Fourth dimension


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3D projection of a tesseract undergoing a simple rotationIn mathematics, the fourth dimension, or a four-dimensional ("4D") space,[dubious – discuss] is an abstract concept derived by generalizing the rules of three-dimensional space. It has been studied by mathematicians and philosophers for almost two hundred years, both for its own interest and for the insights it offered into mathematics and related fields.

Algebraically it is generated by applying the rules of vectors and coordinate geometry to a space with four dimensions. In particular a vector with four elements (a 4-tuple) can be used to represent a position in four-dimensional space. The space is a Euclidean space, so has a metric and norm, and so all directions are treated as the same: the additional dimension is indistinguishable from the other three.

In modern physics, space and time are unified in a four-dimensional Minkowski continuum called spacetime, whose metric treats the time dimension differently from the three spatial dimensions.[clarification needed] Spacetime is thus not a Euclidean space.

Contents [hide]
1 History
2 Vectors
3 Orthogonality and vocabulary
4 Geometry
4.1 Hypersphere
5 Cognition
6 Dimensional analogy
6.1 Projections
6.2 Shadows
6.3 Bounding volumes
6.4 Visual scope
6.5 Limitations
7 See also
8 References
9 External links


[edit] History
The possibility of spaces with dimensions higher than three was first studied by mathematicians in the 19th century. In 1827 Möbius realized that a fourth dimension would allow a three-dimensional form to be rotated onto its mirror-image,[1] and by 1853 Ludwig Schläfli had discovered many polytopes in higher dimensions, although his work was not published until after his death.[2] Higher dimensions were soon put on firm footing by Bernhard Riemann's 1854 Habilitationsschrift, Über die Hypothesen welche der Geometrie zu Grunde liegen, in which he considered a "point" to be any sequence of coordinates (x1, ..., xn). The possibility of geometry in higher dimensions, including four dimensions in particular, was thus established.

An arithmetic of four dimensions called quaternions was defined by William Rowan Hamilton in 1843. This associative algebra was the source of the science of vector analysis in three dimensions as recounted in A History of Vector Analysis.

The fourth dimension was popularised by Charles Howard Hinton, starting in 1880 with his essay What is the Fourth Dimension? published in the Dublin University magazine.[3] He coined the terms tesseract, ana and kata in his book A New Era of Thought, and introduced a method for visualising the fourth dimension using cubes in the book Fourth Dimension.[4][5]

In 1908, Hermann Minkowski presented a paper[6] consolidating the role of time as the fourth dimension of spacetime, the basis for Einstein's theories of Special and General Relativity.[7] But the geometry of spacetime, being non-Euclidean, is completely different to that popularised by Hinton. The study of such Minkowski spaces required new mathematics quite different to that of four-dimensional Euclidean space, and so developed along quite different lines. This separation was less clear in the popular imagination, with works of fiction and philosophy blurring the distinction, so in 1973 H. S. M. Coxeter felt compelled to write:

Little, if anything, is gained by representing the fourth Euclidean dimension as time. In fact, this idea, so attractively developed by H. G. Wells in The Time Machine, has led such authors as J. W. Dunne (An Experiment with Time) into a serious misconception of the theory of Relativity. Minkowski's geometry of space-time is not Euclidean, and consequently has no connection with the present investigation.
—H. S. M. Coxeter, Regular Polytopes[8]
[edit] Vectors
Mathematically four-dimensional space is simply a space with four spatial dimensions, that is a space that needs four parameters to specify a point in it. For example a general point might have position vector a, equal to


This can be written in terms of the four basis vectors (e1, e2, e3, e4), given by


so the general vector a is


Vectors add, subtract and scale as in three dimensions. The dot product also generalizes to four dimensions, like so:


It can be used to calculate the norm or length of a vector,


and calculate or define the angle between two vectors as


The cross product is not defined in four dimensions. Instead the exterior product is used for some applications, and is defined as follows


This is bivector valued, with bivectors in four dimensions forming a six-dimensional linear space with basis (e12, e13, e14, e23, e24, e34). They can be used to generate rotations in four dimensions.

