As a econometrician/statistician I am always looking at data to see patterns and relationships. My large collection of metal tops provides me with lots of data to analyze.
After a conversation with Marc Osgood of Zen Spinning Tops who was making a top that weighed 17g that spun over 17 minutes, and which he named the 1:1 top, I conceived of a simple measure that I called the Zen Ratio in recognition of Marc’s achievement. The Zen Ratio (ZR) is the ratio of the spin time in minutes to the weight of the top in grams. It can be calculated for any, and all, tops, not just long spinners. Marc’s 1:1 top was the first top in my collection to achieve a ZR greater than one.
Most tops have a Zen Ratio less than one. Below is a graph of over 620 tops showing their ZRs against the top weight. The inverse relationship (heavier tops have lower ZRs) is quite obvious. Out of interest, the data points in red are tungsten tops.
Many other collectors have tops with high ZRs. Below I present some data from those collectors of tops with ZRs greater than one. These data were collected over the last year.
The highest ratio recorded to date is 6.12, an incredible value from Tom Griffin with a 1.72g top he made specifically for the challenge.
As indicated above, the zen ratio can be calculated for any spin of any top. Given all the factors that affect spin time – characteristics of the top, and the spinner, and the spin surface, and the environment – it is likely that even the same top will produce different zen ratios on each spin. This highlights one obvious limitation of the zen ratio as a single measure of performance – it is not constant for a given top. But it was never intended to be a single measure, rather one of many ways of describing the performance of a spinning top.