- The greater hexagon
- A short history of my hexagonal thinking
- A short history of Hexnet
- The structure of this site
Greetings, plebeian. If you are like some people, you may be wondering something to the effect of, "What's the deal with this site?" If so, today is your lucky day, for here is an ENTIRE PAGE OF CONTENT dedicated to addressing this very issue.
But first, some interesting facts about Hexnet:
- Legally a church in Massachusetts. Think about it.
- For reasons I don't entirely understand, alt.religion.hexnet is an actual Usenet group.
Anyway, the story of Hexnet is meandering and sordid. The following is a needlessly long summary of it:
The greater hexagon
First and foremost, a point of confusion that I think sometimes arises here is what exactly I mean by "hexagon." I am fond of proper hexagons—regular hexagons, defining a convex hull of six equally-spaced vertices at sixty degrees from each other—but when I speak of "hexagons" in the most general sense, I am really speaking of six-sided plane symmetry in general I guess, and the various geometries, topologies, and combinations pertinent to that. Hexagons, things that look like hexagons, hexagonally-packed circles, et cetera. Specifically in the context of Euclidean geometry, what I guess I am particularly interested in, among other things, is the interplay between circles, triangles, and regular hexagons, their analogues in other dimensions, and their implications for number theory and the ontological underpinnings of mathematics.
So, in the context of general mathematical concepts, when I speak of "hexagons" I am often referring not only to proper hexagons but also to things that resemble hexagons, can somehow be logically mapped to hexagons, or are in some other way relevant to hexagons, six-sidedness, or indeed sixness itself. I am casting a pretty wide net here. The point is that, for me at least, regular hexagons per se serve as a sort of schematic distillation of a set of underlying mathematical and ontological principles, and I would urge the reader not to become too fixated on the shape itself, or on what seems more or less hexagonal at first glance. This is particularly true when seemingly non-hexagonal solutions are clearly better suited for a given application than superficially more hexagonal ones, but where, on closer examination, there may be a deeper hexagonality to the former that far exceeds its surface appearance.
Take for instance the lowly cube: now, cubes are somewhat overrated and definitely overused in our society, but they certainly have legitimate applications. And the cube is clearly a shape with hexagonal implications. And not just because it has six sides—the cube is deeply hexagonal in ways that would take a lifetime to fully understand. So the goal of the hexagonally-aware individual should not be to just replace cubes with hexagonal prisms or even truncated octahedra—that would of course be inane—but rather to understand the hexagonal nature of the cube, to bring this hexagonality to its fullest expression, and to allow this expression to inform and illuminate other aspects of our lives. The point is not to make all things hexagonal, but rather to see the hexagonal in all things—to draw it out, and to behold it.
Though, to be clear, regular plane hexagons definitely form the foundation and ultimate focal point of the hexagonal mysteries. As the minimal spatial representation of sixfold symmetry, they represent the conceptual linchpin holding the whole enterprise together, and are certainly the most important mathematical objects to be considered in the exploration of hexagonal principles. And non-regular hexagons can be quite interesting too, in that they generally fall into the category of "sixness" as mentioned above. For example, Pascal's Theorem, or if you will the Hexagrammum Mysticum, is all very fascinating and hexagonal and doesn't necessarily involve regular hexagons at all.
A short history of my hexagonal thinking
My interest in hexagons began in November of 1994, when I was at school, where I had been banned for two days from the barn. The barn being a building at the school where I—somewhat inexplicably in retrospect—spent most of my time. I was discussing truncated icosahedra with several friends, and for whatever reason hexagons suddenly seemed remarkably interesting. If I'd appreciated at the time what a pivotal development this would prove to be in my life, I probably would've taken the time to record my exact thoughts and actions when these ideas first occurred to me. But I can only assume it must've seemed like a transient fascination at the time, so all I remember are the vague outlines of the day's events. Nonetheless it did indeed prove to be a relatively transient fascination at first. I pursued the matter for several years with varying degrees of enthusiasm, and operated my first hexagon-related website under the auspices of Hexnet.org for a little over one year starting in 1995, but subsequently lost all interest in the matter. Or rather I came to find the whole thing philosophically and ontologically disagreeable. So I turned it into a religion that had nothing to do with hexagons at all (I was a very strange child). In time I came to find this fairly disagreeable as well—and unbearably weird even by my standards—and did my best in the ensuing years to forget the whole episode had ever transpired.