[edit] Orthogonality and vocabulary
In the familiar 3-dimensional space that we live in there are three coordinate axes — usually labeled x, y, and z — with each axis orthogonal (i.e. perpendicular) to the other two. The six cardinal directions in this space can be called up, down, east, west, north, and south. Positions along these axes can be called altitude, longitude, and latitude. Lengths measured along these axes can be called height, width, and depth.

Comparatively, 4-dimensional space has an extra coordinate axis, orthogonal to the other three, which is usually labeled w. To describe the two additional cardinal directions, Charles Howard Hinton coined the terms ana and kata, from the Greek words meaning "up toward" and "down from", respectively. A length measured along the w axis can be called spissitude, as coined by Henry More.

[edit] Geometry
The geometry of 4-dimensional space is much more complex than that of 3-dimensional space, due to the extra degree of freedom.

Just as in 3 dimensions there are polyhedra made of two dimensional polygons, in 4 dimensions there are polychora (4-polytopes) made of polyhedra. In 3 dimensions there are 5 regular polyhedra known as the Platonic solids. In 4 dimensions there are 6 convex regular polychora, the analogues of the Platonic solids. Relaxing the conditions for regularity generates a further 58 convex uniform polychora, analogous to the 13 semi-regular Archimedean solids in three dimensions.

In 3 dimensions, a circle may be extruded to form a cylinder. In 4 dimensions, there are several different cylinder-like objects. A sphere may be extruded to obtain a spherical cylinder (a cylinder with spherical "caps"), and a cylinder may be extruded to obtain a cylindrical prism. The Cartesian product of two circles may be taken to obtain a duocylinder. All three can "roll" in 4-dimensional space, each with its own properties.

In 3 dimensions, curves can form knots but surfaces cannot (unless they are self-intersecting). In 4 dimensions, however, knots made using curves can be trivially untied by displacing them in the fourth direction, but 2-dimensional surfaces can form non-trivial, non-self-intersecting knots in 4-dimensional space. Because these surfaces are 2-dimensional, they can form much more complex knots than strings in 3-dimensional space can. The Klein bottle is an example of such a knotted surface. Another such surface is the real projective plane.

[edit] Hypersphere

Stereographic projection of a Clifford torus: the set of points (cos(a), sin(a), cos(b), sin(b)), which is a subset of the 3-sphere.The set of points in Euclidean 4-space having the same distance R from a fixed point P0 forms a hypersurface known as a 3-sphere. The hyper-volume of the enclosed space is:


This is part of the Friedmann–Lemaître–Robertson–Walker metric in General relativity where R is substituted by function R(t) with t meaning the cosmological age of the universe. Growing or shrinking R with time means expanding or collapsing universe, depending on the mass density inside.[9]

[edit] Cognition
Research using virtual reality finds that humans in spite of living in a three-dimensional world can without special practice make spatial judgments based on the length of, and angle between, line segments embedded in four-dimensional space.[10] The researchers noted that "the participants in our study had minimal practice in these tasks, and it remains an open question whether it is possible to obtain more sustainable, definitive, and richer 4-D representations with increased perceptual experience in 4-D virtual environments."[10] In another study,[11] the ability of humans to orient themselves in 2-D, 3-D and 4-D mazes has been tested. Each maze consisted of four path segments of random length and connected with orthogonal random bends, but without branches or loops (i.e. actually labyrinths). The graphical interface was based on John McIntosh's free 4-D Maze game.[12] The participating persons had to navigate through the path and finally estimate the linear direction back to the starting point. The researchers found that some of the participants were able to mentally integrate their path after some practice in 4-D (the lower dimensional cases were for comparison and for the participants to learn the method).

