Chapter 1: Understanding Randomness

What does randomness truly mean? A random occurrence is one that cannot be anticipated. While computers are capable of generating pseudo-random sequences, if one is aware of the algorithm and has access to preceding numbers in the sequence, predicting the next number becomes feasible. This does not equate to genuine randomness. Authentic random events are those that are completely unforeseeable—phenomena that are beyond human prediction.

The inquiry into whether such fundamentally unpredictable events exist in our universe quickly leads us into profound territory. It touches on some of the most mysterious and essential principles across physics, mathematics, computation, sociology, and theology. Collectively, these principles outline the boundaries of what we can truly comprehend. This is not merely about the current limits of our knowledge that may expand with further discoveries, but rather the absolute confines of science and reason, beyond which we can never proceed, regardless of our ingenuity.

For many years, I have been captivated by a collection of theorems that appear to delineate this boundary. These include:

• Heisenberg’s Uncertainty Principle (Physics): There is a ceiling to how precisely we can gauge the characteristics of physical entities.
• Bell’s Inequality (Physics): This ceiling not only restricts our measurement abilities but also our fundamental understanding of physical objects.
• Gödel’s Incompleteness Theorems (Mathematics): Any attempt to encapsulate everything using a limited set of axioms will ultimately be either incomplete or incorrect.
• Turing’s Undecidability (Computing): There are countless problems that no computer, including the human mind, can resolve.
• Chaitin’s Irreducibility (Computing & Mathematics): Almost every number (with a probability of 1) is indescribable; in essence, the most concise representation of the number is the number itself.
• Arrow’s Impossibility Theorem (Sociology): In any reasonable ranked voting system, it is impossible to amalgamate individual voter preferences into a collective ranking that reflects consensus.

There’s much more to explore regarding each of these meta-theorems. Notice that each of these theorems ends with a negative assertion. They reveal the limitations of what we cannot achieve, where we cannot tread, and what we cannot know under any circumstances. They demonstrate, through the frameworks of mathematics and science, the definitive boundaries of these fields.

Intuition leads us to believe that these six meta-theorems, despite their distinct domains, are interconnected. They seem to arise from the same fundamental phenomenon:

Fundamental randomness is a reality. It is not merely an insignificant blemish on our logical landscape, but rather an unfathomable sea that envelops it. We will never fully understand what exists within this vast ocean of randomness. Instead, we can only catch fleeting glimpses of the contours of our small island of reason, as the theorems and principles mentioned above begin to shed light on our understanding.

Explore the concept of randomness and its implications in this insightful video.

Chapter 2: The Implications of Randomness

Delve into the significance of randomness in various fields, as illustrated in this engaging presentation.

To continue delving deeper into The Divine Random, click on any of the links below:

• Is the Universe There When Nobody’s Looking?

  Objective reality may not exist

• Dethroning the Queen of Sciences

  Why mathematics is not enough

• Ciphers and Superheroes

  How Alan Turing saved the world and doomed computer science

• Everyone Agrees, Except That Guy

  Why randomness is important in Computer Science

• Democracy is a Game of Chance

  Voting is necessary, but is it sufficient?

• Omega Numbers

  The harder we stare, the less we see

• The Wittlest Wobots

  Nanobots within us

• If You Believe in Magic

  With apologies to The Lovin’ Spoonful

• The Chaos Connection

  A bridge from the unknowable

• God Rocks

  The omnipotence paradox in theology

Jim Dutton © 2021