AND LO, MANY YEARS PASSED.
Then, back in the spring of aught six, I was welding scrap metal in a friend's barn one Saturday afternoon and for some reason took to making several hexagonal objects. I had of course never fully renounced the use of hexagonal motifs in art and design—though I tried not to get too enthused about them—so this in itself was not uncharted territory. But for whatever reason it really took this time, and I found myself, seemingly out of nowhere, really fucking interested in hexagons again. Despite my established history with hexagons at this point, as with my initial insight twelve years earlier, I didn't really take too much notice of this development on the day it happened. It was only after some weeks passed and I was still into hexagons again that I realized I would need to come to a new, more integrated understanding of the role hexagons were going to play in my life. This was an unexpected and at first somewhat unwelcome development, as I truly thought I'd put my earlier hexagonal eccentricities behind me for good, and it took some months of further reflection before I was able to fully understand that my return to the hexagonal arts was not, in itself, incompatible with my broader ontological paradigm (which could broadly be described as some species of immanent, panentheistic, idealistic monism).
At any rate, despite a long and diverse track record of cringe-inducing weirdness over the course of my life, I had long held onto the—in retrospect fairly quaint—notion that my "hexagonal phase" was the most conspicuously bizarre of my many bizarre phases, and that it was—uniquely among these phases—something best, like, never mentioned again, at all. This left me in something of a hexagonal closet for the first year or so after my return to hexagonal principles. I would study hexagons in my spare time, working to develop a new, more mature system of hexagonal thought, but I always kept these activities hidden from others—particularly of course from those who might remember my earlier hexagonal obsession.
Events finally forced my hand a year later, when I ran across a Facebook group without an administrator called Hexagons Are Better Than Squares, and took it upon myself to take ownership of the group (as one could do in those days), to make it a focal point for a new, social-media-driven hexagonal movement. (As with most olden-style Facebook groups, HABTS never really went anywhere, and was ultimately rendered effectively defunct under the new group format, but it did however lead to the far more successful Hexagons page, along with its analogue on Google+.) Thus it came to pass that in the fall of 2007 I made my triumphant return to publicly promulgating hexagonal principles.
Around the same time I also released my feature-length Youtube epic, Triumph of the Hexagon, which was originally made specifically to serve as a sort of introductory video for HABTS. Bear in mind that I put this video together fairly quickly, on a tight timetable, in the relatively early days of my neo-hexagonal phase, when I still lacked a great deal of refinement in my thinking vis-a-vis how I wanted to present these ideas. Were I producing this video today, it would obviously be significantly different. There would, among other things, be a deeper mathematical angle, perhaps a bit more diversity vis-a-vis natural imagery, and much, much less Flower of Life crap. But it is what it is, and I continue to stand by it, though I'd like to release an updated version at some point.
The question of what, exactly, prompted and sustained my enduring interest in hexagons is something that I've spent a great deal of time considering in recent years. Certainly my more ontologically comprehensive hexagonal outlook of today casts my youthful hexagonal obsession in a somewhat different light than I perceived it at the time. I was, again, the sort of child who was—moreso than I think is typical—prone to particular obsessions and fixations with things. In early childhood this typically revolved around specific, concrete objects; later this evolved into fixations with the ideas of objects (some real, some imagined or idealized); later still it evolved into a simple fixation with ideas. But it was always one idea—one idea that would become, in effect, my god, and which would consume me completely during its zenith. And even up to the present time I remain the sort of person who is, by nature, always "on" about some particular thing or another. And this was I suppose at the core of my ambivalence about reintegrating hexagonal principles into my later worldview—I had already moved on to my new god, and there wasn't room for two.