[edit] Dimensional analogy

A net of a tesseractTo understand the nature of four-dimensional space, a device called dimensional analogy is commonly employed. Dimensional analogy is the study of how (n − 1) dimensions relate to n dimensions, and then inferring how n dimensions would relate to (n + 1) dimensions.[13]

Dimensional analogy was used by Edwin Abbott Abbott in the book Flatland, which narrates a story about a square that lives in a two-dimensional world, like the surface of a piece of paper. From the perspective of this square, a three-dimensional being has seemingly god-like powers, such as ability to remove objects from a safe without breaking it open (by moving them across the third dimension), to see everything that from the two-dimensional perspective is enclosed behind walls, and to remain completely invisible by standing a few inches away in the third dimension.

By applying dimensional analogy, one can infer that a four-dimensional being would be capable of similar feats from our three-dimensional perspective. Rudy Rucker illustrates this in his novel Spaceland, in which the protagonist encounters four-dimensional beings who demonstrate such powers.

[edit] Projections
A useful application of dimensional analogy in visualizing the fourth dimension is in projection. A projection is a way for representing an n-dimensional object in n − 1 dimensions. For instance, computer screens are two-dimensional, and all the photographs of three-dimensional people, places and things are represented in two dimensions by projecting the objects onto a flat surface. When this is done, depth is removed and replaced with indirect information. The retina of the eye is also a two-dimensional array of receptors but the brain is able to perceive the nature of three-dimensional objects by inference from indirect information (such as shading, foreshortening, binocular vision, etc.). Artists often use perspective to give an illusion of three-dimensional depth to two-dimensional pictures.

Similarly, objects in the fourth dimension can be mathematically projected to the familiar 3 dimensions, where they can be more conveniently examined. In this case, the 'retina' of the four-dimensional eye is a three-dimensional array of receptors. A hypothetical being with such an eye would perceive the nature of four-dimensional objects by inferring four-dimensional depth from indirect information in the three-dimensional images in its retina.

The perspective projection of three-dimensional objects into the retina of the eye introduces artifacts such as foreshortening, which the brain interprets as depth in the third dimension. In the same way, perspective projection from four dimensions produces similar foreshortening effects. By applying dimensional analogy, one may infer four-dimensional "depth" from these effects.

As an illustration of this principle, the following sequence of images compares various views of the 3-dimensional cube with analogous projections of the 4-dimensional tesseract into 3-dimensional space.

Cube Tesseract Description
The image on the left is a cube viewed face-on. The analogous viewpoint of the tesseract in 4 dimensions is the cell-first perspective projection, shown on the right. One may draw an analogy between the two: just as the cube projects to a square, the tesseract projects to a cube.
Note that the other 5 faces of the cube are not seen here. They are obscured by the visible face. Similarly, the other 7 cells of the tesseract are not seen here because they are obscured by the visible cell.

The image on the left shows the same cube viewed edge-on. The analogous viewpoint of a tesseract is the face-first perspective projection, shown on the right. Just as the edge-first projection of the cube consists of two trapezoids, the face-first projection of the tesseract consists of two frustums.
The nearest edge of the cube in this viewpoint is the one lying between the red and green faces. Likewise, the nearest face of the tesseract is the one lying between the red and green cells.

On the left is the cube viewed corner-first. This is analogous to the edge-first perspective projection of the tesseract, shown on the right. Just as the cube's vertex-first projection consists of 3 deltoids surrounding a vertex, the tesseract's edge-first projection consists of 3 hexahedral volumes surrounding an edge. Just as the nearest vertex of the cube is the one where the three faces meet, so the nearest edge of the tesseract is the one in the center of the projection volume, where the three cells meet.
A different analogy may be drawn between the edge-first projection of the tesseract and the edge-first projection of the cube. The cube's edge-first projection has two trapezoids surrounding an edge, while the tesseract has three hexahedral volumes surrounding an edge.
On the left is the cube viewed corner-first. The vertex-first perspective projection of the tesseract is shown on the right. The cube's vertex-first projection has three tetragons surrounding a vertex, but the tesseract's vertex-first projection has four hexahedral volumes surrounding a vertex. Just as the nearest corner of the cube is the one lying at the center of the image, so the nearest vertex of the tesseract lies not on boundary of the projected volume, but at its center inside, where all four cells meet.
Note that only three faces of the cube's 6 faces can be seen here, because the other 3 lie behind these three faces, on the opposite side of the cube. Similarly, only 4 of the tesseract's 8 cells can be seen here; the remaining 4 lie behind these 4 in the fourth direction, on the far side of the tesseract.


