A potentially stupid question...
How does introverted intuition interact with extroverted thinking? It does sound like trying to turn apparent non-sense into 'rational' sense.
I wouldn't say that, although some people would. I think that Ni DOES make sense on some level, and Te just helps give it a structure and presentation that other people can readily understand. The logic is used to streamline the vision and relate it to reality in an understandable way, rather than to analyze and explain the underlying system. The INTJ is a visionary and a strategist. They intuitively understand what's going on, and construct systems and solutions in order to deal with it in a logical way.
If you want to understand "why," and get a practical solution to any issues, you need an INTJ. If you want to understand "how," and get a critical, detailed analysis of the underlying system, you need an INTP.
An INTJ can tell you what to do and why you should do it. An INTP can tell you how something works, why it works that way, and then criticize it based on how they think it should work, and maybe suggest several random ideas about how it could be improved.
The INTP approach works better in engineering or anything that requires a precise understanding of the principles involved, as well as lots of trial and error... while the INTJ approach works better when you need to plan for every possible contingency, and minimize risk.
I originally typed a better version of this, offering more contrast with the INTP, but the stupid backspace key ruined it by sending me back a page (what idiot thought it was a good idea to bind that key to that function?!
), and I was too frustrated to reproduce it at the same level of quality.