Foundations of Computing and Communication Lecture 4. The Mechanical Age

Transcription

1 Foundations of Computing and Communication Lecture 4 The Mechanical Age Based on The Foundations of Computing and the Information Technology Age, Chapter 3 Lecture overheads c John Thornton 2007

2 Lecture Objective To gain an overview of the development of mechanical computation from the scientific revolution through the work of Charles Babbage to the 19th century development of mechanical desktop calculators. Overview of Topics The Industrial Revolution of Steam, Iron and Coal Early Calculators: Schickard, Pascal and Leibniz The Babbage Engines Practical Machines Electricity Dangerous Ideas 1

3 Industrial Revolution Initial slow growth of science: Alchemy, astrology, Neo- Platonism; The term scientist dates from 1820 s; Delayed development of chemistry. Technological innovation: The age of steam; Technology spurs development of science: better instruments, more practical problems, need for mathematical techniques: navigation, engineering, ballistics. Computation: Reliance on human computers and mathematical tables; Existing technology unable to produce reliable computing machines despite good ideas. 2

4 Wilhelm Schickard 1623 Machine based on Napier s Bones: select times table in columns, reveal results of multiplication by moving horizontal slide (image courtesy of the Science Museum, London). Mechanical addition: Result columns added to total by turning knobs; contained an automatic carry device using gears - required significant force to propagate multiple carries. 3

5 Blaise Pascal 1642 The Pascaline: Independently of Schickard, Pascal invented a machine with dial-in numbers added directly to a total (image courtesy of the Science Museum, London). Carries propagated with weights: A number wheel moving from 9 to 0 caused a weight to fall adding one to next column; carries propagated without extra force. Nine s complement subtraction: Weights meant addition could not be reversed, hence use of nine s complement: nine s complement of 48 = (9 4)(9 8) = 51, = 134, (1) + (34) = 35 4

6 Gottfried Leibniz ( ) Philosopher and logician: Envisions universal symbolic language built up of basic ideas; Come, sit down and let us calculate ; anticipates computational logic of today and proposes use of binary numbers. Inventor of stepped drum: Leibniz stepped drum becomes standard for future calculators; Enter complete number using sliders and turn crank to add (image based on Hewlett-Packard Museum diagram). End View Side View 5

7 Leibniz s Calculator Multiplication and division: Enter multiplier 123, turn first crank until stops ( 3), turn second crank (moves to 10s column), turn first crank until stops ( 20), etc, but awkward manual carry mechanism (image courtesy of the Science Museum, London). Thomas Arithmometer: based on Leibniz s machine: automatic carry mechanism + better precision = first commercial machine in 1820, produced until

8 Charles Babbage ( ) Table errors: The world relied on mathematical tables for complex calculation; prepared by human computers ; full of errors and errata of errata; serious consequences for navigation, ballistics, etc. Babbage s dream: calculate and print tables automatically; remove possibility of human error the difference engine. y 1 x 2 1 1st difference 2nd difference 3rd difference Method of Differences:

9 Difference Engine No. 1 Started 1823: 1,500 from the treasury; Partnership with Joseph Clement; Required 25,000 hand made precision parts. Ten years later... Clement quits; Project half finished, 12,000 unassembled parts, no printer, expenses of 17,479; government pulls out (image courtesy of the Science Museum, London). 8

10 Difference Engine No. 2 New start ( ): Babbage redesigns engine using 1/3 of the parts; 2.6 tonnes, 11 feet wide, 31 digit precision, 7 orders of difference; No interest from government, finally constructed in 1991 by Science Museum (image courtesy of the Science Museum, London). 9

11 The Analytical Engine The General Purpose Machine: The circular arrangement of the axes of the Difference Engine round large central wheels led to the most extended prospects. The whole of arithmetic now appeared within the grasp of mechanism. A vague glimpse of the Analytical Engine opened out, and I pursued with enthusiasm the shadowy vision (image courtesy of the Science Museum, London). 10

