Transcript Document

Week 12
The Universal Representation:
The Computer and Digitalization
Sources:
www.iu.edu/~emusic/361/iuonly/slides/digitalaudio.ppt
www.cs.virginia.edu/~evans/cs150/classes/class24/lecture24.ppt
www.computinghistorymuseum.org/teaching/.../pptlectures/History.ppt
www.educationworld.com/a_lesson/TM/computer%20history1.ppt
First Computing Machine:
Abacus
• 3000 BCE, early form
of beads on wires,
used in China,…
• From semitic abaq,
meaning dust.
• Still in use today
Mechanical Reasoning: Logic
Aristotle (~350BC): Organon
Codify logical deduction with rules of inference
(syllogisms)
Every A is a P
X is an A
X is a P
Every human is mortal.
Gödel is human.
Gödel is mortal.
Greek Logic
• Euclid (~300BC): Elements
– We can reduce Geometry to a few axioms and derive the rest by
following rules of
– Propositional Logic
– Constants:
False, True (Binary Logic: Two values)
– Symbols 0,1
– Variables: p, q, r, …
– Punctuation:
()
– Connectives:
• (not p),
–
–
–
–
( p and q),
( p or q),
( p implies q, p only if q, if p then q, conditional),
(p if and only if q)
– Well-formed formula (wff)
Algorithm (825AD)
Mathematical “Recipe” for solving a class of
problems.
Al-Khwārizmī, muslim Persian astronomer and
mathematician, wrote a treatise in the arabic
language in 825 AD, On Calculation with
Hindu–Arabic numeral system.
BLAISE PASCAL
(1623 - 1662)
 In 1642, the French mathematician and
philosopher Blaise Pascal invented a
calculating device that would come to be
called the "Adding Machine".
BLAISE PASCAL
(1623 - 1662)

Originally called a "numerical wheel calculator" or
the "Pascaline", Pascal's invention utilized a train of 8
moveable dials or cogs to add sums of up to 8 figures long.
As one dial turned 10 notches - or a complete revolution it mechanically turned the next dial.
Pascal's mechanical Adding Machine automated the
process of calculation. Although slow by modern
standards, this machine did provide a fair degree of
accuracy and speed.
Gottfried Wilhelm von
LEIBNIZ
(1646-1716)
Computing Machine (1679)
Binary Numbers (1701)
Binary Numbers
1. Computers use Binary Numbers.
2. What is a Character?
3. What are the Characters in the English Alphabet?
A, B, C, …., Z (there are 26 of these)
4. We combine these Characters to make Words:
CAT, HAT, …
5. What are the Characters in the Decimal Number System?
0, 1, 2, 3, 4, 5, 6, 7, 8, 9 (there are how many? 10!)
6. We combine these to make Decimal Numbers:
12, 34, … (we add columns of 10, 100, … as needed)
7. In the Binary Number System, there are only two
characters:
0, 1 …(so we add columns of 2, 4, 8, 16, … as
needed)
8. Now, Let’s learn how to Match a Decimal Number to a
Binary Number…
Binary Numbers
Decimal
10’s 1’s
0
0
0
1
0
2
0
3
0
4
0
5
0
6
0
7
0
8
0
9
16’s
0
0
0
0
0
0
0
0
0
0
Binary
8’s
4’s
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
2’s
0
0
1
1
0
0
1
1
0
0
1’s
0
1
0
1
0
1
0
1
0
1
Jacquard Loom (1801)
Mechanical Computer
• first stored program metal cards
• first computer
manufacturing
• still in use today!
Charles Babbage
• Difference Engine c.1822
– huge calculator, never finished
• Analytical Engine 1833
– could store numbers
– calculating “mill” used punched
metal cards for instructions
– powered by steam!
– accurate to six decimal places
Importance of the Difference Engine
• 1. First attempt to devise a computing machine that
was automatic in action and well adapted, by its
printing mechanism, to a mathematical task of
considerable importance.
