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I believe the term "semi-cursive" is preferable as the primary term for this script. For a similar discussion on terms for all the scripts, pls see Talk: East Asian calligraphy .Dragonbones 09:01, 23 March 2006 (UTC)
To people not familiar with the Chinese characters as they are printed in books and newspapers, this cursive writing may seem impossible to decipher. Not so for the literate Chinese. By using the order of strokes clearly visible on the character, a literate person familiar with the characters can guess what the character really is.
Stroke order cannot necessarily be discerned from the written character and does not play a role in reading. Reading is achieved in part by a "Gestalt" approximation to the regular paradigm, in part by context, and in part by the fact that the cursive approximations are not arbitrary.
As is true with most alphabets, usually the most messy script writing is found in the writings of doctors.