Why Study Uncertainty?

Uncertainty pervades virtually every aspect of our daily lives. In the evolving landscape of the global economy, which increasingly resembles a middleman-driven, asset-management paradigm, a substantial portion of the existing edge collection is now underpinned by leveraging uncertainty, transforming it into a foundation for profit-driven risk. This is essentially what market makers do on a fundamental level, but here are nine ways in which uncertainty interacts with us on the day-to-day:

  1. Clarification of Categorization: For example, a friend may make an assertion that it will rain tomorrow, what what exactly is meant by “rain”; does it need to reach any sort of level in a rain gauge in order to count? Is tomorrow twenty-four hours from the time of the statement or is it midnight to midnight?
  2. Uncertainty in the Immediate: For many questions on a given Trivia Night, one can simply search for the information and find the answer. If there is a geography-related question, you can certainly get the right answer by simply flying over to the location with a band of tour guides, but that will simply not do at the Factory 380 Trivia Night.
  3. Past Occurrence: In the court of law, “guilt” can have two meanings, not mutually exclusive from one another. Guilt can be the certainty of what happens, as well as pleading guilty to the judgement of the court.
  4. Scientific Hypothesis: Does reading Recruiting From Lexington make you smarter? Probably not, actually.
  5. Games of Chance: Poker. (Shoutout Allen Weng)
  6. Performance Bets: When betting in horse-racing, uncertainty is recognized, celebrated, and exploited by those with (relatively accessible) knowledge on each horse.
    1. Performance Bets with Incomplete Information: You never know what’s fully (or even close to mostly) going on in the stock market, and it’s quite near impossible to.
  7. Situational Shifts Between Prediction and Execution: Some can make predictions such as, “If an election is held tomorrow, 56% would vote [political party of your choosing].” However, what if the political party unanimously decides to shoot fireworks at the elderly tonight?
  8. Recommendations of Subjective Value: Health recommendations.
  9. Uncertain Certainties: Let’s say all your life, you’ve written that you were born in 2001 in every single form, and have had no reason to consider otherwise, as it’s what you’ve always heard. Have you ever seen your birth certificate? Many have not, and there have been instances where they have been off by months to years.

Counting

Before we get started on probability, we must learn how to count.

Understanding how to count is fundamental to studying probability because probability, at its core, is about measuring the likelihood of various outcomes within a set of all possible outcomes. Even when it gets complex, ultimately, probability is by definition a ratio. Counting plays a crucial role in identifying both the number of outcomes of interest (favorable outcomes) and the total number of possible outcomes, which are essential components for calculating probabilities.

Furthermore, it introduces us to the concept of a sample space, the set of all possible outcomes of a probabilistic experiment.

Ordered Sets With Repetition

Ordered sets with repetition are identical processes/trials where order doesn’t matter; imagine dice rolls and coin flips.