Okay we have mass and time nailed down. I think the subdivision method should work for length as well. Let's try voltage. Consider two voltage sources that you

Okay we have mass and time nailed down. I think the subdivision method should work for length as well. Let's try voltage. Consider two voltage sources that you want to measure the ratio of. Place one source on one arm of a resistor, and the other through a pulse width modulator, (ideal) low pass filter with a cutoff frequency much lower than the pulse width modulator frequency, and then attach this to the other lead of the resistor. Turn on the voltage sources and adjust the pulse width modulator until the resistor doesn't heat up. You could place it in a cup of water and monitor the temperature. Remember we're free to push up the current in this thought experiment