Ada Augusta Byron, 1815-1852
• born on 10 December 1815.
• named after Byron's half sister,
Augusta, who had been his mistress.
Ada Augusta Byron,
Countess of Lovelace
1842
• Translated Menebrea’s paper into English
• Taylor’s: “The editorial notes are by the translator,
the Countess of Lovelace.”
• Footnotes enhance the text and provide examples of
how the Analytical Engine could be used, i.e., how it
would be programmed to solve problems!
• First Algorithm
• “world’s first programmer”
Logic
Mathematics and
Mechanical Reasoning
• Newton (1687): Philosophiæ Naturalis
Principia Mathematica
– We can reduce the motion of objects (including
planets) to following axioms (laws)
mechanically
Mechanical Reasoning
• Late 1800s – many mathematicians working
on codifying “laws of reasoning”
– George Boole, Laws of Thought
– Augustus De Morgan
• Whitehead and Russell, 1911-1913
– Principia Mathematica
– Attempted to formalize all mathematical
knowledge about numbers and sets
All true statements
about numbers
Perfect Axiomatic System
Derives all true
statements, and no false
statements starting from a
finite number of axioms
and following mechanical
inference rules.
Incomplete Axiomatic System
incomplete
Derives
some, but not all true
statements, and no false
statements starting from a
finite number of axioms
and following mechanical
inference rules.
Inconsistent Axiomatic System
Derives
all true
statements, and some false
statements starting from a
finite number of axioms
and following mechanical
inference rules.
some false
statements
Principia Mathematica
• Whitehead and Russell (1910– 1913)
– Three Volumes, 2000 pages
• Attempted to axiomatize mathematical
reasoning
– Define mathematical entities (like numbers) using
logic
– Derive mathematical “truths” by following
mechanical rules of inference
– Claimed to be complete and consistent
• All true theorems could be derived
• No falsehoods could be derived
Russell’s Paradox
• Some sets are not members of themselves
– set of all Even Numbers
• Some sets are members of themselves
– set of all things that are non-Even Numbers
• S = the set of all sets that are not
members of themselves
• Is S a member of itself?
Russell’s Paradox
• S = set of all sets that are not members of
themselves
• Is S a member of itself?
– If S is an element of S, then S is a member of
itself and should not be in S.
– If S is not an element of S, then S is not a
member of itself, and should be in S.
Epimenides Paradox
Epidenides (a Cretan):
“All Cretans are liars.”
Equivalently:
“This statement is false.”
Russell’s types can help
with the set paradox, but
not with these.
Kurt Gödel
• Born 1906 in Brno (now
Czech Republic, then
Austria-Hungary)
• 1931: publishes Über
formal unentscheidbare
Sätze der Principia
Mathematica und
verwandter Systeme (On
Formally Undecidable Propositions of
Principia Mathematica and Related Systems)
Gödel’s Solution
All consistent axiomatic formulations of number
theory include undecidable propositions.
undecidable – cannot be proven either true or
false inside the system.
Gödel’s Theorem
In the Principia Mathematica system,
there are statements that cannot be
proven either true or false.
Gödel’s Theorem
In any interesting rigid system, there
are statements that cannot be proven
either true or false.
Proof – General Idea
• Theorem: In the Principia
Mathematica system, there are
statements that cannot be
proven either true or false.
• Proof: Find such a statement
Gödel’s Statement
G:
This statement does not
have any proof in the
system of Principia
Mathematica.
G is unprovable, but true!
Gödel’s Proof Idea
G: This statement does not have any proof in
the system of PM.
If G is provable, PM would be inconsistent.
If G is unprovable, PM would be incomplete.
Thus, PM cannot be complete and consistent!
Alan Turing (1912-1954)
• On Computable
Numbers with an
application to the
Entscheidungs-problem
• (1936)
• Code breaking: Enigma
Turing Machines, 1936
Universal Computing machine.
