Sami5001's Journals

The Book of Mozilla

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"about:mozilla" redirects here. For other uses of "about:", see about: URI scheme.

The Book of Mozilla is a well-known computer Easter egg found in the Netscape and Mozilla series of web browsers. The Easter Egg is viewed by having the browser go to the page about:mozilla.

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About The Book of Mozilla

There is no real book entitled The Book of Mozilla. However, apparent quotations hidden in Netscape and Mozilla give this impression by revealing passages similar to the Book of Revelation of the Bible. When about:mozilla is typed into the location bar, various versions of these browsers display a cryptic message in white text on a maroon background in the browser window.

There are three official verses of The Book of Mozilla (official in the sense that they have been included in shipping releases), though various unofficial verses can be found on the World Wide Web. All three official verses have biblical-looking chapter and verse references, though these are actually references to important dates in the history of Netscape and Mozilla.

The three verses all refer to the activities of a fearsome-sounding "beast". In its early days, Netscape Communications Corporation had a green fire-breathing dragon-like lizard mascot, known as Mozilla (after the code name for Netscape Navigator 1.0). From this, it can be conjectured that the "beast" referred to in The Book of Mozilla is a type of fire-breathing lizard, which can be viewed as a metaphor for, or personification of Netscape.

While part of the appeal of The Book of Mozilla comes from the mysterious nature, a knowledge of the history of Netscape and Mozilla can be used to apply some meaning to the verses. Furthermore, the page www.mozilla.org/book has annotations for each of the three verses hidden as comments in its HTML source code. These comments were written by Valerio Capello in May 2004 and were added to the Mozilla Foundation site by Nicholas Bebout in October that year. Neither Capello nor Bebout are 'core' Mozilla decision-makers; and there is no evidence that Capello's interpretations received any high-level approval from the senior management of the Mozilla Foundation.

In some versions of Microsoft Internet Explorer, about:mozilla produces a blank blue page, which some have conjectured refers to the blue screen of death.

Before Netscape 1.1, about:mozilla produced the text "Mozilla rules!".

Apparently there are also translations into several other languages (including swedish).

The Book of Mozilla, 12:10

The Book of Mozilla first appeared in Netscape 1.1 (released in 1995) and can be found in every subsequent 1.x, 2.x, 3.x and 4.x version. The following prophecy was displayed:

And the beast shall come forth surrounded by a roiling cloud of vengeance. The house of the unbelievers shall be razed and they shall be scorched to the earth. Their tags shall blink until the end of days.

from The Book of Mozilla, 12:10

The chapter and verse number 12:10 refers to December 10, 1994, the date that Netscape Navigator 1.0 was released.

Screenshot of The Book of Mozilla, 12:10 in Netscape Navigator 1.1

The page www.mozilla.org/book, which includes all three verses from The Book of Mozilla, contains the following explanation in its HTML source code:

The "beast" is a metaphor for Netscape. The punishments threatened towards the "unbelievers" (most likely non-Netscape users) are traditionally biblical but with the strange threat that their "tags shall blink until the end of days". This probably refers to the fact that invalid tags blinked in Netscape's internal HTML source code viewer (seeing tags blinking in this way would therefore be undesirable), though it could also be a reference to the controversial <blink> HTML element introduced by Netscape.

Viewing the about:mozilla page with a Unix version of Netscape would change the throbber to an animation of Mozilla rising up from behind the "planet" logo and breathing fire. (Images viewable here)

The Book of Mozilla, 3:31

On May 10, 1998, Jamie "JWZ" Zawinski changed The Book of Mozilla verse to reference the fact that Netscape had released its code as open source and started the Mozilla project. This verse was included in all Mozilla builds until October 1998, when a rewrite of much of the Mozilla code meant that the Easter egg was lost. On February 5, 2000, Ben Goodger, then working for Netscape, copied The Book of Mozilla verse across to the new code base. It was included in all subsequent Mozilla builds (until the introduction of the 7:15 verse) and Netscape versions 6 to 7.1.

The verse states:

And the beast shall be made legion. Its numbers shall be increased a thousand thousand fold. The din of a million keyboards like unto a great storm shall cover the earth, and the followers of Mammon shall tremble.

from The Book of Mozilla, 3:31
(Red Letter Edition)

The chapter and verse number 3:31 refers to March 31, 1998, when Netscape released its source code.

