History of Computing: Key Concepts and Figures

The History of Computing: Key Concepts and Figures

• Introduction: The rise of technological change and innovation over recent decades has brought immense societal benefits. Computers, mobile devices, the Internet, the World Wide Web (WWW), and social media are among the advancements that have significantly improved living standards. Computing is any activity that uses computers to manage, process, and communicate critical information integral to modern industrial technology.
• Core idea: A naive view of calculation must be overcome to harness the power of computing; the foundations of computing lie in contributions from many ancient cultures.

Early Civilizations and Foundational Concepts

• The Babylonians (Mesopotamia, present-day Iraq) roughly from 2000 BC to 500 BC
  • Clay cuneiform tables with mathematical texts contain tables for basic arithmetic operations, cubes, and square roots.
  • Numerical system used two symbols (1 and 10) to symbolize numbers; numbers were formed by combining these symbols.
  • Counting boards existed to assist counting and simple calculations; related to the abacus concept.
  • Counting board: wooden, grooves allow beads at any point; abacus: beads with holes placed on specific rods.
• The Egyptians
  • Practical problems: measuring time, floods, land area, bookkeeping, taxes.
  • Base-10 numeral system with distinct symbols for 1, 10, 100, 1,000, 10,000, and 100,000.
  • Rhind Papyrus: a famous Egyptian mathematical manuscript; contains examples of arithmetic and geometric problems.
  • The Rhind Papyrus enabled participation in large-scale building programs (pharaonic projects).
  • Figure reference: Egyptian numerals (visual aid in original handout).
• The Greeks
  • Pythagoras and Thales (~500–600 BC) advanced geometry as a core of mathematics.
  • Pythagoras and the Pythagoreans advocated that number is the essence of all things (a philosophical view); they studied numerical relationships and geometry.
  • Pythagorean theorem often cited as foundational, though Babylonian knowledge predates it by about a millennium.
  • Thales’ theorem (in Euclidean geometry): if A, B, C are points on a circle and AC is the diameter, then the angle ∠ABC is a right angle, i.e., a 90° angle.
  • Conceptual takeaway: geometry and algebra roots in Greek thinking helped shape later computational ideas.
• The Romans
  • Roman numerals: a significant contribution to computing foundations, using letters to symbolize numbers as a sequence.
  • Numeral system: roman symbols are challenging to use for calculations, so abaci remained common tools.
  • Legacy: Roman numerals persist in modern contexts (clocks, cornerstones, film credits, Olympics, etc.).
  • Figure reference: Roman numerals (visual aid in original handout).
• The Islamic Influence
  • Islamic mathematics originated across North Africa, the Middle East, and Spain.
  • Algebra: a continuation and expansion of Greek achievements; algebra treated numbers (rational and irrational) as algebraic objects.
  • Move beyond pure geometry; algebra applied to arithmetic and geometry; study of curves via equations.
  • This era laid groundwork for systematic mathematical methods that would later inform computing theory and practice.

Notable Figures in Computing

• Wilhelm Gottfried Leibniz (Step Reckoner)
  • A German philosopher, mathematician, and early pioneer of mechanical calculation.
  • Developed the binary number system used in digital computers.
  • Built on Blaise Pascal’s calculating machine (the Pascaline) from the early 1670s, recognizing its limitations (addition and subtraction only).
  • Designed and created a calculating machine from 1672–1964 capable of addition, subtraction, multiplication, division, and root extraction; called the Step Reckoner and regarded as the first calculator to perform basic arithmetic operations beyond simple addition/subtraction.
• Charles Babbage (The Difference Engine)
  • Considered a grandfather of computing alongside George Boole.
  • Driven by inaccuracies in mathematical tables due to human error.
  • Designed the Difference Engine (initiated around 1821) to compute mathematical tables and polynomial functions, including logarithmic and trigonometric functions such as sine and cosine.
  • Purpose: to produce precise tables for complex calculations; prototypes existed, and the first working engine was completed later by others.
  • Ada Lovelace is celebrated as the first computer programmer for her work related to this engine.
  • Historical note: Babbage’s original machine was never completed in his lifetime; Swedish engineers George and Edward Scheutz (Schuetz) built the first working Difference Engine in 1853.
• George Boole (Symbolic Logic)
  • Along with Babbage, Boole is considered a grandfather of computing.
  • Developed Boolean algebra, the mathematical foundation for modern computing.
  • Although primarily theoretical, his symbolic logic provided the basis for switching theory and digital circuit design.
  • Published Mathematical Analysis of Logic in 1847, reinforcing the idea that logic is a distinct branch of mathematics, not merely philosophy.
  • Introduced the 0 and 1 quantities, with symbols such as x, y, z representing classes of objects; introduced three basic operators (+, −, and ×) that combine classes of objects in mathematics (interpreted in Boolean logic as OR, AND, and other combinations in later developments).
• Grace Brewster Murray Hopper (COBOL)
  • Computer pioneer and naval officer; Yale mathematics graduate.
  • Led the development and promotion of computer languages such as COBOL (Common Business-Oriented Language) in 1959.
  • The need for standardized business-oriented languages grew as computer use expanded; Hopper’s advocacy helped COBOL become widely adopted.
  • By the 1970s, COBOL was one of the most extensively used programming languages globally.
• Katherine Johnson (Human Computer)
  • In the 1950s, before modern computers, many calculations were performed by human computers, often women.
  • NASA hired mathematicians to perform complex calculations for space missions.
  • In 1962, during the Moon mission era, Johnson studied geometry for space travel, helping determine spacecraft orbits and lunar landing trajectories.
  • Her calculations contributed to successful Moon missions and safe Earth return.
• Gladys Mae West (GPS Technology)
  • Specialized in large-scale computer systems and data processing for satellite data analysis.
  • Key figure in developing a detailed geodetic model of the Earth, foundational for GPS development in the 1960s.
  • Programmed the computer that calculated Earth’s geoid with precision necessary for GPS.
  • Also contributed to radar altimeter satellite developments, guiding advances in satellite geodesy.

