Sunday Morning With Max and Martin

"The Mathematical Universe Hypothesis offers a radical solution to this problem: 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. The external physical reality is therefore more than the sum of its parts, in the sense that it can have many interesting properties while its parts have no intrinsic properties at all."

-- Max Tegmark from "Our Mathematical Universe"

…and in a footnote on the same page Max pushes the idea further, writing:

"Our brain may provide another example of where properties stem mainly from relations. According to the so-called concept cell hypothesis in neuroscience, particular firing patterns in different groups of neurons correspond to different concepts. The main difference between the concept cells for 'red,' 'fly,' and 'Angelina Jolie,' clearly don't lie in the types of neurons involved, but in their relations (connections) to other neurons."

Martin Gardner almost seemed to pre-sage Tegmark when he wrote the following more than a decade earlier (in his essay, "Is Mathematics 'Out There'?"):
 

"No mathematician, Roger Penrose has observed, probing deeper into the intricate structure of the Mandelbrot set, can imagine he is not exploring a pattern as much 'out there,' independent of his little mind and his culture, as an astronaut exploring the surface of Mars.
"In the light of today's physics the entire universe has dissolved into pure mathematics. The cosmos is made of molecules, in turn made of atoms, in turn made of particles which in turn may be made of superstrings. On the pre-atomic level the basic particles and fields are not made of anything. They can be described only as pure mathematical structures. If a photon or quark or superstring isn't made of mathematics, pray tell me what it is made of?"

Or similarly, this from another Gardner piece, "In Defense of Platonic Realism":

"In a curious way, numbers may be more real than pebbles. Matter first dissolved into molecules, then into atoms, then into particles, which are now dissolving into tiny vibrating strings or maybe into Penrose's twistors. And what are strings and twistors made of? They are not made of anything except numbers. If so, the numbers are as much 'out there' as molecules. They could be the only things out there. As a friend once said, the universe seems to be made of nothing, yet somehow manages to exist. As Ron Graham remarked, mathematical structure may be the fundamental reality."