What it is and the problem it solves
It is an automatic mechanical calculator designed to eliminate human error in mathematical tables. It solves the problem of transcription and typesetting mistakes in navigation, astronomy, and engineering tables.
How it works
It uses Newton’s method of divided differences to tabulate polynomial functions. It performs only addition and carry operations. It avoids multiplication and division entirely. Its name comes from the method of finite differences.
What works
The 1991 reconstruction works. It holds eight 31-digit numbers. It tabulates 7th-degree polynomials to 31-digit precision. Its printer produces plaster flongs for stereotype plates. Its 8,000-part, 5-ton mechanism operates within 19th-century manufacturing tolerances.
What does not
It does not compute non-polynomial functions. It does not store intermediate results for reuse beyond its fixed register set. It does not correct input errors. It has no conditional logic or branching. It was never completed in Babbage’s lifetime.
What it changes
It proves that automatic, high-precision, error-resistant polynomial tabulation was mechanically possible in the 1820s. It establishes that 19th-century tolerances were sufficient for complex calculating machinery. It shifts the benchmark for what constitutes a viable mechanical computer from theoretical sketch to buildable design.
Is it worth your time
Yes—if you work on mechanical computation, historical engineering feasibility, or error-resistant calculation systems. No—if you need real-time output, programmability, or integration with other systems. It is a proof, not a tool.