Mathematical Universe

Mathematical Universe

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Mathematical Mystic The Role of Mathematics in Science aims to illustrate the many ways in which mathematical methods have helped discovery in science. It is aimed at a group of readers who are interested in mathematics beyond the level of high school. The authors occasionally use some calculus and more intricate arguments. The book should appeal to college students and general readers with some background in mathematics. The authors state that, ``If we succeed in giving an impression of the beauty and power of mathematical reasoning in science, the purpose of our work will have been achieved.'' What's the answer to the ultimate question of life, the universe, and everything? In Douglas Adams' science-fiction spoof “The Hitchhiker's Guide to the Galaxy”, the answer was found to be 42; the hardest part turned out to be finding the real question. I find it very appropriate that Douglas Adams joked about 42, because mathematics has played a striking role in our growing understanding of our Universe. The Higgs Boson was predicted with the same tool as the planet Neptune and the radio wave: with mathematics. Galileo famously stated that our Universe is a “grand book” written in the language of mathematics. So why does our universe seem so mathematical, and what does it mean? In my new book “Our Mathematical Universe”, I argue that it means that our universe isn’t just described by math, but that it is math in the sense that we’re all parts of a giant mathematical object, which in turn is part of a multiverse so huge that it makes the other multiverses debated in recent years seem puny in comparison. The mathematical universe hypothesis I was quite fascinated by all these mathematical clues back in grad school. One Berkeley evening in 1990, while my friend Bill Poirier and I were sitting around speculating about the ultimate nature of reality, I suddenly had an idea for what it all meant: that our reality isn't just described by mathematics – it is mathematics, in a very specific sense. Not just aspects of it, but all of it, including you. My starting assumption, the external reality hypothesis, states that there exists an external physical reality completely independent of us humans. When we derive the consequences of a theory, we introduce new concepts and words for them, such as “protons”, “atoms”, “molecules”, “cells” and “stars”, because they're convenient. It's important to remember, however, that it's we humans who create these concepts; in principle, everything could be calculated without this baggage. But if we assume that reality exists independently of humans, then for a description to be complete, it must also be well-defined according to non-human entities – aliens or supercomputers, say – that lack any understanding of human concepts. That brings us to the Mathematical Universe Hypothesis, which states that our external physical reality is a mathematical structure. For example, suppose a basketball trajectory is that of a beautiful buzzer-beater that wins you the game, and that you later want to describe what it looked like to a friend. Since the ball is made of elementary particles (quarks and electrons), you could in principle describe its motion without making any reference to basketballs: