See biographies by A. Felix (2002), M. Mabry (2007), and E. Bumiller (2008); J. Mann, Rise of the Vulcans: The History of Bush's War Cabinet (2004); G. Kessler, The Confidante (2007).
See his autobiography Minority Report (1963); A. F. Palmieri, Elmer Rice: A Playwright's Vision of America (1980).
See his Rice (with M. Silver, 1996).
Methods of growing differ greatly in different localities, but in most Asian countries the traditional hand methods of cultivating and harvesting rice are still practiced. The fields are prepared by plowing (typically with simple plows drawn by water buffalo), fertilizing (usually with dung or sewage), and smoothing (by dragging a log over them). The seedlings are started in seedling beds and, after 30 to 50 days, are transplanted by hand to the fields, which have been flooded by rain or river water. During the growing season, irrigation is maintained by dike-controlled canals or by hand watering. The fields are allowed to drain before cutting.
Rice when it is still covered by the brown hull is known as paddy; rice fields are also called paddy fields or rice paddies. Before marketing, the rice is threshed to loosen the hulls—mainly by flailing, treading, or working in a mortar—and winnowed free of chaff by tossing it in the air above a sheet or mat.
In the United States and in many parts of Europe, rice cultivation has undergone the same mechanization at all stages of cultivation and harvesting as have other grain crops. Rice was introduced to the American colonies in the mid-17th cent. and soon became an important crop. Although U.S. production is less than that of wheat and corn, rice is grown in excess of domestic consumption and has been exported, mainly to Europe and South America. Chief growing areas of the United States are in California, Mississippi, Texas, Arkansas, and Louisiana. The world's leading rice-producing countries are China, India, Indonesia, Bangladesh, and Thailand. Total annual world production is more than half a billion metric tons.
It has been estimated that half the world's population subsists wholly or partially on rice. Ninety percent of the world crop is grown and consumed in Asia. American consumption, although increasing, is still only about 25 lb (11 kg) per person annually, as compared with 200 to 400 lb (90-181 kg) per person in parts of Asia. Rice is the only major cereal crop that is primarily consumed by humans directly as harvested, and only wheat and corn are produced in comparable quantity. Plant breeders at the International Rice Research Institute in the Philippines, attempting to keep pace with demand from a burgeoning world population, have repeatedly developed improved varieties of "miracle rice" that allow farmers to increase crop yields substantially.
Brown rice has a greater food value than white, since the outer brown coatings contain the proteins and minerals; the white endosperm is chiefly carbohydrate. As a food rice is low in fat and (compared with other cereal grains) in protein. The miracle rices have grains richer in protein than the old varieties. In the East, rice is eaten with foods and sauces made from the soybean, which supply lacking elements and prevent deficiency diseases. Elsewhere, especially in the United States, rice processing techniques have produced breakfast and snack foods for retail markets. Deficient in gluten, rice cannot be used to make bread unless its flour is mixed with flour made from other grains.
For feeding domestic animals, the bran, meal, and chopped straw are useful, especially when mixed with the polishings or given with skim milk. The polishings are also an important source of furfural and other chemurgic products. The straw, which is soft and fine, is plaited in East Asia for hats and shoes, and the hulls supply mattress filling and packing material. Laundry starch is manufactured from the broken grain, which is also used by distillers. A distilled liquor called arrack is sometimes prepared from a rice infusion, and in Japan the beverage sake is brewed from rice. Rice paper is made from a plant of the ginseng family.
Rice has been cultivated in China since ancient times and was introduced to India before the time of the Greeks. Chinese records of rice cultivation go back 4,000 years. In classical Chinese the words for agriculture and for rice culture are synonymous, indicating that rice was already the staple crop at the time the language was taking form. In several Asian languages the words for rice and food are identical. Many ceremonies have arisen in connection with planting and harvesting rice, and the grain and the plant are traditional motifs in Oriental art. Thousands of rice strains are now known, both cultivated and escaped, and the original form is unknown.
