"You are Israel's teacher," said Jesus, "and do you not understand these things? I tell you the truth, we speak of what we know, and we testify to what we have seen, but still you people do not accept our testimony. I have spoken to you of earthly things and you do not believe; how then will you believe if I speak of heavenly things? No one has ever gone into heaven except the one who came from heaven—the Son of Man. Just as Moses lifted up the snake in the desert, so the Son of Man must be lifted up, that everyone who believes in him may have eternal life. "For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life. For God did not send his Son into the world to condemn the world, but to save the world through him. Whoever believes in him is not condemned, but whoever does not believe stands condemned already because he has not believed in the name of God's one and only Son. This is the verdict: Light has come into the world, but men loved darkness instead of light because their deeds were evil. Everyone who does evil hates the light, and will not come into the light for fear that his deeds will be exposed. But whoever lives by the truth comes into the light, so that it may be seen plainly that what he has done has been done through God."

Sometime around 6000 BCE a nomadic herding people settled into villages in the Mountainous region just west of the Indus River. There they grew barley and wheat using sickles with flint blades, and they lived in small houses built with adobe bricks. After 5000 BCE the climate in their region changed, bringing more rainfall, and apparently they were able to grow more food, for they grew in population. They began domesticating sheep, goats and cows and then water buffalo. Then after 4000 BCE they began to trade beads and shells with distant areas in central Asia and areas west of the Khyber Pass. And they began using bronze and working metals.

The climate changed again, bringing still more rainfall, and on the nearby plains, through which ran the Indus River, grew jungles inhabited by crocodiles, rhinoceros, tigers, buffalo and elephants. By around 2600 BCE, a civilization as grand as that in Mesopotamia and Egypt had begun on the Indus Plain and surrounding areas. By 2300 BCE this civilization had reached maturity and was trading with Mesopotamia. Seventy or more cities had been built, some of them upon buried old towns. There were cities from the foothills of the Himalayan Mountains to Malwan in the south. There was the city of Alamgirpur in the east and Sutkagen Dor by the Arabian Sea in the west.

One of these cities was Mohenjo-daro (Mohenjodaro), on the Indus river some 250 miles north of the Arabian Sea, and another city was Harappa, 350 miles to the north on a tributary river, the Ravi. Each of these two cities had populations as high as around 40,000. Each was constructed with manufactured, standardized, baked bricks. Shops lined the main streets of Mohenjo-daro and Harappa, and each city had a grand marketplace. Some houses were spacious and with a large enclosed yard. Each house was connected to a covered drainage system that was more sanitary than what had been created in West Asia. And Mohenjo-daro had a building with an underground furnace (a hypocaust) and dressing rooms, suggesting bathing was done in heated pools, as in modern day Hindu temples.

The people of Mohenjo-daro and Harappa shared a sophisticated system of weights and measures, using an arithmetic with decimals. Whether these written symbols were a part of a full-blown written language is a matter of controversy among scholars, some scholars pointing out that this and the brevity of grave site inscriptions and symbols on ritual objects are not evidence of a fully developed written language.

The people of Mohenjo-daro and Harappa mass-produced pottery with fine geometric designs as decoration, and they made figurines sensitively depicting their attitudes. They grew wheat, rice, mustard and sesame seeds, dates and cotton. And they had dogs, cats, camels, sheep, pigs, goats, water buffaloes, elephants and chickens.

Tyrannosaurus rex was one of the largest land carnivores of all time; the largest complete specimen, FMNH PR2081 ("Sue"), measured 12.8 metres (42 ft) long, and was 4.0 metres (13 ft) tall at the hips. Mass estimates have varied widely over the years, from more than 7.2 metric tons (7.9 short tons), to less than 4.5 metric tons (5.0 short tons), with most modern estimates ranging between 5.4 and 6.8 metric tons (6.0 and 7.5 short tons). Although Tyrannosaurus rex was larger than the well known Jurassic theropod Allosaurus, it was slightly smaller than Cretaceous carnivores Spinosaurus and Giganotosaurus.

The neck of T. rex formed a natural S-shaped curve like that of other theropods, but was short and muscular to support the massive head. The forelimbs had only two clawed fingers, along with an additional small metacarpal representing the remnant of a third digit. In contrast the hind limbs were among the longest in proportion to body size of any theropod. The tail was heavy and long, sometimes containing over forty vertebrae, in order to balance the massive head and torso. To compensate for the immense bulk of the animal, many bones throughout the skeleton were hollow, reducing its weight without significant loss of strength.

The largest known T. rex skulls measure up to 5 feet (1.5 m) in length. Large fenestrae (openings) in the skull reduced weight and provided areas for muscle attachment, as in all carnivorous theropods. But in other respects Tyrannosaurus’ skull was significantly different from those of large non-tyrannosauroid theropods. It was extremely wide at the rear but had a narrow snout, allowing unusually good binocular vision. The skull bones were massive and the nasals and some other bones were fused, preventing movement between them; but many were pneumatized (contained a "honeycomb" of tiny air spaces) which may have made the bones more flexible as well as lighter. These and other skull-strengthening features are part of the tyrannosaurid trend towards an increasingly powerful bite, which easily surpassed that of all non-tyrannosaurids.The tip of the upper jaw was U-shaped (most non-tyrannosauroid carnivores had V-shaped upper jaws), which increased the amount of tissue and bone a tyrannosaur could rip out with one bite, although it also increased the stresses on the front teeth.