[edit] Shadows
A concept closely related to projection is the casting of shadows.

If a light is shone on a three dimensional object, a two-dimensional shadow is cast. By dimensional analogy, light shone on a two-dimensional object in a two-dimensional world would cast a one-dimensional shadow, and light on a one-dimensional object in a one-dimensional world would cast a zero-dimensional shadow, that is, a point of non-light. Going the other way, one may infer that light shone on a four-dimensional object in a four-dimensional world would cast a three-dimensional shadow.

If the wireframe of a cube is lit from above, the resulting shadow is a square within a square with the corresponding corners connected. Similarly, if the wireframe of a tesseract were lit from “above” (in the fourth direction), its shadow would be that of a three-dimensional cube within another three-dimensional cube. (Note that, technically, the visual representation shown here is actually a two-dimensional shadow of the three-dimensional shadow of the four-dimensional wireframe figure.)

[edit] Bounding volumes
Dimensional analogy also helps in inferring basic properties of objects in higher dimensions. For example, two-dimensional objects are bounded by one-dimensional boundaries: a square is bounded by four edges. Three-dimensional objects are bounded by two-dimensional surfaces: a cube is bounded by 6 square faces. By applying dimensional analogy, one may infer that a four-dimensional cube, known as a tesseract, is bounded by three-dimensional volumes. And indeed, this is the case: mathematics shows that the tesseract is bounded by 8 cubes. Knowing this is key to understanding how to interpret a three-dimensional projection of the tesseract. The boundaries of the tesseract project to volumes in the image, not merely two-dimensional surfaces.

[edit] Visual scope
Being three-dimensional, we are only able to see the world with our eyes in two dimensions. A four-dimensional being would be able to see the world in three dimensions. For example, it would be able to see all six sides of an opaque box simultaneously, and in fact, what is inside the box at the same time, just as we can see the interior of a square on a piece of paper. It would be able to see all points in 3-dimensional space simultaneously, including the inner structure of solid objects and things obscured from our three-dimensional viewpoint.

[edit] Limitations
Reasoning by analogy from familiar lower dimensions can be an excellent intuitive guide, but care must be exercised not to accept results that are not more rigorously tested. For example, consider the formulas for the circumference of a circle C = 2πr and the surface area of a sphere: A = 4πr2. One might be tempted to suppose that the surface volume of a hypersphere is V = 6πr3, or perhaps V = 8πr3, but either of these would be wrong. The correct formula is V = 2π2r3[citation needed].

