How is information inferred from mathematical formulas?
In: 43
Math is used to describe reality. F=ma as a simple example. The force an object applies is equal to its mass times the acceleration it is undergoing. What the specific numbers are is essentially arbitrary, but once we’ve all agreed on a standard they become meaningful as we can compare things against each other from the same frame of reference.
Imagine a large complicated equation as a jigsaw puzzle. Each variable is one of the pieces. If you understand the math sufficiently you can look at that equation and more or less “see” that jigsaw puzzle.
If you’re working in a theoretical field, like for instance particle physics, there’s a decent chance that your math is going to be incomplete. This variable doesn’t jive with that variable, there must be something else in between that’s causing them to behave a bit differently. If you’ve done your research properly you can predict the likely nature of that thing based on how it interacts with what’s around it. Like looking at an assembled jigsaw puzzle and seeing there’s a piece missing. Even if you’ve never seen that piece, if you can see where it has to fit in to the larger picture then you can probably describe it fairly accurately as long as you understand what’s depicted by the overall jigsaw puzzle.
Once you know the likely nature of the thing you may then be able to design an experiment to specifically look for it. This is essentially what happened with the Highs Boson a few years ago. Most scientists agreed that it was probably a particle that had to exist in order to fill a gap in their equations. A Higgs Boson shaped gap in the jigsaw puzzle so to speak. So based on its expected characteristics they then designed a particle accelerator experiment specifically intended to detect the expected shape of that puzzle piece. When they ran the experiment lo and behold they found the missing piece just as they expected it to be. If they had been wrong, then the data would have looked different and they would have had to try again, but in this case they were right.
The ability of a scientific theory to predict something before it is found is usually considered strong evidence of its validity. One good prediction doesn’t mean you’re done, in a lot of ways no science is ever truly “done”, but it does tell you you’re probably on the right track.
Latest Answers