Also called birefringence, (double refraction is) an optical property in which a single ray of unpolarized light entering an anisotropic medium is split into two rays, each traveling in a different direction. One ray (called the extraordinary ray) is bent, or refracted, at an angle as it travels through the medium; the other ray (called the ordinary ray) passes through the medium unchanged.

Double refraction can be observed by comparing two materials, glass and calcite. If a pencil mark is drawn upon a sheet of paper and then covered with a piece of glass, only one image will be seen; but if the same paper is covered with a piece of calcite, and the crystal is oriented in a specific direction, then two marks will become visible.

The (above) Figure shows the phenomenon of double refraction through a calcite crystal. An incident ray is seen to split into the ordinary ray CO and the extraordinary ray CE upon entering the crystal face at C. If the incident ray enters the crystal along the direction of its optic axis, however, the light ray will not become divided.

In double refraction, the ordinary ray and the extraordinary ray are polarized in planes vibrating at right angles to each other. Furthermore, the refractive index (a number that determines the angle of bending specific for each medium) of the ordinary ray is observed to be constant in all directions; the refractive index of the extraordinary ray varies according to the direction taken because it has components that are both parallel and perpendicular to the crystal's optic axis. Because the speed of light waves in a medium is equal to their speed in a vacuum divided by the index of refraction for that wavelength, an extraordinary ray can move either faster or slower than an ordinary ray.

All transparent crystals except those of the cubic system, which are normally optically isotropic, exhibit the phenomenon of double refraction: in addition to calcite, some well-known examples are ice, mica, quartz, sugar, and tourmaline. Other materials may become birefringent under special circumstances. For example, solutions containing long-chain molecules exhibit double refraction when they flow; this phenomenon is called streaming birefringence. Plastic materials built up from long-chain polymer molecules may also become doubly refractive when compressed or stretched; this process is known as photoelasticity. Some isotropic materials (e.g., glass) may even exhibit birefringence when placed in a magnetic or electric field or when subjected to external stress.

Conjugating verbs

In one famous connectionist experiment conducted at the University of California at San Diego (published in 1986), David Rumelhart and James McClelland trained a network of 920 artificial neurons, arranged in two layers of 460 neurons, to form the past tenses of English verbs. Root forms of verbs—such as come, look, and sleep—were presented to one layer of neurons, the input layer. A supervisory computer program observed the difference between the actual response at the layer of output neurons and the desired response—came, say—and then mechanically adjusted the connections throughout the network in accordance with the procedure described above to give the network a slight push in the direction of the correct response. About 400 different verbs were presented one by one to the network, and the connections were adjusted after each presentation. This whole procedure was repeated about 200 times using the same verbs, after which the network could correctly form the past tense of many unfamiliar verbs as well as of the original verbs. For example, when presented for the first time with guard, the network responded guarded; with weep, wept; with cling, clung; and with drip, dripped (complete with double p). This is a striking example of learning involving generalization. (Sometimes, though, the peculiarities of English were too much for the network, and it formed squawked from squat, shipped from shape, and membled from mail.)

Another name for connectionism is parallel distributed processing, which emphasizes two important features. First, a large number of relatively simple processors—the neurons—operate in parallel. Second, neural networks store information in a distributed fashion, with each individual connection participating in the storage of many different items of information. The know-how that enabled the past-tense network to form wept from weep, for example, was not stored in one specific location in the network but was spread throughout the entire pattern of connection weights that was forged during training. The human brain also appears to store information in a distributed fashion, and connectionist research is contributing to attempts to understand how it does so.

The approach now known as nouvelle AI was pioneered at the MIT AI Laboratory by the Australian Rodney Brooks during the latter half of the 1980s. Nouvelle AI distances itself from strong AI, with its emphasis on human-level performance, in favour of the relatively modest aim of insect-level performance. At a very fundamental level, nouvelle AI rejects symbolic AI's reliance upon constructing internal models of reality... Practitioners of nouvelle AI assert that true intelligence involves the ability to function in a real-world environment.

A central idea of nouvelle AI is that intelligence, as expressed by complex behaviour, “emerges” from the interaction of a few simple behaviours. For example, a robot whose simple behaviours include collision avoidance and motion toward a moving object will appear to stalk the object, pausing whenever it gets too close.

Nouvelle systems do not contain a complicated symbolic model of their environment. Instead, information is left “out in the world” until such time as the system needs it. A nouvelle system refers continuously to its sensors rather than to an internal model of the world: it “reads off” the external world whatever information it needs at precisely the time it needs it. (As Brooks insisted, the world is its own best model—always exactly up-to-date and complete in every detail.)

Impulse response

An optical system that employs incoherent illumination of the object can usually be regarded as a linear system in intensity. A system is linear if the addition of inputs produces an addition of corresponding outputs. For ease of analysis, systems are often considered stationary (or invariant). This property implies that if the location of the input is changed, then the only effect is to change the location of the output but not its actual distribution. With these concepts it is then only necessary to find an expression for the image of a point input to develop a theory of image formation. The intensity distribution in the image of a point object can be determined by solving the equation relating to the diffraction of light as it propagates from the point object to the lens, through the lens, and then finally to the image plane. The result of this process is that the image intensity is the intensity in the Fraunhofer diffraction pattern of the lens aperture function (that is, the square of the Fourier transform of the lens aperture function; a Fourier transform is an integral equation involving periodic components). This intensity distribution is the intensity impulse response (sometimes called point spread function) of the optical system and fully characterizes that optical system.

