and tests whether both expressions are logically True while & (when used with True/False values) tests if both are True.
In Python, empty built-in objects are typically treated as logically False while non-empty built-ins are logically True. This facilitates the common use case where you want to do something if a list is empty and something else if the list is not. Note that this means that the list [False] is logically True:
>>> if [False]:
... print 'True'
...
True
So in Example 1, the first list is non-empty and therefore logically True, so the truth value of the and is the same as that of the second list. (In our case, the second list is non-empty and therefore logically True, but identifying that would require an unnecessary step of calculation.)
For example 2, lists cannot meaningfully be combined in a bitwise fashion because they can contain arbitrary unlike elements. Things that can be combined bitwise include: Trues and Falses, integers.
NumPy objects, by contrast, support vectorized calculations. That is, they let you perform the same operations on multiple pieces of data.
Example 3 fails because NumPy arrays (of length > 1) have no truth value as this prevents vector-based logic confusion.
Example 4 is simply a vectorized bit and operation.
Bottom Line
-
If you are not dealing with arrays and are not performing math manipulations of integers, you probably want
and. -
If you have vectors of truth values that you wish to combine, use
numpywith&.