The standard answer you’ll get is that the Liberal Arts were part of the education that was given to free citizens in classical times – an education that was suitable for free people. That is true, but it’s not the whole truth. What people don’t tell you is that it was the kind of education that made people free – free thinkers, free workers. A liberal education wasn’t just liberal, it was liberating. The liberal arts traditionally fell into two groups – word-based and number-based. The first group became the ‘Trivium’ (the meeting point of three pathways) of ‘Grammar, Logic or Dialectic and Rhetoric’ and the number-based subjects were formalised into the ‘Quadrivium’ (the meeting point of four pathways) of ‘Arithmetic, Geometry, Astronomy and Music’. The study of both led to Philosophy, the ultimate goal of which was integration with the mysterious unity at the heart of the universe. In Ancient Egypt, this guiding, unified, integrated and integrating principle was known as ‘Maat’ or ‘right order’. It’s a far cry from the way in which we understand the ‘order’ of authority that treats people as slaves and the planet as something to exploit. You want to go deep? Find meaning in life, lived to the full? A life – your life – lived in harmony with life itself? Explore this introduction to the Integrated approach to the Liberal Arts. It’s a journey that will last your whole life.
Number formed the basis of the ‘Quadrivium’. Arithmetic concerned the study of number in the abstract; Geometry took numbers from plane to solid dimensions; Astronomy involved the study of solid bodies in motion, and thus included physics; Music involved the study of harmony and proportion in relation to sound, but also led to applications in architecture and engineering. All these studies were founded on the mysterious thing which is number – something we can never see or touch, taste or smell. You’ll never find a number seven under your pillow, on your dinner plate or in a cup of tea. And yet, we know number. We can tell number. We can count. This is incredible. And we do this because we know – we know intuitively – that numbers are composed of an essential unit. Take it one level back and you’ll find that that unit is a symbol of an inexpressible unity that underlies everything. Whether you use a metric or an imperial system of measurement, whether you’re measuring Fever in Farenheit or Centigrade, or analysing the song that quote comes from poetically, or musically, you’ll be relating everything you look at to a unit. While the definition of that unit can change, the relationships remain the same. It makes maths a whole lot more interesting when you look at it this way. Has this made you see numbers differently? If so, how? If not, why not?
Euclid’s Elements is a book that is only bested by the Bible in terms of popularity and reach, probably the most widely used textbook of all time, but hardly anyone knows it today. Euclid opens the book with a definition for a point, which is ‘A point is that which has no part’. He goes on to say that a line, which he defines as ‘breadthless length’ ends in two points (Definition 3), and that a straight line is ‘a line which lies evenly with the points on itself’. While Proclus, in his Commentary on Euclid’s Elements, devotes the equivalent of 12 dense pages of print to expounding Euclid’s double definitions of point and line, the compiler of the University of St Andrew’s History of Mathematics website devotes four telling words to them. The four words are simply, ‘This is rather strange’. How can a point, which has no part and a line which has no breadth be drawn, and if they are the basis of geometry, how can we think of studying it? If you want to take this further, explore Proclus’s commentary on Euclid’s first four definitions and see what thoughts emerge for you.
Make a list of 15 or so things that are important to you. Then sort them into things that you want and things you need. Then sort them into three groups – things that are valuable; things that are useful and things that are pleasurable. If some things fit into more than one category, put them in a space between those categories. How can we tell what’s truly valuable? Money or gold are means of exchange, they’re useful only inasmuch as they can help us obtain what is truly valuable – things like learning, wisdom or happiness. Things like ice cream can be both pleasurable and useful, in that we get nutrition and pleasure from them, in varying degrees. I think it was Plato that once said that a good litmus test for telling what was valuable was that valuable things are those it isn’t fashionable or honourable to dismiss. A hero in a story might scorn money, but it would be very strange to find them scorning health, happiness or wisdom. What would you class as your top 10 things that are valuable? How much of your life energy do you invest in pursuing these?
