- On "Useless Knowledge" - permalink

Published On: 02/10/17 Written By: Muhammad It has often been said that certain types of knowledge are "useless". All sorts of knowledge have been accused of this at some time or another. Despite the obvious overall utility of mathematics, pure mathematics in particular has often been the target of these criticisms. It's very easy to turn up examples of people saying this: But here is a case against the uselessness of pure mathematics, leading in with a passage from the mathematical novel The Man Who Counted, written by the late Brazilian writer Júlio César de Mello e Souza. In this passage, the hero of the story, a young Persian savant, named Beremiz Samir, with an extraordinary ability for calculation, becomes the object of the envy of a vizier to the fictional caliph of Baghdad. The vizier insults Beremiz, calling his unique ability frivolous. Beremiz does not become angered, but calmly responds:
"When the mathematician makes his calculations or looks for new relations among numbers, he does not look for truth with a practical purpose. To cultivate science only for its practical purpose is to despoil the soul of science. The theory that we study today, and that appears to us impractical, might have implications in the future that are unimaginable to us. Who can imagine the repercussions of an enigma through the centuries? Who can solve the unknowns of the future with the equations of the present? Only Allah knows the truth. And it is possible that the theoretical investigations of today may provide, within one or two thousand years, precious practical uses. "It is important to bear in mind that mathematics, besides solving problems, calculating areas, and measuring volumes, also possesses much more elevated purposes. Because it is so valuable in the development of intelligence and reason, mathematics is one of the surest ways for a man to feel the power of thought and the magic of the spirit. "Mathematics is, in conclusion, one of the eternal truths and, as such, raises the spirit to the same level on which we contemplate the great spectacles of nature and on which we feel the presence of God, eternal and omnipotent. As I have said, O illustrious Vizier Nahum ibn-Nahum, you have made a slight error. I count the verses of a poem, calculate the height of a star, measure the size of a country or the force of a torrent, and thus I apply the formulas of algebra and the principles of geometry, without concerning myself with the profit I might earn from my calculations and studies. Without dreams or imagination, science is impoverished. It is lifeless."
The Man Who Counted seems modern to me, but I was surprised to find out that it was first published in 1938. And it's managed to be very prophetic indeed. One year later, World War II ensued and, with it, came the conception and implementation of the first general computing devices. The German Z3 and the American ENIAC became the first Turing-complete digital computers. Ever since then, computers have played an ever larger role in all parts of society, and the body of number theory, mulled over even into antiquity, but apparently entirely lacking in any real value for applications, was drastically transformed. Consider that it was once said famously by the legendary mathematician Carl Friedrich Gauss: "Mathematics is the queen of sciences and number theory is the queen of mathematics." Consider also that another not-quite-as-great—an admittedly very high bar to clear—but still great mathematician Leonard Dickson later said: "Thank God that number theory is unsullied by any application." But integers are the essential currency of the digital computer and it stands to reason that the practical value of the study of the integers per se could only have exploded as soon as the digital computer became more widespread. Today there are a great many applications of number theory to computing, including: Even the possibility of contacting alien beings one day is influenced by number theory: the Arecibo message blasted into deep space in 1974 consisted of a number of bits equal to a semiprime, the product of the two prime numbers, in this case 23 columns by 73 rows. This makes for one rectangular arrangement that forms sensible pictures; the other arrangement of 73 columns and 23 rows makes no sense, and all others do not result in a perfectly rectangular shape. So, anyhow, what's the verdict on "useless knowledge"? There is likely knowledge that is really genuinely very useless. The exact number of carbon atoms in my body at any one given time, suggested by the editor, could be one of these very facts, facts that relate to nothing else and signify so very little. But the ascription of "useless" to, for example, pure mathematical knowledge such as number theory is more problematic. Was number theory useless, but then became useful in the 1940s or so? If so, why should it have been pursued before then? One might counter that the framework could have been deemed useless before this time and would have simply been devised on an as-needed basis. A problem here is that t