This was, of course, a fundamentally illusory conflict that worked itself out eventually. The point I want to emphasize here is that I think what ultimately allowed the hexagonal idea to persist and win out over other potential meme-complexes is that it represented, to me at least, a distillation of a certain type of meaning in structure. This rather cryptic conjecture deserves a more thorough treatment than I can give it here, but I will summarize it this way: When I look back over my life, particularly to my various fixations in childhood, I see that there is a certain recurring aesthetic to the things I was drawn to. It's not that such things tended to be aesthetically beautiful per se, but rather that they had a certain type of aesthetic beauty imbued with a particular sort of meaningful, complex structure. Specifically, a type of modular, nested, hierarchical structure, characterized by complex systems of self-contained units and structures that could be arranged and ordered based on simple principles—principles from which they acquired a certain deep meaning. And again not just any meaning, but a particular species of meaning that I find it very difficult to convey the sense of. This sort of attraction is partially I suppose why I was ultimately drawn to mathematics and computer programming, and something vaguely similar may hold true for many people who have followed a similar intellectual trajectory, I don't know. But the end result for me was that there has always been this particular quality of meaning that I would get glimpses of, in complex art, in mathematics, in certain dreams, et cetera, and it was this quality that ultimately, for me, came into greatest focus around the issue of hexagons.
I have tried at times to convey something of this in my writings—of a certain unified form of structure and meaning that seems to emanate from the apparently disparate properties of the hexagon, from the way they seem to emerge organically from the most fundamental concepts of existence, etc. In this I have much work to do. But that is my basic situation at present. Hexagonal principles are the closest thing I have found to an ontological bridge between the formless absolute and the immutable mathematical reality of what is and what can be—the hexagon itself representing nothing less than the origin, the unity, and the archetype of all structure.
This may or may not be "true" in the strictest sense of the term, and it's certainly not a message that resonates with everyone. But it is the course I have charted for myself, and it is one I intend to pursue as far as I can. The present site represents the apex of this process so far. I have many ideas regarding hexagons that I haven't yet tried to express with any great precision, but to the extent I have tried to express my ideas, they are more or less represented here—though sometimes a bit obliquely perhaps.
A short history of Hexnet
The term "Hexnet" was first coined—by me anyway—in February of 1995. It was originally going to be a BBS, back when such things existed. The BBS never materialized, partly I suppose due to the fact that the whole BBS scene was collapsing in those days, but also because I was completely unqualified to implement such a system at the time. I held onto the name though, possibly because it was short, memorable, and you don't have to spell it out for people. One thing I have always avoided, and don't understand why more web entrepreneur-types haven't avoided as well, particularly in recent years, is employing made-up names that are not intuitively simple to spell. As far as I can recall, I've never had to spell out "Hexnet" for a native English-speaker, ever. It is self-evident how to spell it. I think this is quite useful in terms of branding and such, especially with so much information in this vein spread by literal word-of-mouth these days—i.e., passing conversational references to web sites, etc.
As already mentioned, the first iteration of this site, or something resembling it, was launched in the summer of 1995. The site was styled "Hexnet"—more formally "The Hexnet Global Infocenter" or something to that effect—but this was actually before I registered the hexnet.org domain name (domains being relatively expensive at the time). Anyway, my whole shtick at the time was that I sold "hexagons," right, but it was—in addition to being absurd on the face of it—couched in this very over-the-top and vacuous corporate locution (which was simply a style that interested me at the time, entranced as I was by the aesthetic trappings of contemporary capitalism), so it was fairly obvious that I didn't actually sell hexagons (at least not, like, as a self-sustaining business). This had the effect of making the whole site come off as some sort of elaborate joke. Which I suppose it was, in some sense—certainly in retrospect I find it difficult to muster the energy to take anything I did in those days particularly seriously. But, as should be clear by now, I was, in my own weird-ass way, serious about hexagons. I am always serious about hexagons. Nonetheless it was all perhaps a bit too tongue-in-cheek—I presented my ideas in an overly sarcastic, self-deprecating way, and whatever nucleus of substance I was trying to convey was apparently lost in the process. (This has proved to be a recurring problem for me.) Though, again, my hexagonal ideas in those days lacked substance and depth, and were unlikely to impress anyone, regardless of how they were presented.
