Explain this 4D numpy array indexing intuitively

Question

x = np.random.randn(4, 3, 3, 2)
print(x[1,1])

output:
[[ 1.68158825 -0.03701415]
[ 1.0907524  -1.94530359]
[ 0.25659178  0.00475093]]

I am python n

Answer 1

A 4d numpy array is an array nested 4 layers deep, so at the top level it would look like this:

[ # 1st level Array (Outer)
    [ # 2nd level Array
        [[1, 2], [3, 4]], # 3rd level arrays, containing 2 4th level arrays
        [[5, 6], [7, 8]]
    ], 
    [ # 2nd Level array
        [[9, 10], [11, 12]], 
        [[13, 14], [15, 16]]
    ]
]

x[1,1] expands to x[1][1], Let's unpack this one expression at a time, the first expression x[1] selects the first element from the global array which is the following object from the earlier array:

[
    [[1, 2], [3, 4]],
    [[5, 6], [7, 8]]
]

The next expression now looks like this:

[
    [[1, 2], [3, 4]],
    [[5, 6], [7, 8]]
][1]

So evaluating that (selecting the first element in the array) gives us the following result:

[[1, 2], [3, 4]]

As you can see selecting an element in a 4d array gives us a 3d array, selecting an element from a 3d array gives a 2d array and selecting an element from a 2d array gives us a 1d array.