The Lesser Known Revolutions that Created the Modern World
The industrial world was built by practical men, those hearty souls who rolled up their sleeves and got things done. They were men of action, unhindered by the softheaded notions of ivory towers.
Today, however, we no longer live in an industrial world of railroads, furnaces and factories, but one of the visceral abstract, where the common devices that dominate our everyday lives are based on principles that the proverbial “man on the street” would find totally impractical, absolutely nutty.
Every time you use a computer or smartphone, drive a car, use a navigation system or shop at Wal-mart, you are in a very real sense, believing in ideas that defy common sense. These notions were often ridiculed because they defied common experience. In that sense, they were revolutions no less heroic than the physical kind. Here are four:
1. The Inductive Revolution
The concept that every effect has a cause is so obvious and basic that it has been a core axiom that, since ancient times, informed everything from Medieval scholasticism to Descartes’ ontological argument. Eventually, Newton’s laws of motion formalized the concept into one simple equation:
F = ma
The idea that you could calculate force as a specific quantity rather than as an abstract concept underlies much of how we engineered machines for centuries and, indeed, still holds sway today. You can’t build a modern bridge or a skyscraper without it.
However, the fact that every effect has a cause is significantly different than determining what that cause is and by the late 18th century David Hume was beginning to have doubts, which led him to an extreme form of skepticism. He wrote:
That the sun will not rise to-morrow is no less intelligible a proposition, and implies no more contradiction than the affirmation, that it will rise. We should in vain, therefore, attempt to demonstrate its falsehood.
It was an extremely impractical idea. One that a particularly dreamy patent clerk became quite taken with as he stared out his window at a train station with a clock placed in front. He began to wonder how the clock would record time on a train that was moving very, very fast and realized that Newton hadn’t gotten it quite right.
Time and space, he surmised, were relative, not absolute. Then the young man, whom we would come to know as Albert Einstein, expanded the idea a little further to make the general proposition that mass and energy were equivalent and summarized it into a formula almost as simple as Newton’s:
The world was never quite the same.
2. The Geometric Revolution
Geometry is not just something we learn in school, but is intrinsic to our physical world: The basic shapes which we use to build things, lines that connect dots and so on. These ideas have been around for thousands of years and are known as Euclidean geometry.
One of the basic assumptions of Euclidean geometry is that two parallel lines never intersect. However, in the 19th century, men like Gauss, Lobachevsky, Bolyai and Riemann started to think otherwise (e.g. try to draw straight parallel lines around a globe) and they built new forms of non-Euclidean geometry based on curved spaces.
This was, of course, of no practical significance whatsoever, except to entertain a bunch of eggheaded mathematicians. For carpenters, blacksmiths or anybody who wanted to build things, straight lines and ordinary shapes were what mattered.
Well… at least until Einstein theorized that the universe itself was made up of curved spaces created by the gravitational force of massive objects. Now, a lot of the stuff we use is not built in Euclidean space, but in the quantum realm of electrons and very little of it would work if we did not understand the geometry of curved spaces.
3. The Emergent Complexity Revolution
It has long been taken on faith that something significant complex, like a watch for example, requires someone to design it. Then Darwin came along and showed a simple algorithmic process that could create the complexity of life. It was a fairly useless discovery at the time, resulting in debates about evolution more than anything else.
However, the idea of emergence got a boost in the 20th century when Benoit Mandelbrot noticed that simple algorithmic functions could be used to describe a wide variety of incredibly complex phenomena, from word distributions in texts to the flooding of the Nile river to financial markets.
He called the concept fractal geometry and displayed the concept dramatically with his famous equation:
zn+1 = zn2 + c
That simple formula, when graphed, results in the famous Mandelbrot set, an object of almost infinite complexity:
Since then, the idea of emergence has been applied to artificial intelligence methods such as genetic and swarm intelligence algorithms that underlie everything from ordering a flight online to getting a box of cereal to the shelf at Wal-Mart.
4. The Logical Revolution
Probably no concept is more central to common sense than logic, the idea that given a concrete set of inputs, you will get a determinate set of outputs. In other words, given a distinct set of facts, we can decide whether a conclusion is true or not.
That simple notion was blown to bits in 1931 Kurt Gödel and his incompleteness theorems, which showed conclusively that every system will eventually result in a statement that is both true and not true by the rules of the system. Logic, as an absolute concept, was dead. There was no fixing the system because systems themselves are inherently broken.
That led to Alan Turing writing his 1936 paper on computability, which showed that some numbers are not computable. However, it also demonstrated that it was possible to create a universal machine that could “compute any computable sequence,” a concept that led to modern day computers.
Strangely enough, when Gödel and Turing set out to prove the impossible, they paved the way for the rest of us to work within the limits of possibility.
The Visceral Abstract
G. H. Hardy, the great numbers theorist, remarked in his memoirs that he had “never done anything useful.” So why do it? He continued:
The case for my life, then, or for that of anyone else who has been a mathematician in the same sense in which I have been one, in this: I have added something to knowledge and helped others to add more.
Much like Hardy, the ideas of Darwin, Einstein, Gödel and others were utterly useless at the time, of no value whatsoever to practical men immersed in the affairs of everyday life. Their accomplishments were pursued for little reason other than to “add something to knowledge” and they all seemed and, in fact, still seem, a little bit nutty.
However, today we live in the world in the visceral abstract, where these ideas matter. In fact, they are central to our everyday existence.
Even as we do something as simple as make a call from the grocery store, the electrons move through our smartphones in curved space, the location system accounts for the difference in time and space relative to a GPS satellite and the call might be dropped due to an incomputable number. The products themselves arrive at the shelves by way of a genetic algorithm.
It is a curious fact of modern life that we go nonchalantly through our days with the wonders of the universe quite literally at our fingertips, thanks in no small part to the musings of utterly impractical men.