From π to Pi

1
An Illustrated History
of Computation
Bernie Cohen FBCS
Emeritus Professor of Computing
City University
27/9/2013 ©2013 Prof Bernie Cohen OTA13

Computing in Antiquity
The Antikythera analog
astronomical computer
(4thC BC) uses the
Metonic (5thC BC) cycle:
19 solar years
≅
235 synodic months
= 6940 days
Now I, even I, shall
celebrate, in rhymes
inapt, the great immortal
Syracusan ...(3rdC BC).
Showed that 31/7 < π < 310/71
and calculated the number
of grauns of sand in the
unverse(= Eddington's
estimate of 1080 nucleons)
without the use of zero.
Probably invented the
Vitruvius (1stC BC)
odometer: on each
rotation of the wheel. a
pebble (calculus)
dropped into a pot.
The number of pebbles
determined the fare.
27/9/2013 ©2013 Prof Bernie Cohen OTA13 2

Victor 1, the first African Pope
(189-199), fixed Easter on a
Sunday in opposition to the
quartodeciman bishops
of the Eastern Church.
Pope Paul I adopted a computus
developed by the Scythian friar
Dionysius Exiguus (470–544)
aka Dennis the Little
who also introduced the number zero
into Europe and the notation BC/AD
into the calendar (but made at least
three errors that persist to this day!)
The Celtic Church
had its own computus
developed in Iona by
King Oswiu of
Northumbria
convened the
Synod
of Whitby
in 664
to resolve the
conflict.
The Celtic Church lost and
vanished until revived by the
anti-papist Orange Order
1000 years later
(hence the Irish Troubles!)
St Columba

4
When Computors Were Human
John Napier
1550 - 1617
and his bones
Blaise Pascal 1623 -1662
and his Pascaline The Brunswiga
1892-1959
The amazing Curta
invented by Curt Herzstark
(1902 - 1988)
while imprisoned in Buchenwald.
He survived because the Nazis wanted
to give Hitler one for his birthday.
After the war, he manufactured it
in Lichtenstein at the invitation of
Prince Franz Jozef II.

5
Navigation, Longitude and Time
Sextant and chronometer were
useless without tables:
astronomical (here solar to sidereal time)
and mathematical (logs, trig etc.).
Human computors were trained to use
the 'method of differences' to interpolate between
main values calculated by mathematicians.
In 1812, the high incidence of errors in these
tables led ...

6
Charles Babbage
(1791 -1871)
to suggest to Sir John Herschel
that they would be better
'constructed by steam'
and he designed
the Difference Engine to do it.
He soon realised that a machine
could be 'programmed' to do
different calculations and designed
the Analytical Engine.
He never completed it but
a detailed description written by
Luigi Menebrea,
later Prime Minister of Italy,
was translated and expanded with
example programs by the lady
whom Babbage called the
'Enchantress of Numbers'
Augusta Ada Byron,
Countess Lovelace
(1815-1852)

7
The Theory of Computation
Alan Turing
1912 - 1954
Reframed
Gödel's proof
using a universal
model of
computation:
the Turing
Machine
David Hilbert
1862 - 1943
Hilbert's
Programme:
To prove that
mathematics is
complete,
consistent
and decidable.
John von Neumann
1903 - 1957
Polymath.
Stored program
archiecture
Self-replicating
automata
Alonzo Church
1903 - 1995
Ditto using a
different, but
equivalent
model of
computation:
λ-calculus
Kurt Gödel
1906 - 1978
Proved that
mathematics
could not
be both
complete and
consistent
In 1934, Hilbert attended a banquet and was seated next to the new Minister of Education, Bernhard Rust.
Rust asked, "How is mathematics in Göttingen now that it has been freed of the Jewish influence?
Hilbert replied, "Mathematics in Göttingen? There is really none any more."

8
Prof John Rees
1918 – 2013
helped to break
Enigma
'Red' in 1940
using Turing's
Bombe
Colossus, built by ...
Breaking the Codes at Bletchley Park
When you leave valves on,
they don't burn out.
Forbidden to work on ACE
because of the OSA.
I can't tell you how to do it ,
but I wouldn't do it like that.
ca. 1966
to break
Lorenz
Tommy Flowers
1905 – 1998
(BT Dollis Hill & STC)

9
Ferranti Mark 1, 1951
the world's first commercially
available electronic computer
Based on the 'Baby',
designed in Victoria University,
Manchester by Frank Williams
Early British Computers
Pilot ACE, 1946
designed by Turing for
NPL, Teddington
DEUCE, 1955
Made by English Electric
Nelson Research Lab, Stafford
Based on ACE.
60 sold. This one was in
Glasgow University in 1960.
STANTEC-ZEBRA,
1956
Zeer Eenvoudige Binaire
Rekenautomaat
Made by STC, Newport
designed by W. L. van der
Pool of Netherlands PTT
Replaced
in 1964
by
English
Electric
KDF9
runnning
Algol 60.

