If empty space is a “something”, then what is it? Quantum simulations describe spacetime as active not passive:

“…we think of empty spacetime as some immaterial substance, consisting of a very large number of minute, structureless pieces, and if we let these … interact with one another according to simple rules … they will spontaneously arrange themselves into a whole that in many ways looks like the observed universe.” (Ambjorn et al., 2008) p25.

Ignoring time for now, this describes space as an immaterial network that follows simple rules to service observed entities. Taking this approach, space provides the following services:

- Locations. Points that define when objects are in the same locality and so can interact.
- Directions. The neighbors a point can interact with define possible directions from that point.
- Dimensions. The number of independent degrees of freedom that the space extends into.

Locations, directions, and dimensions are services that any space, including our own, must provide to be a space. For example, in Wilson loop networks a point is a volume of our space, and in Penrose spin networks point events interact to give input and output directions (Penrose, 1972). These services define what can be called the structure of a space.

Over two thousand years ago, the Greek Euclid began our geometry by defining the structure of space as follows. He began with a point location of no dimensions that extended in one direction to make a line, that then extended at right angles to give a plane, that he again extended to give a cube. This defined our space as three dimensions whose every point could be represented by three real number coordinates (x, y, z).

This Cartesian coordinate system worked so well for the purposes of geometry that it became the standard, but it doesn’t suit all cases. For example, war-gamers adapted Euclid’s space to the two dimensions of a game board, but as squares only allow four attack directions, their space points are hexagons to allow more attackdirections. Yet most of the current models of physics assume a Cartesian space, including loop quantum gravity (Smolin, 2001), cellular automata (Wolfram, 2002), and lattice simulations (Case, Rajan, & Shende, 2001).

However, in network terms, Cartesian spaces require:

- A maximum size: The size of a Cartesian space must be defined in advance to allocate coordinate memory.
- A zero-point origin: A Cartesian space requires a (0,0,0) point within it to be the absolute center of space.

The maximum size requirement arises because how a Cartesian point is stored depends on the network size. For example, a point stored as (2,9,8) in a 9-unit cube must be stored as (002,009,008) in a 999-unit cube, so it uses more memory. This limit caused our Y2K bug, that nearly crashed our systems in the year 2000. The problem was that most computers stored years as two digits to save memory, so 1949 was stored as “49”, but then the year 2000 was stored as “00” just as the year 1900 was. Changing all our databases to four-digit years meant that any programs accessing them might crash if not modified.

It follows that if our virtual space is Cartesian, its maximum size had to be defined before the first event, to avoid a Y2K bug. But our space has been expanding at the speed of light for billions of years, and is still doing so, with no end in sight, so its final size is undefined. If our space was Cartesian, it should have crashed by now, but it hasn’t, which suggests that it isn’t a Cartesian space.

A Cartesian space also requires an origin point within itself to expand from, so when Hubble showed that every star and galaxy is receding from us, this implied that our Earth is the origin of the universe! But our planet only began recently, so it can’t be the universe’s origin. The discovery that our space is expanding everywhere at once with no absolute center within it means that it can’t be a Cartesian space. In general, Cartesian coordinates work well for small, fixed spaces but not for a space like ours that is expanding indefinitely.