We humans are blackbox physical machines that processes physical inputs to produce physical outputs.
Whether that input goes through processing that is "spiritual" is besides the point. Reproducing "spirituality" is not the goal. The goal is to replicate what is "observable." To produce a machine that when given the same inputs as that given to a human will produce identical (or "better") outputs as the human.
This is definitely an achievable goal as for every set of inputs and output pairs in existence an infinite amount of different machines can be constructed to replicate that exact input/output functionality.
The "spirituality" that goes on within this blackbox machine or humans is irrelevant. It's not even a word that is clearly defined. We aren't trying to replicate "spirituality." We are trying to make a machine that only from an observational standpoint is clearly superior or indistinguishable to a human intelligence.
The understanding the theoretical possibility of singularity is purely within the grasp of a typical person.
Imagine a chat bot designed to be indistinguishable from a human chatter. The inputs are text queries and the outputs are text queries. The domain is every possible text query and the range is every possible text response.
For purposes of simplicity lets say the text input and output is limited to 500 chars. This makes the possible input and output pairs finite. To create a chat bot identical to a human you simply need to create a machine that maps all inputs to certain outputs. Think of it like a giant hash map of strings to strings. Given enough time and enough memory this can be done.
The goal of current AI is to solve this problem more efficiently. To produce logical cores that can dynamically generate outputs from inputs rather than following a gigantic mapping. It can be thought of as form of data compression. The data is the mapping; the compression of that data is the logical core.
The fact that a mapping can even be constructed at all is by logical induction, a proof that a singularity is possible and thus completely invalidating your initial statement of:
>I don't think anything like the singularity will ever be possible