Nonetheless, towards the end of that site's existence, circa late '96, when the web was really filling up with normals for the first time and I had refined my presentation a bit, I found myself being contacted by people with a genuine interest in hexagonal geometry, many of whom could've possibly helped me further develop my hexagonal ideas, had I the patience or interest to engage them. But by then my interest was waning, and I am sorry to say that, to my great regret, I more or less just started ignoring any hexagon-related communication that came my way, leading eventually to the abolition of the entire hexagonal enterprise.
So then, as mentioned, I turned Hexnet into a proper religion, and organized Hexnet as an officially-incorporated church in Massachusetts. The less said about this the better. As alluded to earlier, I myself basically turned into an iconoclastic, monistic idealist. Again, given my tendency to fixate on particular ideas at the exclusion of all others, I came to view my attachment to hexagons as being inappropriate to their relative importance in the structure of the universe—or at least relative to their importance in my new idea-hierarchy of choice. In retrospect, this was an overreaction, or at least a misdirected conclusion, brought on in part by the fact that I had never really applied myself to mathematically teasing out interesting details about hexagons, allowing the whole thing to remain a fairly superficial fascination that was easily set aside in the face of more pressing ontological insights. My views in these days lacked nuance or subtlety. Again, it would take me a further ten years to really integrate hexagonal ideas into my broader ontological worldview, which was itself only starting to take shape around this time.
Eventually this all fizzled out too, insofar as I came to realize realize that I was basically reinventing a wheel that had been invented many, many times before, and which had absolutely no need to be invented again—and which I wasn't doing a particularly good job of reinventing at any rate. Also, by this point it was becoming clear that everything published on the internet would probably be preserved in some form or another until the heat death of the universe, and the prospect of my weird rantings persisting in the human record for that long began to freak me out a bit (as it still does). So, after a few years of atrophy and neglect, Hexnet finally went offline sometime in late 1999 or early 2000. I forget exactly when. I allowed the domain to lapse, someone else came in and used it for some years (and apparently had a site about horses or something, if my present 404s are to be believed). Eventually I had no web presence at all. The early novelty of "having your own website" had worn off by then, and I found myself with little of interest to say. The first stirrings of "Web 2.0" were beginning to be seen in those days, and I contented myself with a more subdued web presence confined to these emerging channels of standardized, organized content.
The hexnet.org domain came available a few years ago, and I bought it up on impulse after my return to hexagonal principles, thinking it might prove useful someday. I tried for awhile to come up with a more expressive domain name for this project ("hexagon."-something, "hexagons."-something, et cetera), but all the good domains were of course taken long ago. At the end of the day, I do feel "Hexnet" has a certain ring to it, and my historical connections to it make it particularly interesting to me. But I do, ultimately, have many reservations about returning to the Hexnetian identity. There is a lot of crap out there with "hexnet" and my name on it—crap I have, again, tried to distance myself from over the years. But it is what it is, and for better or worse I now feel compelled to embrace it as an integral part of my broader, cringe-inducingly weird heritage. Suffice to say though, for the most part I wholly disclaim and dissociate myself from any of the flawed and ultimately rather pointless material I have published under this name in the past. I have come to understand that "Hexnet" is for me something like what "Dymaxion" became for Buckminster Fuller—a fairly arbitrary name that will probably be attached to various hobbies and projects of mine for the rest of my life. (Though unlike Bucky I didn't need to hire a marketing specialist to come up with it.)
At any rate, the upshot of all this is that, after over a decade of inactivity, I have revived the Hexnet name with the ultimate goal of establishing a relatively comprehensive, centralized presentation of my hexagonal ideas and their implications. The internet and the world are different places than they were the last time I had a hexagon-themed Hexnet site up and running. People with weird ideas are in much more regular contact with other people with weird ideas, and the potential for good weird ideas to gain ground in the weird marketplace is as high as its ever been. So it seems like a good time to come forward with weird ideas.