Screenshot of The Book of Mozilla, 3:31 (Red Letter Edition) in Netscape 6

The www.mozilla.org/book page has the following comment in its HTML source about this passage:

Again, the "beast" is Netscape. The text probably refers to Netscape's hope that, by opening its source, they could attract a "legion" of developers all across the world, who would help improve the software (with the "din of a million keyboards"). Some suggest that "Mammon" refers to Microsoft, whose Internet Explorer browser was Netscape's chief competition. The word "mammon," in various semitic languages, is related to money and riches; it appears in English translations of the Bible, and is sometimes used as the name of a demon of avarice. It may therefore imply not only that Microsoft has vastly greater funds to draw on, but that it has greedily abused that fact to further its own position in the marketplace; it also highlights the difference between the purely commercial development of Internet Explorer, and the new community-driven development of Netscape/Mozilla. "Red Letter Edition" may be a reference to so-called Red Letter Editions of the Bible, which print quotations by Jesus in red ink. It could also be a reference to a fact that March 31, 1998 was a red-letter day for the Mozilla project.

The Book of Mozilla, 7:15

The next installment of The Book of Mozilla was written by Neil Deakin. It is included in all versions of Mozilla released since September 2003 (Mozilla 1.5 and above), all versions of Firefox, Camino and the Mozilla Thunderbird email client, the Epiphany web browser (version 1.8.0), and all Netscape versions from 7.2 onwards (except some Netscape Browser prototype releases):

And so at last the beast fell and the unbelievers rejoiced. But all was not lost, for from the ash rose a great bird. The bird gazed down upon the unbelievers and cast fire and thunder upon them. For the beast had been reborn with its strength renewed, and the followers of Mammon cowered in horror.

from The Book of Mozilla, 7:15

The 7:15 chapter and verse notation refers to July 15, 2003, the day when America Online shut down its Netscape browser division and the Mozilla Foundation was launched.

Screenshot of The Book of Mozilla, 7:15 in Mozilla Firefox 1.0

In the HTML source of www.mozilla.org/book, this verse is accompanied by the following annotation:

The "beast" falling refers to Netscape being closed down by its now parent company AOL. The "great bird" that rises from the ash is probably the Mozilla Foundation, which was established to continue Mozilla development. The bird rises from the ash like a Phoenix â�” a reference to the original name of the Mozilla Firefox browser (known as Firebird at the time this verse was written). The bird casts down "fire" and "thunder" on the "unbelievers", which is a direct reference to the Mozilla Firebird (now Firefox) and Mozilla Thunderbird products, which became the main focus of Mozilla development a few months before the events of July 15. The fact that the beast has been "reborn" indicates that the spirit of Netscape will live on through the Foundation (which is made up mostly of ex-Netscape employees) and its strength has been "renewed" as the foundation is less reliant on AOL (who many feel neglected Netscape). Again, the "Mammon" is probably Microsoft, Mozilla's main commercial competitor.

External links

The Book of Mozilla, 12:10
The Book of Mozilla, 3:31
The Book of Mozilla, 7:15
Book of Mozilla, a portal for former Netscape employees

Changes to about:mozilla page

Book of Mozilla on Mozilla.org

The Book of Mozilla (includes annotations in HTML source)
- Bug 217203 â�” Book of Mozilla not on mozilla.org (bug report that led to the creation of www.mozilla.org/book/)
- CVS history for www.mozilla.org/book/index.xml (later replaced by index.html)
- CVS history for www.mozilla.org/book/index.html (replaced index.xml)

Articles about The Book of Mozilla

MozillaZine article announcing the new verse of The Book of Mozilla
Results of a MozillaZine poll on the readers' favourite verse
Some clarifications regarding about:mozilla written by mozilla.org staff member Gervase Markham

Collections of passages

Extracts from The Book of Mozilla â�” a compilation of official and unofficial passages from The Book of Mozilla

Retrieved from "http://en.wikipedia.org/wiki/The_Book_of_Mozilla"

Categories: Mozilla | Netscape | Computer humor | In-jokes

The Meaning of Dreams

From the pharaohs of ancient Egypt to the 20th century Austrian psychoanalyst Sigmund Freud, human beings have tried to decipher the meaning of dreams. In the early 1980s two prominent scientists proposed that dreams are essentially meaningless and represent the brainâ�™s method of forgetting useless information. In a 1997 Scientific American article, however, researcher Jonathan Winson suggests that dreams may play a key part in the development of memories and in the formation of survival strategies.

