If a chicken and a half can lay an egg and a half in a day and a half, how long does it take ONE chicken to lay ONE egg?
What do you think?
Before we discuss the answer to that one, let’s move on to the American House of Representatives. There are 435 people in the House of Representatives. What is the probability that at least two folks in the House share a birthday?
We will return to these two puzzles shortly. Meanwhile…
Imagine that you are one of our distant ancestors foraging for food. You come across something that looks just like a blackberry bush. On it are what appear to be nice ripe blackberries. They feel like blackberries so you pick one. You pop it in your mouth and it tastes like a blackberry. It has the same seeds that you are used to being in a blackberry fruit. It smells like a blackberry. Chances are extremely good that it is, in fact, a blackberry.
Don’t get me wrong. There are some plants out there that could give you trouble! The deadly poisonous amanita mushrooms are said to taste good. And, the white “death angel” has been mistaken for an ordinary field mushroom with deadly results. A single mushroom will kill you but a half a mushroom may only make you wish you were dead.
In general, however, plants, animals, and situations are redundantly coded right at the surface. A blackberry plant has leaves that look like blackberry leaves. It has thorns that look like blackberry thorns and also feel like blackberry thorns. The fruits look like blackberries! They have a texture of blackberry. They smell like blackberries. They taste like blackberries. Though there are some deadly exceptions, in the natural environment, we are generally clued in to what something is by multiple senses. If it looks like a blackberry and smells like a blackberry and feels like a blackberry and tastes like a blackberry, chances are excellent that it really is a blackberry.
When it comes to things produced by human beings, however, we must be much more cautious.
In some cases, such as the puzzles at the beginning of this blog post, the intention is pedagogic. But in other cases, people mislead you for much more nefarious purposes. Someone could intentionally spray the blackberry patch where you go with an odorless, tasteless, invisible poison. It could poison your body and kill you stone cold dead. Or, they could poison you and make you so sick you wish you were dead. Who would do such a thing? Well, the name “Vladimir Putin” springs to mind. He has arranged for the poisoning of his political foes and critics.
It isn’t only your body that is at risk, however. So is your brain. The tricks that people play are not necessarily all deadly. Often, they just want to take your money. So, they will tell you a drink is “All Natural Fruit Drink” because they know that most people care about their health and the health of their families and “All Natural Fruit Drink” sounds like something natural, healthy, and nutritious. But legally, as it turns out, those words mean absolutely nothing in America. That “all natural” drink may be anything but! It could be mainly water and corn syrup! It might have as little as 5% fruit juice.
What do you think is in “Air Freshener”? “Air Freshener” sounds wonderful, doesn’t it? After all, who doesn’t like fresh air? If you’ve been in a musty cabin waiting for the rain to abate and you step outside into the cool, crisp, fresh air, that is a wonderful sensation. Ah! Breathe in that fresh air. And, of course, when you see a commercial for “Air Freshener” on TV, or read the title which might say, “Ocean Breezes Air Freshener” it reminds your brain perhaps of your first trip to the ocean.
What is really in air fresheners is, in many cases, anything but an air freshener. Do you know what a really good air freshener is? Opening your windows. But the sprays that you buy in the store can contain:
Carcinogens
Perfumes
Chemicals that mess with your hormones
Chemicals that deaden your sense of smell
Huh!?
Not exactly an “Air Freshener” is it?
In the puzzles above, the description is also misleading, not because I want to steal your money or poison you, but because I care about my fellow citizens being sold their death warrants packaged as something wonderful. Hopefully, if we become aware of how the surface features of a situation can mislead us, we’ll be less prone to fall for such tricks.
The tobacco companies were good at such tricks. They would sell you something deadly and addictive but advertised to make you think that smoking their product would make you “manly” or “sexy” or “sophisticated” or “urbane” or “adult.” It wouldn’t make you any of those things. It would harm your lungs and your heart and turn your skin gray and make your breath smell bad. But those aren’t very good selling points, you see. Eventually, the government required cigarette companies to put health warnings on the packages. Do you think that the cigarette companies eagerly complied? Guess again. They fought tooth and nail and paid off politicians for years so they wouldn’t have to own up to what their product was really doing to you.
So, let’s return to the puzzles. In the first puzzle, many people are led by the structure of the language presented to answer wrongly.
“If a chicken and a half can lay an egg and a half in a day and a half, how long does it take ONE chicken to lay ONE egg?” The first answer that will likely pop into many minds is “ONE day!” It “seems logical.”
But it’s dead wrong. Consider this analogy: “If nine women can have nine babies in nine months, how long does it take ONE woman to have ONE baby?” One month? No, of course not. It takes nine months. And it will take a day and a half for the one chicken to lay one egg. (Or, a hundred chickens to lay a hundred eggs).
The second puzzle will probably only cause problems if you have been educated about probability.
What? Yes. If you ask a smart ten year old, they will figure it out. Basically, there are only 365 days in a year (or 366 in a leap year). Since the number of Representatives in the House is 435, even if the first 365 people in the House have different birthdays, the next person you look at has to overlap with someone. It’s just like this: Suppose you only have some identical black sox and identical white sox. If you pick three sox in the dark, you have to have at least one match.
If, however, you studied statistics, you may have come across “The Birthday Problem.” As it turns out, if as few as 30 people are in a room, the chances are greater than 50:50 that at least two share a birthday. If the puzzle reminds you of this, your mind runs along lines like this: “Oh, yes, I remember this. It’s “The Birthday Problem” and with even 30 people the odds are good, so with 435 people the probability must be really high. I’d say the odds are 99:1.” No. Wrong. Close, but wrong. There must be at least one match.
It’s very easy for us to rely on the surface of things — including its label or what advertisers say about that thing — as a valid indicator of what’s underneath. And, in nature, that is often true. But in modern society, if you simply believe what someone says, you will certainly lose some money and at some point, you may also lose your entire fortune, your freedom, and your family. It’s happened before. Hitler, to name one famous example, told people he was going to make Germany great and that the “Third Reich” would last a thousand years.
He killed himself in the end. But not before causing the deaths of millions — including millions of Germans. He told people lies that they wanted to hear. He divided people and made people believe that all their troubles would be over if he just had complete power over their lives. Don’t fall for it.
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Essays on America: The Stopping Rule
Essays on America: Where does your Loyalty Lie?
Essays on America: My Cousin Bobby
It’s Not Your Fault; Send me Money
Myths of the Veritas: The Orange Man
