Room Occupancy Matrix becomes House Occupancy Matrix

 

House Occupancy matrix

In the last post, I made a lot of heavy weather about how I could not define an equivalent energy in my room occupancy picture. I had to appeal to the eigenvalues of the transition matrices in a hard-core mathematics paper  that I could never hope to understand...

However, after sleeping on it, I realize one solution was already at hand: each room could have a different ‘temperature’ depending upon how sunny it is (the direction of desirability going up or down depending upon whether it is summer or winter).

Alternatively, I could get out of my two-dimensional thinking and play Snakes-and-Ladders in a real house.

Right, a real house has more than one floor. So you have to look at the elevation of the house as well as its plan, which we looked at in the last post.

And you obviously need to work against gravity to reach a higher floor. So the energy equivalent to the energy level diagram is gravitational energy.

This 3D analogy can be pushed just a little further: energy levels can split when some degeneracy is lifted. While houses can have split levels at one or more floors, even mezzanine floors.

Of course, the analogy is far from perfect: the occupancy of floors does not decrease exponentially as you go upwards...

Never mind!

Bottom-line from a song by Crosby, Stills, Nash & Young: ‘Our house is a very, very, very fine house…”