Now we're familiar with CPUs doing serial processsing and GPUs doing parallel processing.

There's a 2008 TED talk about the left brain doing serial processing and the right brain doing parallel processing, and what happens when one side breaks: https://www.ted.com/talks/jill_bolte_taylor_my_stroke_of_insight

What other situations do this? Companies and countries tend to be either heavily serial (micromanaging/autocratic CEO/Prime Minister) or heavily parallel (delegating CEO/PM). There's not a lot of situations where there are two leaders who do one of either.