Then just fix up a few relays to save reading all those inputs, and maybe an industrial steam-engine to do the heavy-lifting ... hey presto, a difference engine! WFL On 3/14/14, Steve Witham <sw@tiac.net> wrote:
Thinking about calculating pi... if only there were a way to do calculations by hand that was absolutely error-proof, so one wouldn't die having calculated ten thousand digits, only to have an error in digit 7195 detected after one's death.
Well, you could calculate with appropriately-designed puzzle pieces. Think of the basic cell in a multiplication
total factor A input & carry input ^ / \ + + factor B | | factor B output | | input + + \ / factor A v total output & carry output
In decimal, there are 10,000 combinations of the four input digits (of which 9100 are possible). So, just make molds or cutting dies for all those combinations, with appropriate outputs of course. Then you need a frame, and pieces for the edge conditions. On the input and output edges, you could put raised type and print the thing when done.
In fact you could design a set of pieces around the sides, or maybe wires, turning shafts or sliders, to convey all the inputs and outputs to a small area for printing.
If you broke each digit into two pairs of binary-coded-decimal (BCD) bits, you would need four little pieces out of an alphabet of only 64, inside each cell. Then you would need to recode the result as BCD, but there's an issue there.
The bit-pairs for factor A need to be interleaved with the bit-pairs for the carry, in order to get one of each to each upper-right little piece. I can imagine either using signal-crossing pieces, or handling the output of all combinations of (factor A, carry, total) with single pieces out of a set of 1000.
But, a better way to distribute the factor inputs would be as crisscrossing bars lying under the pieces. Then there would still be 64 types of little piece, but only 100 BCD recoder shapes.
--Steve "Did you check your calculations?" "I have my boards, right here!"
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