Why it is necessary to define numbers and rituals
--Because of the common understanding that Hindu scholars define arbitrary numbers, and that the reason they do it is simply out of superstitious stupidity and to control people (which I too used to think).
But then, I myself had the question, like what makes a clean wash, what is the nature of interactions between dust and clothes, and what clothes fibres are made of, and so on. Why did I think about this?
One reason was for me to decide how often I should wash clothes - whether after every wear (which ends after a fresh bath), or after a set number of wears. Definitely, I wouldn't wear the same under-wears after a new bath, because it does itch from experience. Although when we were in school, we would end up wearing dirty vests to class to avoid checking (we'd most often get caught when in the khaki uniform, because of the sweat)
Example of Washing Machine
If you ask someone how many hours or strokes you need to wash a cloth for, they will tell you, "till it's clean, you silly".
But the question has its relevance when you are designing a washing machine.
When you are defining a washing machine, you would want to define the pattern and duration of washing.
One could say that you could test the clothes by making them dirty and see how long it requires you to wash it.
However, that works on the principle of a specific washing method, and it also depends on the type of cloth that you put in.
The details will still have to be defined at some level, and I'm just taking it to the most complete level.
The advantage of this is in designing an efficient washing machine.
It is one thing to define a washing machine that performs a systematic wash based on these principles.
But another form of washing machine can be devised based, that performs a wash until clothes are observed to be clean.
But even that works by not knowing the optimal method of washing.
Therefore, the machine that performs the wash will be less efficient compared to the ideal washing machine.
One could say that this is a difficult task.
But that is what makes products exceptional.