The Meaning of Dreams

Dreams may reflect a fundamental aspect of mammalian memory processing. Crucial information acquired during the waking state may be reprocessed during sleep

By Jonathan Winson

Throughout history human beings have sought to understand the meaning of dreams. The ancient Egyptians believed dreams possessed oracular powerâ�”in the Bible, for example, Joseph's elucidation of Pharaoh's dream averted seven years of famine. Other cultures have interpreted dreams as inspirational, curative or alternative reality. During the past century, scientists have offered conflicting psychological and neuroscientific explanations for dreams. In 1900, with the publication of The Interpretation of Dreams, Sigmund Freud proposed that dreams were the "royal road" to the unconscious; that they revealed in disguised form the deepest elements of an individual's inner life.

More recently, in contrast, dreams have been characterized as meaningless, the result of random nerve cell activity. Dreaming has also been viewed as the means by which the brain rids itself of unnecessary informationâ�”a process of "reverse learning," or unlearning.

Based on recent findings in my own and other neuroscientific laboratories, I propose that dreams are indeed meaningful. Studies of the hippocampus (a brain structure crucial to memory), of rapid eye movement (REM) sleep and of a brain wave called theta rhythm suggest that dreaming reflects a pivotal aspect of the processing of memory. In particular, studies of theta rhythm in subprimate animals have provided an evolutionary clue to the meaning of dreams. They appear to be the nightly record of a basic mammalian memory process: the means by which animals form strategies for survival and evaluate current experience in light of those strategies. The existence of this process may explain the meaning of dreams in human beings.

Stages of Sleep and Dreaming

The physiology of dreaming was first understood in 1953, when researchers characterized the human sleep cycle. They found that sleep in humans is initiated by the hypnogogic state, a period of several minutes when thoughts consist of fragmented images or minidramas. The hypnogogic state is followed by slow-wave sleep, so called because at that time the brain waves of the neocortex (the convoluted outer mantle of the brain) are low in frequency and large in amplitude. These signals are measured as electroencephalographic (EEG) recordings.

Researchers also discovered that a night's sleep is punctuated by periods in which the EEG readings are irregular in frequency and low in amplitudeâ�”similar to those observed in awake individuals. These periods of mental activity are called REM sleep. Dreaming takes place solely during these periods. While in REM sleep, motor neurons are inhibited, preventing the body from moving freely but allowing extremities to remain slightly active. Eyes move rapidly in unison under closed lids, breathing becomes irregular and heart rate increases.

The first REM stage of the night follows 90 minutes of slow-wave sleep and lasts for 10 minutes. The second and third REM periods follow shorter slow-wave sleep episodes but grow progressively longer themselves. The fourth and final REM interval lasts 20 to 30 minutes and is followed by awakening. If a dream is remembered at all, it is most often the one that occurred in this last phase of REM sleep.

This sleep cycleâ�”alternating slow-wave and REM sleepâ�”appears to be present in all placental and marsupial mammals. Mammals exhibit the various REM-associated characteristics observed in humans, including EEG readings similar to those of the awake state. Animals also dream. By destroying neurons in the brain stem that inhibit movement during sleep, researchers found that sleeping cats rose up and attacked or were startled by invisible objectsâ�”ostensibly images from dreams.

By studying subprimate animals, scientists have discovered additional neurophysiological aspects of REM sleep. They determined that neural control of this stage of the sleep cycle is centered in the brain stem (the brain region closest to the spinal cord) and that during REM sleep neural signalsâ�”called pontine-geniculate-occipital (PGO) cortex spikesâ�”proceed from the brain stem to the center of visual processing, the visual cortex. Brain stem neurons also initiate a sinusoidal wave (one resembling a sine curve) in the hippocampus. This brain signal is called theta rhythm.

At least one animal experiences slow-wave but not REM sleepâ�”and, consequently, does not exhibit theta rhythm when asleep. This animal is the echidna, or spiny anteater, an egg-laying mammal (called a monotreme) that provides some insight into the origin of dreaming. The absence of REM sleep in the echidna suggests that this stage of the sleep cycle evolved some 140 million years ago, when marsupials and placentals diverged from the monotreme line. (Monotremes were the first mammals to develop from reptiles.)

By all evolutionary criteria, the perpetuation of a complex brain process such as REM sleep indicates that it serves an important function for the survival of mammalian species. Understanding that function might reveal the meaning of dreams.

