The Einstein black hole equation got me thinking. In a universe where so many things seem random, unexplained, and misunderstood, how can numbers on a paper explain and predict how the universe works?
It blows my mind that this concept (math) is so young relative to the universe and can be used to explain how and why things happen. Where’s the connection?
In: Mathematics
Math was made specifically to judge and explain things.
Imagine distance units, say a foot or meter. The distance itself is arbitrary, someone likely just picked it at random one day. But using that measurement, you can measure the distance between two objects.
Thats all that math is. It was made to explain and predict the world around us, because for 99% of things, everything is predetermined. Time and gravity is constant so we can predict nearly everything else.
A more poetic answer; math mimics the shape of reality like a portrait reveals the form of a person- never encompassing the whole but useful in understanding some.
The short answer is because both Math and our universe obey a set of rules and we can take set the rules of one (math) to approximate the rules of the other (the universe).
Let’s say you work for Ferrari and are tasked with designing a new race car. You have lots of ideas on how to make your car more aerodynamic. But building a whole new car is expensive, and you don’t actually NEED the car to be complete in order to test your aerodynamic designs. For example it doesn’t need a working radio. Or seat belts. Because all that matters is the outside shape of the car. So you build models. As long as those models have the same shape as your goal car you can use them in place of the real thing.
The universe as we know it appears to obey some fundamental rules. Things like the law of gravity, or the law of inertia.
We can use math to make models that give the same results as observing the real universe, or at least close enough to it.
For example, if you want to know where in space the Earth will be in six months you can use a model to figure that out. We know how two objects with a lot of gravity interact so we apply the math using the data we have gathered over the years to build a model of how Earth will move through space.
In reality every object affects every other objects gravity. Your pencil and keyboard are interacting due to gravity. My phone and your phone are interacting due to gravity. And all that junk is pulling on the Earth too.
If that’s the case how can we model what will happen. We cant possibly calculate the effect of gravity from each pair of objects ranging from the sun all the way to a tiny grain of sand on a beach. But we don’t have to. The effects from the sun alone are so much stronger than say, your toothbrush, that we can basically ignore most other things and the models result will be so close to the actual result that any small difference doesn’t matter.
So as long as we have the right information we can use math to model the behavior of various things in the universe, even when we don’t know all the details or can’t measure every little point.
Because in the end it’s all just sets of rules.
Smarter minds than us are still arguing about that (and likely will be for the forseeable future). It’s not obvious why it should be the case, and that’s led more than one respected physicist to entertain the notion that, at heart, the universe IS mathematics, simply because it seems mind-blowing just how well mathematics describes it. There’s even a “Theory Of Everything” candidate along those lines ([Tegmark’s Mathermatical Universe Hypothesis](https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis)).
There are actually physical concepts that have no mathematical backing as of yet but are used because they just work and their results coincide with the rest of the theory. Such as some integrals in QFT where we don’t even know if they exist.
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