10
Ordered in October 1947
by Joe Lyons Tea Shops.
Ran the world's first regular routine
office computer job in 1951.
At present four Government offices have been equipped with computers and orders
have been placed for equipment for a further four. Studies of the possible use of
computers in five more offices have almost been completed.
Jocelyn Simon, Financial Secretary to the Treasury,
House of Commons debate, June 26, 1958
Computers in Business
Ernest Kaye 1922-2012
Engineer and musician.
Last surviving member of the
LEO I development team

11
Programming Languages
The first program run
on the'Baby',
predecessor of the
Machester Mark 1 and
Ferranti Mark 1,
Monday June 21,
1948.

12
Programming Languages
Grace Murray Hopper,
USN, 1906 - 1992
First compiler 1951
COBOL 1959
'DIVIDE CAKE
INTO THREE'
John W Backus,
IBM, 1924 - 2007
FORTRAN 1954
Peter Naur,
U Copenhagen,
1928 -
Algol 60
BNF : Backus-Naur Form
syntactic metalanguage.
Panini (ca. 550BC) constructed a formal
grammar of Sanskrit, the Ashtadhyayi
John G. Kemeny
1926 -1992
Dartmouth BASIC 1964.
Manhattan Project with
John von Neumann.
PhD under
Alonzo Church.
Mathematical assistant
to Einstein.

13
More Programming Languages
Christopher Strachey 1916 - 1975
Scion of the Bloomsbury Group. Designed programming languages
for Elliott and Ferranti. Creator of CPL, 'Christopher's Programming
Language', from which came BCPL, then B, then C, then Unix.
First Prof of Computer Science at Oxford, founded denotational
semantics, the theory of programming languages.
John McCarthy 1927 -2011
Developed LISP at MIT in 1958: a Turing-complete language
with a few simple operators and a notation for functions, which
provided the foundation for Artificial Intelligence.
Robin Milner, 1934 - 2010
City University, Ferranti, Cambridge, Edinburgh, Stanford, etc.
ML, CCS, LCF, pi-calculus. Automatic theorem proving
Advised me not to take the Chair of IT at Surrey in 1984
as I would be more useful in industry. He was probably right.

14
Minis and Mainframes
DEC PDP 8, 1965
up to 32K 12-bit words.
666KHz
IBM 360, 1964
Up to 8Mb 32-bit words, 1MHz
Courier Executerm 60, 1970
IBM 360 compatible remote terminal
DEC PDP 1, 1960
$120,000, up to 64K 18-bit words,
200KHz
The first computer game:
Steve Russell's Spacewar!
20 bought by ITT for
ADX7300 message switch
using Gordon Bell's UART.
The sad tale of
the sheriff and
the IBM sales
engineer

Chips with Everything
William Shockley
1910-1989
Nobel Laureate 1956
co-inventor with
Bardeen and Brattain
of the contact
transistor at Bell Labs.
Set up first 'Silicon
Valley' company:
Beckman Instruments
at Mountain View,
Palo Alto.
The first Fairchildren
including Gordon Moore and Robert Noyce, founders of Intel,
left Beckman Instrunments in 1957 to form Fairchild Semicoductor,
where they developed Silicon Gate Technolgy

16
The Single Chip Microprocessor
Intel 8008,
1971
16Kb
in 8-bit
words
3500
transistors
800KHz,
$120
Intel 4004. 1970, 4kB in 4-bit words, 2300 transistors,
740KHz, $200, designed for the NCM Busicom141-PF,
and signed 'FF', by
Federico Faggin (1941 - )
who also designed the Intel 8008, 4040 and 8080.
Disowned by Intel when he founded Zilog in 1974.

Carver Mead
(1934 -)
Lynn Conway
(1938 -)
The Bible and the Law

18
VLSI
(Very Large Scale Integration)
and the Swiss Watch Industry
Self-Defeating Technology
The Blundell Vector Slide Rule
(1952)
and High Speed Electronic
Circuits

19
Homebrew Computers
The MITS Altair 8800, 1975
$400 kits for electronics hobbyists.
10,000 kits shipped
No software
Microsoft founded to supply a BASIC interpreter.
CP/M OS added later.
Processor Technology Sol-20, 1977
'IBM Blue' case and walnut sides
Video and tape I/O interface boards built-in.
Designed by Lee Felsenstein.
Kansas City data transfer standard.

