On Oils as Offerings

The following is an old post of mine from 2015.  I wrote it a as a guest post for the excellent Quadrivium Supplies, an oil-maker I turn to every so often when I need some real good stuff, and whose oils have never let me down.  She asked me at one point to write a guest post, and I did; it went up in early 2015.  However, she’s since moved platforms and went to a wholesale model, and in that transfer of platforms, her blog got nuked.  While the post went up, it’s no longer there.  I figure I may as well repost it now for posterity, and plus, reading over it reminded me of some good ideas I once had once upon a time.  I hope you enjoy this little relic of writing!


As a ceremonial magician, I go through a lot of supplies.  Yes, there’re the crafting supplies like wood and lead and gold leaf to make Tables of Practice and wands and talismans and the like, but I also go through a lot of consumable supplies like candles, wine, incense, and especially oil.  While I’ve got a grasp of crafting and making some of my own basic supplies, it certainly helps to have friends who can do these things better or who have access to more raw bits and pieces to make better things than I can; after all, while I can make oils for myself, I’d much rather get one of my friends who can expertly create and fine-tune them instead because, well, they know what they’re doing with better equipment and starting goods than I have.

One of my friends owns the lovely Quadrivium Supplies, and she’s an excellent oil-maker that I’ve pinged time and again for very well-made magical oils and advice on how to make a few myself.  My only regret with her work is that I don’t have quite enough income to get some of her oils in bigger quantities!  She knows her recipes well, uses real and natural ingredients that some might shy away from getting, and even makes a series of astrologically-elected oils that are without comparison.  These aren’t cheaply-made garishly-colored artificial oils with a bit of scent, but powerful tools and buffs in their own right.  Recently, she asked me if I’d be interested in writing a guest post on her blog, and I happily obliged.  After thinking for a bit, I figured a good intersection between her work and mine would be a good topic to write on.  Go read my entry there, On Oils as Offerings!

It’s rare that I get the chance to write a guest post for someone else; after all, I have plenty of writing already done and plenty more to do here at the Digital Ambler.  Then again, I’m also not opposed to doing so, since it also gives me a delightful change of pace.


Ceremonial magicians are known for using endless magical tools and magical materia in their works, and I’m no exception; one of the recent choices I had to make in moving to a new house was needing to find a place with a suitable room as my own temple room and magical workshop to house my shrines and altars, as well as providing storage for all my tools and charms that I make.  To be fair, unless tradition dictates otherwise, no system of magic strictly requires material means, but they certainly help, especially in obtaining material ends.  Having a material component in one’s magical work helps to bring down those astral and spiritual forces down, grounding them and giving them a means to work and effect themselves in our world of body and form.  Wands, crystals, talismans, mojo bags, drawn-out circles, engraved candles, and all the rest help in one’s magical works.  Oils are no exception, but they’re also something of a special case.

Not too long ago, I was conversing with one of my spiritual mentors, Saint Cyprian of Antioch, in preparation for a magical undertaking of the Arbatel operation, where one conjures and begins work and initiation with the seven Olympic Spirits associated with the seven traditional planets of Hermetic cosmology.  Saint Cyprian of Antioch, although a Christian saint, was also a powerful magician in his day, and over the centuries has become a steadfast ally to those who call upon him in matters of magic and sorcery of all kinds.  Seeking his advice, he recommended I go through with my plan and conjuration setup: the standard conjuration triangle, crystal scrying medium, incense, yada yada.  However, he suggested one important change: offer the Olympic Spirits a small amount of clear, good oil.  I was considering preparing wine or food, but Saint Cyprian of Antioch turned those down and rather emphatically suggested that I use pure, clean oil as an offering.  He explained that oil has a “volatile” nature, not in the same way as elemental Fire or alchemical Sulfur, but as a magical medium for housing things in a way stronger than water but less than crystal, more pliable than food but less ephemeral than incense.  For housing the soul or power of a spirit, oil would be an excellent offering, especially for entities like those from the Arbatel.

