Or, if you prefer, nine dozen and two.
I don’t know if any of you blog using WordPress, but one of the things you get after a while of using tags (I only started doing that fairly recently) is a list of the ones you use most often. Probably because of the decimal bias of our cultural hegemony, it lists the ten. In my case, this is probably not a good guide to getting more readers but then I’m not particularly interested in doing that, except maybe as a kind of game in which I hope I wouldn’t become emotionally invested. It makes me want to draw a diagram, or rather a pattern:
Apparently this is called a “complete graph” and is described as a simple undirected graph in which each pair of distinct vertices is connected by a distinct edge. The above image shows a K12 , apparently. Because of the decimal bias, my ten tags can be linked up in a similar diagram with rather fewer edges. I used to have hours of “fun” getting computers to draw ever more complicated complete graphs. The distinction also ought to be made between undirected and directed complete graphs of this kind.
There is bound to be an equation which tells you how many edges are needed for a given number of vertices, and in fact there is. It’s:
wn+2=n!en
. . . where “e” is Euler’s constant. No, hang on a minute, that isn’t it apparently as it isn’t necessarily an integer and these obviously will be, so it’s:
(n(n-1))/2
Okay, so plugging in my ten tags gets me (10(10-1))/2, which is forty-five. So much for my title then! I’d worked it out at a hundred and ten but it seems it’s smaller. So then: ninety blog posts.
Here’s what I’m thinking. I have ten tags listed. A fairly crude way of generating blog post ideas would be to combine pairs of them, perhaps in both directions. They are: Philosophy, Ethics, Christianity, Judaism, Veganism, Racism, Evolution, History, Star Trek, Politics. Most of the time, if I blog on one subject on that list it’s likely to involve more than one of the others, which adds to the number of possible combinations in the graph, but it would also be interesting to see what I’ve missed, using those as major foci for a post. For instance, veganism and racism is something I’ve written about before, but not in a “pure”, more focussed sense, and there’s also racism and veganism, which could be something quite different. In pursuit of that combination, there is a lot to be said. For instance, veganism is perceived as a very White project even though, for example, I-Tal diet in its most complete form is RastafarIan and there’s also the question of the growth of supposèdly vegan products in the Third World as cash crops for export and forcing up the prices of something like quinoa, putting it out of reach of the communities which have traditionally eaten it. All very fruitful subjects. There are apparently forty-five pairs of tags in one direction and another forty-five in reverse. Judaism and Christianity is another interesting subject which it would be very easy to write something about, but writing something original and respectful might be a lot harder.
Thinking about writing in this way links mathematics and composition, but as a fairly naïve mathematician I may not be the person to do that. I often find that when I try to connect mathematical activity to something usually considered non-mathematically, I come up with a lot of mind game-type ideas but not much which is particularly applicable, or sometimes something which fits quite well into a particular mathematical activity but is also amenable to common sense. The question in my mind right now is, how useful is it to think of pairs of blog tags as a complete digraph? Is “evolution and Star Trek” a different topic to “Star Trek and evolution”?
Incidentally, the reason “Star Trek” crops up in that list is that I’ve reviewed every episode of “Star Trek TOS” and written several other more general posts on the series. It’s the kind of thing you might expect to generate a lot of views, or maybe not because so many people must be writing about it. I feel, unfortunately, that although it’s a major cultural phenomenon it’s also quite naff to write too much about it.
The above graph apparently also forms the net of an eleven-dimensional simplex, because every complete graph is a projection (the way it’s represented here, in two dimensions) of a simplex of Kn-1 dimensions. Hence this image:
is the net of a tetrahedron. And it clearly is: you can see the faces at the front and back, paired off and seemingly at right angles to each other. Each vertex connects to each other by three edges, and that gives the essence of the simplex in a way. My K10 graph would presumably have each vertex joined to the other nine, each edge forming a polygon enclosing a face, each such polygon enclosing a tetrahedral cell, each tetrahedral cell forming the solid limiting a four-dimensional simplex, and so on. Each one of these encloses a possible combination of tags, more than one this time, and we’re in the realm of factorials and the possibility of more than three and a half million possible blog posts which can be appropriately tagged in various ways from that list, and will be found in the depths, if that’s the right word (it isn’t). This, then, is the hyperspatial approach to blogging. Each tag is located at a precise location relative to the others in hyperspace and since the links between them need not be mere edges but triangles, each blog post can be considered to be written on one of the faces of this nine dimensional simplex, either tapering towards the bottom or getting longer and longer lines as it goes on. You can hold this cluster of blog posts in your nine-dimensional hand-things and turn it this way and that to read each one of the ninety posts, all of which are on the surface of the polytope. If you happen to be a nine-dimensional entity, that is. Some of these are probably already written but I don’t know what they are.
This suggests a way of viewing blog posts via a virtual tesseract, merely four-dimensional and with each face of each of the eight cubes having a post written on both sides, four dozen in all, manipulable via one’s viewing device while wearing 3-D glasses or a VR headset. But all of this is fanciful and it isn’t clear how it would help one blog.
Leaving all that aside, it’s also possible to use the same old AI as I’ve been using for a lot of other things to finish my list of tags with others. It’s quite interesting what happens when I do this, because it fills my list in with the subjects I deliberately avoid on this blog, such as gender identity and trans stuff. InferKit just now gave me this:
Harry Potter
Animals
Politics
Military
Religion
Science
Food
Smart People
Animals and Animals
Writings
David Icke
Family Values
Hot Car Deaths
Holocaust
Asian-American
“Animals and Animals” is a little like “Vulcan And Vulcan” even though it hasn’t seen it. I don’t really want to blog about Harry Potter, although “Hot Car Deaths” is a depressing but possible subject. “Asian-American” strikes me as something you really should be in order to write about it, except that it is interesting how America sometimes seems like the extreme Far East even beyond Asia, so that has possibilities. DeepAI gives me “Science, Education, Welfare, Vacation, Innocent and Damn Law,”, then it seems to turn into a government form of some kind with things like “Pregnancy”, “Birth Year” and the like. This is not very useful and probably reveals the kind of text it thinks I’m writing.
I’ve done all this before, of course.
This blog is naturally a meandering mess of brain dumps, and consequently these two methods vaguely reveal some topics I might want to write about but they’re unlikely to get much readership, and that’s fine. However, I would say this. I suspect that if you’re serious about blogging and already have a blog which has a direction, a focus and a significant readership, you could do worse than to use these techniques. Maybe you’ve written about every combination of tag pairs. Finding out which ones you have and haven’t and colouring in the edges on the resultant complete graph would probably reveal where the large gaps are in your coverage, although some might be nonsensical. I don’t think any of mine would be though, so I suspect yours wouldn’t be either. Just two tags is rather limited, and if you open it up to all combinations, unless you’ve automated the process in some way you just will not have written hundreds of thousands of blog posts, meaning that some of the combinations will be stimulating and novel. As far as predicting tags is concerned, I found it tended to fill in things that I was genuinely interested in but hadn’t blogged about. This would also seem useful. You could also take all the AI-completed tags and build your own complete graph from those. It seems to me that there are likely to be other applications of graph theory to blogging which I have yet to become aware of. Worth investigating maybe?
A Box Of Chocolates 