Spiritual Linear Algebra

My partner Chien is a Scientific Rationalist, Atheist, software architecture engineer, avid gamer, and occasional amateur chemist. Periodically pagans ask me how I can have lived so long and so comfortably with a man who doesn’t share my faith, or any faith at all really, and whose sense of reality encompasses so little of my own.

The short answer is, of course, that he’s a wonderful, brilliant, caring, responsible, and most importantly respectful man, and I actively enjoy sharing my life with him. The longer answer is demonstrated in this post he wrote for me the other day:

I expect that just about everyone learned in grade school about what they called ‘graphing’ where you were required to draw dots on a piece of paper “4 spaces to the left and 3 up” and so forth, teaching about coordinate systems and the fact that you could put a point anywhere on your piece of paper, and for that matter, anywhere on the infinite surface that your paper was a little piece of. Math in high school extended this idea by calling them ‘x’ (left vs right) ‘y’ (up vs down), and adding  ‘z’ which was into the paper vs out of the paper, extending the coordinate system to the real world. These are the ‘three dimensions’ or ‘3D’ that are frequently bandied about, especially for recent television sets and such. Similarly to the 2D case, once you choose an origin (x=0,y=0,z=0), any point in the universe can be specified by providing some value for x,y, and z.

So, when you get to University and take a class called “Linear Algebra”, they add two more bits of complexity: first is that this works for any number of dimensions, although human brains really cease being able to comprehend what dimensions beyond 3 look like. So if you have some problem with 20 dimensions, you can uniquely determine any point in your 20 dimensional space by choosing a value for x,y,z,a,b,c,….for all 20 dimensions, just like the 2 and 3 dimensional cases work.

The second new thing is that the axes of our graphs (x increases to the right and y increases up) are not particularly special, other than they are easy to visualize.   It turns out that just about any set of N arrows pointing in different directions will provide the same ability of “go 5 in this direction and then 7 in that direction” to get to any point in this space of N dimensions. A set of these arrows is called a basis, or a basis set. And there are an infinite number of them, even for one particular dimensionality….

So, what does this have to do with spirituality?

If you visualize that the entirety of human experience is a space with a very large but finite dimension, then in order to encompass all of human experience (i.e. be able to describe every point in that space) you need a basis set for human experience! The two places that I see, having lived and talked with Ember for nearly fifteen years, where such a thing arises, are:


I hesitate to use the word ‘flawed’, but I posit that if we find that a particular Pantheon or Divinatory mechanism fails to adequately cover some particular aspect of human experience, it must be that the Pantheon or Divinatory mechanism fails to contain the proper ‘arrows’ from which that aspect of human experience can be ‘measured’, and therefore is incomplete as a basis set.  The effect of a Pantheon or Divinatory mechanism that fails to be a basis set is that it will be uncompelling to those individuals who are actually having experiences in the parts of human experiences that are unreachable within that Pantheon or Divinatory mechanism.

For example, if you take the deities of Christianity (arguably Father, Son, and Holy Spirit) then it is fairly easy to see that basically the entire feminine part of the human experience is missing, and therefore Christianity is incomplete as a basis set for the human experience.  Even if you were to add in the mythological figures of Christianity, the primary additions to the putative basis set are Mary the Mother, and Mary the redeemed whore, which still leaves vast swaths of the feminine experience basically untouched, and because of the disparity in spiritual power afforded the saints compared with the Trinity, even the axes of ‘mother’ and ‘whore’ are far weaker than any of the Trinity’s.

The Tarot deck seems to be much closer to a basis set, since it has 78 different cards as its axes, and allowing combinations of cards to mean different things than each card by itself further increases the effective size. While I am far from an expert on Tarot, I would expect that much more of the human experience can be derived from one.

So, an interesting aspect of this concept of basis set is that it is possible to work around ‘missing’ aspects if you have the proper materials. For example, a Pantheon or Divinatory mechanism might still be a basis set even if missing ‘mother’ as long as you have the parts in your basis set that could be used to make ‘mother’, like ‘fertility’ + ‘caregiver’ + ‘unconditional love’ + ‘protector’ + ‘family’.