Rice cultivation has been carried into all regions having the necessary warmth and abundant moisture favorable to its growth, mainly subtropical rather than hot or cold. The crop was common in West Africa by the end of the 17th cent. It is thought that slaves from that area who were transported to the Carolinas in the mid-18th cent. introduced the complex agricultural technology, thus playing a key part in the establishment of American rice cultivation. Their labor then insured a flourishing rice industry. Modern culture makes use of irrigation, and a few varieties of rice may be grown with only a moderate supply of water.
Rice is classified in the division Magnoliophyta, class Liliopsida, order Cyperales, family Gramineae.
See Food and Agricultural Organization, Rice (annual); D. H. Grist, Rice (6th ed. 1986); J. A. Carney, Black Rice: The African Origins of Rice Cultivation in the Americas (2001).
It is important to note that Rice's theorem does not say anything about those properties of machines or programs which are not also properties of functions and languages. For example, whether a machine runs for more than 100 steps on some input is a decidable property, even when it is non-trivial. Implementing exactly the same language, two different machines might require a different number of steps to recognize the same input. Where a property is of the kind that two machines may or may not have it, while still implementing exactly the same language, the property is of the machines and not of the language, and Rice's Theorem does not apply.
Similarly, whether a machine has more than 5 states is a decidable property. On the other hand, the statement that "No modern general-purpose computer can solve the general problem of determining whether a program is virus free" is a consequence of Rice's Theorem because, while a statement about computers, it can be reduced to a statement about languages.
Using Rogers' characterization of acceptable programming systems, this result may essentially be generalized to most computer programming languages: there exists no automatic method that decides with generality non-trivial questions on the black-box behavior of computer programs. This is one explanation of the difficulty of debugging.
As an example, consider the following variant of the halting problem: Take the property a partial function F has if F is defined for argument 1. It is obviously non-trivial, since there are partial functions that are defined for 1 and others that are undefined at 1. The 1-halting problem is the problem of deciding of any algorithm whether it defines a function with this property, i.e., whether the algorithm halts on input 1. By Rice's theorem, the 1-halting problem is undecidable.
We identify each property that a computable function may have with the subset of consisting of the functions with that property. Thus given a set , a computable function has property F if and only if . For each property there is an associated decision problem of determining, given e , whether .
Rice's theorem states that the decision problem is decidable if and only if or .
The claim is that we can convert our algorithm for identifying squaring programs into one which identifies functions that halt. We will describe an algorithm which takes inputs a and i and determines whether program a halts when given input i.
The algorithm is simple: we construct a new program t which (1) temporarily ignores its input while it tries to execute program a on input i, and then, if that halts, (2) returns the square of its input. Clearly, t is a function for computing squares if and only if step (1) halts. Since we've assumed that we can infallibly identify program for computing squares, we can determine whether t is such a program, and therefore whether program a halts on input i. Note that we needn't actually execute t; we need only decide whether it is a squaring program, and, by hypothesis, we know how to do this.
This method doesn't depend specifically on being able to recognize functions that compute squares; as long as some program can do what we're trying to recognize, we can add a call to a to obtain our t. We could have had a method for recognizing programs for computing square roots, or programs for computing the monthly payroll, or programs that halt when given the input "Abraxas", or programs that commit array bounds errors; in each case, we would be able to solve the halting problem similarly.
Let us now assume that P(a) is an algorithm that decides some non-trivial property of Fa. Without loss of generality we may assume that P(no-halt) = "no", with no-halt being the representation of an algorithm that never halts. If this is not true, then this will hold for the negation of the property. Since P decides a non-trivial property, it follows that there is a string b that represents an algorithm and P(b) = "yes". We can then define an algorithm H(a, i) as follows:
We can now show that H decides the halting problem:
Since the halting problem is known to be undecidable, this is a contradiction and the assumption that there is an algorithm P(a) that decides a non-trivial property for the function represented by a must be false.