In a machine, three dots in any one box are equivalent to one dot, one place their left.
(Starting with each dot in the rightmost box again worth .)
The values of individual dots throughout this machine come from noting that three ones is , three threes is , three nines is , and so on.
What is the value of a dot in the box to the left (off the screen) next after the s box?
Such a dot is worth three dots in the s place. Keep unexploding to move all these dots into the ss place. Does the count of dots you then see match your answer to the question?
At one point we said that the machine code for the number is .
Do fifteen dots in the machine indeed give one and two s?
What number has code ?
Stabilize this machine that contains dots!
The machine codes for numbers are called ternary or base three representations of numbers. Only the three symbols , , and are ever needed to represent numbers in this system.
There is talk of building optic computers based on polarized light: either light travels in one plane, or in a perpendicular plane, or there is no light. For these computers, base three arithmetic would be the appropriate notational system to use.
