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Nature Doesn't Do Math

Math is a tool that humans have invented and use to model natural occurrences. Don't be confused between the model that depends on math, and what nature does, which never needs to do any math. Nature just does what it does, because it could not do anything else, but it never needs to use math to do it.

Models Are Descriptive​

When we learn physics, we learn equations that describe the motion of things around us. We learn the theory of how things interact, and from that we can predict some thing about the future, like where a thrown ball will land.

It is important to remember that these equations are descriptive: they describe the patterns in nature, but nature does not actually do the math. Things in nature just happen because there is no other way for them to happen. At the micro level these interactions are simple, but when large numbers of them exist together the interactions for a complex system from which emerge new patterns distinct from the underlying behavior.

The emergent behavior is then subject to more mathematical modeling. For example both temperature and pressure are emergent phenomena, and the perfect gas law relates temperature and pressure of gaseous matter in a confined volume. Animal populations are modeled with some kind of population dynamics. All of these models use math of different flavors.

Examples​

Here are a couple of examples that illustrate

  • A planet forms to be very close to spherical, not because it does any geometry. The particles simply attract each other with gravity, and they slosh around until the sphere results because that is the lowest energy arrangement.
  • Soap bubbles form spheres for a similar reason: the molecules in the surface of the bubble are pulling together, and a sphere just happens to be the shape that represents the most amount of pulling can happen. Nature does not calculate the surface area of the sphere, nor does it try to minimize the surface area.
  • When you push an object of certain mass with a specific force, you can calculate the expected acceleration. This is not because nature measures the force, mass, and then calculates the acceleration. Instead, things just interact and move as the only way they can. The equation (F = ma) is a model of that movement, but nature is not aware of the model and does not do any calculations.
  • Gravity falls off as inverse-square not because nature calculates how much pull the sun should give the earth, but because the likelihood of gravitons interacting with matter falls as square of distance. (Think of the likelihood of interacting as the surface of a sphere a distance away, where each area of the surface has equal likelihood, while the surface increases as the square of the distance.) Gravity decreases with distance simply because there are fewer interactions.
  • The ideal gas law describes how pressure and temperature are related in a closed volume. As you squeeze the volume down, both temperature and pressure will go up. Nature does implement some kind of calculator that then "makes" the temperature of the gas be at the right temperature according to the equation. As the volume gets smaller, the pressure goes up because the same number of atoms in a smaller volume means more of them are going to be hitting the edges in a given period of time. The temperature goes up because squeezing them down increases the average energy of the particles. The math of the gas law is a description of how these are related, but nature does not actually do the math.

Don't Confuse the Model with Reality​

We understand the world by modeling it. Your perception of reality is actually a model created in your mind. It is easy and useful to incorporate these scientific models into your own understanding of the world. You actually begin to "see" the world through these models.

Don't confuse the models with reality. Nature itself does not use these models to operate. The "laws" of nature are descriptive. Nothing ever commanded the earth to orbit the sun.

Math itself is not fundamental or universal. Math was invented by humans to aid in model formation. (See also Numbers were Invented.) Numbers, equations, and geometry did not "exist" in the primordial universe so that stars could form as spheres. The math behind nature was not "discovered" because there is no math behind nature.