'For both mathematics and nature involve processes that can be thought of as computations. And then the point is that all these computations follow the Principle of Computational Equivalence...' (
context)
<Blockquote>'But one of the starting points for
the science in this book is that when it comes to more complex behavior mathematics has never in fact done well at explaining most of what we see every day in nature.
Yet at some level there is still all sorts of complexity in mathematics. And indeed if one looks at a presentation of almost any piece of modern mathematics it will tend to seem quite complex. But the point is that this complexity typically has no obvious relationship to anything we see in nature. And in fact over the past century what has been done in mathematics has mostly taken increasing pains to distance itself from any particular correspondence with nature.
So this suggests that the overall similarity between mathematics and nature must have a deeper origin. And what I believe is that in the end it is just another consequence of the very general Principle of Computational Equivalence that I discuss in <a href="[
www.wolframscience.com] chapter</a>.
For both mathematics and nature involve processes that can be thought of as computations. And then the point is that all these computations follow the Principle of Computational Equivalence...'
- Stephen Wolfram, Implications for Mathematics and Its Foundations, page
722</blockquote>