Precise vocabulary: 0, 1
Class of primitive
operations:
Read
Write
Shift Left
Shift Right
Well Formed Sequences
Correctness
Completeness
Equivalence
Complexity
http://aturingmachine.com/
Herman Hollerith (1860-1929)
Herman Hollerith
• Born: February 29, 1860
– Civil War: 1861-1865
•
•
•
•
•
•
Columbia School of Mines (New York)
1879 hired at Census Office
1882 MIT faculty (T is for technology!)
1883 St. Louis (inventor)
1884 Patent Office (Wash, DC)
1885 “Expert and Solicitor of Patents”
Census
• Article I, Section 2: Representatives and direct
Taxes shall be apportioned among the several
states...according to their respective
numbers...(and) every ...term of ten years
• 1790: 1st US census
• Population: 3,929,214
• Census Office
Population Growth:
•
•
•
•
1790
4 million
1840
17 million
1870
40 million
1880
50 million
fear of not being able to enumerate the census in
the 10 intervening years
• 1890
63 million
Computing Tabulating Recording
Company,(C-T-R)
• 1911: Charles Flint
– Computing Scale Company
(Dayton, OH)
– Tabulating Machine
Company, and
– International Time
Recording Company
(Binghamton, NY)
•IBM (1924)
• Thomas J. Watson
(1874-1956)
hired as first president
• In1924, Watson renames
CTR as International
Business Machines
Vacuum Tubes - 1941 - 1956
• First Generation Electronic
Computers used Vacuum Tubes
• Vacuum tubes are glass tubes with
circuits inside.
• Vacuum tubes have no air inside of
them, which protects the circuitry.
HOWARD AIKEN
(1900 - 1973)

Aiken thought he could create a modern and
functioning model of Babbage's Analytical Engine.
He succeeded in securing a grant of 1 million dollars
for his proposed Automatic Sequence Calculator; the
Mark I for short. From IBM.
In 1944, the Mark I was "switched" on. Aiken's colossal
machine spanned 51 feet in length and 8 feet in height.
500 meters of wiring were required to connect each
component.
HOWARD AIKEN

The Mark I did transform Babbage's dream
into reality and did succeed in putting IBM's
name on the forefront of the burgeoning
computer industry. From 1944 on, modern
computers would forever be associated with
digital intelligence.
ENIAC
1946
 Electronic Numerical Integrator And Computer
Under the leadership of J. Presper Eckert (1919 1995) and John W. Mauchly (1907 - 1980) the team
produced a machine that computed at speeds 1,000
times faster than the Mark I was capable of only 2 years
earlier.
Using 18,00-19,000 vacuum tubes, 70,000 resistors
and 5 million soldered joints this massive instrument
required the output of a small power station to operate it.
ENIAC at Moore School,
University of Pennsylvania
Early Thoughts about
Stored Program Computing
• January 1944 Moore School team thinks of better ways
to do things; leverages delay line memories from War
research
• September 1944 John von Neumann visits
– Goldstine’s meeting at Aberdeen Train Station
• October 1944 Army extends the ENIAC contract to
include research on the EDVAC and the storedprogram concept
• Spring 1945 ENIAC working well
• June 1945 First Draft of a Report on the EDVAC:
Electronic Discrete Variable Automatic Computer
First Draft Report (June 1945)
• John von Neumann prepares a report on the EDVAC
which identifies how the machine could be programmed
(unfinished very rough draft)
– academic: publish for the good of science
– engineers: patents, patents, patents
• von Neumann never repudiates the myth that he wrote it;
most members of the ENIAC team ontribute ideas
Manchester Mark I (1948)
Grace Hopper
• Programmed UNIVAC
• Recipient of Computer
Science’s first “Man of the
Year Award”
First Computer Bug
• Relay switches part
of computers
• Grace Hopper
found a moth stuck
in a relay
responsible for a
malfunction
• Called it
“debugging” a
computer
As We May Think
(1945)
TRANSISTOR
1948

In the laboratories of Bell Telephone, John
Bardeen, Walter Brattain and William Shockley
discovered the "transfer resistor"; later labelled the
transistor.
