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.

The jacket 

Leave a comment

This was an awesome jacket.
I saw a kid in my regular coffee house wearing this jacket the other day.  He was wearing this customized leather biker jacket, tricked out like the biker jackets of the punk scene in the late 1970s and 1980s. It had been painted in turquoise, white and maroon paint and adorned with layered rows of metal studs. All the work had been done by hand.

By him.

I call him a kid, but let’s face it, some of those bottle caps are beer caps. He’s probably in his early 20s. I hope.

I asked him if I could photograph some of the detail work. I think he thought I was going to take a picture of him in his jacket, so he put it on. In retrospect I wish I had — but I feel uncomfortable about photographing strangers.

Even strangers wearing clothes they made. Or at least customized.
Still, I was impressed. it was a lot of work, 10 or 20 hours of labor customizing this jacket.

I think that we tend to underestimate the importance of customization in Maker work. But we live in a world absolutely overflowing with cheap manufactured goods. (This jacket, frankly, is not as well made as my jacket from the 1990’s… which isn’t as well made as my girlfriend’s from the 1980s, and definitely isn’t as good as my dad’s leather naval bomber jacket from the 1960s.)

We might disapprove of the message this kid is sending to the world, wearing a studded leather jacket. Or maybe we approve: I certainly do. But rather than purchasing such a jacket pre-made for some fashion line, this kid correctly recognized that there was a DIY ethic at work. He did the work himself. He customized an off the rack leather jacket to express his self-identity to the world.

And maybe we should encourage that in our students more — not because we want everyone walking around in studded leather jackets, but because we would like  people to be able to express their creativity and their hope for a more individualized world, even in off-the-shelf components.

Bookbinding: For the Behenian Stars


Update 23 January 2017: You can buy a copy of these poems through my Etsy store. Would you be interested in buying the book-block, so you can hand-bind the book at home?

A few days ago, a friend asked me if I would make a few of my poetry pieces available for a weekend intensive workshop he’s running. I said yes — but he was planning to photocopy the work, and make seven copies. I thought about this, and decided this was silly. I have the text block more or less ready to go as a PDF file. There are only seven people in this particular intensive… how hard could it be?

Boy, are my fingers tired...

A stack of hand-bound books

Two days later, I have seven “special edition” copies of a book that’s not quite ready for print, and I’ve made a few discoveries I hadn’t expected to make. First of all, this book will need to be longer in the next edition if I intend to bind it using the Coptic stitch, as I did here.  Second, I learned that if you’re going to get all fancy with the stitching, it’s a good idea to get the geometry correct, too — although I do like the star (because a book about stars, and full of star poetry like this, should have a star on it, right?  And it should be worked into the theme and design of the book, right?)

I have a lot of complaints about this edition, as a result.  But I also have a really good idea now of how many copies of a book I can produce in a few days, on short notice — and how many I can produce if I’m really taking my time and being careful with each and every book. I couldn’t be that careful with these; I didn’t have time to slather all over these with a noon deadline for myself today.

But I also learned quite a bit about setting up a production line, as I did with carpentry — make seventeen sets of covers for books; then let them dry while you cut and fold pages; weight the pages while you pierce the covers for the stitching; pierce the pages while you weight the covers again to help them loosen up a bit before stitching.  Stitch the books one at a time while watching cheesy ol’ TV shows to keep yourself seated and on-task making the books. Clean up as you go, or face massive piles of paper.  There’s a Flickr album of photographs from the process if you care to see the process.  Otherwise, you can just admire the books from afar.

Special Edition for Twilight Covening 2016

Always nice to see your name in print… even on your own handiwork.

And now there are seven copies of this book that were not in the world before. In any form.  Are they perfect? No.  Are they real?  Yes.

But real is a tricky thing when it comes to books of poetry, as any working poet will tell you.  We issue chap books for ourselves and our friends quite frequently, and make copies of our work in the hope that it will somehow outlast us.  I spoke to someone only last night, sharing a poem with them, and — when they asked if they could read it to someone else — said that it was part of my immortality spell.  I was only half-joking.

