The Quadrivium: The Lost Tools of STEM
Reminder about this week’s 'first meeting' of the Trivium course:
https://macrobius.substack.com/p/what-classical-teaching-courses-can
The Trivium/Quadrivium Training course for teaching Freshman Year. Getting started is the hardest part and most of the hard work to create the training curriculum for teachers, will be done in Fall 2024.
Specifically:
https://macrobius.substack.com/p/training-course-for-teachers-in-classical
Freshman year of 'The Rhetoric Phase' is coextensive with an American High School. This presents an 'interesting' problem for teaching the Liberal Arts, using the 'Lost Tools of Learning' - the three Arts of the Trivium and the four of the Quadrivium. It is essential to a career in STEM (Science, Technology, Engineering, or Mathematics) that High School students in those careers do the mathematics sequence at the appropriate age. It's good if they can have some introductory courses in the sciences as well, of course. General Biology, General Chemistry, and Physics are usual in American schools.
This creates a problem in that we have to jam most of the Trivium *and* the Quadrivium into two years, or at least make a start at them, assuming the students arrive at High School age completely unprepared. It is essential, from a STEM perspective, that an end be made of made of learning basic Algebra and Geometry no later than the end of Sophomore year. Also, that introduction needs to result in the student knowing what a real Mathematical Proof looks like, and how to reason that way. For hard scientists and engineers, it's a race to get through as much of the Calculus as possible 'before college' as we now say, and somehow along the way pick up Trigonometry and Analytic Geometry.
All this could of been avoided by actually teaching Grammar in Grammar school, and making a start at Logic and Rhetoric as well, along with at least pre-Algebra, in what Americans call 7th and 8th grade. The 'Trivium Revival' of the 20th century, from Dorothy Sayers 'Lost Tools of Learning' address, Sister Miram Joseph's book on the Trivium, and the 1990s introduction into the homeschooling movement via Douglas Wilson's book and the curriculum of Wise and Wise, in The Well-Trained Mind, all have at least a partial solution to the road jam-- but hardly every child will have such advantages, arriving at our notional High School (or being self-taught, or home schooled still).
Besides the pressure placed on it by inadequate preparation and the sudden urgency of STEM, especially Mathematics, that is, the stark necessity, under the circumstances, of mashing together into two short years, 100% of the Trivium and half the Quadrivium, into what amount to an intense, but mostly remedial course, we also have pressure from a different direction -- inherited Anglo-American norms concerning the Liberal Arts:
First, of the Seven Liberal Arts, in Early Modern education -- British, anyway -- Music, the third subject of the Quadrivium -- was entirely suppressed in the college curriculum of the time. This creates a problem in STEM because the subjects of Phonics (Acoustics in modern terminology) and Optics, and indeed ultimately Quantum Mechanics, all depend on a later course in Wave Phenomena which teaches the STEM version of 'Music Theory'. So we end up with the usual Sciences/Humanities split of the same topic, and the inconvenience of having to teach the same subject twice, while paying extra staff, separately trained in different traditions, by more extra staff, to teach what a simple Reigning Master of Liberal Art ('Regent') ought to be able to do, with the aid of a singing Master or Mistress for the practical a capella parts, which every larger parish will have to tackle anyway.
Second, while the British and thence American universities and colleges inherited the Late Medieval curriculum and more or less maintained it intact until just before the American Revolution, the Logic year (Sophomore year) was honoured more in the breach than actually observed to have been taught. This is due to the influence of the late Scholastic school of Petrus Ramus, who taught a 'method' whereby the Trivium could be reduced from three years to two, saving parents quite a bit of money. Famous members of the Ramist school are Descartes and Milton. You might recall something called 'Discourse on the Method {of Petrus Ramus}' or if you look at Milton's complete prose works, you will see his short-form teaching of logic -- the sort of thing an Oxford Tutor gives his _in loco parentis_ ward to read over a weekend and check that subject off the list.
Modern revivals of the Trivium haven't really gone 'full medieval' for these reasons. One of the main ones is that Sayer's, in Lost Tools of Learning, gives the Late Medieval ordering of the Trivium, not the in-practice ordering of colleges in 17th and 18th century. Teaching Logic that early can be done, but not in the modern way, and for all its talk about the Trivium, the homeschooling tradition of the late 20th century, even CCE ('Classical Christian Education') is very modern, and reflects the folk memory of the 19th century alongside the points Sayers was making.
