Geometry Book


Some of the geometry book I'm working on...

Eight pages of geometry

I forget which post Gordon said it in, but at one point he noted that nearly all books prior to the invention of printing were books of magic.  Sure, on the surface they might be called medical textbooks or scientific textbooks or books of geography or mythology or history. But at some level, all these books were books of magic — they were intended to change consciousness at some level.

Rufus Opus said something similar about making lamens. A lamen is usually a disk or a square that you wear on your chest during the conjuration of a spirit.  The act of writing one, of punching a hole in the parchment, and putting it on a string or a chain or a lanyard, is a creative act.  If the emblem you write on the lamen is the signature or symbol of a spirit, your hand is going through a kinesthetic meditation on the nature of the relationship between the conjurer and the spirit.

Something similar is happening as I create this book.  It’s a Moleskine Japanese Album, the larger size, so the pages fold out into this lengthy ‘wall’ or ‘screen’ of emblems — about 5 1/4″ x 8 1/4″ inches per panel, but about 115 1/2″ long — call it about 9′ 7 1/2″.

I think about this project from time to time — more lately, since I’ve been working on it the last few days — and every time I do, I’m somewhat more dismayed at the current state of geometry teaching in the United States.  By all the accounts I’ve found, and by the anecdotal evidence I’ve collected on my own, we’ve stopped teaching students to use rulers and compasses in the study of geometry.  It’s too hard to remember procedures, or students don’t know how to use those flimsy plastic compasses well and the good ones are too expensive, or Euclid isn’t widely available, or … or… or…

The excuses multiply like dandelions after a rainstorm.

I don’t know that this book “will become an heirloom of my house forever,” as one of the somewhat-more-fictional sagas would have it. But I do know that I learned more geometry from the construction of the book than I ever learned in a class.  And I wonder if there’s not a better way to teach geometry embedded in that discovery?

  • Each student gets a good compass, a good ruler, colored pens or pencils, and a blank notebook.
  • Each student learns the construction for a harmonious page layout
  • Each student learns a set of procedures for:
    • Perpendicular bisectors
    • duplication of angles
    • construction of parallel lines
    • construction of similar triangles
    • construction of polygons from given sides
    • construction of polygons within circles
    • transference of a given length or distance to another angle
    • construction of nets for 3-dimensional solids
    • construction of the root-2, root-3, root-4, and root-5 (phi/Φ) proportions
    • division of lines into thirds, fourths, fifths, eighths, ninths, and sixteenths
    • construction of grid and tile patterns
    • construction of simple polygonal combinations to find the sides of super-polygons.

This benefits future craftspeople, because they’re receiving an education in proportions and common mathematical relationships, and it’s not all algebraic notation.  It brings back the beauty of geometry to the mathematics classroom.  It gives all of society a common language for seeing mathematics in the natural world.  It trains future architects and engineers in precision diagramming, and gives future laypeople practice in reading such diagrams.

And it creates hundreds of unique copies of books of practical geometry that are themselves handbooks to a forgotten magic — a magic of beauty, of proportion, of color, of relationship, of graphic design. Students would get to learn ALL of that in the process of producing their own books over the course of a semester or a year. The quality of their book would gradually improve, as their understanding of the geometry improved, and as their love and care of the book improved. Think of all the other studies that could be folded into the creation of the book, too: handwriting, color theory, graphic design, book design, clear writing about mathematics, methodology.  The book is a grade — and students who kept their book up to date would find it useful while taking tests to remember what they had created in their own handwriting. The book itself would be a palace of memory for all the geometry they had learned, just as mine is.

All of the actual constructions are covered in Andrew Sutton’s book Ruler and Compass.  But actually implementing it is on the individual teacher.  And it’s likely the case that the teacher will need some substantial support from an administration that sees and cares about quality instruction.

But it can be done.

31 DoM: petition papers


and not very easily hidden

My petition papers are kinda big

I’m not much of a believer in hiding my work, or my intention. I realize that when it comes to personal business, there’s some value in hiding one’s work — it’s easier to lose weight, for example, if you’re not making a big deal about your exercise and food regime, and just doing it (it’s also incredibly hard to lose weight without a major change in your exercise and diet, but more on that some other time).

