Here are three additional levels of numerology that just don't belong the discipline of software architecture.
Empiricism. Ideally these are from Physics and related "hard" sciences. Psychology or Economics are "hard" sciences in the other sense of hard -- they're difficult because of the subject matter. The magic number 7 ± 2, for example, is a piece of research [miller ] that has some standing. There's some fuzziness to this, and a change in theory or measurement or sample population could refine this.
Mysticism. The idea that every industry is dominated by three major players, or that there are five layers to a good architecture is just mysticism. They are comfortable numbers, they form patterns in our heads, but they aren't natural "laws", or even empirical measurements.
Tautologies. A logical tautology can be framed with numbers to make it seem empirical. "If the solution/consequence does not directly (ie no more than 1 logic jump) tie back to the problem, then something is wrong somewhere." More than one logic jump is just a faux-empirical code for "non-sequitur" or "not directly".
Let's test "more than 1 logic jump". What it if were more than, say, 3 logic jumps? Would that be more or less of an indirect thread of logic? Since it would be equally baffling, the number 1 has no real significance, and is just numerology.
UPDATE
JB Says:
I found this particular rant and your associated personal forum article kind of bothersome. Counting for me is often a way of beginning to make sense when I'm otherwise lost. So, I pondered for a bit, until an insight appeared. It's not about counting. It's about hypothesys formation. It's about doing science.
So, when I'm lost and go start counting things I have no idea what the numbers gathered mean. That's the point, actually. The numbers become additional chunks to mix around and try to find or make some meaning, 27 fizbins observed each day except alternate Tuesdays, when there are literally hundreds. Interesting. Something is different here between alternate Tuesdays and the other days at least as regards fizbins. Now one can begin positing this explanation or that, and testing them.
"Well, perhaps all fizbins have a genetic, cognitive disorder which wires in the twin compulsions of exhibitionsim an an attraction to Tuesdays. Unlikely, as fizbins have no DNA, not being creatures, and are never seen around calendars so they can't know what day it is."
"Is there something interesting about alternate Tuesdays?"
The folly of counting stuff we don't already understand comes not from the counting, but from whipping on the numbers an unrealized belief in some silly, weak, uncontemplated model of the world. Too often the same presumed models are used again and again without even realizing that they are being used. "More is better." "More input makes more output."
Etc.
I don't think it's the counting, so much as the absence of the perspective and the discipline to do science, even in a lightweight manner, with whatever small aspect of the mundane world we decide to count.