You simply can't take a modern book that also mentions Syllogistic in ways that connect to the Trivium, such as Copi's Symbolic Logic or Quine's Methods of Logic, at 'Dialectic Aged children' aged 10-14 and hope something useful will emerge. You can barely do it with late High School students. This despite that fact that 'Computer Logic' is *essential* to STEM now--both Propositional Logic (a mathematical dual of Boolean Algebra), and the First Order Predicate Calculus first articulated by Gottlieb Frege in 1879, which forms the standard 20th century understanding of what a Mathematical Proof is, once formalised.
This doesn't mean it can't be done in either order -- Logic and Rhetoric in practice end up being learned together anyway -- but it *does* mean we need to rethink the relationship between *Computus* (The subject of doing computations, which children are still expected to learn in Elementary School, fortunately), alongside the STEM needs for Computer Science and the practical Art of Programming, and of course relate both properly to symbolic or Mathematical Logic, Algorithms, and how to do Mathematical Proofs. That is a tall order, and no Elementary School or High School programme does it well, today. Classical Liberal Arts can lead the way here, to a more coherent *integration* of the Trivium and Quadrivium -- and in fact we *must* or we can choose to be irrelevant.
This course, then, will have two 'textbooks' being written alongside each other--one, for the Trivium, will just be a commentary on Sister Miriam Joseph's work, as previously explained. It will start with a grammar review and then start walking through the Trivium chapter by chapter. A 'workbook' will be drafted for each meeting (chapter of the book), which will comprise, when it is done, the training curriculum for TEACHERS (or Autodidacts, or Homeschooling Parents with High School aged children).
Meeting 1 begins tomorrow, 9/9/2024, and the chat thread for it is: LINK
Collectively, these books will be e-published as 'The Fish Tank Books'--so-called because the covers will be pictures of George the Orange Cat (Trivium) and Foxy the Grey Cat (Quadrivium), looking at a fish tank. If all goes well, the books will be produced 'in real time' with these two introductory books done this Academic Year. The full set of curriculum materials (workbooks for future years) will be produced 'in real time' or sooner or until I give up the mental ghost or otherwise. So, seven years from now, it should be possible to just 'download it all' and, like Zeph Cochrane, rock and roll!
Although the books will be offered for (inexpensive) purchase at Gumroad, the open source versions will also be available, and instructions provided for finding them -- mostly already given but will be re-iterated. This substack will remain free to all subscribers.
The Quadrivium Fish Tank Book will be serialized as it is written on substack (and other places), and this is the first installment. I like to write 'in the open' with open source following at the github repo (Creative Commons with Attribution or similar). Production works will emerge when the substantial work needed is really completed. I hope to do better than George Martin on this, but totally get it. Tolkien had to type his manuscript, by hand, twice. Even with ten fingers it's a bit of a job. But with the liberal license, you can roll your own, teachers and pedagogues and autodidacts and autists... any time.
Those who take a peak at the Trivium Teachers' Course (and any Classical STEM Teachers out there should) will notice that I delay Chapter 2 of Sister Miriam Joseph's work until I'm ready to take up the Quadrivium. This is my practical response to all the challenges above. In Chapter 2, she starts to introduce the scholastic terminology of what STEM calls Category Theory (commutative diagrams with arrows and homologies and stuff for you Mathematicians, a well known alternative to Symbolic Logic or even Axiomatic Set Theory, which is a SECRET we don't tell normies but maybe should).
I don't fault the Good Sister for this. She was teaching in a 'parochial' and 'post-parochial' setting, for what we would now call TradCath students (the only kind back then), and at a time when she had the full force of the whole of the Third Scholastic and the Papal Encyclical Aeterni Patris at her back, pre-Vatican II. She could get away with just saying... Look, Aristotle, Augustine, and Aquinas all agree on this and this is what you are going to learn.
We in STEM can't get away with that now, anywhere in the West. Why, is a story/narrative/history for some other time... like the next stack in this Grey Cat Fish Tank series...
My approach to Chapter 2 will be to *first* introduce some passages from Linus Pauling's 1930s etc. Chemistry Text, as a prelude to the Biology text (which begins with some allusions to Chemistry). This gets STEM on a familiar ground. In field testing this approach with 'actual Scientists' I've found they find Pauling's rather Scholastic (but very Nominalist and Modern) definitions intelligible. We have to start there -- with what Professor Kirke called 'they teach them in the schools these days'.
The Quadrivium indeed provides the Lost Tools of STEM. But we need to make that case, and above all *provide value* to STEM students. We learned that lesson lesson, about 'The Science' during the COVID crisis and the transition from the 'Before Times' of Neo-Liberalism and the Global Financial Crisis, and 'whatever comes next'. If we do not want another Dark Ages episode, we will begin teaching the Quadrivium now, just like Boethius, SS Cassiodorus and Isidore (the latter, 'Patron Saint of the Internet' if you recall), and the Venerable Bede.