But even a chapbook is a fragile thing.  How many copies do you need to put into the world, for your words to outlive you?  How many beautiful art books must come into the world for a single one to survive the drift of ages?  Likely far more than I can produce by hand.

Unless I make them beautiful.  Unless I make them worthy of love and care and protection. Unless I attend to the effort to make my words and their repositories something larger than simply myself.

These copies are reserved.  I intend to inform the people to whom they are given that this is a gift, and in exchange for this gift I ask them to respect my copyright, and not to publish them, copy them, or hand the book on to someone else.

If you would like a copy, you will have to contact me.  I will be making more; but those will be for sale.

Design: Belgian secret binding 

Leave a comment

Making one book is easy. Making several is hard. A lot of things go wrong when you make a few books. Threads break.  Paper tears. Glue dries faster in the summer heat than you think it should. And it turns out that this design of book works better with an even number of holes in the quires or signatures than an odd number.

But it took making four books to figure out some of the things that go wrong.

The string that I used for binding the cover is ok. It’s not great. It’s not bad. But neither is it the best material — and it turns out that this binding involves a lot of strings pressing against one another and sliding over one another. So using waxed thread instead of un-waxed thread next time would be a good idea.

And it’s also interesting to make three blank notebooks exactly the same way: same covers, same binding, same internal pages. Even so there’s a great deal of variation. None of the three books have the same number of pages. There are a range of small variations even though I was trying to make all three of the owl books the same way.

31 DoM: Free Day


Today’s official 31 Days of Magic post, for the Strategic Sorcery community around Jason Miller, would be to cook a magical meal. But I won’t be home until tomorrow night, so that will have to wait until then.  Today is a “free day”, and the action in this case for me is to “write a poem”.

This evening, I’m acting as the giver of the toast at a combination dinner, dance, and ritual for the EarthSpirit Community at their annual “Stag King’s Masque” at Feast of Lights.  The old hotel where this event used to be held has closed, and as a consequence it’s being held at the Hotel UMASS in Amherst, Massachusetts. And for the first time in forever, dinner is included as part of the celebrations.

The feast is nominally the winter ball of the Stag King — annually chosen and annually feted at this Masque, which celebrates midwinter, wildness, and the growing light as the darkness of the winter solstice is left behind.

Sometime shortly before this post went live, I stood, and called the assembly to attention, and brought them to their feet, thus:

Ladies and gentlemen,
beings of grace and power and purpose,
masked revelers, honorable courtiers, and nimble-footed dancers:

Come, take your feet, rise in honor of our gracious host,
The Lord of these winter revels. 

Here we stand, in the very garden of mid-winter,
with the blossoms and sweet scents of icicles in our nostrils.

We feast this night under spreading branches,
but there in the distance, a growing Light,
glimpsed through the shadow of mighty Antlers!

Beings of grace and power, attend!
Grant him health, long life, prosperity!
Ladies and Gentlemen, the Stag King!

31DoM: Use Tarot Cards


Today’s assignment in the 31 Days of Magic project from the Strategic Sorcery community around Jason Miller is to “Use Tarot/playing cards” in some sort of working.

Yeah.  I can do that.  But as I remarked to Stacey a day or two ago, part of my goal in this series is to get magicians to think differently about magic, and to get teachers to think differently about creativity, and to get us all thinking differently about Making. And so it is that I’m revealing Something Really Important about the magical tradition.

31 DoM: use a card

I. Begin with a pencil drawing…

You see, I don’t think that the teachings in the grimoires about the appearances of angels and demons, or the images of the Planets that one finds in Picatrix, or the images associated with the Mansions of the Moon and the Decans of the Zodiac, are there accidentally.  I think they’re present in these texts not just as visualization tools for calling up spirits.

