I still have problems with the Monty Hall conundrum, and I hope you can straighten me out. Because it seems to me that, as soon as the third door is opened and reveals that there is no car there, then that wave function collapses and you are back to two doors, one of which hides a goat and one of which hides a car. In the table you have above, door #3 has ‘car’ as an option, but as soon as it’s opened, we know that’s not true. (I’m assuming that I, as the contestant, am bright enough to know that choosing door #3 AFTER it has been shown to hold a goat is not going to suddenly produce a car.)

    Regardless of the odds at the beginning, when the third door is opened, it is no longer an issue and you now only have two doors to choose from, one will have a goat and the other will have a car. 50/50.

    What am I doing wrong?

    • To tell the truth, it still seems odd to me too. But the unavoidable fact is that the answer Marilyn gave, though it seems illogical, can be confirmed by experimentation. It seems to me that the key factor is that the game show host knows what’s behind each door, and is therefore going to open a door with a goat behind it. In the wording of the problem, door # 3 is given as an example, but the host would not choose it at random. If he did, it might be accurate to say that the “wave function collapses” , but by knowingly manipulating the options, the host has created a new probability. (Not sure that sounds very logical either, but that’s about the best I can do!) I didn’t become fully convinced that her answer is correct until I looked at the table and imagined each scenario playing out. By the way, I’m even more fascinated by a similar problem that Marilyn also rehashed. It’s sometimes called the Boy Or Girl Paradox. Here’s how her reader worded it: “A shopkeeper says she has two new baby beagles to show you, but she doesn’t know whether they’re male, female, or a pair. You tell her that you want only a male, and she telephones the fellow who’s giving them a bath. “Is at least one a male?” she asks him. “Yes!” she informs you with a smile. What is the probability that the other one is a male?” The answer she gave was one out of three, which REALLY seems illogical, given that the odds of a puppy being male are approximately 50/50, whether another male is in the vicinity or not. But again, her answer can be verified by experimentation. However, after pondering this problem a great deal, I have concluded that it is indeed a paradox of sorts — the answer could be either one out of two or one out of three, depending on whether you interpret the question to be “What are the odds of a puppy being male?” or “What are the odds of having two males compared to the odds of a mixed pair?”

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