Advantages:
increased reliability
1/13 size of vacuum tubes
consumed 1/20 of the electricity of vacuum tubes
were a fraction of the cost
TRANSISTOR
1948
 This tiny device had a huge impact on and
extensive implications for modern computers. In
1956, the transistor won its creators the Noble
Peace Prize for their invention.
Logic
Turing Test (1950)
The First Microprocessor – 1971
• The 4004 had 2,250 transistors
• four-bit chunks (four 1’s or 0’s)
• 108Khz
• Called “Microchip”
Xerox Parc (1970)
ALTAIR
1975
 The invention of the transistor made
computers smaller, cheaper and more reliable.
Therefore, the stage was set for the entrance of
the computer into the domestic realm. In 1975,
the age of personal computers commenced.
Under the leadership of Ed Roberts the
Micro Instrumentation and Telemetry Company
(MITS) wanted to design a computer 'kit' for the
home hobbyist.
ALTAIR 1975
 Based on the Intel 8080 processor, capable
of controlling 64 kilobyes of memory, the MITS
Altair - as the invention was later called - was
debuted on the cover of the January edition of
Popular Electronics magazine.
Presenting the Altair as an unassembled kit
kept costs to a minimum. Therefore, the
company was able to offer this model for only
$395. Supply could not keep up with demand.
ALTAIR
1975
 ALTAIR FACTS:
No Keyboard
No Video Display
No Storage Device
Apple (1976)
 IBM's major competitor was a company
lead by Steve Wozniak and Steve Jobs; the
Apple Computer Inc.
The "Lisa" was the result of their competitive
thrust.
This system differed from its predecessors in
its use of a "mouse" - then a quite foreign
computer instrument - in lieu of manually
typing commands.
However, the outrageous price of the Lisa
kept it out of reach for many computer buyers.
Apple
 Apple's brainchild was the Macintosh. Like
the Lisa, the Macintosh too would make use of a
graphical user interface.
Introduced in January 1984 it was an
immediate success.
The GUI (Graphical User Interface) made
the system easy to use.
IBM (PC)
1981
 On August 12, 1981 IBM announced its
own personal computer.
Using the 16 bit Intel 8088 microprocessor,
allowed for increased speed and huge amounts
of memory.
Unlike the Altair that was sold as
unassembled computer kits, IBM sold its "readymade" machine through retailers and by
qualified salespeople.
IBM (PC)
1981
 To satisfy consumer appetites and to
increase usability, IBM gave prototype IBM PCs
to a number of major software companies.
For the first time, small companies and
individuals who never would have imagined
owning a "personal" computer were now
opened to the computer world.
MICROSOFT (PC)
1983
MACINTOSH
(1984)
 The Apple Macintosh debuts in 1984. It
features a simple, graphical interface, uses the
8-MHz, 32-bit Motorola 68000 CPU, and has a
built-in 9-inch B/W screen.
Digitization/ Binary Numbers
Analog Representations of Sound
Magnified phonograph grooves, viewed from above:
The shape of the grooves encodes
the continuously varying audio
signal.
Analog to Digital Recording Chain
AD
C
Microphone converts acoustic to electrical
energy. It’s a transducer.
Continuously varying electrical energy is an analog of
the sound pressure wave.
ADC (Analog to Digital Converter) converts analog to
digital electrical signal.
Digital signal transmits binary numbers.
DAC (Digital to Analog Converter) converts digital signal in
computer to analog for your headphones.
Analog versus Digital
Analog
Continuous signal that mimics shape of acoustic
sound pressure wave
Digital
Stream of discrete numbers that represent
instantaneous amplitudes of analog signal,
measured at equally spaced points in time.
Analog to Digital Conversion
Instantaneous amplitudes of continuous analog
signal, measured at equally spaced points in
time.
