Gee, this schematic is exactly relevant to my current elemental divination project, though the "paths" are in a different configuration than what I'd been playing with (and that admittedly hadn't worked in any elegant fashion as of yet)...
You've probably posted it for some other reason altogether, but thanks for posting it so you could spur me in new thought-directions! I know nothing about geomancy, so what's inside the "points" doesn't make sense to me, however the geometry itself might be useful.
I'm preparing to ask JMG a Magic Monday question that'll need some supporting illustrations and was thinking I'd pre-think it as a blog post. Would you mind if I also posted your image (with attribution)?
Also, how do you make all these great charts/images? My question's accompanying images are going to have to be hand drawn.
You've probably posted it for some other reason altogether, but thanks for posting it so you could spur me in new thought-directions! I know nothing about geomancy, so what's inside the "points" doesn't make sense to me, however the geometry itself might be useful.
You're welcome!
Mathematically, the geometry is called a unit-distancetesseract graph. (This is the four-dimensional case of a hypercubic graph.) It's effectively the shape that a four-dimensional cube (e.g. a "tesseract") makes if you squish it flat onto a piece of paper.
How does this relate to geomancy? Geomancy is an elemental symbolic system where there are sixteen symbols, each with some of the four elements (fire, air, water, and earth) are either present or not present. (The meaning of each figure depends on which elements are present: for example, the figure "Carcer" is a combination of fire and earth, and means "separation" since these two elements do not mix well and tend to pull in opposite directions.) Each vertex of the graph contains one figure, and has a line to each figure that varies from it by flipping exactly one element. (That is, each figure links to the four figures that are most similar to it.) There are a lot of ways to assign the figures to the vertices (in fact, around 21 trillion ways), but I chose one that has really elegant properties. (One example is that the direction of each line represents an element; another is that the most "mobile" figures appear at the top and the most "fixed" figures appear at the bottom; another is that the most "passive" figures appear at the left and the most "active" figures appear at the right.)
I posted it as a theme for meditation; walking the paths around the overall figure is useful, I find. (In fact, meditation is where I got this in the first place!)
Would you mind if I also posted your image (with attribution)?
Not at all. In fact, attribution isn't necessary (though you're welcome to credit me or link here if you like). Like everything I post, it's in the public domain.
Also, how do you make all these great charts/images? My question's accompanying images are going to have to be hand drawn.
Oh, dear. That's complicated.
The short version is that there are computer "languages" describing how to draw pictures; in this case, the one I used is called Scalable Vector Graphics (or "SVG" for short). It's a text format (in fact, if you're familiar with HTML, it's very similar), and I wrote it out by hand using a text editor. (The text editor I use is an ancient one called Vi, which is basically Notepad or TextEdit.)
I used lots of trigonometry and analytical geometry (which I worked out by hand on paper using a pencil) to construct it. The lines so happen to have a slope of tan(π/8); this is a complicated irrational number (and there's no way I'm dealing with those by hand), so I used a Stern-Brocot tree to find an appropriate integer approximation (in this case, 17/41); from there it was just a couple quiet hours with a calculator. (I have severe chronic fatigue, so I require an extremely large amount of "down time;" I figure I might as well use it as productively as possible.)
I'm a computer programmer by profession, so these are the kinds of tools I use on a daily basis at work! I picked them up bit-by-bit over the last few decades, and I guess I'm just used to them by now.
Well, most of what you do flies right over my head! :D Though I do recall tesseracts from A Wrinkle in Time. Heh.
Also, math is so NOT my strong suit that I just have to nod appreciatively when you say "a slope of tan(π/8)" and pretend I didn't actually get all the way to some form of college-level calculus. How I managed, that, I'll never really know and it seemed to have all been lost along the way since then.
I'm impressed with your "short version" - it sounds quite complicated, or at least very specialized! I'm embarrassed to admit that I wondered if there was a "plug-and-play" graphic image maker. The fact that much work went into making the image is the reason I'd give attribution/credit - though the result is public domain, getting to the result required your expertise, time, brainpower, etc...
Meanwhile...
Hmm, "an elemental symbolic system where there are sixteen symbols, each with some of the four elements (fire, air, water, and earth) are either present or not present." Now that's interesting!