After thinking about this some, I realized that this makes perfect sense.  After candles and incense (and wine, though that’s usually for my own personal use), the material supply I go through the most is a variety of oils.  A full shelf in my supply closet, which is a miniature botanica in its own right, is packed with oils from a variety of distributors and craftspeople, some simple colored-and-scented artificial oils, some intricately developed from the purest extracts all manually taken from herbs and other natural sources.  Most workings that call for candles or talismans will, either due to the recipe or my own inclinations, use an oil in fixing things properly so that a particular power can be fixed.  Abramelin oil, specifically the German recipe, is one I use daily for my own strengthening by anointing my head and palms in prayer.  When using a traditional oil lamp, I’ll mix in some particular oil with the normal fuel for a particular end, like an older cognate to fixing a candle with oil.  I find myself using oils in pretty much any magical operation nowadays; such experimentation has often led me to find alternative uses for oils, sometimes in ways entirely unexpected.

Then again, there are more ways to use oils than in fixing candles or anointing heads.  Among all the oils I have, the one I go through most is common olive oil.  This has a rich history in Mediterranean magic and Western culture generally as a symbol of richness and power, both in this world and in most others.  Simple olive oil can be used towards pretty much any end, not having anything but the pure fruit of the olive tree involved, and when prayed over in a particular manner, can be used on the spot in lieu of any magical oil.  However, I don’t typically use olive oil as a “magical oil”, per se, but as a substance in offering.  For instance, whenever I make an offering to the theoi of the Hellenes, I always pour out an offering of wine with a dash of olive oil.  For one, the Greek gods like the offering of oil with their wine and prayer and incense, but it also suffices to cover the wine and prevent most forms of bacterial or fungal growth in their offerings.  (And yes, the wine still somehow manages to evaporate as the spirits consume it from under the oil, even though this shouldn’t normally be possible, but hey, gods do what they want.)

Of course, I don’t just offer olive oil to the spirits.  Some oils have histories and known uses limited pretty much to offerings, and I’ve taken that route with my own Three Kings oil when working with the Three Wise Men, though they’re also teaching me other methods of using such an oil when working with and under them.  When I need to empower a spirit a particular way, I’ll make them a normal libation but with a few drops of a particular oil that I feel is appropriate.  Household protector spirit needs to be buffed up for an incoming attack?  They’ll get an offering of strong wine with Fiery Wall of Protection oil.  Need to propitiate Aphrodite to help a friend smooth out their relationship?  Sweet wine with Reconciliation oil.  Cleansing a sad spirit who brings in filth?  Clear water with Van Van oil.  Want to placate an angry ancestor with a taste for food?  Good whiskey with turkey drippings (yes, really).  Just as oils can be used to fix a candle or prepare a talisman for ensoulment, oils can also fortify offerings to the spirits and empower them directly.  For that matter, oil can be dedicated to spirits alone for their own use, and if those oils happen to already be consecrated and empowered with herbs or other substances, it can empower the spirit just as strongly as it can empower a talisman.

In the case with the Arbatel spirits, Saint Cyprian of Antioch recommended I use the olive oil as an offering for them to consume, but also to help bring them into the world in their own way.  Oils on their own, according to Saint Cyprian, provide a flexible but useful means to contain the power or presence of a spirit, not unlike talismans or mojo bags, but in a more disposable or usable manner than a set object.  In the case with the Olympic Spirits, Saint Cyprian suggested that I give the spirit pure olive oil to consume and inhabit, then emptying that oil out into the world, allowing the power of that spirit to spread out in our world so it can do its work better in ways that I may not always be able to accomplish.  Oils don’t just evaporate into the air as waters or alcohols do, nor they don’t just vanish into particles like incense or smoke, nor do they stay fixed and firm within a solid containing body.  Oils leak and seep into the world, dispersing themselves and attaching themselves to objects and places, coating things with their powers and imbuing them with their own essences. Oils are much more difficult to get rid of and don’t simply wash away, but they’re not permanent fixtures, either.

Oils, in the end, are just as important a tool as anything else in a ceremonial magician’s temple, if not one of the most important ones.  Sure, not all traditions call for oils in their work, but almost all my workings in a variety of traditions have benefited from including their use for one purpose or another.  I would even rank oil as more important than candles or incense, because a properly prepared oil can take the place of both.  It’s important to remember that oils can be used for many more things than fixing or anointing, but that oils can be used in offerings directly as another method of working with spirits in a way that’s both profound and powerful.

Search Term Shoot Back, November 2014

I get a lot of hits on my blog from across the realm of the Internet, many of which are from links on Facebook, Twitter, or RSS readers.  To you guys who follow me: thank you!  You give me many happies.  However, I also get a huge number of new visitors daily to my blog from people who search around the Internet for various search terms.  As part of a monthly project, here are some short replies to some of the search terms people have used to arrive here at the Digital Ambler.  This focuses on some search terms that caught my eye during the month of November 2014.

