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Mathematics Wizard ™


Does Math Exist?

Is math a real thing in the physical universe,
a storm of the mind, or just an idea?

This video provokes a great deal of thought.


Plato's Euthyphro stumper, which asks whether the rules governing human behavior exist independently of the gods, who simply enforce them, or whether the gods make the rules according to their whims. In other words, is morality objective or subjective? A similar problem occurs when we consider the existence of the rules that govern physical laws ~ the rules of mathematics. Where does math come from? Does it exist independently of human (or other) minds, or is it a human creation? Do we discover mathematical problems or do we invent them?

The question has engendered two positions: mathematical realism, which states that math exists whether we do or not, and that there is math out there we don't know yet, and maybe never can. This position may require a degree of faith, since, "unlike all of the other sciences, math lacks an empirical component." You can't physically observe it happening. Anti-realists, on the other hand, argue that math is a language, a fiction, a "rigorous aesthetic" that allows us to model regularities in the universe that don't objectively exist. This seems like the kind of relativism that tends to piss off scientists. But no one can refute either idea… yet. The video above [below], from PBS's Idea Channel, asks us to consider the various dimensions of this fascinating and irresolvable question.

~ Josh Jones is a writer and musician based in Washington, DC. Follow him at @jdmagness

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There are no rules, mathematics or otherwise, which govern the laws of physics. Rather the empirical nature of the laws of physics govern the mathematical models. The models are designed to describe what nature actually does, which we then use to estimate predictions about what nature will do, or has done, under various circumstances. The knowledge comes from actual measurement, observations, or experimental testing. The mathematical models represent our best understanding, so far, about nature. My confidence in a particular hypothesis grows with careful logical deduction or inductive testing, measuring, or observation. And when a mathematical model is refined to account for all anomalies and conditions, and accurately predicts for every case, of many many cases, after all prior anomaly & condition corrections, we debate calling it a theory or a law.

Both math realism and anti-realism, are ideas chosen in an attempt to impose order on the idea of math. Math is real in the sense of an activity which minds engage in. But if you want to talk about something physical, one needs physical units like, "apples."

Consider the question, does "I have 12," mean anything?, "I have 12 apples," may mean I won't go hungry or I have something to trade. But, "I have 12," has meaning only in pure philosophy or as a claim about process of reasoning. Math is pure philosophy, except with a special constraint of universal consistency. For example, in some sense the mathematical philosophy on equations of lines in 2-dimensions is required by this math philosophy, to be consistent with the math philosophy of matrix algebra in 3-dimsensions. This special requirement of math philosophy need not necessarily apply to nature, physics, or any other philosophy.


If math is invented, the only invention was that of a universally consistent philosophy about numerical quantities. All new contributions to math are discoveries of the mere logical consequences of the original idea, proposing or creating the philosophy of math, as a human activity in exploring the logical consequences of the original conditions of the philosophy.


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