But really, the most important thing to remember is that it’s very hard to get other people involved in your work if you’re not clear about what your work is.  And my work this month, for better or worse, is to showcase some of what I’m learning about Maker Philosophy, and put it into practice through magic; and to use magic to help expound Maker philosophy, and encourage more of my fellow teachers into the practices that will bring Maker philosophy to their classroom and their school.

So for this, the second of the thirty-one days of magic, I’ve written a petition paper.  Now, normally a petition paper is written on a square.  I didn’t have any square paper.  And it’s written in the correct color ink.  I don’t know that I had the correct color ink for anything other than working with Saturn, because Saturn’s color is black.  And today is Saturday (Saturn-Day).  So I guess that’s appropriate that my petition paper is dedicated to him.

As you can see, the petition paper is huge.  Normally, they’re squares, and written and overwritten on top of one another to make a scrawl.  But for me, there’s benefit in making it both readable and beautiful. I want other teachers to be able to read it, and think hey this applies to me. I’m a Maker.  It’s one thing to convince a spirit to make a consciousness shift; it’s quite another to convince another human being.

But, as Gordon has said on other occasions, it’s hard to convince yourself that this is right until it feels right. And the petition to Saturn didn’t feel right.  At various points during the day, I tried making other petition papers. And those felt right.  They felt real, in a way that this more beautiful and calligraphic one doesn’t. Those scribbles were done with heart-power in them, and despite their ugliness they feel far more primal — and far more likely to be effective. So much so that I’m reluctant to photograph them and post them.

Which just goes to show that sometimes the magic is in the beauty, and sometimes it’s in the work.

Tai chi Y4D282: warmth

Leave a comment

I took some time to work on my calligraphy skills yesterday afternoon, writing out the opening verse  of my Neo-Orphic Hymn to to Sun. It didn’t turn out as well as I wanted, but not as bad as I feared, either. 

with broad survey illumines all the sky

Hear Golden Titan whose eternal eye


Today I saw Star Wars: the force awakens, as I did in 1977: a week or so late and seated between my parents. This is not the time for spoilers, or reviews, so I won’t. I’ll simply say that it felt like the torch being passed to a new generation. I deeply enjoyed the film, but I was struck by the previews: so many Space films coming, so many civil war films coming: choose sides, accept your destiny, fight or be destroyed.  My father, who usually doesn’t notice things like this, remarked on it: UN vehicles driving through the desert in Independence Day: resurgence; helicopters and army men against Captain America, surviving in the ruins of the world in The Fifth Wave. (To be fair, there was also a cute bit about sloths.)

Not a hundred steps from my guest bedroom here at my mother’s condo is a narrow stretch of water over to an island; and beyond the island is the Gulf of Mexico.  On all my previous trips to Florida, I’ve been alone swimming at the pool on Christmas Day or Boxing Day, because it’s 50-60 degrees locally, and the Floridians think it’s too cold.  All the kids, the gay couple visiting the more -talkative one’s grandfather, the old ladies ignoring the vultures circling overhead, the painters with their plein-air easels and brushes, the lizards and the black crabs and the pelicans and the black snakes are all out enjoying the weather. So am I. 

At the same time, John Michael Greer’s recent column about how rising waters are affecting western and southern Florida.  Well.  It’s set my danger senses tingling.  I find myself thinking about sinkholes and floodwaters and the transformation of the land into shallow sea over the next hundred years… Or the next fifty… or the next twenty. Nothing like Christmastime to watch and read an ongoing climate horror story surrounded by the mangroves and the Gulf of Mexico just two miles west and eight steps down. Or to consider that the land I’m going home to had warmer temperatures on Christmas Day than I did in Florida, the warmest nativity feast that my state has ever recorded. 

None of this is about tai chi, of course.  But it’s on my mind today as I think about record temperatures, sunny days, and the balance of the dark and the light. Yesterday, a friend of the family took me on a boat ride down the Intracoastal Waterway to get gas at a pump station by an outlet to the Gulf of Mexico. He zoomed along through water labeled as manatee-swimming zones, waved to passing boaters doing the same.  By radio, he commanded the opening of bridges, and  with me and his other guests officiated over some hilarious talk of life in a European army in the 1950s and early 1960s, and his near-miss on serving in Vietnam during his emigration to the US.  

