This is a quote from a fascinating article about Barbara Shipman- a mathematician – whose work with honeybees and a kind of mathematical space called a a ‘flag manifold’ appears to offer intriguing glimpses into how bees manage to communicate. I can imagine her going back in time and guiding Aristotle through the mathematics and natural history involved and in the process blowing his mind for the day:

One day Shipman was busy projecting the six-dimensional residents of the flag manifold onto two dimensions. The particular technique she was using involved first making a two-dimensional outline of the six dimensions of the flag manifold. This is not as strange as it may sound. When you draw a circle, you are in effect making a two-dimensional outline of a three- dimensional sphere. As it turns out, if you make a two-dimensional outline of the six-dimensional flag manifold, you wind up with a hexagon. The bee’s honeycomb, of course, is also made up of hexagons, but that is purely coincidental. However, Shipman soon discovered a more explicit connection. She found a group of objects in the flag manifold that, when projected onto a two-dimensional hexagon, formed curves that reminded her of the bee’s recruitment dance. The more she explored the flag manifold, the more curves she found that precisely matched the ones in the recruitment dance. I wasn’t looking for a connection between bees and the flag manifold, she says. I was just doing my research. The curves were nothing special in themselves, except that the dance patterns kept emerging.

Delving more deeply into the flag manifold, Shipman dredged up a variable, which she called alpha, that allowed her to reproduce the entire bee dance in all its parts and variations. Alpha determines the shape of the curves in the 6-D flag manifold, which means it also controls how those curves look when they are projected onto the 2-D hexagon. Infinitely large values of alpha produce a single line that cuts the hexagon in half. Large values of alpha produce two lines very close together. Decrease alpha and the lines splay out, joined at one end like a V. Continue to decrease alpha further and the lines form a wider and wider V until, at a certain value, they each hit a vertex of the hexagon. Then the curves change suddenly and dramatically. When alpha reaches a critical value, explains Shipman, the projected curves become straight line segments lying along opposing faces of the hexagon.

I especially enjoy how the article shows someone from one discipline using it to offer explanatory mechanisms to another. To employ a detail from the article, ‘casting shadows’ – projecting from one dimension into another – seems an apt metaphor for a kind of thinking I feel an attachment to, where one asks why a resemblance happens. One hypothesises from one ‘dimension’ towards another.

At any rate the description of this projection feels familiar to me from my experiences of thinking about artists’ books in terms of their practice, their makers, instead of their objects. Their objects are the ‘shadow’ that practice casts, if you will, and I fancy that this is true from the originator’s side and from the consumer’s as well. In fact I propose a ‘camera’ metaphor for this, to allow the object to be styled as a ‘lens’ which can project towards either the reader or the author.

Perhaps the maths in the above will turn out wonky, but I think it’s a thrilling find nonetheless. One wonders if the researcher expected to find them. She says not, but it opens out a question about finding patterns. Do we find what we expect to find? Of course this is a familiar methodological bug, but what do we miss if we aren’t primed by a pattern to look for? In a certain way everything we notice is preceded by some sort of interpretive lexicon (that’s my view anyway), so it’s worth hanging around to see if the hypothesis keeps functioning with the observation in some useful way, even if you do suspect it of have been wished into being. Which is what we do anyway. It’s pretty much a waggle dance of its own.