How do we know math isn’t wrong? Like it works but could it only work due to our perception?
In: Mathematics
Plenty of mathematicians think that “math is wrong” if you mean that math is not physically “real” and only a construct of perception. In philosophy of mathematics, this school of thought is called mathematical anti-realism, and there are many different forms of it. Here’s a quote from the book *Measurement* by Paul Lockhart that might help you see what I mean about math being “wrong”:
*”The thing is, physical reality is a disaster. It’s way too complicated, and nothing is at all what it appears to be. Objects expand and contract with temperature, atoms fly on and off. In particular, nothing can truly be measured. A blade of grass has no actual length. Any measurement made in this universe is necessarily a rough approximation. It’s not bad; it’s just the nature of the place. The smallest speck is not a point, and the thinnest wire is not a line.*
*Mathematical reality, on the other hand, is imaginary. It can be as simple and pretty as I want it to be. I get to have all those perfect things I can’t have in real life. I will never hold a circle in my hand, but I can hold one in my mind. And I can measure it. Mathematical reality is a beautiful wonderland of my own creation, and I can explore it and think about it and talk about it with my friends.*
*Now, there are lots of reasons people get interested in physical reality. Astronomers, biologists, chemists, and all the rest are trying to figure out how it works, to describe it. I want to describe mathematical reality. To make patterns. To figure out how they work. That’s what mathematicians like me try to do.”*
Math is largely in our heads, but we can still know if the constructs that we use in math are true based on what we say the constructs are and how we say these constructs relate to others. As a very superficial example: if I define zero as “the number that keeps some number the same when you add it to some number”, then I know for a fact that n+0 = n where n is any number. This doesn’t necessarily have anything to do the objective rightness or wrongness of what “zero” actually means.
You might also like the book The Number Sense by Stanislas Dehaene as a good introduction to a field called “numerical cognition” if you are interested in the relationship between math and the brain/mind.
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