On the Incorrect Framing of Astronomical Probabilities
The odds that you took a dump at 7:30:12 am is 86400 to 1. A rare dump indeed!
How many times have you read some infographic or BuzzFeed list that tries to calculate the odds that you exist? Perhaps it got into all of the billions of starts in the milky way, the number of possible planets, how many possible couplings of men and women, and finally down to which sperm won the race to the egg that made you. The motivation to show you such such astronomical probabilities about everyday occurrences in life can vary from proving the existence of God, to simply trying to impress you.
There is a significant difference between meaningful and meaningless probability. We use probability in a useful way to predict the likelihood of events in the future given unknown variables. Usually we construct a model of a scenario where there are a set of known variables and a set of unknown variables. We then define the possible values that a variable can be and assign a probability to each outcome. Finally through combinatorics we can figure out what the odds of are each specific outcome in the scenario. An example of something we often model in introductory statistics classes is rolling a six sided die. In this scenario, our variable X has a set of six possible outcomes with a probability of occurrence of each. So what are the odds that you roll any particular value? The answer is 6 to 1 for every case as there are six equally probable outcomes for every roll. This is a meaningful probability because we can now use it to make educated guesses about the future.
On the other hand, when these silly articles mentioned above attempt to compute the odds of past occurrences, they always do it with the wrong frame. The set of unknowns are left not well defined. The resulting odds are meaningless. It is prudent to define an unknown that is actually significant to the problem at hand. In the case of the dice roll, the intrinsic unknown of a die is the value that it will tell. It is easy to make the odds of a dice roll meaningless by misdefining the unknown. For example, did you know that the odds of rolling a 6 on a six sided die is not 6 to 1 but actually almost impossible? That’s because the probability that the person who invented the die actually might have invented it anywhere between two and one-hundred sides (perhaps 100 sides is the most you can reasonably fit into an item of this size). The odds that he chose six sides is 99 to 1. Also, the odds that he was born are virtually zero. So therefore the odds that you rolled a six are virtually zero as well because we just multiply those two odds to get the total probability. Wow am I lucky to have rolled a 6 just now! In this scenario we failed to identify the relevant unknowns. We included the odds of the very existence of the die and its inventor rather than assuming that the die exists and then only computing the relevant unknown. This is the folly of these ridiculous statements about the odds you exist, the odds the earth exists, and the odds that the universe exists. They do not work because the unknown being computed is not well defined. In fact, they virtually assume that every variable in the universe is unknown, thereby making the adjective “astronomical” quite literal.
If you took a dump this morning, the odds that you did it at that very second is quite an impressive feat. That millisecond is even more special. You are so lucky! That picosecond!? Well…supernatural forces must have been at work here.
Some people are grammar nazi’s and others cannot stand it when their food touches. I like to see meaningful usage of probability. Thank you for reading and have a nice day.
Disclaimer: I took a jab here only at the folks whom use astronomical odds to justify the existence of a divine being, not the belief in the divine itself. The purpose of this article is not to disprove any religious belief but to promote correct and meaningful use of mathematics.