Key Numerals and Notation

• Roman numerals and their values (historical notation):
  • I = 1,
    \, V = 5,
    \, X = 10,
    \, L = 50,
    \, C = 100,
    \, D = 500,
    \, M = 1000
• Babylonian numerals
  • Used two symbols (1 and 10) to form other numbers by combination; number construction was additive and positional techniques evolved over time.
• Egyptian numerals
  • Base-10 system with distinct symbols for 1, 10, 100, 1,000, 10,000, and 100,000; used for practical computations (measuring time, floods, land area, taxes).
• Geometric and algebraic notations (historical context)
  • Geometry-focused Greek work laid the groundwork for later algebraic approaches.
  • Islamic algebra treated numbers as algebraic objects, enabling the study of curves via equations and applying algebra to arithmetic and geometry.

Concepts, Connections, and Implications

• The continuum from ancient counting tools to modern computing illustrates:
  • A progression from concrete arithmetic (counting boards, abacus) to symbolic logic and algebra, to programmable devices and software.
  • The recognition that reliable, automated calculation reduces human error and expands the scope of problems solvable computationally.
• Theoretical foundations to practical machines:
  • Leibniz’s binary system becomes the basis for digital computers' binary logic.
  • Babbage’s Difference Engine demonstrates the move from manual tables to mechanical computation of complex functions.
  • Ada Lovelace’s work on the Analytical Engine (and association with Babbage) foreshadowed programming concepts.
  • Boole’s logic provides the essential algebra for designing and analyzing digital circuits.
• The social and ethical dimension:
  • With the growing power of computation, new challenges and dangers accompanied its power (industrial, scientific, economic, and societal impacts).
  • The development of standardized business language (COBOL) enabled broad commercial use of computing, expanding access and also raising questions about equity, reliability, and governance.
• Real-world relevance and continuing influence:
  • GPS technology, based on precise geodetic modeling, enables navigation, geolocation services, and satellite communications.
  • Human computers like Katherine Johnson show how human ingenuity contributed crucial insights before widespread digital automation.
  • The historical lineage shows how foundational ideas—from geometry and algebra to logic and programming languages—culminate in today’s computing ecosystems.

Connections to Foundational Principles and Real-World Relevance

• Foundational principles:
  • Abstract algebra and logic underpin modern computation and digital circuitry.
  • Binary arithmetic and logical operators enable reliable, scalable computation.
  • Geodesy and orbital mechanics rely on precise calculations, a lineage from early geometry to modern spaceflight calculations.
• Real-world relevance:
  • The technology stack—from arithmetic devices to binary logic to high-level programming languages—drives almost all modern technology and services.
  • GPS and satellite technologies have become ubiquitous in daily life, transportation, and science.

Ethical, Philosophical, and Practical Implications

• Ethical considerations:
  • As computation becomes more pervasive, questions arise about privacy, surveillance, data security, and equitable access to technology.
• Philosophical implications:
  • The shift from human-computer “computers” to autonomous machines raises questions about the nature of computation, intelligence, and the role of humans in problem-solving.
• Practical implications:
  • The move toward standardized languages (e.g., COBOL) demonstrates the importance of interoperability in scaled, business-critical systems.
  • Understanding historical foundations helps modern practitioners design more robust, efficient, and accessible technologies.

References (as noted in the original handout)

• 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
• IT2221 01 Handout 1 (Property of STI)\n