A Trial of Random Sequences
I was thinking about this because I was reading Alan Moore’s Voice of the Fire. Neil Gaiman wrote in the introduction that Moore quoted someone else when he said that you can start anywhere in a circle. His novel was supposed to be seen as a circular path, I suppose where you could take the end and connect it to the beginning and make a ring out of the line of the story. Gaiman even suggested starting the book wherever you like and then wrapping back to the beginning to finish whatever you had left out.
I was momentarily fascinated by this idea, and it brought to mind sequences of numbers. When I cast for a sequence of numbers, I think about what is random. I have used the 312 pattern before, believing it to be random, and reading Moore’s novel as prescribed by Gaiman would be similar with 231 — starting the novel in the middle and then going back to the beginning. The difference with my 312 is that you’re staring the novel toward the end rather than the middle.
I have to distinguish the meaning of random. It does not mean for me the casting of dice or something similar to get any number that was not provided by voluntary choice. It means the implication that a set of numbers is random because they lack a pattern. In essence, it is an artifice.
So, I realized that you really can’t get a random distribution with just a sequence of three numbers, because they can still imply associations.
A sequence needs at least two numbers. Two numbers can only give you 12 or 21, which implies forward or backward, and there’s nothing random about that. Three numbers gives you 123 and 321, which have the same problem as 12 and 21. As I mentioned, 312 and 231 also create a logic, with you starting somewhere in the middle and then finishing off the earlier parts. That leaves 213 and 132, and the problem I have with them is that one of the numbers remains in its own spot; 3 is in its proper spot in 213, and 1 is in its spot in 132.
Maybe four numbers are needed then. 1234 and 4321 are out for the reasons already established. 2341, 3412, and 4123 are also out because they give us a sequence that begin from somewhere in the middle and move toward the end and then wrap around to finish the rest. Of what’s left over, anything that starts with 1 (such as, 1342, 1423, 1432, 1324, 1243, 1342), have the problem of having at least one number falling in its proper place, and we can also preclude the ones that do it for 2, 3, and 4 (4231, 4132, 2431, 2134, 2314, 3124, 3214, 3241). That leaves a few possibilities that do not have these patterns. But when I look at 4213 and 2413, the implication shows that even numbers are grouped at the start, and with 3142, the odd numbers are at the start. 4312 has the odd numbers in the middle, framed by even numbers, and 3421 has the opposite results. That leaves 2143, and I have to say, if I can see one flaw in this combination of these numbers, it is that the evens are in the odd places, and the odds are in the evens. So, I feel it is impossible to display a random line of numbers without any implied meaning unless I make the sequence larger.
I think five numbers might do it. We already know some of the problems against a random implication, so I won’t bother listing dozens of numbers. I will fish for a number and see if there is anything wrong with it. 34251 might be the answer, and there might be more than one answer to this when using five numbers. It has none of the issues that we have described, but I have a feeling that if we stare at it long enough, a problem will arise, because patterns present themselves when new facets occur to us. After looking for a minute, I actually recognize something that does not bother me as much as the above qualities, and yet it makes me wonder if there isn’t something better. The pattern I found is that you start in the middle and continue a line going backward and forward to the next available number until you run out of numbers. From 3 (the middle), you go back to 4 and then forward to 2, and then back to 5 and then forward to 1. There has to be a better possibility.
25413 feels like it can cover the problem. It looks random, and I cannot demystify it into a pattern with my normal modes of interest. I haven’t looked deeply into the possibilities with a five-number sequence and feel there might be a couple of others.
This makes me think that what interest an artist has with numbers has nothing to do with all possibilities, as it might in math. It has to do with the right number for the right job. It has to be an exact number fulfillment or the work falls apart.
It also makes me think about how the appearance of a random number is anything but random. If it were truly, random, any number would do. You would just blindly pick one from a lineup of available numbers. To an artist, random is the absence of pattern that would intimate some form of meaning. When an artist is talking random, they are talking about the implication of random and not the actual phenomenon.