With the knowledge of the impulse response, the image of a known object intensity distribution can be calculated. If the object consists of two points, then in the image plane the intensity impulse response function must be located at the image points and then a sum of these intensity distributions made. The sum is the final image intensity. If the two points are closer together than the half width of the impulse response, they will not be resolved. For an object consisting of an array of isolated points, a similar procedure is followed—each impulse response is, of course, multiplied by a constant equal to the value of the intensity of the appropriate point object. Normally, an object will consist of a continuous distribution of intensity, and, instead of a simple sum, a convolution integral results.

Many of the cultures employing cuneiform (Hurrian, Hittite, Urartian) disappeared one by one, and their written records fell into oblivion. The same fate overtook cuneiform generally with astonishing swiftness and completeness. One of the reasons was the victorious progress of the Phoenician script in the western sections of the Middle East and the Classical lands in Mediterranean Europe. To this writing system of superior efficiency and economy, cuneiform could not offer serious competition. Its international prestige of the 2nd millennium had been exhausted by 500 BCE, and Mesopotamia had become a Persian dependency. Late Babylonian and Assyrian were little but moribund artificial literary idioms. So complete was the disappearance of cuneiform that the Classical Greeks were practically unaware of its existence, except for the widely traveled Herodotus, who in passing mentions Assyria Grammata (“Assyrian characters”).

The rediscovery of the materials and the reconquest of the recondite scripts and languages have been the achievements of modern times. Paradoxically the process began with the last secondary offshoot of cuneiform proper, the inscriptions of the Achaemenid kings (6th to 4th centuries BCE) of Persia. This is understandable, because almost only among the Persians was cuneiform used primarily for monumental writing, and the remains (such as rock carvings) were in many cases readily accessible. Scattered examples of Old Persian inscriptions were reported back to Europe by western travelers in Persia since the 17th century, and the name cuneiform was first applied to the script by Engelbert Kämpfer (c. 1700). During the 18th century many new inscriptions were reported; especially important were those copied by Carsten Niebuhr at the old capital Persepolis. It was recognized that the typical royal inscriptions contained three different scripts, a simple type with about 40 different signs and two others with considerably greater variations. The first was likely to reflect an alphabet, while the others seemed to be syllabaries or word writings. Assuming identical contents in three different languages, scholars argued on historical grounds that those trilingual inscriptions belonged to the Achaemenid kings and that the first writing represented the Old Persian language, which would be closely related to Avestan and Sanskrit. The recognition of a diagonal wedge as word-divider simplified the segmentation of the written sequences. The German scholar Georg Friedrich Grotefend in 1802 reasoned that the introductory lines of the text were likely to contain the name, titles, and genealogy of the ruler, the pattern for which was known from later Middle Iranian inscriptions in an adapted Aramaic (i.e., ultimately Phoenician) alphabet. From such beginnings, he was eventually able to read several long proper names and to determine a number of sound values. The initial results of Grotefend were expanded and refined by other scholars.

Next the second script of the trilinguals was attacked. It contained more than 100 different signs and was thus likely to be a syllabary. Mainly by applying the sound values of the Old Persian proper names to appropriate correspondences, a number of signs were gradually determined and some insight gained into the language itself, which is New Elamite; the study of it has been rather stagnant, and considerable obscurity persists. The same holds true for the Old Elamite of the late 2nd millennium.

The third script of the Achaemenian trilinguals had in the meantime been identified with that of the texts found in very large numbers in Mesopotamia, which obviously contained the central language of cuneiform culture, namely Akkadian. Here also the proper names provided the first concrete clues for a decipherment, but the extreme variety of signs and the peculiar complications of the system raised difficulties which for a time seemed insurmountable. The serious external divergencies between older and newer types of Akkadian cuneiform, the distribution of ideographic and syllabic uses of the signs, the simple (ba, ab) and complex (bat) values of the syllables, and especially the bewildering polyphony of many notations were only gradually surmised by scholars. Once the Semitic character of the language had been established, the philological science of Assyriology developed rapidly from the closing decades of the 19th century onward, especially because of scholars like Friedrich Delitzsch and, later, Benno Landsberger and Wolfram von Soden.

Once Akkadian had been deciphered, the very core of the system was intelligible, and the prototype was provided for the interpretation of other languages in cuneiform. Until the 20th century Sumerian was not definitely recognized as a separate language at all but rather as a special way of noting Akkadian. Even when its independent character was established, the difficulties of interpretation were appalling because of its strange and unrelated structure. After Sumerian finally died out as a living language toward the middle of the 2nd millennium, it lingered on as a cult idiom of Babylonian religion. To facilitate its artificial acquisition by the priesthood, grammatical lists and vocabularies were compiled and numerous religious texts were provided with literal translations into Babylonian. These have facilitated the penetration of unilingual Sumerian texts, and Sumerian studies advanced greatly through the efforts of such scholars as Delitzsch, François Thureau-Dangin, Arno Poebel, Anton Deimel, and Adam Falkenstein.

Form of computing in which DNA molecules are used instead of digital logic circuits. The biological cell is regarded as an entity that resembles a sophisticated computer. The four amino acid bases that are constituents of DNA, traditionally represented by the letters A, T, C, and G, are used as operators, as the binary digits 0 and 1 are used in computers. DNA molecules are encoded to a researcher's specifications and then induced to recombine (see recombination), resulting in trillions of “calculations” simultaneously. The field is in its infancy and its implications are only beginning to be explored.