How can one effectively expand their purview from the tangible and perceptible to the abstract and unseen? Human minds are predisposed to search for causality. Our biology drives us to create associations among events, crafting a narrative that expounds upon specific outcomes. These constructed narratives make our reality appear destined in hindsight. But, suppose that far beyond our current purview, there exists a space with infinite outcomes and therefore infinite causal chains. Under this perspective, how often would our widely accepted causal narratives remain true?
Super Bowl LIV was a fantastic football game. The prolific Kansas City Chiefs offense matched up against the stout defense of the San Francisco 49ers, with many pundits predicting a 49ers victory. A 49ers victory seemed certain after the Chiefs offense turned the ball over with twelve minutes left in the fourth quarter, giving Jimmy Garropolo a chance to increase the 49ers 10-point lead. However, the great Mahomes had different plans. The Chiefs offense never looked back after retaking the field giving the Chiefs their first Super Bowl in 49 years.
This is the story of Super Bowl LIV as observed from our reality (purview). But in the realm of the infinite, the determinism we assign to rationalizing the end result is ill-advised. Many view the Chiefs victory as obvious. The narrative states that Mahomes’ comeback prowess, coupled with Garropolo’s ineffectiveness in crunch time, ensured a Chiefs victory. However, assigning this level of certainty to the outcome of Super Bowl LIV is extremely misguided.
Back to the point of this piece. Human sight is defined by a cone vision. This cone enables us to view things that occur within a certain area of a circle as pictured below:
Suppose we abstract our physical cone of vision to its probabilistic equivalent – probabilistic sight. When considering the picture above in terms of probabilistic sight, the white region represents the outcomes that we witness in our reality while the blue region represents those outcomes that we do not witness, but that exist in alternate realities.
Yet, using the two-dimensional images above fails to treat the incredible number of outcomes that exist in infinite realities with proper respect. Indeed, the two-dimensional circle represents a simple causal chain – X impacts Y –but the randomness in the relationship between these two variables generates infinitely many outcomes. In essence, the mechanism that generates the outcome in two-dimensional space is unknown, but it is known that one variable generates the outcome.
As the number of variables affecting our outcomes increases, so does the dimensionality of our infinite realities, causing our reality to comprise a far smaller share of our infinite space. Consider the diagram below, which is a three-dimensional image used to simplify an n-dimensional hyperplane:
Our reality is represented by the purple cube show above. As the number of possible realities increases, so does the size of the light blue cube. Consequently, as the volume of this larger cube increases (while the purple cube’s volume stays fixed) less significance should be assigned to deterministic interpretations of events that occur in our specific reality since it comprises a smaller share of the total number of realities.
This visualization attempts to communicate the idea that a probability is nothing more than one outcome’s proportion of the total number of outcomes. Hopefully, the discussion above makes the idea of probability feel more concrete, as it can be difficult to internalize such an abstract concept. To drive the point home, suppose an effective statistical model predicts that Team A will defeat Team B in a game of basketball 75% of the time. If I am asked, “what team will win the game?” I have several methods to use when crafting my response:
- Use my “understanding” of both teams to pick a winner (heuristic)
- Perform an analysis of each teams’ strengths and weaknesses to pick a winner (analysis)
- Abide by the statistical model’s prediction (probability)
Suppose I select method (1) under the assumption that Team B’s height will lead them to victory over Team A. In making my selection based on height differentials, I am implying that Team B will beat Team A in every matchup – the same logic applies if I select a different immutable heuristic to determine the winner. Such a methodology lacks intellectual honesty and respect for the variety of paths the game may take to reach its outcome because it implies a single variable (or a collection of them) has enough predictive power to anticipate the outcome with certainty. Similarly, using method (2) to select the team creates the same issue – while my analysis and rationale for selecting a winner may be more elaborate, I am implying that the team I select will win with certainty. Once again, this methodology ignores the randomness that exists in basketball games.
However, using method (3) to select a winner implies something entirely different. Under method (3), I should select Team A because they are most likely to win across all possible realities. Before the game is played, I am uncertain of which reality will become my reality. But I do know that, 75% of the time, Team A will be the victor of the reality I personally witness. To maximize the chances that I select the winner of the game correctly, I should select Team A, even though I must admit that I am not certain that Team A will win the game. Thus, selecting an outcome that is most likely to occur does not imply that it will occur with certainty. Rather, it simply maximizes the chances that you will correctly predict the outcome of the reality you witness, given that you cannot know the outcome before the game is played.
Making decisions based on probabilistic forecasts requires humility. Indeed, people who are equipped with the philosophy of probability never deal in absolutes because they have respect for the range of outcomes that can be generated across every possible reality. Such humility promotes intellectual honesty and skepticism, as these individuals do not accept narratives at face value. They accept that certain outcomes are the result of complex systems that may be impossible to fully understand. Consequently, they make decisions with respect to what is likely to happen, remaining skeptical of those who are certain of what will happen.
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