[edit] See also
Wikisource has original text related to this article:
Flatland
Euclidean space
Euclidean geometry
4-manifold
Exotic R4
Dimension
Four-dimensionalism
Fifth dimension
Sixth dimension
Polychoron
Polytope
List of geometry topics
Block Theory of the Universe
Flatland, a book by Edwin A. Abbott about two- and three-dimensional spaces, to understand the concept of four dimensions
Sphereland, an unofficial sequel to Flatland
Charles Howard Hinton
Dimensions, a set of films about two-, three- and four-dimensional polytopes
Miegakure, A puzzle platforming video game in 4-dimensional space.
List of four-dimensional games
[edit] References
^ Coxeter, H. S. M. (1973). Regular Polytopes, Dover Publications, Inc., p. 141.
^ Coxeter, H. S. M. (1973). Regular Polytopes, Dover Publications, Inc., pp. 142–143.
^ Rudolf v.B. Rucker, editor Speculations on the Fourth Dimension: Selected Writings of Charles H. Hinton, p. vii, Dover Publications Inc., 1980 ISBN 0-486-23916-0
^ Hinton, Charles Howard (1904). Fourth Dimension. ISBN 1-5645-9708. http://www.archive.org/details/fourthdimension00hintarch.
^ Gardner, Martin (1975). Mathematical Carnival. Knopf Publishing. pp. 42, 52–53. ISBN 0 14 02.2041 0.
^ Hermann Minkowski, "Raum und Zeit", 80. Versammlung Deutscher Naturforscher (Köln, 1908). Published in Physikalische Zeitschrift 10 104–111 (1909) and Jahresbericht der Deutschen Mathematiker-Vereinigung 18 75–88 (1909). For an English translation, see Lorentz et al. (1952).
^ C Møller (1952). The Theory of Relativity. Oxford UK: Clarendon Press. p. 93. ISBN 0198512562.
^ Coxeter, H. S. M. (1973). Regular Polytopes, Dover Publications, Inc., p. 119.
^ Ray d'Inverno (1992), Introducing Einstein's Relativity, Clarendon Press, chp. 22.8 Geometry of 3-spaces of constant curvature, p.319ff, ISBN 0-19-859653-7
^ a b Ambinder MS, Wang RF, Crowell JA, Francis GK, Brinkmann P. (2009). Human four-dimensional spatial intuition in virtual reality. Psychon Bull Rev. 16(5):818-23. doi:10.3758/PBR.16.5.818 PMID 19815783 online supplementary material
^ Aflalo TN, Graziano MS (2008). Four-Dimensional Spatial Reasoning in Humans. Journal of Experimental Psychology: Human Perception and Performance 34(5):1066-1077. doi:10.1037/0096-1523.34.5.1066 Preprint
^ John McIntosh's four dimensional maze game. Free software
^ Michio Kaku (1994). Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension, Part I, chapter 3, The Man Who "Saw" the Fourth Dimension (about tesseracts in years 1870–1910). ISBN 0-19-286189-1.
[edit] External links
Wikibooks has a book on the topic of
Special Relativity
"Dimensions" videos, showing several different ways to visualize four dimensional objects
Science News article summarizing the "Dimensions" videos, with clips
Garrett Jones' tetraspace page
Flatland: a Romance of Many Dimensions (second edition)
TeV scale gravity, mirror universe, and ... dinosaurs Article from Acta Physica Polonica B by Z.K. Silagadze.
Exploring Hyperspace with the Geometric Product
4D Euclidean space
4D Building Blocks - Interactive game to explore 4D space
4DNav - A small tool to view a 4D space as four 3D space uses ADSODA algorithm
MagicCube 4D A 4-dimensional analog of traditional Rubik's Cube.

Wireless Technology: Communicating the Wi-Fi WayWi-Fi wireless technology is the biggest thing to hit the Internet since the Internet was first conceived. But it can be risky if you don’t take the proper precautions.
By Gary Orlando CEO, Tech Services Short for wireless fidelity, Wi-Fi is a new global standard based on the IEEE 802.11 protocol describing rules for all manufacturers to adhere to when designing and installing their wireless equipment. Any products tested and approved as Wi-Fi Certified® by the Wi-Fi Alliance (an organization made up of leading wireless equipment and software providers) are certified as interoperable with each other, even if they are from different manufacturers. Most commercial laptops have an option for a certified Wi-Fi adapter, or else it comes as standard equipment. The connection speed is fantastic—as fast as or faster than cable modems. Hotspots make it easy to connect to the world. Using Wi-Fi technology is similar to using a cell phone, except the cells are called hotspots and you use a computer for communication instead of a phone. A hotspot is a local area that is serviced by Wi-Fi-compliant equipment, and the number of hotspots is rapidly increasing. There are currently 59,874 Wi-Fi hotspots in 96 countries around the globe. The country with the greatest number of hotspots is the United States, followed by the United Kingdom, Germany, France, and Japan. The top five Wi-Fi cities in the world are London, Tokyo, New York, Paris, and Singapore. To search and browse for Wi-Fi hotspot locations wherever you are or plan to be, you can visit JiWire’s advanced search page at http://ibs.jiwire.com/search-hotspot-locations.htm. Most hotspots are offered by companies or services where a person is already a paying customer, such as at hotels, cafes, or ISPs. There are even a lot of free hotspots available in public places and restaurants, but free access to hotspots may not last very long. As more ISP companies get on the bandwagon they will be putting together service packages with guaranteed access to certified Wi-Fi-serviced areas. On the free (non-certified) areas, there is no guarantee of service; you get what you pay for.

