In your example of pancakes versus photosynthesis I wouldn't consider either one smart. Both have expertise in different categories. The smart person is the one who understands to defer to person A about plant related topics and person B on culinary issues. Being smart is sometimes just getting out of your own way and not being stupid. Stupid people think they know about things they don't and are rigged when presented with new information.
A stupid person is a person that insists he can make pancakes beter than you because he knows about photosythesis and you don't.
The whole phenominon is regarded as the Dunning Kreuger Effect.
One of the most prolific things a person can ever understand. I highly reccommend everyone seeking to understand behavior in general familiarize themselves with it.
http://en.wikipedia.org/wiki/Dunning–Kruger_effect
Its why Soulja Boy thinks he's Rakim, and why Canibus will tell you he is not Rakim.. when by all accounts he has probably surpassed him.