The History of Computing

  • Computing is any activity that utilizes computers to manage, process, and communicate critical information that is an integral part of modern industrial technology.

  • The rise of technological change and innovation over the last decades has brought immense significance to society, including the Internet, the World Wide Web (WWW), mobile devices, and social media, which have led to significant benefits and improvements in the standard of living.

  • This course material emphasizes the foundational role of early contributions to computing as the basis for modern technology.

Early Civilizations

  • Babylonians (Mesopotamia, present-day Iraq) from about 2000 BC2000\text{ BC} until about 500 BC500\text{ BC}

    • Clay cuneiform tablets with mathematical texts included tables for basic arithmetic operations, cubes, and square roots.

    • Numerical system used two symbols (1 and 10); numbers were formed by combining these symbols.

    • Counting boards existed to assist with counting and simple calculations; similarities with an abacus.

    • Counting board: usually wooden with grooves; beads could be placed at any point in a groove.

    • Abacus: beads on rods with holes enabling placement on specific rods.

  • Egyptians

    • Practical problems solved: measuring time, measuring floods, calculating land area, bookkeeping, taxes.

    • Base-10 numeral system with distinct symbols for 1, 10, 100, 1000, 10^4, and 10^5.

    • Rhind Papyrus (Egyptian papyrus) contained examples of arithmetic and geometric problems and aided participation in the Pharaoh’s building program.

    • Egyptian numerals and arithmetic knowledge supported large-scale construction and administrative tasks.

    • Source note: Figure 1. Egyptian numerals (context in handout).

  • Greeks

    • Pythagoras and Thales (roughly 500–600 BC) made notable contributions to geometry.

    • Pythagoras (philosopher/mathematician) studied Egyptian mathematics; led to the Pythagorean school (number as essence of all things).

    • The Pythagorean theorem is attributed to Pythagoras (Babylonians may have known it earlier).

    • Thales’ theorem (Euclidean geometry): if A, B, and C are points on a circle with AC as the diameter, then the angle ∠ABC is a right angle.

  • Romans

    • Roman influence on computing through the Roman number system (letters symbolizing numbers).

    • Roman numerals were difficult to use, so an abacus was often used for calculation.

    • Roman numerals continue to influence modern life today (clocks, building cornerstones, movie credits, and sports events such as the Olympics and the Super Bowl).

    • Figure 2. Roman numerals (referenced in handout).

  • The Islamic Influence

    • Islamic mathematics originated across North Africa, the Middle East, and Spain.

    • Algebra development continued from Greek achievements; a comprehensive theory treated rational and irrational numbers as algebraic objects.

    • Algebra extended to arithmetic and geometry; curves studied using equations.

    • The rise of algebra and systematic computation contributed to the true potential of computing, enabling unprecedented power for science, industry, and business, alongside new difficulties and dangers.

  • Babylonians (Mesopotamia, present-day Iraq) from about 2000 BC2000\text{ BC} until about 500 BC500\text{ BC}

    • Clay cuneiform tablets with mathematical texts included tables for basic arithmetic operations, cubes, and square roots.

    • Numerical system used two symbols (1 and 10); numbers were formed by combining these symbols.

    • Counting boards existed to assist with counting and simple calculations; similarities with an abacus.

    • Counting board: usually wooden with grooves; beads could be placed at any point in a groove.

    • Abacus: beads on rods with holes enabling placement on specific rods.

  • Egyptians

    • Practical problems solved: measuring time, measuring floods, calculating land area, bookkeeping, taxes.

    • Base-10 numeral system with distinct symbols for 1, 10, 100, 1000, 10^4, and 10^5.

    • Rhind Papyrus (Egyptian papyrus) contained examples of arithmetic and geometric problems and aided participation in the Pharaoh’s building program.

    • Egyptian numerals and arithmetic knowledge supported large-scale construction and administrative tasks.

    • Source note: Figure 1. Egyptian numerals (context in handout).

  • Greeks

    • Pythagoras and Thales (roughly 500–600 BC) made notable contributions to geometry.

    • Pythagoras (philosopher/mathematician) studied Egyptian mathematics; led to the Pythagorean school (number as essence of all things).

    • The Pythagorean theorem is attributed to Pythagoras (Babylonians may have known it earlier).

    • Thales’ theorem (Euclidean geometry): if A, B, and C are points on a circle with AC as the diameter, then the angle ∠ABC is a right angle.

  • Romans

    • Roman influence on computing through the Roman number system (letters symbolizing numbers).

    • Roman numerals were difficult to use, so an abacus was often used for calculation.

    • Roman numerals continue to influence modern life today (clocks, building cornerstones, movie credits, and sports events such as the Olympics and the Super Bowl).

    • Figure 2. Roman numerals (referenced in handout).

  • The Islamic Influence

    • Islamic mathematics originated across North Africa, the Middle East, and Spain.

    • Algebra development continued from Greek achievements; a comprehensive theory treated rational and irrational numbers as algebraic objects.

    • Algebra extended to arithmetic and geometry; curves studied using equations.

    • The rise of algebra and systematic computation contributed to the true potential of computing, enabling unprecedented power for science, industry, and business, alongside new difficulties and dangers.