After we fueled up, we zoomed out into the Gulf, and cruised along the beach for a while before returning up the ICW to base.  Sunlight dappled the water where fishermen, barbequers, sailboarders, would-be surfers, thugs, drug-dealers and who knows what else enjoyed their warm day in the sun. All through the IntraCoastal Waterway, piles of silt called “spoils” from the work of the Army Corps of Engineers show where the mud has been dumped from channel-making to accommodate the passage of boats: some cargo, mostly showy pleasure craft that allegedly fish. It all seems like precious little to hang a rescue mission on, hundreds of miles across the Gulf to Alabama or Louisiana or northern Florida, in the event of major flooding. 

But it won’t be major flooding, of course. The sea level will rise in increments, an Nichols here, a centimeter there. The high tides will be higher, the low tides will be less low. The moon’s pull will be exceptionally strong during this full moon, and the next, and the next… until at last the height of the tides won’t quite be attributable to the moon.  Something else will be responsible. Something else will be to blame.

I imagine that my mother’s condo will be underwater, and not in the crash of 2008-sense of a house with more on the mortgage than it can be sold for. This year, next, in ten years, in twenty? I wonder how long the party will last, how long I will hear stories at Christmastime of riding parties in Rhineland woods with the army while drinking beer on the deck of a Florida party boat. 

And so I do tai chi: between watching the force awaken, and a lat afternoon swim; between morning Druidry and an evening cocktail; between a morning slice of toast and jam, and an evening plate of leftovers from a celebration of the Light coming into the World. 

The tai chi practice is… perfunctory? Simple? Basic? Ordinary? Normal, for me.  It feels like it carries a complicated range of emotions around it today.  My breathing is off.  My spin and half spin don’t quite work on the carpet here. I work through the postures a little too fast. I’ve drunk more in the last few days than I usually drink in a few months. The surf hits the boardwalk outside. It is wake stirred up by a Ski-Doo.  The sky is a brilliant blue.  The sea is a gunmetal gray. 

The change, for good or ill, is incremental to my perceptions. One day rarely makes much difference.  In an hour or so, high tide will come when the moon rises.  

Thirty Days of Making: Stave-Book, Finished.


I’m in Day 30 of a short series: Thirty Days of Making. Every day for the next thirty days, I intend to make something, anything, that is in some way connected to school. There won’t always be pictures, and I reserve the right to credit myself for things that I help my kids make. But I’ve decided that I need thirty days of maker success and maker failure under my belt to be a better designer.

I’ve decided that artwork counts, but not writing (unless it’s part of the art, like calligraphy). Digital work counts, but it has to be useful or publishable.

Some days there will be pictures, some days there won’t be. Each blog entry will contain a list of some of the materials and tools, a quick review of the success or failure of the Making, and a reflection on what I think I learned from the endeavor. (My friend Alicia is beginning a new series along these lines, 12 weeks of the Artist’s Way — I wish her well in her process, go check her out!).  Also, there was a technical glitch with Day 24, which is now posted.

Reason for the Project:

Yesterday, while I was searching Andrew Carle’s website for a specific article to reference in yesterday’s Thirty Days of Making article, I came across Bre Pettis‘s “The Cult of Done” Manifesto:

  1. There are three states of being. Not knowing, action and completion.
  2. Accept that everything is a draft. It helps to get it done.
  3. There is no editing stage.
  4. Pretending you know what you’re doing is almost the same as knowing what you are doing, so just accept that you know what you’re doing even if you don’t and do it.
  5. Banish procrastination. If you wait more than a week to get an idea done, abandon it.
  6. The point of being done is not to finish but to get other things done.
  7. Once you’re done you can throw it away.
  8. Laugh at perfection. It’s boring and keeps you from being done.
  9. People without dirty hands are wrong. Doing something makes you right.
  10. Failure counts as done. So do mistakes.
  11. Destruction is a variant of done.
  12. If you have an idea and publish it on the internet, that counts as a ghost of done.
  13. Done is the engine of more.

And I realized that I really wanted to finish some of the projects that I’d started but not finished in this thirty days. The four big ones were my shirt, and the last few detail stitches on my pencil case, the stave-book, and a lotus wand.  There was also a gauntlet-glove to assemble, although that didn’t turn out so well. So I devoted today to “Done”.

