“Another day goes by and I didn’t use algebra once.”
So begins Professor James Franklin’s latest article and podcast on ABC: a discussion of the philosophy of mathematics and why it matters. Statements such as the one above are often proudly stated by those who are perhaps unaware of the mathematics which surrounds their everyday life – and it is these statements that Prof. Franklin hopes to debunk with a little philosophy, rationality, and of course, mathematics.
Many people – often students – question the usefulness and applicability of mathematics to their everyday life. Basic arithmetic may be everywhere, but more complex mathematical ideas can be harder to spot. It can seem frustrating to persevere with a subject that many consider as abstract and purely academic. Yet this this vastly incorrect: mathematics is all around us, in nature, in life, and indeed, in philosophy.
To really address this issue, Prof. Franklin imagines a world millions of years ago. A world predating humans and mathematical concepts, yet a world still abundant with mathematical occurrences. Some concepts that Prof. Franklin addresses are symmetry, flow, continuity, and discrete patterns.
“There were many such properties—symmetry, for one,” Franklin explains. “Like most animals, the dinosaurs had approximate bilateral symmetry. The trees and volcanoes had an approximate circular symmetry with random elements—seen from above, they look much the same when rotated around their axis. The same goes for the dinosaurs’ eggs…
Other mathematical properties that existed in the pre-human world are flow and continuity (of rivers, for example); discrete patterns such as grasses coming in clumps; and ratios (for example, large dinosaurs are more ponderous than small ones because the weight ratio of big to small dinosaurs is much more than their muscle cross-section ratio).”
So once again, the question is: how does this relate to my life? As Franklin explains, this Jurassic world explanation demonstrates how mathematics is not abstract and it can be quite literal in its interpretation – symmetry, for example, is often identified purely by visually recognition. “Those properties can exist not just in an abstract world of numbers or sets but in the very world we live in,” he says.
But there is more, and the importance of mathematics is underscored by all disciplines: reasoning in law and politics, intuition in arts, observation in science. Dig deep enough, and you can find mathematics at the root of almost anything.
“A proper understanding of mathematics can also help us think more intuitively about the world around us,” Franklin says. “To get to the truth in natural sciences like physics and biology, there is no choice but to get out and observe what happens to be true. Swans can be white or black or blue—there is no way of knowing which they are without observation. Mathematics is not like that. It just needs hard thinking, and the results are true—and must be true—in this world and in all possible worlds.”
We strongly recommend you take a few minutes and listen to this excellent podcast, or read the article in its entirety on ABC.