I remain,
Chien D’Arren D’Or

I can’t comment much on the mathematics of his suggestion, since I only understand it as he’s explained it to me. I do have some notes of my own to expand and clarify:

1: He is referring, obviously, to what I call “token based” divination – i.e. systems based on a finite set of symbols, like the Tarot, or the Runes. It also applies to systems like Astrology, where the tokens are not randomly drawn, but determined by an established sequence of steps. The practical result is the same for his purposes.

Oracular trance does not have this artificially confining feature, although it does have the organic equivalent. My ability as a seer or dreamworker to interpret messages is limited to the ambient symbolic language my brain translates such input into – that language is naturally comprehensive to my experience, but if my experience doesn’t overlap the with the needs of the querent the relevant area, I may not be able to translate the message sufficiently for the querent to interpret my answer correctly. When that happens, the solution is to seek a different seer, hoping their life experience will have provided them with the appropriate referents.

2: He acknowledges that the Christian Trinity is not considered a polytheism from within Christianity, so the use of “pantheon” in this context is understandably loose. For the purposes of this question,  the Christian “pantheon” functionally includes the many intercessors and adversaries – saints, apostles, prophets, angels, demons, Satan, etc. although Protestant practice does not emphasize prayer via intercessors, nor the existence of demons, and I’m not sure what the actual canonical theology is regarding adversaries in the Catholic or Orthodox traditions. Functionally, it doesn’t matter what is canonical – folk theology is also part of practice.

There are actually at several Marys in the New Testament, and the reformed prostitute is yet another figure, though she is often conflated with Mary, Lazarus and Martha’s sister, in confusion, and from there conflated with Mary of Magdalene. For the sake of folk consciousness, however, the “damage” is long since done. Even “Mary, Mother of God” is not actually the peer of the Divine Trinity, theologically – She is merely the greatest of the intercessors. This does indeed create a problem that feminist theology was developed to address, and that the Goddess movement also arose to address. Abrahamic tradition actually does include the divine feminine if you go back far enough, but until these movements made a point of exploring Them, They were not generally included in mainstream consciousness, and arguably still aren’t.

3: I think what happens with actual Polytheistic pantheons is that when something turns out not to be covered in the basis set, either existing deities take on those roles as they arise, or new gods are born. Sometimes deities combine or split, for similar reasons. Greece and Rome were happy to have new deities.

Other cultures were more likely to attribute to existing deities. A lot of cultures would pull gods from their neighbors’ pantheons as they encountered new needs, since those new needs were as often introduced by their neighbors anyway.

Syncretism also helps a great deal in this regard, as lining up deities of our own with the symbols and thus needs met by our neighbors deities helps us expand our understanding of all Powers involved, and thus has the effect of expanding our basis set.

And of course, in traditions where ancestor elevation is possible (such as the canonizing of saints, to get back to his Christian example), expanding the basis set comes naturally as time passes, and impressive people are revered for what they did in a more modern lifetime, thus automatically incorporating new needs and realms into the pantheon as we go.

4: “[N]early 15 years”! Wow, I guess it has been that long… 😀



About EmberVoices

Ember Cooke has been a member of Hrafnar and Seidhjallr for more than a decade, where she trained to be a Seidhkona, Galdrakona, and Gythia. She founded the Vanic Conspiracy and made ordination vows to the Vanir and her congregation in the summer of 2013. She has contributed to several publications on Heathen and Northern Pagan subjects and regularly presents rituals and workshops at festivals. Her personal practice is more diverse, as the Vanir have lead her into cross-training and service for the wider Pagan community. This has including medium and servitor training in American Umbanda, clergy training with the Fellowship of the Spiral Path, and jail ministry for local counties. She holds a BA with honors in Religious Studies from Santa Clara University. Ember has lived all her life in the south San Francisco Bay Area, and is intimately bound to the valley of her birth.
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