“wicks for middle eastern oil lamp” — Honestly, for those little clay, metal, or terracotta lamps you find from the Middle East, the best type of wicks are those you make yourself from a cotton ball.  Every cotton ball is actually a tiny roll of cotton; simply unroll it into a flat-ish sheet, then roll it again tightly lengthwise like a dreadlock.  Stick it into the spout of the lamp, soak in oil for five minutes before lighting, and boom, you have yourself a perfectly good wick.  Follow the rest of the rules for oil lamps here.

“seven sphere rufus opus”, “‘seven spheres’ opus”, “seven spheres rufus opus”, “rufus opus seven spheres”, “seven spheres by rufus opus” — Yes, Fr. Rufus Opus (my instructor, who is not me) released a book this month, “Seven Spheres” by Nephilim Press.  It is an awesome book (that I did not write).  You should totally buy it from him (who is not me).  I have my copy that I’m working through, and it’s truly an awesome text.

“cinnamon powder spell benefits to sprinkle in four corners” — I don’t know of any, myself, but cinnamon is used to sweeten things up, as well as bring prosperity and joy into one’s life; given its connections to the Sun (cassia and Saigon cinnamon are a little spicier and given to Mars), it also has some mildly protective benefits in magic.  Some ideas for sprinkling cinnamon in this fashion would be to do so in an hour of Jupiter in the day of the Sun, praying for prosperity and happiness to fill up your home, hearth, and house, that all rooms in the house and all places on the property be blessed with the grace of the Lord.  Simple stuff like that, perhaps also setting a white candle dressed in cinnamon oil in each room.

“how to relate question to geomancy houses” — The twelve houses of geomancy are the same twelve houses in astrology.  You, as the querent, have a query to ask.  That query has a topic.  Find the house that best relates to that topic: e.g., if marriage then house VII, if children then house V, if job then house X, if curses then house XII, etc.  It really doesn’t get any simpler than that.  If your query doesn’t have a topic, then you don’t have a query.  If your query can be associated with several houses equally, then inspect each of those houses.  Take your time.  There is no rush to ask a question of geomancy.  Make sure your query is clear, concise, and concrete enough for you to handle instead of being vague, complicated, and abstract.

“tetractys divination” — This is an idea I’ve been experimenting with, using the Tetractys (especially in mathesis) for divination.  I haven’t yet found a suitable way to do so, but there are opportunities here I may not be looking at yet.  My idea would be to use two ten-sided dice (2d10) from a tabletop gaming set, with the 0-9 die given to “answer #1” (where you’re coming from, where you’re based out of, past experiences) and the 00-90 die given to “answer #2” (where you’re headed to, what you need to become, future experiences).  The number on each die could be associated with one of the ten sphairai on the Tetractys, such that if I rolled a 3 and a 50, that’d indicate the sphairai of Fire and of Salt, respectively, indicating that it’s time for me to reduce myself from pure action in the world to a base of nothing, to burn out completely, to focus on the substance that keeps me burning rather than focusing on the results of acting.  That kind of thing.  It’s a side project, but one that could be useful.

“penis growth curse” — …is this really a curse? I mean, usually you’d want to shrink or remove the penis as an effective curse, which is actually a cultural phenomenon in Africa known as koro.  People actually get killed for being accused as wizards or witches there who shrink or disappear away men’s penises, so this is a pretty big thing, but cursing a penis to get bigger?  Dude, that’s like a fetish of everyone who likes penises, especially their own, unless you’re talking about something so big that it’d crush cars.  Even then, there’s a fetish for that, too (hyper and/or macro).

“huge dick images.” — You won’t find any of those on this blog, sadly; I may be a little colorful with my vocabulary, but nothing here is generally NSFW.  I do make the “big anointed wand” joke occasionally, though.

“how to use elohim gibor in prayer” — Technically, you don’t.  From my point of view, you let him use you.  Elohim Gibor (lit. “Strong God”) is one of the names of God, associated in Western qabbalistic practice to the sephirah of Geburah and thus to the planet Mars.  I’ve used this name when working with a martial aspect of God or when working with martial spirits who respond to this name of God.  However, the process is the same otherwise as with any other name of God: you seek the aid of God for his blessing, grace, guidance, and protection that his will be done and not your own lest it be in accordance with his, that you work with the authority of God that God may work through you, etc. etc.  So, really, the answer to this turns out like that Soviet Russia joke, with Elohim Gibor using you.  Beyond that, gematrialize it, intone it, contemplate it, meditate on it, calligraphy it, and whatever else you want to use to figure the name out.

