HS #95 2023.6.8
Three Body Problem
Have you ever noticed the allure of the number “three”? In sports, for example, hockey has the hat trick (three goals), three strikes in baseball, three medals in the Olympics, three hits in volleyball, three seconds in the lane in basketball. What other examples can you think of?
Interestingly, “three” sometimes gives rise to stability and sometimes to instability. Wind turbines have three blades. Those are needed to keep it balanced. If just two blades, then it could change direction too quickly when the blades are vertical. A stool or camera TRIpod needs three legs for maximum stability. More than three legs leads to potential rocking.
Relationships, on the other hand, seem most stable between just two people. When dining at friends’ homes, my father liked to quip, “I brought my bad wife with me and left my good wife at home. Isn’t that big – a’ – me?” But he also conceded that bigamy was forbade in the Bible. His proof text: “No man can serve two masters.”
Non-PC joking aside, folks in the job market sometimes reference the “Two body problem” - the challenge of a married couple both finding employment in a given location.
But this phrase actually comes from a deeper scientific challenge called the "Three Body Problem." It turns out that the relationship between three things often leads to surprising difficulties and counterintuitive surprises.
The three-body problem originated in physics. Understanding and predicting the motion of two heavenly bodies under the influence of mutual gravity is rather simple. It’s a college-level physics problem. But, introduce a third body and calculating the motion of the three bodies becomes impossible, except with the aid of computer approximation and simulation. This led the 19th century physicist/mathematician Henri Poincare’ (one of my heroes) to develop chaos theory, an apt term since the motion of the bodies was often chaotic and unpredictable.
The intriguing mutual relationship of three things is seen even in the children’s game Rocks-paper-scissors. Isn’t it counterintuitive to you that three things can each beat something that beats something that beats itself?
I use a physical example of the game as a party trick using three knives and three cups. Set the cups on a table in the shape of a triangle so that the distance between each pair of cups is a bit more than a knife’s length. The challenge then is to place the three knives – extending horizontally from the top of the cups – so as to form a stable platform in the center of the triangle. You can do it – just interweave the ends of the knives.
A more profound example of this three-way relationship exists in Christian doctrine – in fact it’s exposed in the Apostle’s Creed. Any mathematician (or lawyer or philosopher) will tell you that you need to define a term before you can use it. Yet the Apostles Creed seems to violate this principle. Reading through it, one comes to the phrase (concerning Jesus) “conceived of the Holy Spirit” and only afterwards does one recite the phrase “I believe in the Holy Spirit.”
Isn’t that faulty writing? Shouldn’t the existence of the Holy Spirit be acknowledged before the action of the Holy Spirit is referenced? Seems so. However, the Spirit was sent by the Father to glorify the Son, so Jesus needs to be acknowledged before the mission of the Holy Spirit can be understood. So just like Rocks-paper-scissors, one is forced to cut into the three-way relationship of the Trinity at some point.
This challenge of three-way relationships also exists in voting. In 1972 the economist Kenneth Arrow received the Nobel prize for showing that it’s impossible to form a voting method to choose the winner among three candidates that will always satisfy three commonsense objectives. In particular, if you want a system where the final outcome i) ranks A over B if each voter ranks A over B, and ii) is not affected by including irrelevant alternatives into the voting choices, then that voting system is susceptible to the Rocks-paper-scissors dilemma. That is, A beats B, B beats C, and C beats A. (How? Suppose Beth’s order of preference is A, B, C. Tim’s order is B, C, A; and Dan’s is C, A, B. Then in a two-way vote, A beats B, B beats C, and C beats A.)
Alas, my parents were all too familiar with this shortcoming since those often seemed the voting outcomes of my two siblings and me.
