Benjamin DeHass | Monterey, CA
The Monday after I drove out to the benitoite mines, I could not stop thinking about owning every mineral ever discovered. Not buying them, finding them, each one pulled out of the ground myself. I was in my evening block, the hours I keep for my own projects, already partway into building a small autograd engine to learn how backpropagation works. The mineral thought landed on top of that. Granting it breath, I found mining claims (a person can stake a piece of land and work it) which opened into another thread, and another. Each one gets added to a list that grows until I run out of room and they all fall back into the dark to be found again some other day.
The problem showed itself at dinner. I sat down to watch something and could not pick. In one week I had opened seven threads and every one wanted the hour. A video on the chemical structure of benitoite. The autograd build. Where a person learns to scuba dive, because that had started to sound interesting too. I did a version of all three at once; one playing in front of me, one open on the side screen, one running in my head. None of them absorbed. It was just me and my brain at the table, and the table was full.
For a long time I read this as a discipline problem, and some of that was true. But splitting one dinner three ways, the real story came through, and it was not about willpower. It was about rate.
A queue has two rates. Work arrives at some average rate (the arrival rate) and gets served at some average rate (the service rate). Utilization is the ratio between them. If work arrives slower than you clear it, the line stays finite and everything is eventually served. If it arrives faster, utilization passes one, and the queue is called unstable. An unstable queue does not settle at some large size. It grows without bound, and the wait climbs toward infinity, no matter how fast the server runs.
Instability is not slowness, and a faster server does not fix it. If new interests arrive faster than anyone could ever finish them, no amount of effort closes the gap, because the gap is not made of effort. Working harder lifts my service rate and leaves the arrival rate untouched, and the arrival rate is the term that broke the system.
You cannot slow the world down. The mines, the videos, the friend who mentions the one thing you have never heard of, the cool object seen in passing, these arrive at whatever rate they arrive. The service rate has a hard ceiling too, set by the hours and the one body moving through them. Both natural levers are fixed. What is left is the one nobody thinks to touch, because it feels like loss. You cap how many items are in service at once and hold the rest at the door; not forever, just not yet.
It is for this reason that a closed system admits a new job only when a current one departs. The seat is not open until the customer in it stands up. Completion is not the end of a thing, it is what makes room for the next one. Seen that way, the cap is not deprivation but an ordering, a structure laid over the pile so the work already on the plate gets all of me instead of a third of me. The guilt I felt going all in on one thing while six others waited was the system telling me something false. Finishing was never the betrayal of the other six, it was the only thing that would ever let them in.
I am capping the occupancy. A few things in service, the rest in a queue I am allowed to ignore, nothing new admitted until something is done. The benitoite waits for the autograd engine. The scuba waits for the benitoite. They lose nothing by waiting, and there’s always new to look forward to.
An unstable queue serves no one. Neither does an unstable mind.