Hi all, When we create new datatypes, we have the option to make new choices for the new datatypes [0] (not the existing ones). The question is: Should every NumPy datatype have a scalar associated and should operations like indexing return a scalar or a 0-D array? This is in my opinion a complex, almost philosophical, question, and we do not have to settle anything for a long time. But, if we do not decide a direction before we have many new datatypes the decision will make itself... So happy about any ideas, even if its just a gut feeling :). There are various points. I would like to mostly ignore the technical ones, but I am listing them anyway here: * Scalars are faster (although that can be optimized likely) * Scalars have a lower memory footprint * The current implementation incurs a technical debt in NumPy. (I do not think that is a general issue, though. We could automatically create scalars for each new datatype probably.) Advantages of having no scalars: * No need to keep track of scalars to preserve them in ufuncs, or libraries using `np.asarray`, do they need `np.asarray_or_scalar`? (or decide they return always arrays, although ufuncs may not) * Seems simpler in many ways, you always know the output will be an array if it has to do with NumPy. Advantages of having scalars: * Scalars are immutable and we are used to them from Python. A 0-D array cannot be used as a dictionary key consistently [1]. I.e. without scalars as first class citizen `dict[arr1d[0]]` cannot work, `dict[arr1d[0].item()]` may (if `.item()` is defined, and e.g. `dict[arr1d[0].frozen()]` could make a copy to work. [2] * Object arrays as we have them now make sense, `arr1d[0]` can reasonably return a Python object. I.e. arrays feel more like container if you can take elements out easily. Could go both ways: * Scalar math `scalar = arr1d[0]; scalar += 1` modifies the array without scalars. With scalars `arr1d[0, ...]` clarifies the meaning. (In principle it is good to never use `arr2d[0]` to get a 1D slice, probably more-so if scalars exist.) Note: array-scalars (the current NumPy scalars) are not useful in my opinion [3]. A scalar should not be indexed or have a shape. I do not believe in scalars pretending to be arrays. I personally tend towards liking scalars. If Python was a language where the array (array-programming) concept was ingrained into the language itself, I would lean the other way. But users are used to scalars, and they "put" scalars into arrays. Array objects are in some ways strange in Python, and I feel not having scalars detaches them further. Having scalars, however also means we should preserve them. I feel in principle that is actually fairly straight forward. E.g. for ufuncs: * np.add(scalar, scalar) -> scalar * np.add.reduce(arr, axis=None) -> scalar * np.add.reduce(arr, axis=1) -> array (even if arr is 1d) * np.add.reduce(scalar, axis=()) -> array Of course libraries that do `np.asarray` would/could basically chose to not preserve scalars: Their signature is defined as taking strictly array input. Cheers, Sebastian [0] At best this can be a vision to decide which way they may evolve. [1] E.g. PyTorch uses `hash(tensor) == id(tensor)` which is arguably strange. E.g. Quantity defines hash correctly, but does not fully ensure immutability for 0-D Quantities. Ensuring immutability in a world where "views" are a central concept requires a write-only copy. [2] Arguably `.item()` would always return a scalar, but it would be a second class citizen. (Although if it returns a scalar, at least we already have a scalar implementation.) [3] They are necessary due to technical debt for NumPy datatypes though.