What was the impetus for the creation of a ''computing'' machine?

Increasing demands in science, engineering, business, etc. for large computation intensive calculation that pushed the limits of the abilities of human computers to perform them within the limited times available with a minimum of errors.

The first occurrence of this was in the 1830s and Charles Babbage responded with his inventions of the Difference Engines and Analytical Engine, but was unable to secure adequate funding to complete the machines.

The second occurrence of this was shortly before 1890 when the US Census Bureau recognized they would not be able to complete the upcoming census on time to meet the deadline in the constitution and Herman Hollerith responded with his invention of his electromechanical semiautomatic punchcard tabulation system.

The third occurrence of this was around the beginning of the 20th century and several people in various universities responded with inventions of various types of analog computers, culminating in MIT's gigantic electromechanical Differential Analyzerin 1929.

The fourth occurrence of this was in the late 1930s thru early 1940s and several people (Zuse in Germany, Atanasoff in US, Flowers in UK, Eckert & Mauchley in US, Turing in UK, etc.) responded ultimately resulting in the invention of the modern general purpose programmable electronic digital computer.