I recently finished reading Max Tegmark’s book Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, and I found it to be a truly amazing and transformative experience. This book, along with Complexity: A Guided Tour by Melanie Mitchell, which I read several years ago, has had a significant impact on my understanding of the world and my intellectual journey.
Our Mathematical Universe has provided clarity for several of the big questions that have been troubling me since grad school. I had expressed to my advisor, Josh, that my interests felt too broad—I wanted to understand intelligence, life, and reality, as well as build artificial versions of each to learn from the process. This book has helped to clear up much of my confusion and guide me in my pursuit of these answers.
Tegmark’s book starts by exploring reality from various angles.
First, the book takes a cosmological perspective, delving into the history of our universe. It explains how physicists have been able to extrapolate the 14-billion-year history of our observable universe, leading to the conclusion that the universe began with the Big Bang. Years ago, I was skeptical about the Big Bang theory because it seemed like an extreme extrapolation that went too far. However, the book provides a wealth of evidence to support this theory, specifically, our observable universe seems to be quite flat in spacetime, and I now find the extrapolation quite convincing.
The book also introduces the inflation theory, developed in 1979, as a potential explanation for the cause of the Big Bang. According to this theory, the universe underwent rapid expansion due to the doubling of matter in every dimension. This idea is compatible with general relativity and has gained acceptance among many physicists. I personally find this theory satisfying and see it as a potential starting point for further exploration if I want to delve into cosmology.
Next, Tegmark delves into the microscopic world, discussing the debate between Einstein and Bohr over the nature of quantum mechanics. When I first learned this debate years ago, I had initially sided with Einstein, believing that there must be some mechanisms behind the apparent randomness of quantum mechanics–“God does not play dice with the universe”. The book introduces Everett’s Many Worlds interpretation, first proposed in 1957, which posits that the wavefunction never collapses and that parallel universes exist. I find this idea intriguing and think that Einstein might have appreciated it as well. In comparison, the widely accepted Copenhagen interpretation, dating back to the 1920s, seems more like a higher-level model of reality—useful, but not the ultimate.
Additionally, the book covers the concept of decoherence, which explains why we don’t observe quantum superposition on a macroscopic scale. This idea was first introduced in 1970 by H. Dieter Zeh, but Tegmark also discovered this independently. Decoherence is now well-accepted in the field and could serve as a starting point for further investigation if I want to delve into the microscopic realm.
Tegmark takes a step back and discusses three different types of reality: internal, external, and consensus reality. Internal reality is what we perceive and the world model created in our brain, akin to Anil Seth’s “controlled hallucination”, while external reality is the ultimate, objective, independent reality. Consensus reality lies somewhere in between, as it is the shared understanding of reality among people. The idea of consensus reality particularly resonates with me, as it seems to be the most important reality for ordinary people. For example, a wall is a wall not because it exists independently from human observers, but because most people agree that it is a wall. However, at a more fundamental level, we know that it is just a collection of protons, neutrons, and electrons.
The book proposes that the ultimate external reality is a mathematical object, which is an intriguing but speculative idea. While I am open to the possibility, I would like to see more evidence before fully accepting it.
In discussing the mathematical nature of reality, Tegmark emphasizes the distinction between mathematical structures and their descriptions. For example, the ideas of addition and multiplication are the structures, and we can describe them using either natural language, like ancient Greeks did, or using equations, like modern students do. The description can vary from culture to culture, but the mathematical structure doesn’t change. He also explores the fundamental properties of mathematical structures, such as symmetry and relation. Regardless of whether mathematics is the ultimate reality or merely describes the reality, his elaboration deepens my understanding of mathematics.
Finally, the book touches on fascinating topics inside the reality, like the nature of life and consciousness. Tegmark suggests that life is not a binary category but a spectrum defined by complexity. Similarly, he proposes that consciousness arises from the brain’s computational processes as a byproduct of understanding the self and the world.
While I have chosen to disregard some of the more speculative ideas in the book, the concepts that resonated with me have significantly influenced my understanding of the world. I feel incredibly fortunate to have encountered so many valuable ideas in one book. As I continue my intellectual journey, I eagerly anticipate reading more works by Max Tegmark and others who delve into these fascinating subjects.
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