Classical vs Quantum Fingernail growth rate

So, myself, Max and co. hop on the subway and head towards Porter Square to get us some sushi at Kotobukiya, this marvelous inexpensive sushi place at the Porter Exchange. Along the way, Max and I start to discuss issues of fingernail growth; following is an approximation of the ideas that we came upon:

Max suggested that if his fingernails were to grow twice as fast he could bite his nails twice as fast. From this, I disagreed saying that he could bite his nails twice as often. There was then agreement that the nails could not be bitten off twice as fast, but Max introduced as an alternative that they could be bitten off in chunks twice as large in size. From these two methods of dealing with nails that grow twice as fast comes a simple theory. Suppose there is a frequency with which nails may be bitten (we'll call it w because it's like a little omega) and suppose that there is a size, or amplitude, of bitten off nail chunks (we will call this a), then we can say that their product will be a constant (say C, just because) that is proportional to the rate of fingernail growth. This theory can be written in the form w*a=C; this is what we will call the fundamental theory of classical fingernail growth.

Max then theorized a non-classical form of fingernail growth when he stated that he would like to have quantum fingernails. This led to a discussion of how quantum fingernail growth would work. Our best theorization of the matter is that since everything is a probability distribution you can never know how long your fingernails are or how fast they are growing unless you bite them. As such you will not know how long your nails are until you bite them, but then you will not know how long it will take until you need to bite them again.

Postscript: I do not encourage biting one's nails; personally I use nail clippers. Nail biting was just the context that the conversation took at the time.