A few weeks ago my friend Michelle called me a little after one in the afternoon. The ring of the telephone woke me up and I stumbled across the room to answer her call. I looked down at the little display, saw that it was Michelle, and then put on my best telephone face to accept her “Hello, Joshy.”

Michelle called to tell me that she had accepted a new job—she was in need of a new one, believe you me. This was fantastic news. Usually Michelle can spot my false wakefulness, even over the phone, like one of those empaths from Star Trek (or something). But this time, her excitement—in conjunction with my keen theatrical abilities—distracted her from the reality of my slumber, which is exactly what I was aiming for.

I wasn’t, but the question still remains: could I have justifiably been upset at Michelle for waking me up? Well, yes but mostly no. It was one in the afternoon. Most people are awake when the sun’s up. So, Michelle was right to operate on the assumption “people are awake when the sun’s up.” The world is a crazy and complicated place. We have to live our lives despite only having access to a very small amount of knowledge about our environment. Therefore most of our judgments aren’t certain. Instead, they’re best guesses that approximate what we should do if we actually knew everything there was to know. Thankfully, we’re not totally in the dark.

People are very good at working with probabilities because lots of the events in the world have a high probability of certainty. That tree in the park you saw this morning on your way to work will probably still be there during your commute home later tonight. The position and function of the knobs and buttons on your stove are not going to switch themselves around when you’re not looking—with high probability. So it’s not surprising that people believe that there are certainties in life. And maybe if you were able to know everything about everything at every time, then the world would work according to a small set of fixed laws. Unfortunately, no one—as far as I know—has that sort of depth of knowledge and understanding. So, for practical purposes, we’re left interacting with probabilities.

Now we get into trouble when we confuse probabilities for certainties. Then we become locked into a stereotype. That’s right, I think stereotypes are simply misapplied probabilities. Several years ago some fledging stand-up comedian trying to break it big played the Conan O’Brien Show. He included two “postive stereotypes” that stuck with me. “All Jews can fly and Mexicans are made out of candy,” he claimed. Being (sort of) both Jewish and Mexican, I can say from experience that very few Jews whom I know can fly and even fewer Mexicans are made out of candy. So what makes his stereotypes wrong? Well, probabilistically his claims aren’t well supported.

Here’s another perhaps less inflammatory claim: men are taller than women. I bet a lot of you agree with that. But let’s hold up just a second and see just what the sentence is saying. There are a lot of words missing that really ought to be there. My claim doesn’t mean all men are taller than all women. If you cite your friend from college on the women’s basketball team who towers over everyone else in a crowd, you haven’t disproved anything. What I really mean to say is that on average men are taller than women; i.e., if you pull a random man and a random woman off the street and compare their heights, record the answer, and then repeat the experiment several times over, then in general, you will find that the man is taller than the woman.

So what are assumptions: they are the most probable results from a distribution of possible results that we adopt as fact based on our experience. Experience varies, so assumptions vary. The key is to remember that sometimes outlying events can happen, and we must be open to the possibility that they do. Most Mexicans aren’t made out of candy, but don’t let me fool you into believing that none of us are.

All that said, Michelle should’ve known, given her previous experience, that there was a high likelihood that I would be sleeping at one in the afternoon. Don’t forget that not all assumptions apply in all contexts. These things are conditional, after all. So, she’s only partially excused.

And while I’m on my soapbox, it’s worth pointing out that because people almost exclusively interact with probability distributions, probability and statistics really need to be given more attention in school curricula. Over emphasis on deterministic systems tricks students into believing that the world really operates on certain events. I can’t think of anything further from the truth.

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