“rufus opus review” — Dude’s cute but in a relationship, also straight, so I typically don’t have my eye out for him like that.  He’s charismatic, for sure, especially once he’s got a few whiskeys in him.

“do males born on a leo/virgo cusp have big dicks” and also “do guys born on a leo/virgo cusp have big penises like greek god hermes” — I’m not surprised I got these searches (again), though I am surprised that they came apart several days away from each other.  Either this is one very concerned searcher, or two separate searchers who have similar tastes and problems.  Hermes, if you look at his Homeric Hymn, would actually be born sometime around the end of Pisces or the start of Aries (a few days after the third New Moon after the winter solstice), and he’s not generally the most sexualized of the gods (though he has his own thing going on), and isn’t exactly a god of giant endowments.  Then again, he might be totally the god to go to if you have a koro curse to enact on someone, which would be hilarious for everyone except those who’d get killed in Africa for it, so I dunno.

“geomancy blog” — While this blog covers many topics, I do occasionally write about geomancy.  A while ago, I wrote a 20-post series on geomancy that covers each of the 16 figures in depth and at length along with four aspects of geomantic technique. the I even wrote a translation of a medieval text on geomancy, which is available on my Etsy that you should check out!  Spread the word, check it out, and I hope it helps.

“congo men biggest cocks” — Since I’ve never slept with someone from the Congo region of Africa, I can’t say whether this is true or not. Also, seriously, I know the US had two federal holidays this past month, but if having two extra days off (for only a percentage of the population here, mind you) gets you that hot and bothered that I’m getting a higher than average hit count for people looking for giant pictures of dicks or for people with giant dicks, I seriously question why you’re using Google and WordPress and not Grindr or Scruff.  Tumblr’s where I go to get my porn, generally speaking, so you might also check that out.

“material used in summoning a spirit” — Technically speaking, you don’t need anything material to summon a spirit; intent, prayer, and a mental connection are all you strictly need.  Some people do a bit of centering prayer to contact a spirit, some people go to their astral temples, and other people just see them, flag them down, and have a conversation with them.  That said, many people (including myself) find it extraordinarily useful to have material tools, for which I suggest a scrying medium (e.g. crystal ball, glass of water, mirror), a summoning platform (e.g. Triangle of Art, Table of Practice), a tool of will (wand or knife or dominant index finger), a few candles, some appropriate incense, and the usual stuff.  Again, none of it is strictly needed, but it helps.

“books on loan from australian libraries about hinese and japanese astrology specifically nine star ki” — I know literally nothing about any of these these things.  I am definitely not an Australian library, nor have I ever been to one nor gotten a book out on loan from one. I’ve talked about these things exactly zero times on my blog or my Twitter.  Why did Google lead you here.  I apologize.

“adherent bandage and jelq” — For those who don’t know, jelqing is a method some men use to increase their penis size (both length and girth) by forcing more blood than normal into it with an extra-firm grip, using an almost udder-milking technique.  The jury’s out on whether this works, but I’ve heard good things with it, so long as you keep at it regularly like any workout; the idea is that you’ll slowly stretch the blood cavities in the soft tissue of the shaft, which allows it to hold more blood when you get an erection, which means getting a bigger hardon.  It’s not recommended for everyone, and there are definitely unsafe ways to do this.  Since you’re forcing more blood into the cock than normally goes in, if you have a cut or scrape or other wound on it that requires a bandage, you really really shouldn’t be handling it that roughly, if at all.  But then, who am I kidding, if you’re already into jelqing then you’re probably not looking to play by all the rules.

“do quadrivium.oils work” — Absolutely!  Some of my favorite oils comes from Quadrivium Supplies, and I’m a big fan of her work.  She charges a pretty reasonable amount for pretty powerful magical oils, and occasionally stocks some other useful and interesting supplies.  By all means, take a look; this time of the year, she has some good sales going on, so have at!

