Mathematics, whether a source of anxiety or passion for many, plays a crucial role in explaining and guiding a large portion of scientific activities. From medical experiments to the development of artificial intelligence, there is one mathematical principle that has dominated many fields of the modern world: Bayes’ Theorem.
Bayes’ Theorem, developed by Thomas Bayes – an amateur mathematician in the 18th century, has today become a cornerstone in many scientific disciplines. This simple formula allows us to predict and model various phenomena in life, from weather forecasting and stock markets to predicting the outcomes of sports events.
In the book “Everything is Predictable” by award-winning science writer Tom Chivers, Bayes’ Theorem is introduced as an indispensable tool for understanding and predicting the future. This book, with its lively and accessible writing style, has made it to the shortlist of the Royal Society Trivedi Science Book Prize 2024.
The future can be predicted, but to a certain extent.
Can you predict the future? The answer is yes, at least to a certain degree. For some phenomena in nature, we can make predictions with near-absolute accuracy. For instance, you can be sure that in a few seconds, you will inhale and exhale, your heart will beat, and the sun will rise tomorrow at a predetermined time.
Some predictions that are more quantitative, such as the time a train arrives at the station or whether your friend will arrive on time, depend on various factors like the quality of transportation services or your friend’s habits. Similarly, we can predict that the world population will increase until the mid-21st century and then gradually decrease, or that global temperatures in 2030 will be higher than in 1930.
Clearly, the future is not always murky and elusive. Some parts of it are easier to predict than others. Universal laws, such as the movement of planets according to Newton’s laws, can be predicted for thousands of years, while chaotic phenomena like the weather can only be forecasted for a few days. However, we can still look into the future, even if it is not entirely clear.
The future is not always murky and elusive. (Illustrative image).
When it comes to predicting the future, many people immediately think of the mystical or supernatural visions. In reality, humans always make predictions in their daily lives based on information and experiences accumulated from the past. For example, when you predict that the store near your house will have a certain cereal you need, you rely on your habits and experiences rather than on some supernatural intuition.
However, these predictions are not always accurate. The universe may be a completely predictable system if we had perfect information about every particle of matter, as posited by physicist Laplace. But in reality, we only have partial information and imperfect senses. Instead of seeing the entire universe, we can only observe small, inaccurate parts, from which we make predictions based on limited information.
Bayes’ Theorem allows us to update our beliefs about an event as new information becomes available. (Illustrative image).
Meanwhile, Bayes’ Theorem is a powerful tool in probability theory, allowing us to update our beliefs about an event as new information comes to light. Simply put, it helps us answer the question: “What is the probability of event A given that event B has occurred?” For example, in medicine, we can use Bayes’ Theorem to calculate the probability of a person having a disease based on test results; in finance, Bayes’ Theorem can be used to predict the likelihood of a stock price increase based on economic indicators and market news…
However, Bayes’ Theorem cannot predict the future with 100% accuracy. There are several reasons for this:
- Data: The quality and quantity of data used to calculate probabilities greatly influence the results. If the data is incomplete or inaccurate, the predicted outcome will be unreliable.
- Modeling: How we construct probability models also affects the outcomes. An overly simplified model may overlook important factors, while a model that is too complex may lead to overfitting.
- Random events: Many events in life are random and cannot be fully predicted.
Bayes’ Theorem is a powerful tool but not a magic wand. It provides a scientific approach to making decisions based on data, but we need to combine it with expertise and experience to make more accurate predictions. (Illustrative image).
In a world full of change and complexity, Bayes’ Theorem helps us make decisions and predictions with a relatively high degree of accuracy based on the information we have. Life is not like a chess game, where every move can be calculated precisely. Instead, it resembles a game of poker, where players must make decisions based on incomplete information and the changing environment.
Bayes’ Theorem is the equation that helps us cope with that uncertainty. With this theorem, we can calculate the likelihood of an event occurring based on prior information and new data. It is an essential tool in various fields, from healthcare to economics and even artificial intelligence.
