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)– Symbols0,1– 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 Binary10’s 1’s 16’s 8’s 4’s 2’s 1’s 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 2 0 0 0 1 0 0 3 0 0 0 1 1 0 4 0 0 1 0 0 0 5 0 0 1 0 1 0 6 0 0 1 1 0 0 7 0 0 1 1 1 0 8 0 1 0 0 0 0 9 0 1 0 0 1

• first stored program - metal cards

• first computer manufacturing

• still in use today!

Jacquard Loom (1801)Mechanical Computer

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

Derives some, but not all true

statements, and no false statements starting from a

finite number of axioms and following mechanical

inference rules.

incomplete

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 nothave any proof in thesystem of PrincipiaMathematica.

G is unprovable, but true!

Gödel’s Proof IdeaG: 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, 1936Universal Computing machine.Precise vocabulary: 0, 1Class of primitiveoperations:

ReadWriteShift LeftShift Right

Well Formed SequencesCorrectnessCompletenessEquivalenceComplexity

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 stored-program 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 KeyboardNo Video DisplayNo 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 "ready-made" 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

ADC

Continuously varying electrical energy is an analog of the sound pressure wave.

Microphone converts acoustic to electrical energy. It’s a transducer.

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

AnalogContinuous signal that mimics shape of acoustic sound pressure wave

DigitalStream 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”

[a.k.a. “sample word length,” “bit depth”]Precision of numbers used for measurement: the more bits, the higher the resolution.

Example: 16 bit

Analog to Digital Overview

Sampling RateHow often analog signal is measured

Sampling Resolution

[samples per second, Hz]Example: 44,100 Hz

Sampling Rate

Nyquist Theorem:Sampling rate must be at least twice as high as the highest frequency you want to represent.

Determines the highest frequency that you can represent with a digital signal.

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

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.

Which rates can represent the range of frequencies audible by (fresh) ears?

3-bit Quantization

A 3-bit binary (base 2) number has 23 = 8 values.

0

1

2

3

4

5

6

7

A rough approximation

Am

plit

ud

e

Time — measure amp. at each tick of sample clock

4-bit Quantization

A 4-bit binary number has 24 = 16 values.

0

2

4

6

8

10

12

14

Am

plit

ud

e

A better approximation

Time — measure amp. at each tick of sample clock

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 theargument:

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".

New Media Initiative

Art/Design

Humanities

Technology

Rhetoric

Philosophy

BAMPFA

Art History

Film Studies

EECS

IEOR

Public Health

Journalism

Architecture

Music

Art Practice

iSchool

ME

BioE

Theater

Education

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/micro.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.