There are some good long answers already, so I'm going to try to give as short an answer as possible.

A quantization of X is some X_hbar depending on a parameter hbar (occasionally q=e^hbar instead) such that X=X_0 and X_hbar is generically "less commutative" than X. This is by analogy with quantum physics where X_0 is classical physics and hbar measures the failure of position and momentum to commute.

There are some good long answers already, so I'm going to try to give as short an answer as possible.

A quantization of $X$ is some $X_\hbar$ depending on a parameter $\hbar$ (occasionally $q=e^\hbar$ instead) such that $X=X_0$ and $X_\hbar$ is generically "less commutative" than $X$. This is by analogy with quantum physics where $X_0$ is classical physics and $\hbar$ measures the failure of position and momentum to commute.

There are some good long answers already, so I'm going to try to give as short an answer as possible.

A quantization of X is some X_hbar depending on a parameter hbar (ocassionaly q=e^hbar instead) such that X=X_0 and X_hbar is generically "less commutative" than X. This is by analogy with quantum physics where X_0 is classical physics and hbar measures the failure of position and momentum to commute.

There are some good long answers already, so I'm going to try to give as short an answer as possible.

A quantization of X is some X_hbar depending on a parameter hbar (occasionally q=e^hbar instead) such that X=X_0 and X_hbar is generically "less commutative" than X. This is by analogy with quantum physics where X_0 is classical physics and hbar measures the failure of position and momentum to commute.