# Gardening the Manifold

Who needs a hair dryer when you can think about infinity instead? But seriously, what do we label “infinite”? It’s often associated with recursion or fractals. Recursion is common in programming, and here is a fact:

Recursion and iteration (looping) are equally powerful. Any recursive algorithm can be rewritten to use loops instead. The opposite is also true. Any iterative algorithm can be written in terms of recursion only. In a sense, all recursion is an illusion. At the machine level, you have an iterative process for fetching and executing instructions. All function calls (including the recursive ones) are implemented via a runtime stack to keep track of the return addresses, actual parameters, and local variables associated with function calls. [Steven J. Zeil]

So, both recursion and iteration may or may not be infinite. We may count “1, 2, 3, ad infinitum”, but the last symbol is actually the end of counting, breaking the loop. Boring!

But there’s a phenomenon which may be really infinite: map compression aka infinite ignorance. Take all the unknown, perhaps unobservable space-time, then call it “The Universe” – we’re done, let’s go for a lunch at The Restaurant at the End of the Universe, or maybe play the new Manifold Garden game!