The 13 Most Important Numbers in the Universe
Some numbers, such as your phone number or your Social Security number, are decidedly more important than others. But the numbers on this list are of cosmic importance: they are the fundamental concepts that define our universe, that make the existence of life possible and that will decide the ultimate fate of the universe. Here they are, in the order in which science first became aware of them.
1. The Universal Gravitational Constant
Maybe 2013 hasn’t been such a great year, but 1665 was a whole lot worse - especially if you happened to live in London. That was the year of the last great outbreak of bubonic plague, and even though Londoners didn’t know a whole about medicine, they knew that it was a good idea to get out of town. The court of King Charles II departed London for Oxfordshire, and Cambridge University shut down. One of its undergraduates, Isaac Newton, went back home to Woolsthorpe, where he spent the next eighteen months opening the door to the modern world.
We live in a technological era that would be impossible without the ability to make quantitative predictions. And the first great example of quantitative prediction was to be found in Newton’s theory of universal gravitation. Starting from the hypothesis that the gravitational attraction between two masses is directly proportional to the product of the masses and inversely proportional to the square of the distance between them, Newton figured out that the orbit of a planet was an ellipse with the sun at one of the foci. Johannes Kepler had reached this conclusion from years of painstaking observations, but Newton was able to do so with no more than the assumption of gravitational attraction and the mathematical tool of calculus (which he had invented for this purpose).
The invention of the cannon during the Middle Ages showed that the speed of sound was finite; you could see a cannon fire long before you heard the sound of the explosion. Shortly thereafter, several scientists, including the great Galileo, realized that the speed of light was finite as well. Galileo devised an experiment that might well have proved this, involving telescopes and men pointing lights at each other over a great distance. But the extreme rapidity of the speed of light, combined with the technological limitations of the 1600s, made this experiment unworkable.
By the end of the nineteenth century, technology had advanced so far that it was possible to measure the speed of light within 0.02 percent of its actual value. This enabled Albert Michelson and Edward Morley to demonstrate that the speed of light was independent of direction. This startling result led eventually to Einstein’s theory of relativity, the iconic intellectual achievement of the 20th century and perhaps of all time.
3. The Ideal Gas Constant
In the 17th century, scientists understood three phases of matter - solids, liquids and gases (the discovery of plasma, the fourth phase of matter, lay centuries in the future). Back then, solids and liquids were much harder to work with than gases because changes in solids and liquids were difficult to measure with the equipment of the time.
Robert Boyle was perhaps the first great experimentalist, and was responsible for what we now consider to be the essence of experimentation: vary one or more parameter, and see how other parameters change in response. Boyle discovered the relationship between the pressure and volume of a gas, and a century later, the French scientists Jacques Charles and Joseph Gay-Lussac discovered the relationship between volume and temperature. To obtain the required data, Gay-Lussac took a hot-air balloon to an altitude of 23,000 feet, possibly a world record at the time. The results of Boyle, Charles and Gay-Lussac could be combined to show that in a fixed quantity of a gas, temperature was proportional to the product of pressure and volume. The constant of proportionality is known as the ideal gas constant.
It’s easy to make heat. Humans have been able to capture or create fire since prehistoric times. Producing cold is a much more difficult task. The universe as a whole has done a very good job of it, as the average temperature of the universe is only a few degrees above absolute zero. And it has done so the way that we do it in our refrigerators: through the expansion of gas.
Michael Faraday, who is far better known for his contributions to the study of electricity, was the first to suggest the possibility of producing colder temperatures by harnessing the expansion of a gas. Faraday had produced some liquid chlorine in a sealed tube, and when he broke the tube (and thereby lowered the pressure), the chlorine instantly transformed into a gas. Faraday noted that if lowering the pressure could transform a liquid into a gas, then perhaps applying pressure to a gas could transform it into a liquid - with a colder temperature. That’s basically what happens in your refrigerator; gas is pressurized and allowed to expand, which cools the surrounding material.
Pressurization enabled scientists to liquefy oxygen, hydrogen and, by the beginning of the 20th century, helium. That brought us to within a few degrees of absolute zero. But heat is also motion, and a technique of slowing down atoms by using lasers has enabled us to come within millionths of a degree of absolute zero, which we now know to be slightly more than -459 degrees Fahrenheit. Absolute zero falls in the same category as the speed of light. Material objects can get ever so close, but they can never reach it.
