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Computation

January 1st, 2006 | Filed under: Backgrounds | No Comments »

The Analytical Engine
From “computers� in the Encyclopædia Britannica online:
“While working on the Difference Engine, Babbage began to imagine ways to improve it. Chiefly he thought about generalizing its operation so that it could perform other kinds of calculations. By the time the funding had run out in 1833, he had conceived of something far more revolutionary: a general-purpose computing machine called the Analytical Engine. The Analytical Engine was to be a general-purpose, fully program-controlled, automatic mechanical digital computer. It would be able to perform any calculation set before it…. Augusta Ada King, the countess of Lovelace, was the daughter of the poet Lord George Gordon Byron and the mathematically inclined Anne Millbanke. One of her tutors was Augustus De Morgan, a famous mathematician and logician. … Lady Lovelace attended Babbage’s soirees and became fascinated with his Difference Engine. … She went on to become the world’s only expert on the process of sequencing instructions on the punched cards that the Analytical Engine used—that is, she became the world’s first computer programmer.â€?

Computer
From Wikipedia: “In current usage, a computer is a device which is used to process information according to a well-defined procedure.

The word was originally used to describe people who were employed to do arithmetic calculations, with or without mechanical aids. The famed Gottfried Wilhelm von Leibniz himself complained of the time he expended in performing calculations. Starting in the 1950s computing machine was used to refer to the machines themselves; finally, the shorter word computer took over the term computing machine. Originally, computing was almost exclusively related to arithmetical problems, but modern computers are used for many tasks unrelated to mathematics, as their cost has declined, their performance has increased and their size is reduced.

However, the above definition includes many special-purpose devices that can compute only one or a limited range of functions. When considering modern computers, their most notable characteristic that distinguishes them from earlier computing devices is that, given the right programming, any computer can emulate the behaviour of any other (limited only by storage capacity and execution speed), and, indeed, it is believed that current machines can emulate any future computing devices we invent (though undoubtedly more slowly). In some sense, then, this threshold capability is a useful test for identifying “general-purpose� computers from earlier special-purpose devices. This “general-purpose� definition can be formalised into a requirement that a certain machine must be able to emulate the behaviour of a universal Turing machine. Machines meeting this definition are referred to as Turing-complete. While such machines are physically impossible as they require unlimited storage and zero crashing probability, the attribute Turing-complete is sometimes also used in a lax sense for machines that would be universal if they had more (infinite) storage and were absolutely reliable. The first such machine appeared in 1941: the program-controlled Z3 of Konrad Zuse (but its Turing-completeness was shown only much later, namely, in 1998). Other machines followed in a flurry of developments around the world. See the history of computing article for more details of this period.�

Turing Machine
From Wikipedia: “The Turing machine is an abstract model of computer execution and storage introduced in 1936 by Alan Turing to give a mathematically precise definition of algorithm or ‘mechanical procedure’. As such it is still widely used in theoretical computer science, especially in complexity theory and the theory of computation. The thesis that states that Turing machines indeed capture the informal notion of effective or mechanical method in logic and mathematics is known as the Church-Turing thesis.

The concept of the Turing machine is based on the idea of a person executing a well-defined procedure by changing the contents of an infinite amount of ordered paper sheets that can contain one of a finite set of symbols. The person needs to remember one of a finite set of states and the procedure is formulated in very basic steps in the form of “If your state is 42 and the symbol you see is a ‘0’ then replace this with a ‘1’, remember the state 17, and go to the following sheet.

Turing machines shouldn’t be confused with the Turing test, Turing’s attempt to capture the notion of artificial intelligence.

A Turing machine that is able to simulate any other Turing machine is called a universal Turing machine or simply a universal machine as Turing described it in 1947:

It can be shown that a single special machine of that type can be made to do the work of all. It could in fact be made to work as a model of any other machine. The special machine may be called the universal machine.�

What Are the Implication of the Universal Turing Machine?

The Fabric of Reality: The Science of Parallel Universes-And Its Implications
by David Deutsch
From Amazon: “In The Fabric of Reality, Deutsch traces what he considers the four main strands of scientific explanation: quantum theory, evolution, computation, and the theory of knowledge.�

Computationalism: New Directions
by Matthias Scheutz (Editor)
From the dust jacket: “Classical computationalism—the view that mental states are computational states—has come under attack in recent years. Critics claim that in defining computation solely in abstract, syntactic terms, computationalism neglects the real-time, embodied, real-world constraints with which cognitive systems must cope. Instead of abandoning computationalism altogether, however, some researchers are reconsidering it, recognizing that real-world computers, like minds, must deal with issues of embodiment, interaction, physical implementation, and semantics. This book lays the foundation for a successor notion of computationalism. It covers a broad intellectual range, discussing historic developments of the notions of computation and mechanism in the computationalist model, the role of Turing machines and computational practice in artificial intelligence research, different views of computation and their role in the computational theory of mind, the nature of intentionality, and the origin of language.�

Turing’s Man: Western Culture in the Computer Age
by J. David Bolter
From Amazon, by Ivan Askwith: “Although Turing’s Man is a little bit dated — it was published in 1984, before the internet had even taken on a significant presence in modern life, it suggests and foreshadows a number of themes which have become more prominent since the text was printed. Beginning with an overview and survey of technological evolution, from the Ancient World right up through the present, Bolter does a fine job of articulating the complex process through which technology changes and is changed by the society into which it is introduced.â€?

Age of Spiritual Machines
by Ray Kurzweil
From Barns and Noble: “After establishing that technology is growing exponentially, Kurzweil forecasts that computers will exceed the memory capacity and computing speed of the human brain by 2020, with the other attributes of human intelligence not far behind.�

Machines Who Think: A Personal Inquiry into the History and Prospects of Artificial Intelligence
by Pamela McCorduck
From Amazon, from Scientific American: “The enormous, if stealthy, influence of AI bears out many of the wonders foretold 25 years ago in Machines Who Think, Pamela McCorduck’s groundbreaking survey of the history and prospects of the field. A novelist at the time (she has since gone on to write and consult widely on the intellectual impact of computing), McCorduck got to the founders of the field while they were still feeling their way into a new science.�



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