Galileo wrote that philosophy is written in the language of mathematics.
We don't know who started applying mathematics to scientific study, but it is possible that the Babylonians discovered the underlying pattern of eclipses nearly 3000 years ago. It took 2,500 years for the invention ofNewtonian physics to explain the patterns.
Since then, most major scientific discoveries have used mathematics in some form because it is more powerful than any other human language. Many people claim that the universe is created by a mathematician and that mathematics is more than that.
Is it possible to imagine a universe in which mathematics doesn't work?
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The Pythagorean theorem was invented in ancient Greece.
The hypothesis says that you can't discuss a concept unless you have the language to describe it.
We need to describe concepts that don't work in a human language. One can describe an electron, but when we start asking questions like "What color is it?", we realize the weakness of English.
An electron has no color, or more accurately, all colors, because the color of an object depends on the wavelength of light reflected by it. The question is meaningless. The answer is, in principle, simple. The behavior of an electron is described in an equation written by Paul A.M. Dirac. When we look at the details, it isn't simple.
An electron is a tiny magnet. The calculation of the magnitude is very difficult. Explaining an Aurora requires us to understand magnetic fields and atomic physics, but at the end of the day, they are just more mathematics.
When we think of the individual, we realize that a human commitment to logical, mathematical thinking goes much deeper. The decision to overtake a car does not involve the integration of the equations of motion, but we do it. A car on autopilot will solve them.
We should not be surprised that mathematics is the only language for describing the external world. It doesn't mean that something can be predicted.
The discovery of chaotic systems has been one of the most remarkable discoveries of the last 50 years. Many systems are chaotic. We can't predict hurricanes in the Caribbean with all the power of modern computers.
The equations that describe weather are chaotic so we can make accurate predictions in the short term, but they become unreliable over time. We know what predictions cannot be made precisely thanks to quantum mechanics. One can calculate the properties of an electron, but we can't predict what one will do.
We can't predict when a hurricanes will happen. The fact that we can't predict an event doesn't mean we can't describe it. It is generally accepted that the universe was created in the Big Bang and we have a remarkably precise theory of that.
A lot of social phenomena, from the stock market to revolutions, lack good predictive mathematics.
How about personal relationships? Love is blind, but relationships are predictable. The vast majority of us choose partners inside our social class and linguistic group, so there is absolutely no doubt that is true in the statistical sense. It is also true in the local area. A host of dating sites make their money by using software that makes them look like they're trying to match you to your ideal mate.
A universe that could not be described in a mathematical way would need to be irrational. Even if a theory is implausible, we can still describe it.
I don't think we live in that universe, and I think we can't imagine a non-mathematical universe.
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