History of computer

“Sketch of the Analytical Engine” by L. F. Menabrea, translated and with extensive commentary by Ada Augusta, Countess of Lovelace. This 1842 document is the definitive exposition of the Analytical Engine, which described many aspects of computer architecture and programming more than a hundred years before they were “discovered” in the twentieth century. If you have ever doubted, even for a nanosecond, that Lady Ada was, indeed, the First Hacker, perusal of this document will demonstrate her primacy beyond a shadow of a doubt. (This document was revised in 2006 to improve appearance and readability and requires a modern Web browser with style sheet and Unicode support. If your browser lacks such refinements, the original 1998 edition remains available.)
“On the Analytical Engine”, Chapter VIII of Charles Babbage's 1864 autobiography, Passages from the Life of a Philosopher.
The Report of the Committee of the British Association for the Advancement of Science which, in 1878, recommended against constructing the Analytical Engine.
“The Analytical Engine”, paper by Major-General Henry P. Babbage (Charles Babbage's son), read at Bath on September 12th, 1888; published in the Proceedings of the British Association, 1888. (The 1998 edition remains available for users with older browsers.)
“Babbage's Analytical Engine”, a 1910 paper by Henry P. Babbage published in the Monthly Notices of the Royal Astronomical Society 70, 517-526, 645 [Errata] (1910), describing his construction of a portion of the Mill and Printing Apparatus, used to compute a table of multiples of Pi.
“Pascal's Calculating Machine”. After years of work, in 1645 Blaise Pascal built a gear-based mechanical adding machine. This document is Pascal's disclosure of the operation of the machine and the grant of a patent upon it in 1649 by Louis XIV, king of France. This is the original text; even if you're comfortable reading modern French, you'll probably find this seventeenth century document rather quaint.
The Analytical Engine Emulator
Programming Cards. A detailed description of the various cards used to program The Analytical Engine emulator, including a number of ready-to-run examples.
The Java Applet Emulator describes an Analytical Engine emulator which runs as a Java applet within a Web page. If your browser supports Java, you can run Analytical Engine simulations with no additional software or installation.
The Command-Line Emulator. Documentation, in Unix manual page style, of aes, a command-line emulator for The Analytical Engine which you can download in either ready-to-run object code or source code form, which runs on any computer with a compatible Java virtual machine implementation.
Is the Emulator Authentic? discusses the challenges one faces in developing an emulator for a machine which was never actually built, and the rationale behind some of the design decisions made in implementing it. Various aspects of The Analytical Engine are compared to those of both early electronic and present-day computers.
The Mathematical Function Library. Babbage immediately recognised that one great advantage of the Engine was that once a given formula was prepared for it, the cards for that formula could be placed in a library and called on whenever evaluation of it was needed in the future. This document describes a modest library of cards for evaluating the elementary transcendental functions, illustrating how the Engine might compute them.
Glossary of Babbage's Terminology
Download
These are ZIP compressed archives, some of which contain subdirectories; be sure to specify the appropriate options when extracting to preserve the directory structure. In addition, the source and object code archives contain long, upper and lower case file names. If extracted with a utility which flattens such names into MS-DOS FILENAME.EXT format, they will neither compile or execute correctly.
Source code for the mathematical function library. Includes the examples from the function library document and test programs for each function.
Object code (.class files) for the command-line emulator.
All examples of programs for The Analytical Engine emulator which appear in documents linked to this page.

