The original sentence:
We set out to explore how it is that we can all live in the same universe yet see reality so differently.
The compared sentence:
We set out to explore how we can all live in the same universe yet see reality so differently.
I would like to know the meaning and usage of the phrase "how it is that". In particular, I would like to know:
What is the difference in meaning between these two sentences?
What is a possible answer to that how-clause?
Because of how, an adjective is chosen.
It is amazing…?
Is "how it is that" considered as a standard pattern?
Are there other usages of that pattern?
"It also showed me how it is to be a student."
The expression … how it is that we can all live in the same universe… acknowledges that we do live in the same universe though we see reality differently.
Using it is that… means that the speaker believes that what follows is true.
The expression … how we can all live in the same universe, though we see reality so differently. could mean that the speaker believes we may not be able to live in the same universe (metaphorically), and is looking for ways to correct that. How to do it? That is a possible interpretation, but the sentence as given could mean the same as the other version.
For explore how it is that, something longer and more explanatory than amazing would likely follow.
Without it is that, and seeing how as asking for a means, it might want something like by being considerate of each others’ points of view.
Yes, that is a normal way to assert that the speaker believes what follows is a fact.
There can be other uses of the same pattern, but the example you propose isn’t the same, since it doesn’t introduce a clause saying that anything is a fact. In your example, the how is referring to a general description of the experience of being a student.