12 Grandfather of Computing First computer architecture: Analytical Engine anticipated modern computer: the store (primary memory) held variables in numbered columns (addresses), the values of variables were copied to registers in the mill (CPU) where calculations were performed, and results copied back to the store. First programming language: Machine to be controlled by punched cards (based on Jacquard loom), cards for variables, values and operations (+,,, ). Machine could decide which cards to select next on basis of internal calculation conditional branching and looping all arithmetic procedures can be encoded. 11

13 Eventual Fame Ada Lovelace: With advent of electronic computers, Babbage finally recognised as a genius. Ada Lovelace, collaborator and patron recognised as first computer programmer (image courtesy of the Science Museum, London). Ideas developed: Analytical Engine partially built by son Henry, several difference engines constructed + ideas for an anticipating carriage were picked up. 12

14 Ideas before their Time Inappropriate Technology: Babbage s machines were too slow, expensive, cumbersome and dangerous. Needed electronic technology to make them practical. Most of his ideas rediscovered independently in 20th century. Babbage foresaw basic architecture of the computer + basic requirements of a programming language - what was missing? Boolean Algebra: Although some flow of control logic, Babbage did not see that logical procedures could be expressed as calculation. Leibniz started thinking this way, George Boole formalised it in 1854: logical operations (and, or, not, implies) expressed as calculations involving binary (true/false) variables - becomes basis of 20th century circuit design and programming. 13

15 Practical Machines Scheutz Difference Engine: Built in Sweden 1853, Babbage viewed it in 1854, winner of Grand Exhibition Gold Medal. British government builds Scheutz engine for 1,500, used to calculate and print more than 600 tables. Variable toothed gears: Desktop calculators become possible with reduction of size of Leibniz drum variable toothed gear (1870s) (image based on Hewlett-Packard Museum diagram). Side View A Pin Interior View 14

16 Key-Driven Machines Comptometer: Dorr Felt designs mechanism to handle carries faster than a key can be repressed (1/150 second) in Makes key-driven entry practical - no need to set up number and turn a crank - up to ten times faster for addition and subtraction - turns simple desktop calculation into a reality (image courtesy of the Science Museum, London). Mechanical calculator evolution ends... similar machines to the comptometer in use until 1970s in offices and shops. 15

17 Turning-on the Light Bulb Industrial society: Factory system and urban living become the norm; Age of steam, iron and coal; Railways and steam ships open up the world; Telegraph, telephone and radio start mass communications; Large scale industrial war becomes possible. Science flourishes: Chemistry: Mendeleev s periodic table of elements (1869); Physics: atomic theory of matter (Dalton 1803), electro-magnetic fields fill the void (Maxwell 1873), existence of electrons proposed (Stoney 1874) and demonstrated (Thomson 1897) harnessing of electric power. Over-confidence: There is nothing new to be discovered in physics now, all that remains is more and more precise measurement. (Lord Kelvin 1900) 16

18 Dangerous Ideas Darwin: Origin of Species (1865) acts as a bombshell to prevailing beliefs: life evolved through natural selection + random mutation; humankind evolved from apes; no plan or design and no designer; God is dead Nietzsche s famous phrase refers to the shared cultural belief in a Christian God (1887) - Christian teaching hard to reconcile with findings of science - humanity empowered by science replaces God as the master of destiny - scientific materialism - birth of socialism and Marxism - Freud (1900) investigates an unconscious filled with repressed sexuality. 17

19 Lecture Exercises Using the nine s complement method calculate (show your workings). Draw a table that shows how the method of differences arrives at a common difference in the expansion of x 4 (show the expansion up to x = 6). Provide a half page description of the similarities between Babbage s idea of the Analytical Engine and a modern day computer. Write a brief (one page) summary of the key ideas put forward by the following thinkers: Charles Darwin, Freidrich Nietzsche, Karl Marx and Sigmund Freud. 18