Right, this entry is basically for Ben, who wants to know what on earth non-euclidean geometry has to do with Ursula Le Guin.

It might actually be a bit hard to write, because I can't find my copy of the essay 'A Non-Euclidean View of California as a Very Cold Place to Be'. This is what happens when you photocopy essays and then put them in a pile with other photocopied essays. I really need to buy Dancing on the Edge of the World from Amazon, the only problem is we only just placed an Amazon order last month, and the shipping is so expensive we try and make it a once a year thing.

For those of you who don't know, Ursula Le Guin is a speculative fiction author from Portland. She's not hard science fiction. While she is informed by it, the science is not the dominant part of her stories. Like all the best speculative fiction, the science in Le Guin's novels is just a novum or enabling device that allows her to alter things and speculate.

In her Hainish novels (The Dispossessed and the Left Hand of Darkness) her ansible allows instantaneous communication. This lets two cultures interact and introduces the possibility of an outsider in the narrative. Le Guin's stories often have outsiders, people who have as little information about a speculative culture as the reader. When you are seeing a world through the eyes of an outsider, the narrative demands that things be explained more explicitly and you are afforded more information. In the case of the Dispossessed, the fact that Shevek is from an anarchistic moon, but visiting a culture more like our own, lets us see a capitalist society through fresh eyes. Because we are looking at a society like our own through the eyes of an outsider, we get a fresh perspective and must look a second time at things that we usually take for granted. This is called cognitive estrangement, because the eye of the outsider divorces what we are seeing from our experiences and allows us to view them cognitively in a new way.

In Always Coming Home, Le Guin uses the Earth Sciences to reshape California into a new place, but one that still has echoes of the 'home', or the California we know. She uses information science to create a computer network that connects her distant society, so that even though they live in small towns, they are connected through the 'city of the mind'.

She uses science to connect cultures, and also to find solutions. In Always Coming Home, she says that the only difference that she can see between the Kesh (her people who may or may not live a very long time from now in Northern California) and our own culture is that there are not so many of them. While the fact that there are less of them means less conflict, and the fact that they can tread more lightly on the earth, she doesn't want them to be benighted or unknowledgable (as I guess can happen in small insular cultures), so she gives them the city of the mind, to connect them. An information network. An Infocalypse, I guess. She destroys the world as we know it through physical distasters and plague and warfare, but then she gives them the best thing that we had ; information.

So science is really just something that she uses in her 'getting to' utopia. The science isn't part of the utopia, it is a vehicle. She is more informed by anthropology, the social sciences, Taoism, anarchy. She is the daughter of Emma Goldman and Kropotkin and Lao Tzu.

That said, she uses scientifc paradigms to illustrate her point very well. And this is where we get to non-euclidean geometry. Although I have decided that it actually has very little to do with the geometry, and everything to do with the non-euclidean paradigm. The idea of the quantum world.

First thing to remember : 'getting to' Utopia is more important to Le Guin than being there. Utopia means 'no place'. Some people percieve this to mean that utopia is impossible, is unattainable, because how can we have a perfect society? Things that explore this concept : Dostoyevsky's Grand Inquisitor and Yevgeny Zamyatin's We ; the idea of Freedom vs. Happiness. You can be free or you can be happy, but you cannot have both. Therefore, utopia is unattainable. Le Guin explores this idea in 'The Ones Who Walk Away from Omelas', a story about a perfect society, bar one child who is suffering and alone. The whole society knows that they are happy, but that their happiness depends upon this child's suffering.

Le Guin's utopian visions are what you might call 'critical', or ambiguous (as she subtitled The Dispossessed). Things are not perfect, but they are an improvement. When I read a story by Le Guin, I see the idea of a world done differently. I consider the fact that there are alternatives to the here and now.

And the chance to stand in the here, now and look forward and imagine ways in which we might do it better. Darko Suvin describes Utopia as 'an historically alternative wishful construct'. The desire for something better, but also a signpost on how to get there.

So, Always Coming Home is set a long, long time from now in Northern California. Le Guin said in an essay once "My world, my California, still needs to be made." and, to me, the book is her holding out her hands and giving us a gift, the chance to make it.

Back to the non-euclidean stuff.

In 'A Non Euclidean View of California as a Very Cold Place to Be', Le Guin describes her approach to utopia.

She is subverting the usual connotations you expect when you encounter words like 'cold'. In this essay (and in Always Coming Home) cold is not neccesarily a bad thing to be. Nor is passive. It is anathema to the ideas society currently holds about progress, that it is ever expanding, growing, bright, forceful, aggressive. She is denying the Western idea of progress and offering an alternative for the future.

How is this non-euclidean?

Euclid's fifth axiom states that for any given line there is only one parallel line going through any given point. I always took this to mean that the two lines would always meet, but that was before I actually made any effort to understand it.

Anyway, you know I don't care about the actual maths anyway.

Let's just look at the paradigms instead. The euclidean world view is linear, deterministic, generalised. You could say that it was a dominant scientific paradigm, in that in Science, generalisations normally include homogeneity, relative independence of remote parts and simplicity of the elementary facts.

Considering that Hyperbolic (one type of Non Euclidean) geometry is about extremely small differences (The difference between the two intersecting lines is tiny, if you saw them both on a piece of paper you would think there was only one line. You would need to extend them for millions and millions of miles to begin to see them separating), you could say that it is anything but general.

[Also, just trying to write this, I have suddenly realised that perhaps the fact that you have to extend the lines so far is also important. Maybe Le Guin is using the idea 'non-euclidean' to imply great distances, a far reaching view. Something that will take a long, long time to observe/experience/get to.

I never expected it to be that simple.]

Non-Euclidean geometry was embraced by physicists in the twentieth century, giving rise to a new quantum paradigm : the idea of a space-time embedded, experiential reality.

Generalised deterministic-predictive models demand the removal of a particular possible space from its encompassing space-time embedded context, not to mention the transposition of that space into euclidean spatial coordinates and linear time.

I guess this means that a problem in science can face us in two ways : the euclidean/classical problem confronts us on a particular [linear?] web strand, but the non-euclidean/quantum choice is to percieve the problem as some kind of trouble we are immersed in as inhabitants of this web.

We are invested in humanity's future. We are not outside the web, this world. We are deeply involved, responsible, hopeful for this particular problem's outcome.

We already know that Le Guin is not particularly in favour of the idea of linear time (the people in Always Coming Home seem as if they could be as much from the past as the future. They are a people of the distant future looped back on the past, but also situated in one potential future). She rejects the linear idea of progress and offers an alternative. So to call her view 'non-euclidean' seems to be a futher rejection of linear models and deterministic prediction. Instead, she favours an experiential, non-linear, subjective alternative (that she offers as one of many possible futures). She offers us immersion and the ability to follow the smallest differences in lines to the point where they separate, diverge, the place where we find a new future. The gold under the rainbow, the 'bell-curved hill of possibility'

This has to be the longest entry I have ever written. I hope it made sense.