This paper has two main purposes, One is a scientific theory for the Hangul writing system. It is a mathematical model which is formulated a logical characteristics involved in the compositionality principle of Hun Min Jung Um[6], and is based on the traditional scientific methodology and theory. The other is an engineering model for the Hangul writing system. It has proven that the model is more theoretical and practical that the conventional models called Hangul automata. This paper also shows the reasons why Korean has a great national pride in Hangul[3]. Consequently, we suggest that Hangul writing system has a potential capability as an ultimate human interface connecting human, computer and information.