Compose a short story of at least 300 words describing the process of building a complex mechanical computer. The narrative must focus on the intricate gears, the logic of the machine, and the inventor's obsession. The entire text must be a lipogram: you cannot use the letter 'e' (uppercase or lowercase) anywhere in the story. Pay close attention to common words like 'the', 'he', 'she', 'where', and 'computer' which must be avoided or rephrased.