A Tribute to Numerals
I was diagnosed with advanced testicular cancer nine days after my 23rd birthday. Contrary to what some people might expect, facing my mortality at such a young age turned out to be an enriching use of my time—and brought home for me why humans have spent countless millennia waging war against the scientific ignorance of a state of nature. Moreover, it opened my eyes to the fact that our species’ war against cancer, as with our battles against small pox, Alzheimer’s, and hunger, are fought as much through the inventive language of mathematics as they are in the laboratory or the clinic. And this war fought with numbers has an objective charm: it encapsulates the fractal beauty of a cancerous tissue unsullied by regard to its devastating effects.
For thousands of years, humans navigated the world only able to count the so-called natural numbers: the positive integers. Even today, children are taught counting with natural numbers–if you have two apples, and you buy two more, you’ll have four apples. But nature, beneath its superficial exterior, does not operate only in natural numbers–it utilizes fractions, negative numbers, irrational numbers, zero, and infinity. In a remarkable display of foresight (or luck), our ancestors accounted for this with one of humankind’s most immortal inventions: our contemporary numeral system, which, unlike analogous systems–think Roman Numerals or tally marks–was such a radical revolution in human thought that it is now being used for purposes never envisioned by its creators.
A disease like cancer follows beautiful and precise mathematical formulas that take advantage of quantities which run counter to human intuition. But as daunting a foe as cancer is, our numeral system is powerful in its own right, for it is not just any method of counting. It is a positional decimal system, which means that no number is too large or too small to be represented. Complex and irrational numbers give notation to quantities which take no physical form, and calculus uses limits, a consequence of infinity and zero, to measure probabilities and other concepts which we can’t see.
In our species’ noble fight against our demons, such elusive notions—those which can’t be seen using natural numbers alone—are of critical importance. These notions have always existed in nature, hidden from perception, but like invisible ink, are exposed only when confronted by the power of our numerals.
Ironically, many of these concepts were once considered monsters themselves. The French mathematician Henri Poincaré once famously griped that the Weierstrass function, which is continuous everywhere but differentiable nowhere, was “an outrage against common sense.” The idea of a mathematical construction which couldn’t be visually observed using existing methods made Poincaré, like many before him, uneasy. Today Weierstrass’s outrage is being used to model physiological signals such as heartrates and is thus playing an important role in developing our understanding of our own bodies.
The beauty of our numerals is that they are full of outrages against common sense, and that’s what makes them work. The idea of negative numbers is absurd to children who are learning to count using apples, as it no doubt was to the first mathematicians who envisioned them. Even more ridiculous are imaginary numbers, so much so that perhaps their most well-known function today is as the punchline of mathematical jokes (to the rare class of people who are inclined to such humor). Yet, such absurdities can be clearly shown using the basic axioms of our numerals, and this is where their versatility shines: in their ability to take tools built for one purpose, and generalize them to entirely new, unexpected uses.
It’s easy to take this property for granted until we are reminded of the timeless role it plays in our survival. Likely first created to facilitate basic commerce, numerals nowadays combine with stem cells to build artificial organs in people who need them, and algorithms model how congenital heart defects express themselves in populations–literally applying our millennia-old method of counting to solving problems the inventors of numbers could never have imagined existing.
Our ancestors have made a long and unprecedented rise from being just another hominid in a long line of primates, to one which now has the power to reflect on its own destiny. Considering their efforts, do we not have an obligation to use our numeral system – misunderstood by most, too often perceived as menacing, but with the power to be one of our most formidable allies if approached without trepidation – towards pushing our understanding of ourselves and our world further than it’s ever been pushed before?
The sheer brilliance of numerals, and the brilliance of our forbearers who created and applied them, demand no less.
Rohit Raghunathan is a biostatistics student from Plymouth, Michigan. His interests include almost everything.
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