The structure of this site
This site is, ultimately, dedicated to both hexagons and hexagon-related ideas. I have decided that a major subfocus of the site will be dozenalism, or the advocacy of a base twelve number system. I have had an interest in dozenalism for many years, going back to my earliest hexagon days, when I tried to develop a base six positional notation system, and quickly realized that base twelve made a lot more sense. There are obviously geometrical and mathematical areas of overlap between these ideas, but since it is at least theoretically possible that this site could become some sort of hub for dozenal activity, I feel the need to point out that dozenalism per se is something that makes so much sense, on so many different levels, that it really stands on its own as a system worth advocating for without requiring one to buy into any of my eccentric ideas about hexagons. If you have come to this site via some sort of dozenal link or search or what have you, please be assured that you can probably enjoy the dozenal content provided here without subscribing to any of the hexagonal ideas also presented.
This site is fundamentally composed of content articles called nodes. When this was a Drupal site (2010 – 2013) I wanted to suppress the term "node," as it was conspicuously distinctive of Drupal, so I called everything a "post." Now that I've moved from Drupal to a custom Rails application, I have returned to calling them "nodes," since I find it a pleasant and vaguely futuristic sounding word.
Node content can be accessed through the following major site areas:
Bear in mind all of these pages are essentially different presentations of the same material, though some are limited to particular subsets. The library is a curated collection of primary, feature-length content articles that address the core concerns of the site. The blog consists of nodes specifically flagged as blog posts, and does not generally include non-time-sensitive posts. The gallery contains every "featured" node image, and has links back to every image node, but obviously does not include non-image nodes. The node index contains all published nodes, sortable by publish date, last comment date, &c., and is the only comprehensive list of all node content. "Categories" is (circa 2013) a new node view that I originally intended to replace the old, curated library, but it's not quite up to this task yet, so I leave it here now as a weird, standalone, taxonomic tool. It doesn't really make a lot of sense at present but may be interesting to some people, I don't know. The tag directory should be self-explanatory.
In addition to published nodes there are a number of static pages containing core content, including our Links page, and the "About Hexnet" page that you are presently reading. These can generally be accessed from the "Featured Resources" block in the sidebar. Beyond this, there are several other non-node resources of interest, such as our news feeds, and the Hexagonbot tweet feed.
If you are new to either hexagons (as, like, a concept), or dozenalism, please consider reading these two brief articles I have been putting together, which can be found in the library:
There are several olden articles on dozenalism in the library as well, which are well worth reading if you have any interest in the subject.
This site is still very much a work in progress. I wrote most of the original content here in the early months of 2010, and intermittently added more over the following years. After a 2011 overhaul, I committed myself to the "everything should be a blog post" school of thought, after which all content—even standalone images with minimal text associated with them—were published as blog posts. I have since pulled back from this philosophy, and as of the latest incarnation of this site (circa fall of 2013), I explicitly disavow it. Henceforth only time-contextual posts, current news, site announcements etc. will be featured in the blog. Other content—images, media, and feature-length articles—will simply be published and categorized appropriately in the existing hierarchy of tags, categories, library sections, etc.
Please note that, in content paragraph form at least, I generally employ underlined links for external resources, and non-underlined links for internal Hexnet resources. (For anyone writing content for the site, in comments or elsewhere, external links can be given the CSS class "ex.") Special groups of links, lists of links, or links in the main menus are not generally styled like this, if is obvious from the context that they lead to external sites. Where possible I avoid opening links in new windows/tabs, since I find this behavior obnoxious as fuck when it is forced on me by other sites. Two exceptions to this that I can think of off the top of my head are the print view links for nodes, and the Amazon search button on the search page.
In closing, thank you for your time, for visiting my strange little site, and for reading the bulk of this rather long-winded introduction for some reason. And thank you for choosing hexagons. Please enjoy the rest of your time at Hexnet.org, and your continuing existence.
– Graham, May 11B6; (2010)
Revised & updated, November 11B9; (2013)