More about Technology

Modern examples
There are an extraordinary number of examples how science and technology has helped us that can be seen in society today. One great example is the mobile phone. Ever since the invention of the telephone society was in need of a more portable device that they could use to talk to people. This high demand for a new product led to the invention of the mobile phone, which did, and still does, greatly influence society and the way people live their lives. Now many people are accessible to talk to whoever they want no matter where any of the two people are. All these little changes in mobile phones, like Internet access, are further examples of the cycle of co-production. Society's need for being able to call on people and be available everywhere resulted in the research and development of mobile phones. They in turn influenced the way we live our lives. As the populace relies more and more on mobile phones, additional features were requested. This is also true with today’s modern media player.
Society also determined the changes that were made to the previous generation media player that the manufactures developed. Take for example, today’s media players. At the beginning, cassettes were being used to store data. However, that method was large and cumbersome so the manufactures developed compact disks, which were smaller and could hold more data. Later, compact disks were again too large and did not hold enough data that forced today’s manufactures to create MP3 players which are small and holds large amount of data. Today’s society determined the course of events that many manufactures took to improving their products so today’s consumers will purchase their products.

[edit] Economics and technological development

Nuclear reactor, Doel, Belgium
Looking back into ancient history, economics can be said to have arrived on the scene when the occasional, spontaneous exchange of goods and services began to occur on a less occasional, less spontaneous basis. It probably did not take long for the maker of arrowheads to realize that he could probably do a lot better by concentrating on the making of arrowheads and barter for his other needs. Clearly, regardless of the goods and services bartered, some amount of technology was involved—if no more than in the making of shell and bead jewelry. Even the shaman's potions and sacred objects can be said to have involved some technology. So, from the very beginnings, technology can be said to have spurred the development of more elaborate economies.
In the modern world, superior technologies, resources, geography, and history give rise to robust economies; and in a well-functioning, robust economy, economic excess naturally flows into greater use of technology. Moreover, because technology is such an inseparable part of human society, especially in its economic aspects, funding sources for (new) technological endeavors are virtually illimitable. However, while in the beginning, technological investment involved little more than the time, efforts, and skills of one or a few men, today, such investment may involve the collective labor and skills of many millions.

[edit] Funding
Consequently, the sources of funding for large technological efforts have dramatically narrowed, since few have ready access to the collective labor of a whole society, or even a large part. It is conventional to divide up funding sources into governmental (involving whole, or nearly whole, social enterprises) and private (involving more limited, but generally more sharply focused) business or individual enterprises.

[edit] Government funding for new technology
The government is a major contributor to the development of new technology in many ways. In the United States alone, many government agencies specifically invest billions of dollars in new technology.
[In 1980, the UK government invested just over 6-million pounds in a four-year program, later extended to six years, called the Microelectronics Education Programme (MEP), which was intended to give every school in Britain at least one computer, software, training materials, and extensive teacher training. Similar programs have been instituted by governments around the world.]
Technology has frequently been driven by the military, with many modern applications being developed for the military before being adapted for civilian use. However, this has always been a two-way flow, with industry often taking the lead in developing and adopting a technology which is only later adopted by the military.
Entire government agencies are specifically dedicated to research, such as America's National Science Foundation, the United Kingdom's scientific research institutes, America's Small Business Innovative Research effort. Many other government agencies dedicate a major portion of their budget to research and development.