I think they’re there as a curriculum in drawing and visual representation.  Consider the following description, taken from the Fourth Book of Occult Philosophy allegedly but probably not by H.C. Agrippa:

The Spirits of Jupiter appear with a sanguine and choleric body; they are of middle stature; their motion is “horrible and fearful,” but they are mild of countenance and gentle in speech. They are of iron colour, which ought to have connected them with Mars; their motion is that of flashing lightnings, and withal thunderous; their sign is the apparition of men about the circle who seem to be devoured by lions. Their particular forms are a king with drawn sword riding on a lion; 2 a mitred personage in a long vestment; a maid crowned with laurel and adorned by flowers; a bull; a stag; a peacock; an azure garment; a sword; a box-tree.

This is a description, or more accurately a set of descriptions, that can be followed:  red and yellow, middle height, weirdly-angled body parts, human looking faces.  Reddish skin, lions, a man with a sword riding on a lion, a bishop, a woman with a laurel crown and flowers, a bull, a male deer with a suite of antlers, a peacock, a sword, a box-tree or topiary.  In other words, says the author of the Fourth Book, “don’t just look for these spirits… try drawing them, too.”

Maybe I’m wrong.  Maybe there’s no intention on the part of these late Medieval and early Renaissance artists to provide their students with a drawing curriculum.

But it feels right.  Consider the engravings of the 1600s and 1700s associated with alchemy.  The artists and artisans who produced those elaborate illustrations for the Rosicrucian pamphlets knew how to draw — wheeled fortresses and flying beakers, angels and angles and geometric figures of stunning complexity.  The creators of the illustrations were working within a tradition, and no one among them really appeared to fear Church arrest and persecution — they were the makers of the Church’s books and altarpieces, at first.  The Church could not have done without their illustrative powers.  And those powers of illustration, of illumination, of communication-in-pictures, had been passed down in some form since well before the Fall of Rome.

So maybe the Tarot isn’t just a divination system. Maybe it’s the end product of a complex course in drawing, designed to teach its users how to communicate in pictures.  It’s a simple way to learn how to paint miniatures for the medieval book trade.  It’s a simple way to learn to handle the tools of the medieval artist: the pen, the brush, the paint pots.  It’s a simple way to work with line are and a limited palette of colors.


More than that, though, whenever I create a card like this, I discover what a powerful artist Pamela Colman Smith really was. The card I did tonight, the Eight of Cups, is usually understood to be the acceptance of the spiritual against the love of the material.  But what I see is that the cups are stacked on the wrong side of a dive filled with water: our side.  The figure is renouncing the cups, perhaps, and seeking the mountains in the distance — but then, he or she was facing a long-way-around journey to come to the cups in the first place.  We the viewers have the cups, not the renunciate.

Is that significant? Maybe.  But I wouldn’t have noticed it, one way or the other, without drawing ehe card first.  And maybe that’s it — that it’s not just about drawing the card from the deck, but drawing-in-the-sense-of-duplicating the card that is equally important.  You don’t know what you’re looking at if you haven’t studied it, and if you draw it yourself, then you’ve studied it far more effectively than if you just looked at it.

The Visual Curriculum

Every card has an entire curriculum within it:  how to draw figures, for example.  How to duplicate proportions.  How to color.  How to portray light, and show angles.  How to express distance through size and through height above the baseline of the card.  How to demonstrate depth.  How to curve and straighten lines so that vertical and horizontal surfaces are seen. How to compress three dimensions of information into two.

How to learn how to draw.

Then as now, in Smith’s time as in Agrippa’s time as in the days of Hermes Trismegistus, drawing was hard.  Distance, proportion, color, angle of shadow, angle of light source, shade, hue, line — none of these things come naturally to anyone.  They have to be practiced just like writing or arithmetic. There was no place for drawing in the traditional medieval curriculum.  It is literally hidden in plain sight — in the lavish illustrations that adorn illuminated manuscripts, right alongside the texts describing the seven liberal arts.


