Wilhelm Schickard

Wilhelm Schickard

Calculating instruments, astronomy, and languages · 1592–1635 · Württemberg

Schickard's calculating instrument is an important case in reconstructing technology from incomplete evidence. Surviving descriptions show an early attempt to combine arithmetic aids. They do not give us an original machine whose reliability we can measure today.

The person and the surviving evidence

Schickard studied at Tübingen, receiving a BA in 1609 and an MA in 1611. He became professor of Hebrew there in 1619 and later professor of mathematics and astronomy. His work included teaching aids, surveying, engraving, and collaboration with Johannes Kepler. These activities establish a varied technical career without an invented childhood apprenticeship or a hereditary explanation for his abilities. MacTutor biography

Letters to Kepler dated 20 September 1623 and 25 February 1624 describe his calculator. The latter reports that a partly completed machine intended for Kepler was destroyed in a workshop fire. The descriptions combine multiplication-table cylinders, based on Napier's rods, with toothed wheels for addition and subtraction. Multiplication required reading partial products and transferring results; calling the whole process automatic hides the operator's work. Letters quoted and discussed by MacTutor

The Computer History Museum reproduces a sketch dated 1624, credited to the University of Tübingen. That is a historical drawing, not a photograph of a surviving seventeenth-century calculator. Schickard sketch

Tübingen's catalog identifies its exhibited machine as a reconstruction dated 1957. A reconstruction can test whether an interpretation is workable. It cannot prove that every reconstructed detail was present in the original, or that an original worked equally reliably. University museum object record

Worked mechanism: a six-digit decimal accumulator

This is an original logical model of an accumulator, not a gear-accurate reconstruction. Assume six decimal positions, each storing a digit from 0 to 9. The register represents an integer from 0 through 999999. Addition proceeds from the least significant position to the most significant.

For each position, calculate s = old_digit + input_digit + carry. Store s mod 10 and pass floor(s/10) to the next position. The carry entering the units position is zero.

Trace 099997 + 000008:

Position	Sum including incoming carry	Stored digit	Outgoing carry
Units	7 + 8 = 15	5	1
Tens	9 + 0 + 1 = 10	0	1
Hundreds	9 + 0 + 1 = 10	0	1
Thousands	9 + 0 + 1 = 10	0	1
Ten-thousands	9 + 0 + 1 = 10	0	1
Hundred-thousands	0 + 0 + 1 = 1	1	0

The result is 100005. A carry is information crossing a position boundary. In a physical machine, energy must also cross that boundary or be supplied locally. A mathematical rule saying "carry one" does not solve friction, tooth engagement, timing, or the load imposed by a long carry chain.

If the same input 8 is added to 999997, the six stored digits become 000005 and an outgoing carry remains. The mathematical total is 1000005. The register alone represents the result modulo one million; an overflow signal is needed if the application requires the full total. Whether a particular historical design signals overflow is a separate question about its mechanism.

Combining lookup and accumulation

To calculate 347 × 82, a multiplication aid can supply 347 × 8 = 2776 and 347 × 2 = 694. The operator must align the first result as tens:

2776 × 10 = 27760
             694
sum        28454

A device supplying those partial products is doing useful work, but it is not equivalent to a machine that accepts both factors and automatically sequences the complete multiplication. An error entering 2776 instead of 27760 survives perfectly reliable addition. The distinction is between correct components and a correct overall procedure.

Likewise, a dial holding a number is storage, but naming it "RAM" imports a later architecture. Random-access memory includes an addressing model and read/write operations; a set of retained digit positions does not establish those properties.

Evaluating a reconstruction

Useful tests should stress mechanisms rather than merely demonstrate easy cases. Additions without carries test digit entry. A single rollover tests one transfer. A chain of five carries tests interactions. Overflow tests a capacity boundary. Repeated operations test reset and retained state. Passing these tests is evidence about the tested reconstruction under the tested conditions, not a proof about all inputs or a lost original.

The Computer History Museum's overview is useful for comparing Schickard and Pascal, but its broad category "four-function calculator" should be read with these operating distinctions in mind. Museum overview

Exercises

1. Trace 087659 + 009784 in the six-digit model. Show every outgoing carry and check the resulting value independently.
2. Design four addition tests that distinguish correct digit entry, a failed carry between the tens and hundreds positions, a failed long carry chain, and unreported overflow. Give expected outputs and explain what each test can and cannot establish.
3. A reconstruction computes 347×82 correctly after an operator enters two partial products. A report concludes that Schickard built a fully automatic multiplier in 1623. Separate the mathematical, operational, and historical gaps in that conclusion.

Compare your reasoning with the worked solutions

1. From the right, the sums are 13, 14, 14, 17, 9, and 0. The outgoing carries are respectively 1, 1, 1, 1, 0, and 0. The stored digits, read left to right, are 097443. Independently, 87659+9000=96659, and 96659+784=97443. Agreement checks the trace but does not test a physical mechanism.
2. 123456+111111=234567 uses no carries. 000090+000010=000100 isolates a tens-to-hundreds rollover. 099999+000001=100000 demands a long chain. 999999+000001 must yield stored 000000 plus an overflow indication in our specified model. A passing no-carry test says little about transfers; a passing chain test does not prove operation under every speed, wear level, or load. Inputs and required outputs must be documented before interpreting the results.
3. The arithmetic verifies one product, not every product. The operator performs selection, alignment, and transfer, so the demonstrated system is not a fully automatic multiplier. Finally, a modern reconstruction is evidence about one interpretation of surviving descriptions. Dating the idea or a reported construction to 1623 requires the letters; demonstrating modern operation does not independently establish the lost original's exact construction or reliability.