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Notable Figures in Computing

  • Wilhelm Gottfried Leibniz (Step Reckoner)

    • German philosopher, mathematician, pioneer in mechanical calculation.

    • Developed the binary number system used in digital computers.

    • Built on Blaise Pascal’s calculating machine (Pascaline) from the early 1670s.

    • Recognized Pascaline’s limitations (only addition and subtraction) and designed a calculating machine (the Step Reckoner) capable of addition, subtraction, multiplication, division, and extraction of roots.

    • The Step Reckoner was the first calculator to run the basic arithmetic operations; time frame noted as 1672–1964 in the handout (note potential typographical error in the source).

  • Charles Babbage (Difference Engine)

    • Often regarded as a grandfather of computing along with George Boole.

    • Motivated by the errors in human-generated mathematical tables; sought to reduce human error.

    • Designed the Difference Engine in 1821 to compute polynomial functions and logarithmic and trigonometric functions (e.g., sine, cosine) for producing mathematical tables.

    • Intended to be more advanced than Pascaline and the Step Reckoner.

    • Ada Lovelace is associated as an analyst for the Analytical Engine and is often considered the first computer programmer.

    • Babbage prototypes existed, but the machine was not completed during his lifetime; the first working Difference Engine was built in 1853 by Swedish engineers George and Edward Scheutz.

  • George Boole (Boolean Algebra)

    • Co-credited as a founder of computing alongside Babbage.

    • Developed Boolean algebra, the foundation for modern computing.

    • Although largely theoretical, his symbolic logic provided the mathematical model for switching theory and digital circuit design.

    • Key work: "Mathematical Analysis of Logic" (1847).

    • Argued that logic could be treated as a separate branch of mathematics, not merely philosophy.

    • Introduced the binary values 0 and 1 to represent absence and presence, respectively, and used symbols like x, y, z to represent classes of objects.

    • Introduced three operators (+, −, ×) that combine classes of objects in mathematics.

  • Grace Murray Hopper (COBOL)

    • Computer pioneer and naval officer; graduate in mathematics from Yale.

    • Pioneered development of high-level programming languages, including COBOL (Common Business-Oriented Language) in 1959.

    • Promoted the standardization and adoption of COBOL by military and private sector users.

    • By the 1970s, COBOL was considered the most extensively used computer language in the world.

  • Katherine Johnson (Human Computer)

    • In the 1950s, computers as we know them did not exist; humans performed complex calculations—“computers.”

    • Hired by NASA to compute calculations for space travel.

    • In 1962, supported NASA’s moon mission by studying geometry for space travel, determining spacecraft trajectories to orbit Earth and land on the moon.

    • Johnson’s calculations enabled NASA to send astronauts to the moon and back.

  • Gladys Mae West (GPS Technology)

    • Focused on large-scale computer systems and data-processing for satellite information.

    • Second Black woman hired at the Naval Proving Ground in Virginia in 1956.

    • Most notable contribution: creating a detailed geodetic model of the Earth, which became the basis for GPS development in the 1960s.

    • Programmed the computer that calculated Earth’s geoid to achieve the precision needed for GPS.

    • Influential in radar altimeter satellite development and teaching how to improve satellite geodesy with advancing technology.

  • References cited in the handout for further reading:

    • Bagchi S. (2021). Techtonic shift: A brief history of computing and the web. Orange Publishers.

    • O’Regan, G. (2021). A brief history of computing. Springer.

    • Forbes (2021). GPS only exists because of two people: Albert Einstein and Gladys West [Web Article]. Retrieved on June 22, 2022, from https://www.forbes.com/sites/startswithabang/2021/02/18/gps-only-exists-because-of-two-people-albert-einstein-and-gladys-west/

    • NASA (2020). Who was Katherine Johnson? [Web Article]. Retrieved on June 22, 2022, from https://www.nasa.gov/audience/forstudents/k-4/stories/nasa-knows/who-was-katherine-johnson-k4

    • YaleNews (2017). Grace Murray Hopper (1906-1992): A legacy of innovation and service [Web Article]. Retrieved on June 22, 2022, from https://news.yale.edu/2017/02/10/grace-murray-hopper-1906-1992-legacy-innovation-and-service

Mathematical and symbolic references

  • The Roman numerals and their practical usage:

    • I=1I = 1, V=5V = 5, X=10X = 10, L=50L = 50, C=100C = 100, D=500D = 500, M=1000M = 1000

  • Binary system (Leibniz) underpins digital computation.

  • The move from geometry-centric mathematics to algebra and logic laid the groundwork for modern computing concepts and hardware design.

Real-world relevance and implications

  • The progression from counting boards and abaci to symbolic logic (Boolean algebra) and high-level programming languages demonstrates the increasing power and abstraction in computation.

  • Ethical and practical considerations arise with the true potential of computing, including power for science and industry alongside risks and dangers.

  • Early computational work directly enabled modern technologies such as GPS (via West), spaceflight (Johnson), and business computing (Hopper, COBOL).

Summary connections to broader themes

  • Foundational role of counting tools (counting boards, abaci) in developing numerical methods.

  • The shift from concrete counting to abstract algebra and logic as enabling technology for hardware and software.

  • The enduring impact of individual contributions on today’s computers, programming languages, and navigation systems.