A series of “snapshots”
Analog to Digital Overview
Sampling Rate
How often analog signal is measured
[samples per second, Hz]
Example: 44,100 Hz
Sampling Resolution
[a.k.a. “sample word length,” “bit depth”]
Precision of numbers used for measurement: the more
bits, the higher the resolution.
Example: 16 bit
Sampling Rate
Determines the highest frequency that you can
represent with a digital signal.
Nyquist Theorem:
Sampling rate must be at least twice as high as the
highest frequency you want to represent.
Capturing just the crest and trough of a sine wave
will represent the wave exactly.
Aliasing
What happens if sampling rate not high
enough?
A high frequency signal
sampled at too low a rate
looks like …
… a lower frequency signal.
That’s called aliasing or foldover. An ADC has a
low-pass anti-aliasing filter to prevent this.
Common Sampling Rates
Which rates can represent the range
of frequencies audible by (fresh) ears?
Sampling Rate
Uses
44.1 kHz (44100)
CD, DAT
48 kHz (48000)
DAT, DV, DVD-Video
96 kHz (96000)
DVD-Audio
22.05 kHz (22050)
Old samplers
Most software can handle all these
rates.
3-bit Quantization
A 3-bit binary (base 2) number has 23 = 8 values.
7
6
Amplitude
5
4
3
2
1
0
Time — measure amp. at each tick of sample clock
A rough approximation
4-bit Quantization
A 4-bit binary number has 24 = 16 values.
14
12
Amplitude
10
8
6
4
2
0
Time — measure amp. at each tick of sample clock
A better approximation
Quantization Noise
Round-off error: difference between actual signal and
quantization to integer values…
Random errors: sounds
like low-amplitude
noise
The Digital Audio Stream
It’s just a series of sample numbers, to be interpreted
as instantaneous amplitudes: one for every tick of the
sample clock.
This is what appears in a sound file, along with a
header that indicates the sampling rate, bit depth and
other things.
Common Sampling Resolutions
Word length
Uses
8-bit integer
Low-res web audio
16-bit integer
CD, DAT, DV, sound files
24-bit integer
DVD-Video, DVD-Audio
32-bit floating point Software (usually only for
internal representation)
FIRST GENERATION
(1945-1956)
 First generation computers were characterized by
the fact that operating instructions were made-to-order
for the specific task for which the computer was to be
used. Each computer had a different binary-coded
program called a machine language that told it how to
operate. This made the computer difficult to program and
limited its versatility and speed. Other distinctive features
of first generation computers were the use of vacuum
tubes (responsible for their breathtaking size) and
magnetic drums for data storage.
SECOND GENERATION
(1956-1963)
 Throughout the early 1960's, there were a
number of commercially successful second
generation computers used in business,
universities, and government from companies
such as Burroughs, Control Data, Honeywell,
IBM, Sperry-Rand, and others. These second
generation computers were also of solid state
design, and contained transistors in place of
vacuum tubes.
SECOND GENERATION
(1956-1963)
They also contained all the components we associate
with the modern day computer: printers, tape storage,
disk storage, memory, operating systems, and stored
programs. One important example was the IBM 1401,
which was universally accepted throughout industry, and
is considered by many to be the Model T of the computer
industry. By 1965, most large business routinely processed
financial information using second generation computers.
THIRD GENERATION
(1965-1971)
Though transistors were clearly an improvement over
the vacuum tube, they still generated a great deal of heat,
which damaged the computer's sensitive internal parts.
The quartz rock eliminated this problem. Jack Kilby, an
engineer with Texas Instruments, developed the
integrated circuit (IC) in 1958. The IC combined three
electronic components onto a small silicon disc, which was
made from quartz. Scientists later managed to fit even
more components on a single chip, called a
semiconductor.
THIRD GENERATION
(1965-1971)
As a result, computers became ever smaller
as more components were squeezed onto the
chip. Another third-generation development
included the use of an operating system that
allowed machines to run many different
programs at once with a central program that
monitored and coordinated the computer's
memory.
