# Mathematical formulation of 'Indra's net' [closed]

Quoting Wikipedia:

"Imagine a multidimensional spider's web in the early morning covered with dew drops. And every dew drop contains the reflection of all the other dew drops. And, in each reflected dew drop, the reflections of all the other dew drops in that reflection. And so ad infinitum. That is the Buddhist conception of the universe in an image." Alan Watts

What logic could be used to sufficiently model such framework? More specifically, suppose if I wanted to model a network of hypergames or a quantum Turing machine what tools would I need?

I just want a hint to get started.

On page 689 of D.Hofstadter's Goedel, Escher and Bach he mentions that there are three authors $Z$, $T$ and $E$. And $Z$ exists only in a novel by $T$, $T$ only in a novel by $E$ and $E$ in a novel by $Z$. He represnted with three nodes, Z,T,E where one arrows point from $Z$ to $E$, $E$ to $T$ and $T$ to $Z$. Now Hofstadter further states that if this authorship is possible and he says that by a "trick" which is all three authors are themselves characters in another novel...by $H$.

So, basically this prompted me to look up Indra's net in his other section for $n$-dimensional generalization. However, he briefly touched on it. Further online research yielded an area called Tensor Product Networks.

This led me to think how to model a hypergame network. Consider the Quine atom Q. Now Q={Q}. Is it then possible to construct a lattice of Q which in turn contains Q and if so, how to represent it symbolically?

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## closed as unclear what you're asking by Lord_Farin, Bookend, drhab, TravisJ, hardmathMay 16 '15 at 14:11

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Absolutely incomprehensible. – Gerry Myerson Oct 10 '12 at 6:16
I'm not sure if I know what logic could be used, but there is a good book called 'Indra's pearls' by D. Mumford that discusses this. – Alex Oct 10 '12 at 7:08
@Alex That was my inspiration actually, but that book seemed to be a text more on fractals unless I missed the portion that gives a logical treatment of such network. – Sniper Clown Oct 10 '12 at 7:35