TOK: The Math KI!

Knowledge Issue: We can use mathematics successfully to model real-world processes. Is this because we create mathematics to mirror the world or because the world is intrinsically mathematical?

Mathematics from my point of view was never qualitative, meaning that it could not wholesomely describe how a process is undertaken. However, it is true that the world is intrinsically mathematical in my point of view. Creating math to mirror the world is an incomplete claim, because our knowledge right now is limited and there are many problems yet to be answered.

Our current knowledge is limited in a sense that we constantly discover more mathematical problems and solutions in the world. It must mean then that the world is intrinsically mathematical because our discoveries in math are proven by the observing other processes. Before we discovered triangles, pies, the number lines, the world must have already had these values for in itself to function and for us to actually discover it. It must have already been present before us, because naturally, you wouldn’t be able to find something that was never there in the first place, let alone formulate something out of nothingness.

If one could find the answer to a specific problem or recreate a specific process, then it must be able to apply to something else. By saying that the world is intrinsically mathematical must mean that the math that can be applied to a process must also be proven to be useful to other similar processes. In quantitative chemistry, the math that we use consists of moles or Avogadro’s constant, numbers that are mind-boggling and are as large as 6.23 to the 23rd power. These values, though they are finite, are too massive to be counted and too difficult to be used in practical applications, yet the theories that revolve around the link between chemistry and math work. The periodic table formed through the dependence of carbon-12 and moles are still in use, and produce tangible and reasonable processes in discovering the number of formula units, particles, molecules, etc.

Though there is one problem that arises from claiming that the world is intrinsically mathematical, and though it does not necessarily dispute the claim, gives us reason to think that we created math to mirror the world instead. First of all, if the world is intrinsically mathematical, it must mean that whatever we find in the world that is mathematical is 100% true. Yet, there is always an uncertainty in all the equations that are formulated. Even if they are proven, it does not mean that it is 100% true. Equations can be replaced by others, meaning that the first one was not entirely correct and the second must be the “correct” one. Later on, we find out that the second equation wasn’t entirely correct either and a third one was made to replace it. Hypothetically, if this was to keep persisting and the replacements would go on, it must mean that even if the world is intrinsically mathematical, we are not able to grasp the absolute 100% solution of math.

Eventually it must mean that neither of these claims are independent from each other. We as humans create our own math and discovering is merely extracting certain portions of the mathematical world. It is impossible to say right now that the world is intrinsically mathematical because human discoveries are ever-changing. We have to consider though, that if the world is truly mathematically intrinsic, it doesn’t necessarily mean whatever we take is absolutely correct. It could be mathematically intrinsic, but whatever we grasp is not entirely correct, and the solution that is not entirely correct therefore becomes the mathematics we created to mirror the world.

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