“san lazaro bead pattern” — San Lazaro, more commonly known in English as Saint Lazarus, can be a bit confusing for some people, since there are two Lazaruses in the Bible.  One is Saint Lazarus of Bethany, the brother of Mary and Martha and the one who was raised by Jesus Christ from the dead after being in his tomb for four days.  The other is…well, he has no formal appellation, just “Lazarus” from the parable of Jesus known as “The Rich Man and Lazarus”, from the Gospel of Luke.  San Lazaro kinda merges these two Lazari, mostly from the second, and is often depicted as a beggar covered in sores, walking on crutches, and licked upon by dogs.  He’s syncretized with the orisha Babaluaye, the orisha of illness, poverty, death, and the like.  However, there are many paths or aspects to San Lazaro, each possessing their own name, focus, and bead pattern for their elekes.  While you should always go to your local olorisha or Santero/a for real information, you can find some information online that may not be as trustworthy.

“hermes/mercury and legba” — They’re all pretty cool guys who don’t afraid of anything.  However, they are not the same entity, and you’d do well to take heed of that.  Hermes is Greek, Mercury is Roman; these two basically grew up together, with Mercury being solidly based on Hermes (the name “Mercurius” literally means “god of the merchants” and isn’t a native Roman god).  Legba is one of the variants of the name Eleggua, the childlike trickster and messenger of the crossroads who opens the ways.  Yes, they both preside over crossroads, messages, pranks, children, medicines, and many other things, but there are also important differences, too.  Legba, specifically, indicates more of a Haitian variant from Vodou, which has its own means of contacting Legba than Santería does Eleggua.  I highly suggest against conflating Legba with another crossroads gods, especially from a white or European culture.

Pythagorean Correspondences to the Tetractys

As many of my readers know, as well as those in Western occulture generally, correspondences are a big thing for us.  Based on our shared philosophical and educational lineages, we like to say that “A is like B”; we understand that the light of the Sun is much like the heat of fire, which itself is like the luster of gold based on certain shared properties.  In recognizing these shared properties, we immediately come to a system of symbols, where one thing can stand in for another, as well as to a system of harmonic relationships, where two things can be used compatibly with each other because they share the same ideas.  On a large scale, we call this system of symbolism one of correspondence, where something corresponds to something else.  This is often used in emanationist frameworks, where these correspondences cross levels of manifestation.  For instance, the Sun being an astrological planet is on a higher level than the element of Fire, which is itself on a higher element than actual fire or gold.  However, we can use any of these things to represent or produce a harmony with the other since they’re all corresponded to each other.

Probably one of the most valuable resources for this comes from the Second Book of Occult Philosophy by Cornelius Agrippa, where Agrippa presents a set of correspondences that link various names of God, planets, choirs of angels, ranks of the blessed, elements, prophets, and the like to each other based on certain shared properties.  Crucially, however, Agrippa organizes this by number.  Thus, he has a Scale of Four (book II, chapter 7) to correspond things that are easily divisible into one of four groups, a Scale of Seven (chapter 10) for things grouped into sevens, a Scale of Ten (chapter 13), and so forth.  Each of these are immensely useful for magicians, since they provide us with symbols and ritual ideas at a glance.  Aleister Crowley’s famous Liber 777 and, more recently, Stephen Skinner’s Complete Magician’s Tables offer these but on a much grander scale, corresponding far more things together on a qabbalistic basis than Agrippa does in his Scale of Ten.

Of course, finding systems of correspondence is an old thing, and even back in classical and antique times do we see the foundations of these systems of correspondence set up and used.  And, well, you can see where I’m taking this, aren’t you?  The Tetractys, that venerable Pythagorean symbol, was seen to contain within itself the foundations of all life and existence in every conceivable form, and not just in a strictly emanationist way.  Each rank of the tetractys, based on whether it related to the Monad, Dyad, Triad, or Tetrad, was associated to something else that formed part of the cosmos.

One good source for this comes from Iamblichus’ Life of Pythagoras, where he gives a good overview of the life of Pythagoras (duh) as well as a number of his teachings (though nowhere in depth as I’d like).  The Taylor translation linked above, however, also contains an extensive collection of other Pythagoreans who followed Pythagoras and wrote down what the Teacher (ostensibly) said, as well as a set of notes where Taylor inspects the things Iamblichus says and expands on them where the original author was annoyingly terse to our modern readers.  Part of this expansion is where Taylor talks about how the Tetractys wasn’t just a number but a graphical mnemonic, if you will, of various things

