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Against Myths? Some category theory and set theory at the end…

This is Gustave Moreau’s painting, Oedipus and the Sphinx 1863-43. Gustave Moreau is a Symbolist painter, or perhaps the father of symbolism. This is in contrast to the prevailing realism schools of art. Symbolism prioritized the dream world, the unconscious, the subjective, the individual, artifice – some of these – all of these. Also there is the notion that perhaps these paintings tell a story in a different way, through indexical symbols rather than, or inadition to drama and tension. Symbolic paintings are meta-textual, their richness comes from associations within their cultural context.

I am an enormous fan of Moreau. I love worldbuilding. His paintings are rich, weird, and alive. When I saw this at the Met in NYC, my lover and I sat down and stared at it for hours. Then we got up and saw it was Moreau’s!

For most of my adult life, I have also been a lover of myth. I still am. I was taken with a teen, by the prompt of Joseph Cambell to find the new planetary myths of our age that will help us make sense of the changing world.I have thought and studied technology and the stories we tell about technology, modern and ancient that could help us understand our relationship with computers, planetary computation, and its ensuing catastrophic impact on the environment and on society.

How does change happen? I think of the Sorites Paradox – How does a grain of sand become a heap? The general explanation is that our language is too vague – so this is really a problem of language not a philosophical problem. From the standpoint of complexity theory, we can understand a heap to be an emergent property or state of adding grains of sand, just like heating water will change the state from liquid to gas.

But how does change happen in the world of humans, not just in the world of atoms and sand. How does change happen in society? I have some ideas but I am just going to ask the question for now.

In many of Socrates’ dialogues, there is a recourse to myth. I always felt this was because there was a limit to reason, or to what reason could tell us – and that these other “truths” were only available via myth.

In terms of computation, there are some problems that we can compute (that are reducable to algorithms) and some problems we cannot. These non-computational problems can be solved by what alan turning called an oracle machine. This is another way of stating the distinction between logos and mythos – Socratic reasoning and greek mythology.

So why do we need oracles, the sphinx, or myths? Because there are some decisions and events that are beyond computation and our current decision-making technologies. In the past, I thought that myth was a technology for decision-making. But today, I feel this is wrong, and I am channeling the Dialectic of Enlightenment by Horkheimer and Adorno. That mythology is the collapse of reason, not a technology for an alternative to reason. Some myths may be wise or true, but what tools to we have to determine those?

Mythology looks like the way oracle machines are implemented today: black boxes that cover up a gap in an algorithmic system, a way to obfuscate a state change or phase transition, a way to obfuscate how change happens. From here, I am thinking of the hermeneutics of suspicion, Paul Ricoeur, and the disciplines of suspicion, which must be decoded to be understood. There is a relationship between the disciplines of suspicion and structuralism – that there is something behind the event that explains the event – the mythos behind the logos- the story behind the reason. But today, this feels like it just hides away the violence at the heart of change and at the heart of structure.

Maybe instead of new myths what we need are understandable oracle machines. Instead of the

On that note- I am going to leave you with some open-generated logical analysis of the grimm fairy tale, The Summer Garden and the Winter Garden – discussed in other pages of this blog. I think this is fascinating as a pedagogical tool in learning different mathematical/logical systems.