If you think you managed, you didn’t. You either drew ‘a’ pen, or ‘the’ pen, or a symbol for pen. If you found this impossible, then don’t worry. You’re human, and you’re not the only person who’s found it impossible. Think about it. If you reflect on the experience, and the qualities of ‘penness’ associated with each of the stages, you’ll notice that ‘the pen’ is the most specific; ‘ a pen’ is more general and ‘pen’ is the most abstract, but the most wide-ranging. With simple old ‘pen’, you’re free to include memories, intuitive information, concrete and abstract associations, connections and much, much more if you let your imagination soar and expand. At its most poignant, you could even say you become ‘pen’, become totally involved in the experience of contemplating ‘pen’, so there is no division between you and ‘pen’. In doing so, you really get ‘penness’, you really understand it, allowing you to be so much more eloquent and engaged when you narrow the focus of thinking down to ‘a pen’ and then ‘the pen’. You’ve started to integrate the metaphysical with the physical; your intuition with your intellect; your emotions and your reason; your essence and your being. This is deep stuff – where can you take it?
You won’t find this in most grammar books, but English verbs can be grouped according to 3 ways in which we perceive time. On level 1, the bottom level, you have past, present and future – I have been reading, I am reading, I will be reading. This is a specific moment or span of time as we experience it in relation to the present moment. We can look back on our memories of the past and forward to our project projections for the future. On level 2, the next level up, we have two forms of verbs describing recurring action – action that happens outside time as we experience it, but that happens in perpetuity, in a perpetual motion cycle: I read every night; I (used to) read every night. Things can’t happen in perpetuity in the future. On the third level, the level of eternity, or infinity, we have the infinitive, the verb form that describes an action happening outside time, but within an eternal frame of reference ‘to read’, ‘to be’.
Aristotle set himself this task once. I like to think of him sitting down and looking at amphora, perhaps. He came up with 10 distinct ways we have of thinking about something – they’ve become known as ‘Aristotle’s 10 Categories of Being’. They’re not taught in school, which is a shame, because they give us a really good handle on understanding how we think. You look up Aristotle’s categories on line, if you’re curious. Then analyse your list against Aristotle’s. How many ways of thinking did you come up with compared with him? Try looking at the world comprehensively using all 10 categories consciously for a while. You’ll probably find it frees something up inside you. This stuff goes deep.
One of things people used to learn as part of the Liberal Arts Grammar curriculum was the distinction between words that have definitions and can fit into categories (words such as nouns and verbs, for instance) and words that can’t be easily defined (words such as ‘and’, ‘if’ or ‘but’, for instance). These words were known as ‘syncategorematic’ words and in the Middle Ages, in particular, scholars got really excited about the fact that every day they used loads of words they couldn’t find ways of defining, so they wrote books about them. Now you don’t have to read them, but it’s as important today to realise that most of the words we lean on to convey meaning are words we can’t define. They’re reminders, within language, that language is just an artificial construct and that the reality which lies behind language, the reality that makes us—and language—tick is not language. It’s related, but it’s different and it’s impossible to pin down rationally. We have to approach it intuitively. What does this tells you about the way you approach life?
In simple terms, the golden mean is a proportion, typically found between the sides of a regular pentagon within a five- pointed star and the length of the side of a point of that star measured from the apex to the point where it meets the pentagon. If the side of the regular pentagon is 1, then the long side of the triangle above it will be 1.6180339887… it’s a number that transcends reality because it can never be measured accurately, and yet, it exists. The ratio between the side of a regular central pentagon in a five- pointed star and the long side of any of the triangles that form the star’s points will always, whatever the measurements of the lines, be the golden mean or ration of 1.6180339887… - wow! I find that amazing! In his book, The Golden Meaning (Kairos, 2013), Keith Critchlow argues that it is this ratio that helps us maintain a balance between too much sameness and too much difference in being. He goes way beyond Geometry in applying this to life. In a conversation, for instance, he argues that if you impose your views on someone else, or invade their space too much, you’re distorting the golden mean. Speak too softly; retreat or withdraw too far, and you’re distorting it in the opposite direction. The golden mean allows space for speaking and for listening. It shifts from one party to the other. If one part is greater than the other, what do you relate it to in your view? Speaking or listening? What do you think is most conducive to bringing about effective communication?