At first sight, Babbage's 31 digits in the Difference Engine seems quite ludicrous. But I think he was not just trying to compensate for the "lack of floating point" with more digits. As I understand it, the Difference Engine was built to calculate tables through polynomial extrapolation, a process which is notoriously ill conditioned except for very low polynomial degrees. That means that you need to have much more precision to represent the intermediate results than whatever you get in the final result.
Babbage was overreaching, but I wonder how many digits he would have needed for the Difference Engine to be practically useful.
That's a great point, thank you Toivo. I guess that Babbage had a bit of a dilemma: build something simple that worked but risk it being dismissed as trivial or something more ambitious and see it fall short. In one sense he ran the first big failed IT project!!
Nice article!
At first sight, Babbage's 31 digits in the Difference Engine seems quite ludicrous. But I think he was not just trying to compensate for the "lack of floating point" with more digits. As I understand it, the Difference Engine was built to calculate tables through polynomial extrapolation, a process which is notoriously ill conditioned except for very low polynomial degrees. That means that you need to have much more precision to represent the intermediate results than whatever you get in the final result.
Babbage was overreaching, but I wonder how many digits he would have needed for the Difference Engine to be practically useful.
That's a great point, thank you Toivo. I guess that Babbage had a bit of a dilemma: build something simple that worked but risk it being dismissed as trivial or something more ambitious and see it fall short. In one sense he ran the first big failed IT project!!
four arithmetic arithmetic operations
What would I do without you? Thanks so much and now corrected. PS Hope more posts coming soon on your Substack too.