Layman’s Corner: Is Math “Real”?
As poor as I am at math, I certainly hope the answer to the question of “Is math real?” is an emphatic “no”.
This, my first in what will certainly be many attempts to make a fool of myself on weighty philosophical topics, I want to discuss the nature of mathematics and its relation to the “real” world. I want to preface this post by saying I’m not apologizing for this Promethian action: a layman with an average education discussing a subject that belongs only to the Olympians of Academia.
I do not, however, take up themes like this lightly, and hopefully I do so with a humility that would invite those with more profound understanding of these subjects to condescend and engage in the discussion. It is my naive dream that such subjects might eventually become commonplace themes of discussion, open to the laity that might be interested in such subject matter. If I’m really pushing the reality of this dream, I hope that those of us with interest in these topics may even be able to eventually contribute to the conversation. These posts are not intended to be exhaustively researched nor particularly conclusive, just open-ended thoughts of discussion that might invite a conversation over a beer perhaps.
The question at hand for today: Does math constitute an underlying “true fundamental reality”? Is math simply a very useful tool for us to construct a logical, descriptive representation of “reality”? At the risk of setting up a false dichotomy, these are essentially the two questions I will explore, and I answer the former question in the negative and the latter question in the affirmative. Also, for the sake of simplicity and brevity, please forgive the somewhat whiggish and linear historical approach to math and science.
Let’s look at four major revolutions in science and mathematics, which are all related, but I believe support the idea that we change mathematical concepts to fit our description of reality rather than vice versa: Euclid’s geometric world, Newton’s (Kepler’s) calculus world, Einstein’s relative world, and the spooky mathematics of quantum theory.
Take the essentially two-dimensional, plane-driven reality of the ancient greeks and Euclid; the math behind these Greek systems wasn’t simply an abstraction to them, or mathematical tool, it was math revealing ultimate reality. So much so that mathematicians such as Pythagoras developed mythical math cults that truly believed they had tapped into the secrets of the universe and numbers were the underlying reality “behind” this world. They thought this world was the abstraction of the math and not vice versa. Plato certainly believed this to more than a large degree and goes into detail in his origins stories in Timaeus about his math/atomic structure of the world.
But a deeper understanding of reality was needed when Newton was prompted to invent his calculus to account more for moving objects, adding an element of time and space as necessary to be more accurate and mathematically descriptive of Newton’s reality. I think by the time of Newton and certainly later by the time of Einstein, it clearly can be shown that Euclidean geometry really doesn’t have the kind of basis in reality the Greeks understood. Once time and space (and certainly time as a 4th dimension and the curvature of space) are added as variables, Euclidean geometry becomes a neat little exercise in logic and perhaps carpentry, but is no longer useful in any descriptive sense of our reality. It certainly seems goes by the wayside as any underlying universal truth revelation.
Once again, when general and special relativity is stumbled upon by Einstein, the calculus of Newton, still works in a Newtonian sense, and in a Newtonian descriptive analysis of the world, but a deeper, more thorough mathematical representation of time and space is necessary in the math of relativity. So goes it for subatomic particles in quantum mechanics, and I predict a new sort of math will be invented to solve the next level of micro and macro investigations in the future. Do we yet know the mathematics behind dark matter and dark energy? Some may claim so, but it seems to me it is just as likely that these are placeholder ideas that are awaiting a new view of the universe and therefore a new mathematical paradigm to be descriptive of our new universal realities.
I think these examples show that we use math as a descriptive tool in each instance, rather than a revealing of an underlying mathematical truth in which the universe is constructed. Other than the examples used, I also believe this is the case because of the nature of numbers. I think that infinity exists in just the space between 0 and 1, or just in the space between 0.0 and 0.1 ad infinitum (if such a concept has any real meaning). This leads me to believe that math is infinitely malleable to use as a tool for any descriptive abstraction of our past, present, and future representation of reality.
So, I do not believe that numbers “exist” in any Platonic sense, or that we are revealing deep universal secrets through math. I come down on the side that math, like science, is a very powerful tool that is unbounded and therefore can be used for any description of our understanding of reality – even when our reality changes.