Excerpted with permission from Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, by Max Tegmark. Available from Random House/Knopf. Copyright © 2014.
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.
Math, math everywhere!
But where's all this math that we're going on about? Isn't math all about numbers? If you look around right now, you can probably spot a few numbers here and there, for example the page numbers in your latest copy of Scientific American, but these are just symbols invented and printed by people, so they can hardly be said to reflect our Universe being mathematical in any deep way.
But where's all this math that we're going on about? Isn't math all about numbers? If you look around right now, you can probably spot a few numbers here and there, for example the page numbers in your latest copy of Scientific American, but these are just symbols invented and printed by people, so they can hardly be said to reflect our Universe being mathematical in any deep way.
Because of our education system, many people equate mathematics with arithmetic. Yet mathematicians study abstract structures far more diverse than numbers, including geometric shapes. Do you see any geometric patterns or shapes around you? Here again, human-made designs like the rectangular shape of this book don't count. But try throwing a pebble and watch the beautiful shape that nature makes for its trajectory! The trajectories of anything you throw have the same shape, called an upside-down parabola. When we observe how things move around in orbits in space, we discover another recurring shape: the ellipse. Moreover, these two shapes are related: the tip of a very elongated ellipse is shaped almost exactly like a parabola, so in fact, all of these trajectories are simply parts of ellipses.
We humans have gradually discovered many additional recurring shapes and patterns in nature, involving not only motion and gravity, but also areas as disparate as electricity, magnetism, light, heat, chemistry, radioactivity, and subatomic particles. These patterns are summarized by what we call our laws of physics. Just as the shape of an ellipse, all these laws can be described using mathematical equations.
Equations aren't the only hints of mathematics that are built into nature: there are also numbers.
As opposed to human creations like the page numbers in this book, I'm now talking about numbers that are basic properties of our physical reality. For example, how many pencils can you arrange so that they're all perpendicular (at 90 degrees) to each other? 3 – by placing them along the 3 edges emanating from a corner of your room, say. Where did that number 3 come sailing in from? We call this number the dimensionality of our space, but why are there 3 dimensions rather than 4 or 2 or 42? And why are there, as far as we can tell, exactly 6 kinds of quarks in our Universe? There are also numbers encoded in nature that require decimals to write out – for example, the proton about 1836.15267 times heavier than the electron. From just 32 such numbers, we physicists can in principle compute every other physical constant ever measured.
As opposed to human creations like the page numbers in this book, I'm now talking about numbers that are basic properties of our physical reality. For example, how many pencils can you arrange so that they're all perpendicular (at 90 degrees) to each other? 3 – by placing them along the 3 edges emanating from a corner of your room, say. Where did that number 3 come sailing in from? We call this number the dimensionality of our space, but why are there 3 dimensions rather than 4 or 2 or 42? And why are there, as far as we can tell, exactly 6 kinds of quarks in our Universe? There are also numbers encoded in nature that require decimals to write out – for example, the proton about 1836.15267 times heavier than the electron. From just 32 such numbers, we physicists can in principle compute every other physical constant ever measured.
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