FOURTH GENERATION
(1971-Present)
In 1981, IBM introduced its personal
computer (PC) for use in the home, office and
schools. The 1980's saw an expansion in
computer use in all three arenas as clones of the
IBM PC made the personal computer even more
affordable. The number of personal computers
in use more than doubled from 2 million in 1981
to 5.5 million in 1982.
FOURTH GENERATION
(1971-1990)
Ten years later, 65 million PCs were being used.
Computers continued their trend toward a smaller size,
working their way down from desktop to laptop
computers (which could fit inside a briefcase) to palmtop
(able to fit inside a breast pocket). In direct competition
with IBM's PC was Apple's Macintosh line, introduced in
1984. Notable for its user-friendly design, the Macintosh
offered an operating system that allowed users to move
screen icons instead of typing instructions
Contemporary
Computers
Logic
Robotics and Automation
• Both involve: computers, physical world, geometry
• Both engage many disciplines
• “robota”
coined in 1920 (Capek)
– Emphasizes unpredictable environments like homes, undersea
• “automation” coined in 1948 (Ford Motors)
– Emphasizes predictable environments like factories, labs
robotics
automation
Short Films on Computing
Logic by Machine (Computer and
the Mind of Man)
http://www.archive.org/details/logic_by_machine_1
14 min
http://www.archive.org/details/logic_by_machine_2
15 min
Lev Manovich on New Media
What is New Media ?
New media are often defined as digital/computational. I'd like to explore an alternate definition where
digital/computational media are one example of a broader class of "New" media. Here's a sketch of the
argument:
1. medium: from latin: "medius": intervening element
an element that facilitates transformation from A to B
eg, change in form: clay, paint, plastic, ...
special case: an element that facilitates
communication between A and B. eg. printing press,, radio, internet, ...
thus: a medium is an agent for transformation.
2. consider two classes of medium:
singular:
can be used once: eg, paint, thermoset polymers
reconfigurable: can be reused: eg, radio, thermoplastic polymers (plastics)
3. reconfigurable media are essentially flexible, available for use (cf. Bestand, Gestell).
ie: reconfigurable media are tranformable agents
for transformation. (doubly transformative)
4. proposal: define "new" media as reconfigurable media
eg, new media are tranformable agents for transformation.
(always available, doubly transformative, postmodern technology)
examples: computers, the intert, nanotechnology, stem cells,
(includes digital/computational but is much broader)
We might define New Media as "Means without Ends".
Humanities
Philosophy
Rhetoric
Journalism
Education
iSchool
Art History
Architecture
Public Health
Film Studies
Theater
IEOR
BAMPFA
Music
EECS
Technology
Art Practice
ME
BioE
New Media Initiative
Art/Design
Mission
To critically analyze and help
shape developments in new
media from para-disciplinary and
global perspectives that
emphasize humanities and the
public interest.
bcnm.berkeley.edu
BIBLIOGRAPHY
Information was gathered from the
following sites:
http://www.pbs.org/nerds/timeline/mic
ro.html (Triumph Of The Nerds)
http://www.digitalcentury.com/encyclo
/update/comp_hd.html (Digital Century)
http://humlink.humanities.mcmaster.ca/
~dalberto/comweb.htm (History of
Computers)
FIFTH GENERATION
(Future)
Many advances in the science of computer design and
technology are coming together to enable the creation of
fifth-generation computers. Two such engineering
advances are parallel processing, which replaces von
Neumann's single central processing unit design with a
system harnessing the power of many CPUs to work as
one. Another advance is superconductor technology,
which allows the flow of electricity with little or no
resistance, greatly improving the speed of information
flow.
FIFTH GENERATION
(Future)
Computers today have some attributes of
fifth generation computers. For example,
expert systems assist doctors in making
diagnoses by applying the problem-solving
steps a doctor might use in assessing a patient's
needs. It will take several more years of
development before expert systems are in
widespread use.