I'm working with 25 combinations because Spirit is regarded as one "elemental" component in the modern Ogham tradition. The schematic I'm trying to discover or locate (if there is one) has to arise out of some of the pairings' specific qualities. This schematic might not be possible given what I know so far about the ways the elements combine, but that's essentially what I've been gnawing on for awhile now. Also trying to see links and disjunctures, transitions and relations between the 25.
I may end up needing to at least dip into the descriptive text on geomancy, just to see how elements and their combinations are conceived. While some of that is likely to be non-Druidical in nature (and thus different from my Ogham-derived system), there's probably some "genetic" similarity (both coming from Western occultism) that might be useful to explore.
I'm embarrassed to admit that I wondered if there was a "plug-and-play" graphic image maker.
😅 As you can see, my Mercury and Saturn are dignified and my Venus is a mess! So I'm afraid I do things the hard way, and don't know about such programs.
I'm working with 25 combinations because Spirit is regarded as one "elemental" component in the modern Ogham tradition.
That makes sense to me: 25 is the number of each pairing of 5 elements where order matters (that is, fire+water is different from water+fire). That reminds me of the I Ching (which has 8 "elements" and a similar ordering requirement). (This is a bit different than a geomancy-like system involving spirit, since it would include a total of 32 figures, and only the presence or absence of an element would matter and not the order.) Your project sounds really interesting, I'd love to hear more about it! I've never thought about "spirit" as an element, before, so I'm curious what it's associations would look like.
As far as geomancy goes, Greer's books (Earth Divination, Earth Magic and The Art and Practice of Geomancy, they're basically the same as far as this is concerned) are the best ones I've seen on the topic. Super briefly, the figures you want are:
I think the direction(s) I'm heading are definitely influenced by the I Ching - that was the divination method I had the most experience with prior to trying and failing to connect with Ogham. Early on in this in-the-works system I toyed with whether it revealed transitions (i.e. changes or yi/I of Yijing/I Ching), but that didn't "ping" too strongly.
Right now I mostly have a lot more questions than answers about what I'm doing, but maybe I'll start posting a bit about it so as to tickle the hive-mind and learn from all the experienced members of the wider ecosophia community.
Thanks for that list, by the way - I can see already where the elements have different connotations in the two systems, but too, there are similarities worth considering.
And yes, you're correct that fire+water (aka Fire of Water) is different from water+fire (Water of Fire).
Speaking of the I Ching, I find I'm really jealous of the beauty of the hexagram system - and the way you lay out the geomantic figures above reminded me of that. I don't have anything nearly so ... concise (AND evocative of meaning) for what I'm working on, but it's early days yet, so you never know. :)
As for beauty, I agree that the I Ching and geomancy both have a real mathematical purity and elegance to them, which I find enchanting. I bet the more you meditate on your system, the more I imagine it'll click into place... I often find I need complication to erect a structure that ends up simple once all the scaffolding is pulled away!
This is seriously cool. I am glad to find another computer and occult nerd in here! Also, kudos for Vi! I cheat a little since I use MS Code with a ViM plugin but hey...
May I ask how are you using this set of correspondences? I am nowhere near of using Stern-Brocot trees at work. What kind of computer stuff do you do?
My first job was under a grumpy old French Canadian UNIX sysadmin who insisted I learn to use the POSIX tools for everything, since if you need to fix a broken server in single user mode in the middle of the night, they're all you're gonna have. Sound advice, I've ended up in that situation more times than I can count! But now I just use vi, sed, awk, grep, etc. for everything.
May I ask how are you using this set of correspondences?
I mostly use it for meditation on the figures. This is a very visual arrangement of all the building blocks of geomancy, so it helps make some things more apparently (like how the figures relate, etc.) Following the paths can tell stories, too. But also note that the overall arrangement shows some peculiarities: mobile figures are at the top of the page, stable figures are at the bottom of the page; yin figures are on the left of the page, yang figures are on the right of the page, that sort of thing. (There's a lot more than that, but I wouldn't want to take away all your fun of studying it!) So it also makes a very good geomancy cheat sheet, and I have a copy on my wall for just that reason!
What kind of computer stuff do you do?
I've been programming for almost thirty years! Once upon a time, I made video games; more recently, I owned a tech startup; after selling it, I now work for a tech giant. In that time I've done a lot of different things, but image processing, statistics, and data visualization were some of the big ones. I've mostly worked on the server side at very large scale (millions or tens of millions of consumers), so tricks to make the computer process things very quickly have been important (for example, knowing your trig identities so you don't have to compute cosines in a tight loop). I've also had to deal with numerical stability issues a lot, so things like Stern-Brocot trees, which lets us work with integers instead of floats, help avoid those kinds of problems.
