Fake science, 1793 style
I've often read about the decimal hours and decimal months that were supposed to go with the metric system. I hadn't seen a picture of a decimal clock before.
From an 1888 French book on horology,
here's an 'equation dial'
showing the two systems together.
As with most metric units, these hours are toooooo loooooooong for practical use.
There was a good HUMAN reason for the 12/12 pattern, just as there was a good HUMAN reason for the 12-month calendar. There's nothing natural about 10s except finger-counting.
Both 12s arose from an initial division into four seasons. The year-seasons represented the work of plants, and the day-seasons represented the work of humans. In both cases the four seasons can be described as sleep, preparation for work, work, and rest from work. As human society got more detailed and organized, each of the four was divided into start, middle, and end; or intro, story, and outro. The day-pattern was divided again by 2s.
The revolutionaries tried to invoke science for their new units, but the connections were abstract and numerical, not tied to human work. They named their 10 months after plant-related events, but the 10 could never synchronize with four seasons, so the plan failed from the start.
Weeks have always been the outlier. Presumably the pattern of work 6 and rest 1 was determined by long experience and natural negotiation between workers and employers. But 7 doesn't sync with months or years no matter how you parse them, and 7 doesn't divide into internal parts.
Do we have 12s in our nervous system? Hard to say. We have clear evidence for natural brackets of 3 in counting and language, but not much for the outer brackets of 4.