The Shape of Code

What were the events that drove organizations to fund the creation of the first computers?

I suspect that many readers do not appreciate how long scientific/engineering calculations took before electronic computers became available, or the huge number of clerical staff employed to process the paperwork associated with running any sizeable business.

If somebody wanted to know the logarithm of some value, or the sine/cosine of an angle, they looked up the answer in a table. Individuals owned small booklets of tables supplying some level of granularity and number of significant digits. My school boy booklet contains 60-pages of tables, all to five digits of output accuracy, with logarithm supporting four-digit input values and the sine/cosine/tangent tables having an input granularity of hundredth of a degree.

The values in these tables were calculated by human computers; with the following being among the most well known (for more details, see Calculation and Tabulation in the Nineteenth Century: Airy versus Babbage by Doron Swade, and The History of Mathematical Tables: from Sumer to Spreadsheets edited by Campbell-Kelly, Croarken, Flood, and Robson):

• In 1624 Henry Briggs published logarithms for the integer ranges 1-20,000 and 90,001-100,000 (to 14 decimal places), followed some years later by tables of sine and logarithm of sine; in 1628 Adriaan Vlacq publishing tables that filled in the missing values (to 10 decimal places). In 1783 Jurij Vega published a bug-fixed and extended version of Vlacq’s tables.

  In 1827 Charles Babbage (that Babbage) published Table of Logarithms of the Natural Numbers from 1 to 10800. These tables were based on corrected versions of these tables, a rigorous nine-stage proofreading process was followed to prevent new mistakes creeping in.

  Today, one person can publish A reconstruction of the tables of Briggs’ Arithmetica logarithmica (1624), with an appendix containing 300 pages of calculated values,

• between 1794 and 1799, Gaspard de Prony employed sixty to eighty computers to calculate the logarithms of the integers from 1 to 200,000 to fifteen significant digits (rounding issues sometimes required calculating 25 decimal digits; published in eighteen volumes). Around 400 man-years.

Logarithms and trigonometric functions are very widely used, creating incentives for investing in calculating and publishing tables. While it may be financially worthwhile investing in producing tables for some niche markets (e.g. Life tables for insurance companies), there is an unmet demand that will only be filled by a dramatic drop in the cost of computing simple expressions.

Babbage’s Difference engine was designed to evaluate polynomial expressions and print the results; perfect for publishing tables. While Babbage did not build a Difference engine, starting in 1837, engines based on Babbage’s design were built and sold commercially by the Swede Per Georg Scheutz.

Mechanical calculators improve accuracy and speed the process up. Vacuum tubes are invented in 1904 and become widely used to process analogue signals. World War II created an urgent demand for the results of a variety of time-consuming calculations, e.g., accurate ballistic tables, and valve computers were built. The plot below shows the cost per million operations for manual, mechanical and valve computers (code+data):

To many observers at the start of the 1950s, the market for electronic computers appeared to be organizations who needed to perform large amounts of scientific/engineering calculation.

Most businesses perform simple calculations on many unrelated values, e.g., banks have to credit/debit the appropriate account when money is deposited/withdrawn. There is no benefit in having a machine that can perform hundreds of calculations per second unless it can be fed data fast enough to keep it busy.

It so happened that, at the start of the 1950s, the US banking system was facing a crisis, the growth in the number of cheques being written meant that it would soon take longer than one day to process all the cheques that arrived in one day. In 1950 Bank of America managed 4.6 million checking accounts, and were opening 23,000 new account per month. Bank of America was then the largest bank in the world, and had a keen interest in continued growth. They funded the development of a bespoke computer system for processing cheques, the ERMA Banking system, which went live in 1959. The plot below shows the number of cheques processed per year by US banks (code+data):

The ERMA system included electronic storage for holding account details, and data entry was speeded up by encoding account details on a magnetic strip included within every cheque.

Businesses are very interested in an integrated combination of input devices plus electronic storage plus compute. There are more commerce oriented businesses than scientific/engineering businesses, and commercial businesses usually have a lot more money to spend, i.e., the real money to be made by selling computers was the business data processing market.

The plot below shows the decreasing cost of hard disc storage (blue, right axis), along with the decreasing computing cost of valve based computers (red, left axis; code+data):

There was a larger business demand to be able to store information electronically, and the hard disc was invented by IBM, roughly 15 years after the first electronic computers.

The very different application demands of data processing and scientific/engineering are reflected in the features supported by the two languages designed in the 1950s, and widely used for the rest of the century: Cobol and Fortran.

Data processing involves simple operations on large quantities of data stored in a potentially huge number of different combinations (the myriad of mechanical point-of-sale terminals stored data in a myriad of different formats, which evolved over time, and the demand for backward compatibility created spaghetti data well before spaghetti code existed). Cobol has extensive functionality supporting the layout and format of input and output data, and simplistic coding constructs.

Scientific/engineering code involves complex calculations on some amount of input. Fortran has extensive functionality supporting program control flow, and relatively basic support for data input/output.

A third major application domain is real-time processing, such as SAGE. However, data on this domain is very hard to find, so it is not discussed.