I suspect there's an occult angle to the deep study of algorithms, but honestly in practice I think one becomes a good programmer mostly by having a lot of silver bullets in your toolbox!
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no subject
Date: 2020-10-11 05:11 pm (UTC)You've probably posted it for some other reason altogether, but thanks for posting it so you could spur me in new thought-directions! I know nothing about geomancy, so what's inside the "points" doesn't make sense to me, however the geometry itself might be useful.
I'm preparing to ask JMG a Magic Monday question that'll need some supporting illustrations and was thinking I'd pre-think it as a blog post. Would you mind if I also posted your image (with attribution)?
Also, how do you make all these great charts/images? My question's accompanying images are going to have to be hand drawn.
no subject
Date: 2020-10-11 06:27 pm (UTC)You're welcome!
Mathematically, the geometry is called a unit-distance tesseract graph. (This is the four-dimensional case of a hypercubic graph.) It's effectively the shape that a four-dimensional cube (e.g. a "tesseract") makes if you squish it flat onto a piece of paper.
How does this relate to geomancy? Geomancy is an elemental symbolic system where there are sixteen symbols, each with some of the four elements (fire, air, water, and earth) are either present or not present. (The meaning of each figure depends on which elements are present: for example, the figure "Carcer" is a combination of fire and earth, and means "separation" since these two elements do not mix well and tend to pull in opposite directions.) Each vertex of the graph contains one figure, and has a line to each figure that varies from it by flipping exactly one element. (That is, each figure links to the four figures that are most similar to it.) There are a lot of ways to assign the figures to the vertices (in fact, around 21 trillion ways), but I chose one that has really elegant properties. (One example is that the direction of each line represents an element; another is that the most "mobile" figures appear at the top and the most "fixed" figures appear at the bottom; another is that the most "passive" figures appear at the left and the most "active" figures appear at the right.)
I posted it as a theme for meditation; walking the paths around the overall figure is useful, I find. (In fact, meditation is where I got this in the first place!)
Not at all. In fact, attribution isn't necessary (though you're welcome to credit me or link here if you like). Like everything I post, it's in the public domain.
Oh, dear. That's complicated.
The short version is that there are computer "languages" describing how to draw pictures; in this case, the one I used is called Scalable Vector Graphics (or "SVG" for short). It's a text format (in fact, if you're familiar with HTML, it's very similar), and I wrote it out by hand using a text editor. (The text editor I use is an ancient one called Vi, which is basically Notepad or TextEdit.)
I used lots of trigonometry and analytical geometry (which I worked out by hand on paper using a pencil) to construct it. The lines so happen to have a slope of tan(π/8); this is a complicated irrational number (and there's no way I'm dealing with those by hand), so I used a Stern-Brocot tree to find an appropriate integer approximation (in this case, 17/41); from there it was just a couple quiet hours with a calculator. (I have severe chronic fatigue, so I require an extremely large amount of "down time;" I figure I might as well use it as productively as possible.)
I'm a computer programmer by profession, so these are the kinds of tools I use on a daily basis at work! I picked them up bit-by-bit over the last few decades, and I guess I'm just used to them by now.
no subject
Date: 2020-10-11 08:35 pm (UTC)Well, most of what you do flies right over my head! :D Though I do recall tesseracts from A Wrinkle in Time. Heh.
Also, math is so NOT my strong suit that I just have to nod appreciatively when you say "a slope of tan(π/8)" and pretend I didn't actually get all the way to some form of college-level calculus. How I managed, that, I'll never really know and it seemed to have all been lost along the way since then.
I'm impressed with your "short version" - it sounds quite complicated, or at least very specialized! I'm embarrassed to admit that I wondered if there was a "plug-and-play" graphic image maker. The fact that much work went into making the image is the reason I'd give attribution/credit - though the result is public domain, getting to the result required your expertise, time, brainpower, etc...
Meanwhile...
Hmm, "an elemental symbolic system where there are sixteen symbols, each with some of the four elements (fire, air, water, and earth) are either present or not present." Now that's interesting!
