Venn Diagrams, sines, cosines, tangents, logarithms, antilogarithms, Pythagoras theorem, the Fibonacci sequence, and imaginary numbers. To a lot of people, that doesn't sound like fun - and to them it certainly doesn't sound like a fun way of spending an evening.
But not me. I love maths and I was genuinely quite excited to log on to Skeptics in the Pub - Online last night to hear Michael Brooks, author of 13 Things That Don't Make Sense and The Quantum Astrologer's Handbook, deliver a talk called The Art of More:How Mathematics Created Civilisation. A talk in which he would make a case, a very strong one, that maths should be taught as a humanity rather than, or as well as, a science.
Michael Brooks believe we'd be better served as a society if we understood not just the technicalities of mathematics but the culture, or cultural impact, of maths. His talk outlined some examples of what he meant and if it was, in places, a little scattershot (any narrative that was there was loose to begin with and got looser as the evening went on) that didn't stop it being very interesting.
Brooks, an enthusiastic a speaker as he is a fan of right angles, began with a brief introduction to three people he felt were among the greatest, and most important, mathematicians of all time. Two I had never heard of and the third I had never had down as a mathematician. We'll come to her in a bit but first up was Shulgi or Ur, the second king of the Third Dynasty of Ur, who lived, and ruled, in what is now south-western Iraq over four thousand years ago.
Shulgi transformed his kingdom using his mathematical skills and was soon so renowned for his ability with numbers he was actually worshipped. People sang hymns about his numerical ability. So what were his amazing skills?
He could count, he could add up, and he could subtract. He never quite mastered multiplication or division but, back in the days of Ur, this was enough for him to be considered a genius. That and his own rampaging ego. His mathematical skill set saw him arranging compulsory audits for civil servants and traders and set Ur on the path to becoming the largest, and most powerful, city in the world at the time.
Under Shulgi, the people of Ur built roads, they built ziggurats, and they built alliances. Jump forward to the 17th century and simply being able to count was no longer enough to have you hailed as a genius. John Napier, a Scottish laird, used the properties of those much loved right angle triangles to create an exhaustive table of logarithms.
With over ten million entries, it took Napier two decades to complete but it was a huge huge boon for astronomers, Johannes Kepler was childishly excited by Napier's work, and led to the invention of the slide rule which until the advent of the modern pocket calculator became an essential piece of kit for anybody needing maths in their life.
The slide rule powered the Industrial Revolution, was used in the Manhattan Project to help develop the atomic bomb, and was instrumental in calculations required to ensure a man landed safely on the moon.
The slide rule was a bigger deal than I had ever realised. Brooks' third great mathematician is none other than Florence Nightingale. The Lady with the Lamp is more famous for her nursing and social reform than her way with an abacus but she had studied maths from an early age and used it often in her career.
After a brief discursive story about how Nightingale would lock up the other nurses at night and sleep with the key under her pillow (she was worried by tales of nurses sleeping with soldiers), Brooks told us how she would, during her career, collect and collate hospital data and statistics. In Scutari, she analysed death rates and saw that field, or battle, hospitals had much lower rates of mortality than larger permanent hospitals.
It soon became apparent that more army personnel were dying of diseases caught in these hospitals than they were of wounds received in battle. Nightingale instigated huge reforms in military medical practices and was even elected the first ever female member of the Royal Statistical Society.
While numbers, it seems, came natural to Nightingale, Napier, and Shulgi that's not the case for many of us. That's because numbers are difficult and mathematics isn't normal or natural for us. According to Michael Brooks, maths is not what you think it is. It is not something that was always there. It is something we invented and it is something that raises us above all other species on the planet.
Animals can't count and we are, essentially, animals. Or at least animals can't count above 3 and nor, historically, could we. Counting, before maths, went, roughly - one, two, three, more. For the Piraha tribe in the Amazon it still does. They get lost after three. They see no need for it. If there is four, seven, twenty-eighth, or three thousand this can all be quite easily summed up by the word 'more'. Or even 'lots'.
Our invention of mathematics has given us the ability to deal with qualities larger than our brains can naturally comprehend. Our invention of counting led, eventually, to accounting. It led to the invention of money which led to trade, business, commerce, and even revolution.
After the Babylonian times, maths never really reached the West. Instead its development took place in China and India before arriving in Europe via North Africa many centuries later. But once it arrived we soon started putting it to good, and not so good, use.
Jacques Necker, a Genevan banker who served as finance minister for Louis XVI, was eager to reduce the French national debt and to do this he carried out an audit that revealed the royal court's indulgence and profligacy. Louis XVI and his court were not best pleased that their wastefulness had been exposed so Necker lost his job.
If not, like many of that era, his head. That would have taken nominative determinism to a new level. Necker's revelations were a key influence on the French Revolution and when the Bastille was stormed in 1789 the revolutionaries carried a picture of Necker on a banner with them. Around the same time, in the United States, Alexander Hamilton, the Founding Father and now star of a hit musical, used his admiration for the English and Dutch methods of accountancy to help build the new America on a foundation of financial prudence.
Geometry was used for ship building, navigation, and, ultimately, converting 'infidels' to Christianity (quite an affront considering much of the groundbreaking work in that discipline had come from the Islamic scholar Ibn al-Haytham around the turn of the first millennium). Algebra (another Islamic invention) became a financial tool and was used to make loan revenue projections and to enhance military logistics (such as the angle a cannon should fire at to ensure maximum death) and, with the contribution of John Nash (who Russell Crowe plays in Ron Howard's 2001 film A Beautiful Mind) and his developments within the field of game theory, to create nuclear equilibrium and detente.
When Brooks spoke about calculus (which was used to create the Spitfire fighter aircraft) and imaginary numbers he lost me a little. Which just goes to show that even a keen fan of mathematics like myself hasn't really learned much new about the subject since I left school. In that I am far from alone.
While Brooks touched on subjects as diverse as Christopher Columbus, Leonardo da Vinci (who hated fractions!), GPS, perspective, the Hagia Sophia in Istanbul (built by two mathematicians, apparently), and Albrecht Durer's visit to Bologna these were mere dressing to a talk whose main point he never wavered far from and even kept to during a Q&A that took in Euclid and exponential growth curves and cast doubt on the very existence of Pythagoras.
That was Brooks' idea, or conceit to some, that maths should be studied as a humanity as much as it is studied as a science. To Michael Brooks, and after attending this lecture I am inclined to agree, mathematics give us a sense of ourselves, it helps us temper our darker impulses and inclinations, and it gives us the tools to build societal structures that may not always be perfect but help advance us a species. That's Numberwang.
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