Should we treat alternative mathematicians the same way we treat alternative archaeologists or historians?

A fractal by Auntie K.

Here’s a post I’ve been trying to write for months. Discussion on Sharon Howard’s site and at the Hall of Ma’at has given me another prod into having a go. It’s not that I have a problem identifying what to say, it’s a matter of trying to say it politely. What do you do when someone spouts demonstrable nonsense at an academic conference or in a paper? For instance I’ve been told far too many times by different people that a person is a fractal of society. Now there are many responses to that, but my first is always that I’d like to ask “How have you calculated the Hausdorff dimension?”

Yet I can’t help feeling that would be a bit rude. My usual action has been to leave it. If there’s no value in what they’re saying then I thought no-one would apply it in their own work. Chris Gosden does in his book Archaeology and Colonialism in a section where it almost makes sense talking about how individual identity is constructed. He uses an example from Melanesian ethnography where people are ‘dividuals’ rather than individuals. They’re the sum of their component parts rather than being socially atomic. This all makes sense to me and how I think of the scale of social activities. I’m happy with the idea of people being driven by urges which are like sub-individual forces and these tying into the wider social sphere and demographic influences. I can see there’s dialogue between who we are and the society we’re in. But the line saying that the individual is a fractal of society tells me nothing.

For a start it’s untrue. A fractal is a shape that appears similar at all scales of magnification. One of the effects of this is if you’re looking at a fractal you can’t tell what scale the diagram is just by looking at it. It’s usually quite easy to tell if you’re looking at an individual or a society. If you’re really stuck then you can always count the legs and divide by two. If the answer is one or less then there’s a strong probability you’re looking at an individual. Sarcastic yes, but hopefully makes it clear how the notion of an individual being a fractal isn’t possible without doing severe violence to the word ‘fractal’.

Worse than that though is that the line “the individual is a fractal of society” obscures meaning. A fractal works on one set of rules throughout. Is the author really saying the laws that govern individual behaviour are identical to the laws that govern societies? Is this really a homology? The eighties and nineties in archaeology were trek away from the idea that we could find universal laws of human behaviour. In one mathematical step we’ve leapt to the conclusion that there are laws after all, we know what they are and they’re identical at all scales and we didn’t even need a phantom tollbooth.

Perhaps when people say this they’re not talking about a homology, they’re talking about an analogy. An individual is a mass of social tensions like a society. That makes sense, but we already have a good word for saying something is like something. The word is ‘like’. I could understand the use of the term fractal if archaeologists routinely dealt with fractals but most don’t. They’re exotic items to archaeologists. So when someone says “the individual is a fractal of society” no only are they not telling us anything helpful, it’s clear they don’t understand exactly what they’re talking about.

How do you tackle this? I’ve used Chris Gosden’s book as an example because, apart from that line, it’s fantastic. The misuse of ‘fractal’ fortunately doesn’t diminish his arguments and it’s a really helpful book. In contrast I’ve heard a paper by another professor built entirely on this broken metaphor. In the same talk she also informed us that ‘chaos’ and ‘surprise’ were synonyms – which came as an amazing chaos to the mathematicians in the audience. I tried raising this at the conference and I was told that it’s a matter of opinion, some mathematicians do use the terms interchangeably. You can test this for yourself. Here’s a link to arXiv’s nonlinear dynamics search form. Search the abstracts for the word surprise. Now search for chaos. If you actually read the abstracts to see what context the word surprise is used in then the comparison is painful. I suppose it is a matter of opinion but as far as I can tell the difference is my opinion’s right (please correct me below if I’m wrong – I could be missing a better way to search elsewhere).

This isn’t an isolated case. I’d also like know how to deal with people who think chaos is non-deterministic and others who use the term nonlinear to mean ‘nice’ – only not as precisely as that. There are people who do know they mean when they say nonlinear, but it’s a minority who are explicit is saying what they mean.

The reason I’ve brought it up now is tomorrow’s post. I’m happy with the idea that there are some unscrupulous authors peddling rubbish, but not all alternative archaeologists are like that. I’m also aware that there are some academic archaeologists who take time to think about what they’re doing, especially when they do interdisciplinary work, but I’m also aware they’re not all like that. Attacking alternative archaeologists merely because they’re not ‘academic’ is, if you’re an academic, cowardice.

Surely as a matter of integrity you should debunk poor history or archaeology wherever it comes from. Even more so from academics in fact because they’re paid to produce books, while a lot of people on the fringe engage with alternative archaeologies in their free time on a voluntary basis. So while I don’t agree with many alternative archaeologies I think the people who connect with them, if they’re sincere, deserve respect rather than ire. This is why I’m not that bothered by druids at Stonehenge.

People out to make money recycling demonstrably false ideas, that’s a different matter. —–