Leibniz's monadology is often viewed as too counterintuitive a metaphysical theory and disenchants many. Could we draw a philosophically significant analogy between Leibniz's monads and Mandelbrot's fractals so that we make better sense of Leibniz's goals in monadology and his philosophical views in general? Could we make a model of Leibnizian metaphysics out of the theory of fractals with possible contributions from other formal tools?

For the sake of being facilitative, here are two quotes from Benoit B. Mandelbrot:

The Fractal Geometry of Nature 2nd edition, 1982, p. 419

The Fractal Geometry of Nature 2nd edition, 1982, p. 419.

Fractals and Chaos: The Mandelbrot Set and Beyond, 2004, p. 183

Fractals and Chaos: The Mandelbrot Set and Beyond, 2004, p. 183.

  • If you are asking users here to come with their own analogies that would be off-topic. You can ask if philosophers drew analogies between monads and fractals in the literature, but then please rephrase the question to make that clear.
    – Conifold
    Sep 14 at 19:55
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    Stephen Wolfram recalls that he himself had hopes for something a bit similar to this question, (Dropping In on Gottfried Leibniz), but Wolfram could never quite get a good handle on what monads were, at least not enough to build up his own system with monads.
    – agc
    Sep 14 at 21:04
  • @Conifold To my knowledge, there's no considerable study to understand Leibniz theory of monads through fractals. I had come to think about a connection that might be exploited to grasp Leibniz's goals long before I came across Mandelbrot's remarks. I wondered whether anybody else holds similar ideas to discuss. But, yes, now I view that the issue is too broad as a question, perhaps better to draw it back. Sep 14 at 21:12
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    Deleuze's Fold: Leibniz and the Baroque comes to mind, and Bouquiaux, L'harmonie et le chaos if you read French.
    – Conifold
    Sep 14 at 23:03

We discussed fractal cosmologies here: What would a fractal universe tell us about Time? I'd say there is a serious risk of saying something like 'these are two complicated things so they are the same' - an approach generally based on baffling the uninitiated with jargon, rather than making true headway (widely found in pseudoscience claims about how quantum behaviour is weird & consciousness is weird so they must be the same thing). We can link minds to complexity theory and emergence, sure. But we just don't find infinite-levelled self-similar structures like in Mandelbrot's maths, in our world - the Planck scale & size of the universe provide defined limits.

I'd say there is a fundamental parallel between what Plato is doing with his Forms, with the monism of Shankaracharya in Hindu thought, and with Leibniz's monads. That is, creating a framework which can relate cultural & religious diversity, into a single structure. While not consciously motivated by political aims, I'd suggest this methodology fits a kind of 'spiritual entrepreneurialism', where it gained attention & support for providing a basis for cultural unity, without requiring homogenisation.

Leibniz aimed to bridge the math-cult Plato took from Pythagoras, with his religious ideas, unifying mathematics & spirituality. On the mathematical monism part of that, I'd say Lisi's proposals about E8, are a better candidate for manifesting something compatible with Leibniz's ideas, than fractals.

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