Prelude: Computing from Ancient Times to the Modern Era - The Technical and Social History of Software Engineering - page 25

The decimal point seemed to have originated in India during the ninth century,
but it was John Napier who made the concept important in Western mathematics
around 1620. Napier also invented logarithms and an interesting manual calculator
called “Napier's bones.” Logarithms were used in the first slide rules and hence
are an important background topic for analog computation.
The concept of zero seemed to have several independent sources. It was used
in Babylon with base 60 math, but apparently as a placeholder rather than actual
calculations. This use was about 2,500 years ago.
The Olmecs and Mayans both used zero as a true number, and it was used for
calendar calculations, which were quite complex. This use of zero seems to date
to around 400 AD .
The use of zero in India dates to about 458 AD when it was found in a text on
mathematics. Whether this was an indigenous invention or inherited from Babylon
is not certain. Later in the 600s, the famous Indian mathematician Brahmagupta
wrote a paper on the uses of zero, which moved past zero itself into negative num-
bers.
Decimal numbers, the decimal point, and zero were all important precursors
leading to computers and software calculations.
Digital Computers
Later chapters in this topic will discuss the evolution of digital computers and
associated software from the mid-1930s through 2010, with projections to 2019.
Suffice it to say that software was created specifically to operate on digital com-
puters. Without digital computers, there would be no software. Without software,
digital computers would have no major purpose and would probably not have sup-
planted analog computers.
Higher-Level Programming Languages
I started as a young programmer in the 1960s. Programming using both machine
language (mainly for patches and bug repairs) and basic assembly language was
how I first programmed IBM 1401 computers.
My firsthand experience was that machine language was very error prone
and also rapidly fatiguing due to the high attention span needed to deal with it.
Assembly language was a step in the right direction, but not a very big step. Hav-
ing to use dozens of assembly instructions to handle calculations or format printed
output was time consuming and actually boring. Higher-level languages, starting