The teeth of T. rex displayed marked heterodonty (differences in shape). The premaxillary teeth at the front of the upper jaw were closely packed, D-shaped in cross-section, had reinforcing ridges on the rear surface, were incisiform (their tips were chisel-like blades) and curved backwards. The D-shaped cross-section, reinforcing ridges and backwards curve reduced the risk that the teeth would snap when Tyrannosaurus bit and pulled. The remaining teeth were robust, like "lethal bananas" rather than daggers; more widely spaced and also had reinforcing ridges.Those in the upper jaw were larger than those in all but the rear of the lower jaw. The largest found so far is estimated to have been 30 centimetres (12 in) long including the root when the animal was alive, making it the largest tooth of any carnivorous dinosaur.

If I speak in the tongues of men and of angels, but have not love, I am only a resounding gong or a clanging cymbal. If I have the gift of prophecy and can fathom all mysteries and all knowledge, and if I have a faith that can move mountains, but have not love, I am nothing. If I give all I possess to the poor and surrender my body to the flames, but have not love, I gain nothing. Love is patient, love is kind. It does not envy, it does not boast, it is not proud. It is not rude, it is not self-seeking, it is not easily angered, it keeps no record of wrongs. Love does not delight in evil but rejoices with the truth. It always protects, always trusts, always hopes, always perseveres. Love never fails. But where there are prophecies, they will cease; where there are tongues, they will be stilled; where there is knowledge, it will pass away. For we know in part and we prophesy in part, but when perfection comes, the imperfect disappears. When I was a child, I talked like a child, I thought like a child, I reasoned like a child. When I became a man, I put childish ways behind me. Now we see but a poor reflection as in a mirror; then we shall see face to face. Now I know in part; then I shall know fully, even as I am fully known. And now these three remain: faith, hope and love. But the greatest of these is love.

Builders of computer systems often need information about floating-point arithmetic. There are, however, remarkably few sources of detailed information about it. One of the few books on the subject, Floating-Point Computation by Pat Sterbenz, is long out of print. This paper is a tutorial on those aspects of floating-point arithmetic (floating-point hereafter) that have a direct connection to systems building. It consists of three loosely connected parts. The first Section, "Rounding Error," on page 173, discusses the implications of using different rounding strategies for the basic operations of addition, subtraction, multiplication and division. It also contains background information on the two methods of measuring rounding error, ulps and relative error. The second part discuses the IEEE floating-point standard, which is becoming rapidly accepted by commercial hardware manufacturers. Included in the IEEE standard is the rounding method for basic operations. The discussion of the standard draws on the material in the Section , "Rounding Error," on page 173. The third part discusses the onnections between floating-point and the design of various aspects of computer systems. Topics include instruction set design, optimizing compilers and exception handling.

I have tried to avoid making statements about floating-point without also giving reasons why the statements are true, especially since the justifications involve nothing more complicated than elementary calculus. Those explanations that are not central to the main argument have been grouped into a section called "The Details," so that they can be skipped if desired. In particular, the proofs of many of the theorems appear in this section. The end of each proof is marked with the * symbol; when a proof is not included, the * appears immediately following the statement of the theorem.

Squeezing infinitely many real numbers into a finite number of bits requires an approximate representation. Although there are infinitely many integers, in most programs the result of integer computations can be stored in 32 bits. In contrast, given any fixed number of bits, most calculations with real numbers will produce quantities that cannot be exactly represented using that many bits. Therefore the result of a floating-point calculation must often be rounded in order to fit back into its finite representation. This rounding error is the characteristic feature of floating-point computation. "Relative Error and Ulps" on page 176 describes how it is measured.

Since most floating-point calculations have rounding error anyway, does it matter if the basic arithmetic operations introduce a little bit more rounding error than necessary? That question is a main theme throughout this section. "Guard Digits" on page 178 discusses guard digits, a means of reducing the error when subtracting two nearby numbers. Guard digits were considered sufficiently important by IBM that in 1968 it added a guard digit to the double precision format in the System/360 architecture (single precision already had a guard digit), and retrofitted all existing machines in the field. Two examples are given to illustrate the utility of guard digits.

The IEEE standard goes further than just requiring the use of a guard digit. It gives an algorithm for addition, subtraction, multiplication, division and square root, and requires that implementations produce the same result as that algorithm. Thus, when a program is moved from one machine to another, the results of the basic operations will be the same in every bit if both machines support the IEEE standard. This greatly simplifies the porting of programs. Other uses of this precise specification are given in "Exactly Rounded Operations" on page 185.