Monad Dyad Triad Tetrad
Number 1 2 3 4
Doubling Progression 1 2 4 8
Tripling Progression 1 3 9 27
Even Geometry Point Line Polygon Solid
Odd Geometry Point Open curve Closed curve (circle) Cylinder
Element Fire Air Water Earth
Platonic Solid Tetrahedron Octahedron Icosahedron Cube
Growth of Vegetation Seed Length Breadth Depth
Communities Individual Family Town State
Power of Judgment Intellect Science Opinion Sense
Parts of an Animal Rational Irascible Epithymetic Body
Seasons Spring Summer Autumn Winter
Ages of Man Infancy Youth Adulthood Old Age

Well, would you look at that, it’s a table of correspondence along the same path as Agrippa’s Scale of Four.  It’s not quite the same (Agrippa gives Summer, Spring, Winter, and Autumn instead of Pythagoras’ Spring, Summer, Autumn, Winter, and I’m personally in favor of using Agrippa’s associations or a variation thereof, especially considering how Athenians started their year at the summer solstice), and there are a few hard-to-understand terms and progressions, but for the most part it’s definitely something useful in seeing how emanation works in everything.

I mean, sure, the can of Monster energy drink next to me is something that emanated from the Source just as I did, but it has a different body and different contents than I do.  Consider the body of the can, the metallic mostly-cylindrical shape the drink comes in.  The can wasn’t born, so it can’t age in the way a human ages, but consider how soft drink cans are made for a bit.  The cylindrical can was stretched out from a circular cut from a flat sheet of aluminum; from this, we got the tetrad-corresponded cylinder from the triad-corresponded circle.  Of course, this circle itself has depth, since it’s a cutout from an aluminum sheet which is a body; all bodies have three dimensions (length, breadth, and depth), without any one of which it’d only be a two-dimensional shape.  So, whence the circle itself?  The circle itself is a form, not a body, an idea that can interact with others.  Whence the form of a circle?  The form of a circle is made from a curved line traveling around a point.  After all, all circles only need two points for a definition: a center and a boundary.  The curved line demonstrates motion and direction, both of which are relative concepts (in order to move, you need something to move from both in terms of location, speed, orientation, etc.).  The curved line, then, comes from the single point, the Monad of all shapes and forms and bodies.

So why is the tetradic form of a circle a cylinder and not a sphere?  After all, isn’t the sphere the thing most like a circle in the third dimension?  Sorta, yeah, but a sphere is (according to Pythagoras and other Pythagoreans) a perfect body, and there is nothing we can make in the cosmos that is perfect due to the constant actions of Difference, Existence, and Sameness as well as the upheaval and drama in the four elements.  Rather, the tetradic form of a circle is a circle with depth, the most straightforward of which is a stack of circles, forming a cylinder.  It makes sense, though a little counterintuitive.

Between Agrippa and Taylor’s exposition of the correspondences of fourfold things to the Tetractys, a lot of intellectual work has already been cut out for us in studying how the Tetractys can relate to individual things.  Then again, that’s just it; this kind of analysis is good for understanding individual things, and it’s the relationships of those things that are just as important, if not moreso.  In fact, one of the more famous divisions of things is the Quadrivium, literally “four ways”: four types of mathematics used throughout the classical, medieval, and Renaissance worlds.  In this, arithmetic is an understanding of bare number (Monad), followed by music (in the broad sense) as an understanding of relationship and modulation (Dyad), followed by geometry as an understanding of static form (Triad), followed by astronomy which is an understanding of moving bodies (Tetrad).  Just as one can’t study astronomy without a knowledge of geometry, and geometry of music (for the study of proportions and ratios is a type of music in the classical, ideal sense!), and music of arithmetic, the Tetractys itself indicates that the relationships between things are where the real action lies in the cosmos.

After all, wasn’t that the whole point of my developing mathesis, anyway?  To discover relationships more than units?  To understand the changes between the different methods of manifestation rather than the methods themselves?  Something is still missing, and that’s where mathesis becomes mathematic, in our modern sense of numbers and relationships.  After all, if we’re still trying to analyze stuff as individual units, then we’re dealing with things as individual monads.  A Dyad is more than just two monads put next to each other; it is a relationship between the two that makes two monads into a Dyad.  That relationship is often called “music” in Pythagorean literature, but it’s not necessarily the music of instruments or sounds.  Music, in this case, is the means of progression, movement, and patterns.  It is not enough to study sheer quantity in the arithmetic sense, and it is yet too much to study harmony in the geometric sense.  Another type of analysis-and-synthesis is needed for the Dyad.