Process and Results:

A lot of these projects were finished (or at least chivvied along toward finished) in ten and twenty-minute blocks of time throughout the day.  I needed to wait for the drama teacher to finish one appointment, so I sewed the bottom hem of my shirt in place while I waited. Thank goodness the sewing machine didn’t break like yesterday.

Thirty days of making: pencil case details

only one, pink zipper left in the drawer… oh well.

I was waiting for my class this morning, while they finished a math test.  So I put in the final stitches in my pencil case, which was admired several times throughout the day.  I was really pleased with the reaction to it; I think I need to make a dozen more or so, and distribute them as rewards for project completion in other parts of the school.  They’ll attract notice, and draw some new kids into the programs I’m running.

Thirty days of making: gauntlet gloves

I like the left-hand pattern more than the right-hand one.

The gauntlet needed four minutes with a glue gun.  So I did that during a math class that was meeting in the Design Lab.  I’m not sure anyone in the class realized that I’d done the work while they worked on building a triangular truss bridge out of popsicle sticks. Another project, completed. How many projects can be moved along the curve to “complete” in a single day, at the end of a month of preparation and forward-leaning intention? Quite a lot, it turns out. I couldn’t put the cuffs on the sleeves of my shirt, unfortunately, but I could finish these two projects — and I also had enough time in that math class to build a small section of a truss bridge all by my lonesome. Building some small projects gives you the creative confidence to attempt more, and succeed. The math students were all stressed out about perfection. I knew mine wasn’t going to be perfect — so it gave me the go-ahead to do mediocre work as a learning exercise.

Thirty days of making: geomancy stave book.

kids lit up today when I said, “the lab has a pyrographer now.” They were disappointed when it turned out to be a wood-burner.

And mediocre work, or even terrible work, is the first step toward making great work.  The great work does not come at the beginning of the effort, but at the end.  Therefore, make the first few mistakes, and then a few more, and then a few more yet beyond that.  The great work emerges from the mediocre, and the Great Work emerges from the great work which precedes it.

The completion of the stave-book with my poem, Quatrains on Geomancy, took the longest. Maybe most of an hour.  I was working on other stuff in the lab, so I would scribe a line, putter in the lab for a bit while the fine tip re-heated, and then do another line, and so on.  THis was the most tedious part of the day’s work — not so much creative work, as deliberate carrying-out of a creative vision already decided upon. Sometimes “Done” means executing an existing plan, regardless of whether it’s the right plan or not.

Thirty days of making: geomancy stave book.

the completed book

On the other hand, the results seem to live up to my intention.  I have a book of eight staves or wooden panels. Each panel has two quatrains on it, each of which takes as its topic or theme one of the sixteen characters of geomancy.  The result is a small, ceremonial-style book that explains some aspect of the sixteen signs.  This is by no means the most-complete text on geomancy ever written, nor even the most accurate; but it is at the least a useful introduction to the subject.


Four projects (one not shown here, because I’d forgotten my phone up in my classroom when I was down in the costume shop waiting for a colleague, and using the sewing machine).  Four projects that are off my to-do list.

Thirty days of making, completed.    All in all, a very productive October.  The whole collection of Thirty Days of Making entries can be viewed here.

There are still projects to finish. The Mercury book, for example, and the geometry textbook. Even a page of those two projects is a couple of hours apiece.  I’ll have a good program in place to finish those two projects, but that’s not what this was about. Which brings me to…

Reflection on My Learning:

I’m a lot better at architecture, sewing, graphic design, and general creativity after thirty days of this stuff.  I’ll be better after sixty days, or a hundred days, or a year… but I don’t think I could sustain this level of attention to the writing about my creative process for more than thirty days at a time.  It’s often been an hour for the creative process, and an hour for the reflection upon it.

All the same, I’ve learned a lot from the process, I think.  I’m a lot better than I used to be about just starting, and just keeping going.  I don’t let myself get bogged down in mistakes — it’s not going to be perfect anyway, so keep moving. Get the thing done, get it finished, get it on someone else’s plate to consider and think on and reflect upon, and make it happen.  Then do the next thing.

