A lot of cosmology insight can be gained by simply looking at and contemplating this lattice. Here are the first five of my top ten interesting insights:

1. Say each blue bar is now 1 km long, but we somehow 'grow' the length of each bar (not the cubes) at a steady rate of one meter per year. The distance between any two red cubes will then grow at n meters per year, where n is the number of bars between them. This is equivalent to Hubble's law - the apparent recession speed of a distant galaxy is proportional to its distance from us. The 'Hubble constant' (H-zero, or Ho) of the lattice would be one meter per year per km distance. Take note that it is a distance divided by a time and a distance, so the unit of measure is essentially one over time. If we divide Ho into 1000, we get the Hubble time of this lattice as T

_{H}= 1000/1 = 1000 years. The factor 1000 is just the number of meters in a km.

2. An observer somewhere near any red cube (say at the viewpoint in the diagram) will get the impression that she is at the center of a large expanding system of cubes, with all cubes moving away from her at speeds depending upon their relative distance. To her, the color of distant red cubes will appear redder than nearby cubes (light with longer or 'stretched' wavelengths), from which she will be able to deduce that more distant cubes recede faster than nearby ones. Whether she attributes the reddening to Doppler shift or to stretching of the wavelengths does not matter at this point, but it is equivalent to the distance/redshift relationship that astronomers use.

3. If our observer extrapolates backwards in time, she will conclude that if the individual growth rates of bars have always been one meter per year, the red blocks must have been touching each other at a certain time in the past. With all bars one km long and a stretch rate of at one meter per year, this must have happened 1000 years ago. So, our astronomer may conclude that expansion of the lattice have probably started 1000 years ago. This is not necessarily the age of the lattice, since she does not quite know what may have happened before the time when the cubes (presumably) touched each other. The ‘age’ of our universe is determined in a similar way.

4. Since we are working with a (scaled down) toy model here, let us say the speed of light in this lattice is an extremely pedestrian one km per year, so that in 1000 years, light would have traveled only 1000 km. Later we will replace kilometers with light-years, but for now, please bear with me. If our cube-astronomer should use a telescope to look as far as she possibly can, what will she see? Due to the finite speed of light, she must be looking back in time - she would be seeing every successive cube at an earlier time, i.e. at the time when the light left it. At some distance, she must be looking back to the time when all the cubes were touching each other. Unless the cubes were all transparent, she could not observe anything more distant, or to an earlier time, for that matter. This is equivalent to our present observation of the cosmic microwave background (CMB) radiation, the most ancient observable light.

5. Shortly after the bars started to expand, light could however move through the lattice. Suppose our lattice astronomer knows the natural color (and hence the wavelength of emissions) of the ancient cubes, but presently she detects them at a wavelength that is a thousand times longer. She could deduce that the length of the (now one km long) blue bars must then have then been only one meter. Because of her assumption of a steady growth in the length of one meter per year for each bar, she can also estimate the time when the light has left the most distant visible cubes: about one year after the expansion started, or roughly 999 years ago. This is equivalent to our present observation of the CMB radiation, which is stretched by a factor of 1088, coming from approximately half a million years after expansion started.

The black background that you see when you ‘look down the shaft’ at the bottom-left of the lattice represents the CMB of the toy-model. The cubes do not stop there; you can just not see the ones farther out, towards infinity…

I think this is more than a mouthful already. I will proceed with the last five of my top ten ‘lattice insights’ in a follow-on post. Any feedback would be welcomed.