Published on September 30, 2024
Why base 6? To make a long story short, it's easy to count to high numbers, and it's good for calculating RPMs.
Walking to a college class at the Allison Road Classrooms (ARC), probably to a generic class like general chemistry, I don't remember.
I was tired and delirious and started counting my steps in my head: "one," "two," "three,"… At some point, I was walking faster than I could count because the numbers were multisyllabic and was starting to forget what number I was on.
So I decided I would offload some of this effort onto the only convenient placeholders I had: my fingers. I forgot what number I was on and started over.
I counted ten steps and got lazy, so on my left hand I used 1 finger to represent those ten and started counting aloud at 1 again. I repeated this until I had all 5 fingers up on my left hand.* I had counted to ten, but run out of fingers on my left hand. So on the next restart, I raised 1 finger on my right hand and closed my fingers on my left hand. (Note, when raising fingers one at a time starting from my thumb, I struggle once I reach ring/pinky fingers. So now I start with my pinky.)
*Initially, I wasn't paying attention to detail, and when my 5th finger was raised, I immediately closed my left hand and carried the one over to my right hand. As opposed to when my fifth finger is raised AND I count to 10 aloud again. This error led me to be counting in base 5 on my left hand.
Base 6 allows me to count quickly and record accurately.
With a stopwatch, this is especially good for counting RPM. Once your watch hits 60 seconds, stop counting. Take your number in base 6 and divide by 60 seconds. What is 60? Well, it factors into 6×10. We can divide our number by these two factors one at a time.
So take your base-6 number and divide by 6; that is, move the decimal point to the left one place. The base-6 number is now an order of magnitude smaller, and therefore slightly easier to work with.
Now convert this smaller number to base 10. Multiply by the 1/6ths place, 6ths place, and the 36ths place and sum them. Take the new base-10 number and divide by 10, the second factor. That is, move the decimal point to the left one place (again).
One place value is auditory. The second is your left hand. The third is your right hand. The fourth is a number you imagine in your head.
You have now almost mindlessly calculated an RPM with up to 4 significant figures of precision with nothing but a minute and a stopwatch.
You can just truncate after the decimal if you don't want the precision.
Why don't we count in base 11?