I don’t think I know how to “think like a Russian” either. Most Russians I know all think different things just like most Americans.
Undoubtedly true, but some Russians like to believe otherwise — hence the proverbial:
Умом Россию не понять! [Umom Rossiju ne ponjat’!]
“Russia is not to be understood with the mind” or “Russia defies understanding.”
P.S. For Ron and others, this is actually the first of a four-line verse by the 19th-century poet Fjodor Tjutchev:
Умом Россию не понять,
Аршином* общим не измерить:
У ней особенная стать —
В Россию можно только верить.
(Russia cannot be understood by the mind,
She cannot be measured by a common yardstick*
She has a special character/substance —
One can only “believe in” Russia.)
So, the supposedly inscrutable nature of Russia, Russians, and Russian-ness is older than Churchill’s formulation “riddle wrapped in a mystery inside an enigma”!
*If you want to be super-pedantic about it, “a stick measuring about 28 inches, or 71 cm” — this unit of length was called an arshin in Russian.