Random

Probability can easily lay claim as the most misconstrued concept in mathematics. Random means random. Some number, between 0 and 1 represents the likelihood that an event will happen. Simple as that. Probability is the knowledge of uncertainty. It is not that hard, but it can feel a little counterintuitive unless you think very clearheaded about it.

How many times must we hear otherwise intelligent, educated individuals say things like, “Mr. ______ should go the casinos, he kept rolling 7’s!”? Complete nonsense! Past results have no bearing whatsoever on future results. Humans are super pattern-finding machines; we see patterns even when they don’t exist! Thus some people cling to irrational notions of lucky or unlucky streaks. Past results are next to irrelevant! We only use sampling to estimate true probabilities when the true probabilities are otherwise unknowable, which is far from the case with simple dice. Others cherish the ill-conceived notion that the numbers should “even out” somehow. Again, the past results are irrelevant. We would only expect the results to exactly match their true probabilities as the sample size approaches infinity. Because we will not be sitting here rolling the dice until the universe ends, you should not expect the numbers to “even out” necessarily!

I love probability as a concept, so it pains me to witness these fallacies uttered like ignorant grunts by my colleagues in education, some of whom actually teach high-level mathematics! Some mathematicians see geometry, ratios, or calculus in everything. I see probability. Randomness is everywhere. Randomness is beautiful!