[edit] Private funding
Research and development is one of the biggest areas of investments made by corporations toward new and innovative technology.
Many foundations and other nonprofit organizations contribute to the development of technology. In the OECD, about two-thirds of research and development in scientific and technical fields is carried out by industry, and 20 percent and 10 percent respectively by universities and government. But in poorer countries such as Portugal and Mexico the industry contribution is significantly less. The U.S. government spends more than other countries on military research and development, although the proportion has fallen from about 30 percent in the 1980s to less than 100 percent.[1]

[edit] Other economic considerations
Appropriate technology, sometimes called "intermediate" technology, more of an economics concern, refers to compromises between central and expensive technologies of developed nations and those which developing nations find most effective to deploy given an excess of labour and scarcity of cash.
Persuasion technology: In economics, definitions or assumptions of progress or growth are often related to one or more assumptions about technology's economic influence. Challenging prevailing assumptions about technology and its usefulness has led to alternative ideas like uneconomic growth or measuring well-being. These, and economics itself, can often be described as technologies, specifically, as persuasion technology.
Technocapitalism
Technological diffusion
Technology acceptance model
Technology lifecycle
Technology transfer

[edit] Sociological factors and effects
See also: Social construction of technology

Downtown Tokyo (2005)
The use of technology has a great many effects; these may be separated into intended effects and unintended effects. Unintended effects are usually also unanticipated, and often unknown before the arrival of a new technology. Nevertheless, they are often as important as the intended effect.
[edit] Values
The implementation of technology influences the values of a society by changing expectations and realities. The implementation of technology is also influenced by values. There are (at least) three major, interrelated values that inform, and are informed by, technological innovations:
Mechanistic world view: Viewing the universe as a collection of parts, (like a machine), that can be individually analyzed and understood (McGinn 1991). This is a form of reductionism that is rare nowadays. However, the "neo-mechanistic world view" holds that nothing in the universe cannot be understood by the human intellect. Also, while all things are greater than the sum of their parts (e.g., even if we consider nothing more than the information involved in their combination), in principle, even this excess must eventually be understood by human intelligence. That is, no divine or vital principle or essence is involved.
Efficiency: A value, originally applied only to machines, but now applied to all aspects of society, so that each element is expected to attain a higher and higher percentage of its maximal possible performance, output, or ability. (McGinn 1991)
Social progress: The belief that there is such a thing as social progress, and that, in the main, it is beneficent. Before the Industrial Revolution, and the subsequent explosion of technology, almost all societies believed in a cyclical theory of social movement and, indeed, of all history and the universe. This was, obviously, based on the cyclicity of the seasons, and an agricultural economy's and society's strong ties to that cyclicity. Since much of the world is closer to their agricultural roots, they are still much more amenable to cyclicity than progress in history. This may be seen, for example, in Prabhat rainjan sarkar's modern social cycles theory. For a more westernized version of social cyclicity, see Generations: The History of America's Future, 1584 to 2069 (Paperback) by Neil Howe and William Strauss; Harper Perennial; Reprint edition (September 30, 1992); ISBN 0-688-11912-3, and subsequent books by these authors.

[edit] Ethics

Technology development.

The distinction between science, engineering and technology is not always clear. Science is the reasoned investigation or study of phenomena, aimed at discovering enduring principles among elements of the phenomenal world by employing formal techniques such as the scientific method.[8] Technologies are not usually exclusively products of science, because they have to satisfy requirements such as utility, usability and safety.
Engineering is the goal-oriented process of designing and making tools and systems to exploit natural phenomena for practical human means, often (but not always) using results and techniques from science. The development of technology may draw upon many fields of knowledge, including scientific, engineering, mathematical, linguistic, and historical knowledge, to achieve some practical result.
Technology is often a consequence of science and engineering — although technology as a human activity precedes the two fields. For example, science might study the flow of electrons in electrical conductors, by using already-existing tools and knowledge. This new-found knowledge may then be used by engineers to create new tools and machines, such as semiconductors, computers, and other forms of advanced technology. In this sense, scientists and engineers may both be considered technologists; the three fields are often considered as one for the purposes of research and reference.[9]