Inside the Narrative Mind: Is Math a Universal Language?

 

Mathematics is sometimes described a "universal language," because its concepts are the same across all times and cultures. People were so sure of this that they used mathematics as a way to communicate with potential alien readers on the golden record of the Voyager space probe: Starting from the width of a hydrogen atom (the most common element in the universe), the record explains successively larger units of measurement, eventually working up to the location of Earth in the universe based on the positions of a series of pulsar stars relative to the Andromeda galaxy where the probe is eventually headed. This precision of mathematical measurements also can be used to estimate the scientific knowledge of different cultures, as in a widely cited passage from the Bible that allows one to calculate pi (roughly) from the dimensions of a basin in Solomon's temple. The more precise a culture's measurements, the more scientifically advanced it is understood to be. Plato went so far as to argue that mathematics is more true than observable reality, a reflection of the world of pure forms. Some contemporary writers extend Plato's transcendent view of mathematics to the possibility that life as we see it is a form of virtual reality, operating on some substrate of numbers and equations that remains invisible to us.

Ben Orlin's book Math for English Majors explains math in this way: "Math begins with numbers. Though numbers and words differ in a few notable ways, both are systems for labeling the world. Numbers, like words, let us reduce a complex experience (say, a lakeside stroll) to something far simpler. In the case of words, a description ("there were lots of expensive dogs"); in the case of numbers, a quantity ("3 miles"). After numbers come calculations. Calculations generate new numbers from old numbers, which is to say, new knowledge from old knowledge. For example, if our 3-mile lake is a rough circle, then I can calculate the distance across the lake to be approximately 1 mile. ... Algebra, like literature or philosophy, takes a step back from the everyday world. We leave behind particular numbers (177) and particular calculations (177 / 3) to study the nature of calculation itself."

The fact that math allows for abstraction is why Plato felt it was more true than reality -- the circumference of a circle is always the 2pr, regardless of where you find the circle, what color it is, whether it describes a physical object like a temple basin or is just a drawing, etc. That's indeed an interesting property of math. But as I have argued elsewhere, every language permits abstraction in this way, and all languages are products of the Narrative Mind. To reprise an example from my original Two Minds paper, the creature sleeping by my feet can be identified with progressively abstract terms as a miniature poodle, a dog, a canine, a mammal, an animal, and a living being. He can also be identified as Midnight, his specific name; or in a more formal context as Champion Winks James, King of the Ninja Moodles, GC (his AKC name, under which he won several dog shows, which also conveys his winning status and the fact that he completed an AKC "canine good citizen" obedience course). Abstractions, thus, can tell us a lot. In the article, I pointed out that linguistic abstractions help us to make predictions about the world -- e.g., that Midnight is likely to bark at a cat instead of meow. However, none of these abstractions adequately convey the warm, fluffy, good-natured creature beside me, an experiential truth that is best known to the Intuitive rather than the Narrative mind.

What's missing from Narratives is the embodied reality of life. We sometimes confuse the symbol for the thing symbolized -- based on long experience with dogs, for example, we automatically respond with a happy "oh!" of recognition when a poodle is mentioned or pictured in a book. But those aesthetic experiences are not the same as meeting the poodle himself. This may be why math leaves some people feeling cold: It is almost pure Narrative, in its algebraic forms specifying abstract relationships between things that are themselves abstract -- x and y and z. If it were about poodles, rather than xs, people might find it easier to follow. But it would also trade in some of its abstract power for those helpful specifics.

Mathematics does, however, have an aspect of Intuitive understanding for some people. Some people see a beauty in equations and numeric concepts, but you have to know where to look. The Pythagoreans regarded mathematics as a religious practice, with secret knowledge that was revealed only to the initiated, such as the existence of a perfect 12-sided solid geometric form (the dodecahedron -- a solid that's familiar to Dungeons and Dragons players as the d12). You had to be an initiate of the Pythagorean mysteries before the existence of this "perfect" form was revealed to you, because of a belief that outsiders would not adequately appreciate it. Ben Orlin provides a more modern example of Intuitive appreciation of math, in describing Welsh numbers: un for one, dau for two, tri for three; then a shift after 15 (pymtheg) to add numbers one at a time -- unarbymtheg or one-and-fifteen for 16, dauarbymtheg or two-and-fifteen for 17. He is particularly charmed, though, by the Welsh word for 18, with is deunaw or "two nines." This is a different way of breaking up the sum than we are used to in English (eighteen = "eight and ten," a base-10 system), but one that is equally true (18 is indeed two 9s, and that total is much more symmetrical than our lopsided eight-and-ten). Yet the base-10 system allows for easier calculations: Add up the ones column, carry the remainder, add up the tens, and voila you have a sum. "Two nines" might be more useful in some limited situations, such as dividing by three, but "eight and ten" has more widespread benefits. Still, someone who appreciates the aesthetics of numbers in this way is responding to Intuitive characteristics of numbers, the beauty of patterns and relationships between them, and the alternative possibilities for expressing a single number. Similar Intuitive characteristics of other languages are what is captured by the Whorfian hypothesis, the idea that language shapes reality, which I have written about recently.

At its heart, though, mathematics is probably the most Narrative of Narrative-Mind activities, the closest to pure abstract description of nature. Intuitive-level aspects of math will always be an acquired taste.