20
Xerox PARC
The Star, or Dandelion, outperformed the Sun
but, at $16,595, was overpriced
and was abandoned as a product line by Xerox.
The Xerox 914 copier, 1959,
generated so much profit that Xerox founded a non-profit
research lab in Palo Alto with instructions not to make product.
Unfortunately they hired some crazy people who developed
the mouse, the graphical user interface and the ethernet
which they put together into the
Alto personal computer, 1973
which inspired Steve Jobs to design the Apple
and Stanford University to develop the Sun workstation.
The Alto was developed into the
Xerox 8010 Star, 1981,
powered by a Symbolics LISP chip

Alan Kay 1940 -
1966: worked with Ivan Sutherland (1938 -)
on Sketchpad (1962), the first GUI
The best way to predict the future is to invent it.
1968: worked with
Seymour Papert(1928 -) on Logo
1973: worked in Xerox Parc with
Doug Engelbart (1925-2013) on the mouse,
and Adele Goldberg (1945 -)
on Smalltalk, which became
Squeak and Tweek,
In 1968,
conceived Dynabook,
prototype of the laptop,
tablet and e-book reader,
which became
One Laptop Per Child.
1983: Chief Engineer at Atari
then Apple then Disney, now
Viewpoints Research Institute

22
The 1977 Trinity
Apple II
Commodore PET Tandy/Radio Shack TRS-80
Jack Tramiel 1928-2012
Commodore and Atari
Auschwitz survivor
Steve Jobs 1955-2012 Charles Tandy 1918-1978
Texas leather company

23
Personal Computers
Atari 400, 1979
The original games machine
4 million sold
IBM thought of buying the
company to get it, but instead
designed ...
The IBM PC, 1981
4.77MHz Intel 8088, up to 256Kb RAM
2 floppy disk drives, open architecture
Operating system MS-DOS by Microsoft
based on QDOS, based on CP/M
$1565

24
Home Computers
Commodore 64, 1982
$595, 17 million sold
BBC Model A/B, 1981
Acorn (ARM)
£235, Millions sold
Sinclair ZX Spectrum, 1982
£125, 5 million sold
(not including clones)
Amstrad CPC464, 1984
£249, 3 million sold
Raspberry Pi, 2012
£20, ??? Sold
Sinclair ZX80, 1980
£99.99, 100,000 sold

25
WIMP: the Xerox PARC Legacy
Apple Macintosh, 1984
8MHz Motorola 68000
MacPaint, MacWrite,
Mac Draw
128k, $2495
256k, $2795
Windows 1.0 1985,
2 years late, slow and buggy
Windows 2.0 1987
Mac look-alike,
Aldus Pagemaker, Excel, Word,
Corel Draw

26
Meanwhile … on the telephone
Almon Brown
Strowger
1839 - 1902
Undertaker
First exchange
La Porte, IN, 1892
75 subscribers.
First UK automatic
exchange
Epsom, 1912
Alexander Graham Bell
1847 - 1922
Prof of Elocution.
Founder of Bell Labs.
Invented telephony,
aeronautics, hydrofoil and
much else.
In 1876, the President of
Western Electric declined to
buy Bell's patent for
$100,000, claiming that the
telephone was just a toy.
Two years later,
he offered $2,000,000 for it.

27
Digital telecoms
First digital telephone exchange
Moorgate PCM, ITT-STC 1971
(now demolished and replaced by
the 'ski slope' building in Fore St)
Alec Reeves 1902-1971
Pulse code modulation
STC 1937
Gottfried Ungerboeck
1940-
Trellis coded modulation
IBM Zurich 1980
(now at Broadcom)
Massively increased
transmission rates made
data comms feasible.
Vint Cerf
TCP/IP
on Arpanet
DARPA 1972

28
Convergence Tim
Berners-Lee
CERN
Hypertext,
1980
plus Internet
= WWW, 1989
Martin Cooper
Motorola
DynaTac
('The Brick')
1973

Moses, meet Steve.
He's going to upgrade
your tablet.
Meanwhile,
on a different cloud ...

Recursion and Invariance
Dijkstra's Ball Game The Mutilated Chessboard

From π to Pi

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