Kick at the rock, Sam Johnson, break your bones: But cloudy, cloudy is the stuff of stones. ~ Richard Wilber

The very notion of impenetrability, so basic to our everyday understanding of the material world, turns out to be something of a mathematical illusion. Why don’t we fall through the floor? Why did the rock rebound when Dr Johnson kicked it? Because two solids can’t interpenetrate each other, that’s why. But the reason they can’t has nothing to do with any sort of intrinsic stuff like solidity. Rather, it’s a matter of numbers. To squash two atoms together, you’d have to put the electrons in those atoms into numerically identical quantum states. And that is forbidden by something un quantum theory called the “Pauli exclusion principle,” en.wikipedia.org/wiki/Pauli_exclusion_principle which allows two electrons to sit directly on top of each other only if they have opposite spins.

As for the sturdiness of individual atoms, that too is essentially mathematical. What keeps the electrons in an atom from collapsing into the nucleus? Well, if the electrons were sitting right on top of the nucleus, we’d know exactly where each electron was (right in the center of the atoms) and how fast it was moving (not at all). And that would violate Heisenbert’s uncertainty principle, which does not permit the simultaneous determination of a particle position and momentum.

So the solidity of the ordinary material objects that surround us – tables and chairs and rocks and so forth – is a joint consequence of the Pauli extension principle and Heisenberg’s uncertainty principle. In other words, it comes down to a part of abstract mathematical relations. As the poet Richard Wilber wrote, “Kick at the rock, Sam Johnson, break your bones:/ But cloudy, cloudy is the stuff of stones.”

At its most fundamental, science described the elements of reality in terms of their relations to one another, ignoring any stuff like quiddity those elements might possess. It tells us, for example, that the electron has a certain mass and charge. But these are mere propensities for the electron to be acted upon a certain ways by other particles and forces. It tells us that mass is equivalent to energy, but it gives us no idea of what energy really is – beyond being numerical quantity, that when calculated correctly, is conserved in all physical processes. As Bertrand Russell noted in his 1927 book “The Analysis of Matter,” when it comes to the intrinsic nature of the entities making up the world, science is silent. What it presents us with is one great relational web: all structures, no stuff. The entities making up the physical world are like the pieces in a game of chess: what counts is the role defined for each piece by a system of rules that say how it can move, not the stuff that the piece is made of. ~ Page 187 - 188 ( Why does the world exist - Jim Holt)