Reflection on General Learning:

Do you find that other people always seem to be standing still?  I find that I feel that way now.  The more creative projects I do, the more skilled I am in other areas.  I met with a colleague today about Keynote, the presentation software from Apple Computer.  I showed her how to use the color-picker function, which allows you to click on an existing color and transfer the color from one photograph or object to another.  She’s a creative type, so she immediately saw its usefulness.  In a short while, after I’d shown her two or three things that she could do, she took over from me, and made a much more beautiful project than I’d ever have believed possible for a beginner.  Creative people learn new creative skills faster.

There’s more to say about that someday, but not today.  The big takeaway for me is that if you want to be creative, you compel yourself to be creative with a challenge that you must meet, in a public and obvious way. The results pay dividends which are unexpected but useful.


Five of five stars.  It doesn’t matter that some of the projects are bad — they all taught valuable lessons that established my skills and helped me deepen my own creative confidence.  Sooner or later I’m going to be able to stand tall and claim that October 2013 was a major milestone for my work as a designer — it’s where I established my own confidence in my abilities, and decided to take the necessary command over my desire to do, to make and to build, instead of merely to dream.

Creative Work For Others

Leave a comment

Scroll of Power
Originally uploaded by anselm23

I’ve had much more success lately at doing interesting and useful work for others, than for myself. A few months ago, I was asked to assist in doing some prosperity work involving a fountain dedicated to Jupiter at a local shop — which, as near as I can tell, worked. Odd, that. What was odder still was that the fountain broke after a few months, right after a major repair to the shop’s infrastructure was required. The owner had the money to pay for the repairs, but then the fountain broke. And one of the employees there has been asking me to do something new.

It’s been my experience that magic, like design, never quite works the same way the second time around. It’s part of the reason Apple never recycles its hardware cases from one design to the next: they design a completely new case or frame to go around a redesigned machine for a reason, and that reason has a lot to do with the dream and hope of the “new and improved”.

So, it’s a little early to tell if this is going to work for the shop in the way that they, and I, want. She only got it this morning, after all. But, it feels good to do work for someone else, and provide them with a tangible object of material benefit.

What’s the relationship between magic, and Design Thinking? It’s a harder question to answer. The late-Medieval/early-Renaissance author Henry Cornelius Agrippa states that the magician’s power lies in knowing the three-fold virtues of the universe, namely the virtues of plants and stones and woods; the virtues of measurements and patterns rooted in mathematics; and finally the realm of spirits and spiritual qualities. I’m paraphrasing, but I think that there’s a powerful relevance to design, and to design thinking. If a magician’s job is to know the three-fold virtues of the universe, then a designer’s job is likewise to know the three-fold virtues of the universe — because the designer, like the magician, is tasked with the duty of taking real-world materials and tools, measuring them and parcelling them out in the proper ways according to rules of mathematics and science, and making something to excite the human spirit with love and wonder.

Increasingly I think of myself as a designer rather than as a teacher, or a magician. But I don’t think I could have been a designer without being a teacher or a magician first. I needed to wrestle with the core concepts of those three-fold virtues of the universe before I could see that Design Thinking involves using real-world tools and materials to excite the human spirit.

The exciting thing, of course, is how much excitement I get out of being a designer-magician. I may not be any good at it, but it certainly delights my soul and my spirit to be a creator of things, above and beyond what mystical benefits accrue to the present owner of this scroll of power.  And it’s another way to bring more diversity into the world, which I think is A-OK.

Via Flickr:
A friend of mine runs a shop, and has been experiencing some of the ups and downs of the current economy. We tried doing some magical work to keep her shop running a while ago, using the energies of Jupiter — bringer of generosity. The earlier work was some Jupiter sigils attached to a fountain; that worked surprisingly well. But, then the fountain broke; the parts to the fountain have been sitting in a back room of her shop for a while.

So, last Thursday I started this scroll of the Orphic Hymn to Jupiter. I finished it last night, and gave it to her this morning — charged with Jovian, Solar and Lunar energies. For my first major piece of “calligraphy” (with a Sharpie pen!), I think it turned out rather well. Jupiter’s face is a little off-balance and crazy, but on the whole it turned out pretty well.

I didn’t use the traditional “medieval” page-layout that I’ve been experimenting with for this particular page, but there is an underlying geometry behind it, particularly on the illumination in the lower-right. All in all, it obeys Henry Cornelius Agrippa’s model of the three-fold virtues.