Math and Nature
My brother sent me a YouTube video titled “Is math discovered or invented?” and it inspired me to write another short piece here. It is a brilliantly animated TED.Ed talk by Jeff Dekofsky. You can watch it yourself, but in short it ponders the question of whether math is something discovered by humankind while observing nature or invented by humankind to describe nature. It ends with a good summary line:
“If there are a number of trees in a forest, but there’s no one there to count them, does that number exist?”
This got me thinking, and I wanted to explain how I see the role of mathematics in the natural world.
Math is a tool used to describe observations in the natural world. Scientists first observe something new in nature and say “Huh? What’s up with that?” Based on their observations, they make a guess at what type of mathematical expression might describe what they are seeing. Once an equation is formed to describe an observed phenomenon, scientists can adjust the input values to provide testable predictions outside of their initial observations. If the tests succeed, the equation gains more respect. If tests fail, the equation gets adjusted or rejected. This is nature of scientific progress. Math is a man-made structure that is used to approximate the forces of nature. It works very well, and has led us to a great understanding of the world we live in. Math keeps expanding as our understanding of nature expands.
To help drive this home, a good analogy might help.
Think of mathematics as a super-accurate scaffolding that perfectly aligns with a curve occurring in the natural world. The scaffolding itself is built very strictly using the rules of an equation. Scientists can walk along the scaffolding in any direction and measure to see if there are any tiny (or big) gaps between it and the natural curve. If gaps are found, the scientists tweak the equation to try to make it fit perfectly, or toss it out and start over with the newly gained test evidence. If they don’t find any gaps, then the equation can be considered an accurate representation of the curve — but the equation isn’t the curve itself. It is a tool used to predict the behavior of the natural curve.
Another interesting expansion on this analogy relates to the development of better and better test equipment as technology progresses. Imagine that the scaffolding mentioned above has some *really* tricky places to get to on it. We can’t check for gaps in those areas until we build a machine that can get us there to look. When better telescopes are designed, advancements and refinements are made to astrophysics. Very large and expensive instruments like the Large Hadron Collider allow for the field of particle physics to advance. Those machines allow the scientist to climb higher and access the trickier bits of the scaffolding to check if their equations match the curves of nature.
Scientists have been doing this for a very long time, and equations have come and gone and have been modified often. Mathematics is a tool used to quantify and describe the moving target of scientific understanding, and everything keeps changing all the time. The things that seem to not change are just things that we understand really well at this point.