I'm working with 25 combinations because Spirit is regarded as one "elemental" component in the modern Ogham tradition. The schematic I'm trying to discover or locate (if there is one) has to arise out of some of the pairings' specific qualities. This schematic might not be possible given what I know so far about the ways the elements combine, but that's essentially what I've been gnawing on for awhile now. Also trying to see links and disjunctures, transitions and relations between the 25.
I may end up needing to at least dip into the descriptive text on geomancy, just to see how elements and their combinations are conceived. While some of that is likely to be non-Druidical in nature (and thus different from my Ogham-derived system), there's probably some "genetic" similarity (both coming from Western occultism) that might be useful to explore.
no subject
Date: 2020-10-11 09:16 pm (UTC)😅 As you can see, my Mercury and Saturn are dignified and my Venus is a mess! So I'm afraid I do things the hard way, and don't know about such programs.
That makes sense to me: 25 is the number of each pairing of 5 elements where order matters (that is, fire+water is different from water+fire). That reminds me of the I Ching (which has 8 "elements" and a similar ordering requirement). (This is a bit different than a geomancy-like system involving spirit, since it would include a total of 32 figures, and only the presence or absence of an element would matter and not the order.) Your project sounds really interesting, I'd love to hear more about it! I've never thought about "spirit" as an element, before, so I'm curious what it's associations would look like.
As far as geomancy goes, Greer's books (Earth Divination, Earth Magic and The Art and Practice of Geomancy, they're basically the same as far as this is concerned) are the best ones I've seen on the topic. Super briefly, the figures you want are:
no subject
Date: 2020-10-13 04:15 am (UTC)Right now I mostly have a lot more questions than answers about what I'm doing, but maybe I'll start posting a bit about it so as to tickle the hive-mind and learn from all the experienced members of the wider ecosophia community.
Thanks for that list, by the way - I can see already where the elements have different connotations in the two systems, but too, there are similarities worth considering.
And yes, you're correct that fire+water (aka Fire of Water) is different from water+fire (Water of Fire).
Speaking of the I Ching, I find I'm really jealous of the beauty of the hexagram system - and the way you lay out the geomantic figures above reminded me of that. I don't have anything nearly so ... concise (AND evocative of meaning) for what I'm working on, but it's early days yet, so you never know. :)
no subject
Date: 2020-10-13 05:08 am (UTC)As for beauty, I agree that the I Ching and geomancy both have a real mathematical purity and elegance to them, which I find enchanting. I bet the more you meditate on your system, the more I imagine it'll click into place... I often find I need complication to erect a structure that ends up simple once all the scaffolding is pulled away!
no subject
Date: 2021-03-02 05:26 am (UTC)May I ask how are you using this set of correspondences?
I am nowhere near of using Stern-Brocot trees at work. What kind of computer stuff do you do?
no subject
Date: 2021-03-02 12:25 pm (UTC)My first job was under a grumpy old French Canadian UNIX sysadmin who insisted I learn to use the POSIX tools for everything, since if you need to fix a broken server in single user mode in the middle of the night, they're all you're gonna have. Sound advice, I've ended up in that situation more times than I can count! But now I just use vi, sed, awk, grep, etc. for everything.
I mostly use it for meditation on the figures. This is a very visual arrangement of all the building blocks of geomancy, so it helps make some things more apparently (like how the figures relate, etc.) Following the paths can tell stories, too. But also note that the overall arrangement shows some peculiarities: mobile figures are at the top of the page, stable figures are at the bottom of the page; yin figures are on the left of the page, yang figures are on the right of the page, that sort of thing. (There's a lot more than that, but I wouldn't want to take away all your fun of studying it!) So it also makes a very good geomancy cheat sheet, and I have a copy on my wall for just that reason!
I've been programming for almost thirty years! Once upon a time, I made video games; more recently, I owned a tech startup; after selling it, I now work for a tech giant. In that time I've done a lot of different things, but image processing, statistics, and data visualization were some of the big ones. I've mostly worked on the server side at very large scale (millions or tens of millions of consumers), so tricks to make the computer process things very quickly have been important (for example, knowing your trig identities so you don't have to compute cosines in a tight loop). I've also had to deal with numerical stability issues a lot, so things like Stern-Brocot trees, which lets us work with integers instead of floats, help avoid those kinds of problems.
I suspect there's an occult angle to the deep study of algorithms, but honestly in practice I think one becomes a good programmer mostly by having a lot of silver bullets in your toolbox!