Maybe, more importantly, drawing and the copying of drawings is a way to show students the practice effect at work. Here is the first copy of a Tarot card I ever did for myself. It’s a terrible rendition of the Eight of Pentacles. You can see that I’m starting to experiment with the idea of depth, with the idea of angles.   But if you want to get better, you have to do the work more frequently.

Because that’s part of this story too.  When I went to darken the green of the hills, and to paint in the boots and cloak of my human figure — I found that my ink pens had dried up.  I’ve been so busy with other things, like carpentry and string theory and design process, that I let this project to produce my own Tarot deck fall by the wayside for a while, and my kit was partially dried up.  Although I did a number of cards, including the Chariot, and used them to dispense some magical advice once upon a time… I’ve fallen out of practice.  I’m mostly picking up where I left off — but I’ve let some of my tools reach their expiration dates.

And it’s a useful reminder that all things face Saturn — death and endings — sooner or later.  Is drawing a part of the magical curriculum for you? If so, it’s time to get started.


31DoM:Use a Seal


For the 31 Days of Magic today, I’m supposed to use a sigil (e.g, of Solomon).  For me, this tends to mean the images from, say, the Clavicula Solomonis.  But I also think about it from the perspective of the images of the Decans of the Zodiac, or the Mansions of the Moon, from Picatrix.

Twenty-Fourth mansion of the Moon

after Nigel Jackson and Christopher Warnock’s book

I’d already done some work with the 24th Mansion of the Moon, as you can see.  The 24th Mansion represents a new beginning, as shown by a mother giving milk to her child.  It represents new starts, beginning new work, and represents a kind of balance or energetic equilibrium between Mercury (flitting here and there) and Saturn (establish boundaries).

This one is in a book, so I’m reluctant to mess with bit much; it’s already been ‘activated’, but tonight I made use of it in new ways.

31DoM: sealI also went back to the Clavicula Solomonis.  I don’t want to reveal which of the pentacles I intended to create; I’ll say that my goal was to achieve some greater level of insight into my students and colleagues.  But that isn’t the one I made. At some point, I hit the scroll button, up or down, and the seal changed; or maybe I flipped a page that shouldn’t have been flipped.   I read the wrong instructions, and produced the wrong seal.  So I think it will be interesting to see what results from this.  The seal I actually created is supposedly for helping make spirits visible when they try to be invisible.  And so I wonder what the result will be, especially since it’s in my notebook that serves as my bullet journal, my vademecum or grimoire, and project notebook.

From an artistic point of view, I think about the value of the work of reproducing seals. It’s a chance to think about letters as shapes, certainly; and to think about scaling.  It’s a chance to think about geometry and imagery.  It’s a chance to consider symmetry and beauty and ugliness.  And it’s a chance to think about color and design.

But it’s also a chance to reflect on actual magic.  I mean, from the perspective of the ‘outsider’ it’s hard to see this emblem as anything other than occult.  It’s mysterious (especially since my ability to write or draw in Hebrew is severely challenged, especially when I’m reading not-particularly-well-reproduced drawings by a Victorian occultist reproducing the work of a medieval author who probably didn’t really know Hebrew).  Of all the activities I’m planning to do during these 31 days of magic, this is the image which has the most potential to get me into serious trouble.

But think about that — if we live in a physical, materialist universe, then this is just an act of historical reproduction.  It has no power to affect any thing or any one. There are no spirits that are invisible, which can be conjured to visible sight; and at the same time, there is no conjuration which will actually conjure spirits at all.  The act of reproducing such a seal is a futile action in a physical, materialist universe, except maybe to display a kind of madness.  But if that’s the case, then saying this is an example of historical reconstruction is an utterly harmless if eccentric pastime; and there’s no reason to get in trouble for making it at all.

And if it’s not the case that we live in a physical, purely materialist universe, then I have some interesting times ahead.  New beginnings indeed.

Older Entries