The Nature of Numbers
Updated: Aug 31, 2022
Initially published in the Raleigh NEWS & OBSERVER on 23 March 2016 “Mathematics is the language by which God has written the universe,” said Galileo. This metaphorical language of Galileo suggests that from the sub-atomic level of particle physics to cosmology, nature is inherently mathematical.
Mathematics is not just more of the arithmetic we were taught in grade school, as many sadly and mistakenly imagine. Mathematics deals with ideas, concepts, fundamental physical constants and properties of our universe, and is true whether you “believe in it,” or whether or not you are “comfortable with it.”
For example: if you toss up something into the air, its trajectory will always takes the shape of an upside down parabola. The St. Louis Gateway Arch looks like an upside down parabola, but mathematically, it is a catenary. The parabola is expressed by the simple equation y=x^2. The “y” expresses the upward, vertical position and the “x” expresses the horizontal position. These values vary by the initial speed and direction of the toss, but the trajectory shape will always be a parabola.
The elegant equation e=mc^2 expresses the concept that mass and energy are equal and convertible. For example, if we get a particle going really fast – approaching the speed of light – like they do at the CERN Large Hadron Collider, where recently the Higgs particle was experimentally discovered (4 July 2012), then the mass of that particle will become energy.
Humans have invented symbols and units by which to count, and to describe fundamental physical constants and properties. Centimeters, miles, seconds, pounds and volts are all human units of measurement.
Your weight – and you really mean to say your mass – as measured in pounds or kilograms, is not a fundamental property of our universe. It will vary from day to day and varies depending whether you’re on Earth or the moon which is 1/6 of the Earth’s gravity, or on Mars which is 1/3 gravity. If you really want to “lose weight,” than you should go to Mars where a 180 kg person will weigh 60 kg.
If you want to communicate your weight in a more useful fashion you should express it in GeV – gigaelectron volts. And by the mass=energy equivalence you can do that. Yes, GeV is another human unit of measurement. But at least it’s tied to a fundamental property of the universe; therefore someone from another galaxy might understand it because one GeV is the mass of a proton (proton mass is actually 0.938 GeV) and the mass of a proton is the same wherever you are at in our universe.
Another human measurement is the light-year, which is the distance that light travels in one year (about 5.88 trillion miles) at its constant rate of 186,000 miles per second. A light year is a measure of distance, not a measure of time as I’ve heard it erroneously implied by some, including by newscasters.
I’m not sure intelligent beings from another galaxy would understand miles per second; but they would know the speed of light, (as expressed in their language) because it is constant whether you’re on Earth or Alpha Centauri. Light from our Sun takes eight minutes to reach us. We have observed light from galaxies so distant it has taken billions of years to reach us.
A telescope is a time machine. Furthermore it has been conjectured that numbers are basic properties of our natural world. An example is 3 – the number of dimensions in our particular universe. Why are there three dimensions instead of four or more? And from particle (sub-atomic) physics, why are there 6 kinds of quarks?
Nature is full of pure numbers, imaginary numbers, irrational numbers, dimensionless numbers and transcendental numbers – and they are all every bit as intriguing as their names suggest. A pure number expresses a concept involving no human units of measurement. Examples are pi, e, and the golden ratio. These are purely mathematical constants, and using a computer can be calculated out to many decimal places. Other mathematical constants are determined only experimentally. Perhaps pi is the best known example of a pure and transcendental number. Pi is the 16th letter of the Greek alphabet. The symbol pi represents the universal physical property that the circumference of a circle (or sphere) divided by its diameter equals an irrational number approximately equal to 3.14… .
An irrational number is not a number that’s crazy; it’s a number that cannot be expressed as a ratio. Another irrational number is the square root of 2. That c/d equals pi, is true for golf balls, bowling balls, tires and the Earth. This basic property of our universe is true on Earth or at the Andromeda Galaxy.
To ponder that our universe is inherently mathematical is to me exhilarating and the noblest intellectual inquiry of all.