«Mathematics is the language in which God has written the universe.» Galileo
Mathematising the world has been the initiative which enabled science to understand and gain some power on it. Mathematics keeps amazing physicists by its power of prediction! Many physical laws have been discovered by applying a mathematical tool which was created by a mathematician only to satisfy his own logic. As if the intimate fabric of the universe was mathematical!
Max Tegmark gathered his reflexions in his book: “The Mathematical Universe Hypothesis: My quest for the ultimate nature of reality.” (2014).
«If my life as a physicist has taught anything at all, it’s that Plato was right: modern physics has made abundantly clear that the ultimate nature of reality isn’t what it seems.»
And Tegmark: the son of a mathematician and physicist himself, continues:
«Our reality isn’t just described by mathematics – it is mathematics, in a very specific sense.»
«At the bottom level, reality is a mathematical structure, so its parts have no intrinsic properties at all! In other words, the Mathematical Universe Hypothesis implies that we live in a relational reality, in the sense that the properties of the world around us stem not from properties of its ultimate building blocks, but from the relations between these building blocks.»
In this important and entertaining book Tegmark applies very fruitfully his experience as a teacher at MIT. He knows how to present a question and what will illustrate the answer in the best way.
As an example here is how he explains the crucial discoveries in the 1920s that the universe is expanding. He asks to imagine oneself giving a lecture and discovering that the attendees sitting just in the first row are all very old. And the further one looks, the younger the attendees are! With babies laying at the farthest seats! Just in front of a black void! That’s how our universe looks like when we look for galaxies: the farthest they are, the younger!
Everyone fond of astronomy knows this of course, but it’s rare to find an illustration that speaks as much to the imagination! And Tegmark’s book is full of such nice findings.
He presents the findings of “the precision cosmology” to show how it “highlight the mysterious utility of mathematics for understanding our world.” Then he expands the concepts laid by the inflation model of the universe and Quantum Mechanics to define different levels of Multiverses. Tegmark suggests that “Fine-tuning is arguable evidence for the Level II Multiverse“. I.e. that the explanation behind the astounding fine-tuning of the 32 constants that make our Universe suitable for life and intelligence is that there are an infinity of these, each with different values for these constants and that we live in the only one that, by chance, have the good values!
Level III Multiverses are Hugh Everett’s ones. Here again, Tegmark illustrates the Many Worlds hypothesis in new and clear illustrations.
Information is introduced and its importance emphasized. “The quantum weirdness doesn’t go away, it just gets censored” (about the difference between microphysics and macrophysics). Or “I concluded that quantum mechanics requires secrecy: an object can only be found in two places at once in quantum superposition as long as its position is kept secret from the rest of the world.” “Quantum observation isn’t about consciousness, but simply about the transfer of information.“
The last part of the book describes the M.U.H or Mathematical Universe Hypothesis.
The M.U.H implies that we live in a relational reality, in the sense that the properties of the world around us stems not from properties of its ultimate building blocks, but from the relation between these building blocks.”
Strangely, Tegmark doesn’t “bet on a computable universe.” Even if all his work seems to point towards Simulism!
So the universe would be a structure, a purely mathematical object, thus a set of informations, which is compatible with Simulism.