When Freud wrote The Interpretation of Dreams, the physiology of sleep was unknown. In light of the discovery of REM sleep, certain elements of his psychoanalytic theory were modified, and the stage was set for more neurologically based theories. Dreaming came to be understood as part of a biologically determined sleep cycle. Yet the central concept of Freud's theoryâ�”namely, the belief that dreams reveal a censored representation of our innermost unconscious feelings and concernsâ�”continues to be used in psychoanalysis.

Some theorists abandoned Freud altogether following the neurological discoveries. In 1977 J. Allan Hobson and Robert McCarley of Harvard Medical School proposed the "activation-synthesis" hypothesis. They suggested that dreaming consists of associations and memories elicited from the forebrain (the neocortex and associated structures) in response to random signals from the brain stem such as PGO spikes. Dreams were merely the "best fit" the forebrain could provide to this random bombardment from the brain stem. Although dreams might at times appear to have psychological content, their bizarreness was inherently meaningless.

The sense, or plot, of dreams resulted from order that was imposed on the chaos of neural signals, Hobson said. "That order is a function of our own personal view of the world, our remote memories," Hobson wrote. In other words, the individual's emotional vocabulary could be relevant to dreams. In a further revision of the original hypothesis, Hobson also suggested that brain stem activation may merely serve to switch from one dream episode to another.

Reverse Learning

Although Hobson and McCarley had presented an explanation of dream content, the basic function of REM sleep admittedly remained unknown. In 1983 Francis Crick of the Salk Institute in La Jolla, Calif., and Graeme Mitchison of the University of Cambridge in England proposed the idea of reverse learning. Working from the Hobson-McCarley assumption of random neocortical bombardment by PGO waves and their own knowledge of the behavior of stimulated neural networks, they postulated that a complex associational neural network such as the neocortex might become overloaded by vast amounts of incoming information. The neocortex could then develop false, or "parasitic," thoughts that would jeopardize the true and orderly storage of memory.

According to Crick and Mitchison's hypothesis, REM sleep served to erase these spurious associations on a regular basis. Random PGO waves impinged on the neocortex, resulting in erasure, or unlearning, of the false information. This process served an essential function: it allowed the orderly processing of memory. In humans, dreams were a running record of these parasitic thoughtsâ�”material to be purged from memory. "We dream to forget," Crick and Mitchison wrote.

The two researchers proposed a revision in 1986. Erasure of parasitic thoughts accounted only for bizarre dream content. Nothing could be said about dream narrative. Furthermore, dreaming to forget, they said, was better expressed as dreaming to reduce fantasy or obsession.

None of these hypotheses seems to explain adequately the function of dreaming. On the one hand, Freud's theory lacked physiological evidence. (Although Freud had originally intended to describe the neurology of the unconscious and of dreams in his proposed "Project for a Scientific Psychology," the undertaking was premature, and he limited himself to psychoanalysis.) On the other hand, despite revisions to incorporate elements of psychology, most of the later theories denied that dreams had meaning.

Exploring the neuroscientific aspects of REM sleep and of memory processing seemed to me to hold the greatest potential for understanding the meaning and function of dreams. The key to this research was theta rhythm.

Theta rhythm was discovered in 1954 in awake animals by John D. Green and Arnaldo A. Arduini of the University of California at Los Angeles. The researchers observed a regular sinusoidal signal of six cycles per second in the hippocampus of rabbits when the animals were apprehensive of stimuli in their environment. They named the signal theta rhythm after a previously discovered EEG component of the same frequency.

Theta rhythm was subsequently recorded in the tree shrew, mole, rat and cat. Although it was consistently observed in awake animals, theta rhythm was correlated with very different behaviors in each species. For example, in marked contrast to the rabbit, environmental stimuli did not induce theta rhythm in the rat. Rats demonstrated theta rhythm only during movement, typically when they explored. In 1969, however, Case H. Vanderwolf of the University of Western Ontario discovered there was one behavior during which the animals he studied, including the rat, showed theta rhythm: REM sleep.

In 1972 I published a commentary pointing out that the different occurrences of theta rhythm could be understood in terms of animal behavior. Awake animals seemed to show theta rhythm when they were behaving in ways most crucial to their survival. In other words, theta rhythm appeared when they exhibited behavior that was not genetically encodedâ�”such as feeding or sexual behaviorâ�”but rather a response to changing environmental information. Predatory behavior in the cat, prey behavior in the rabbit, and exploration in the rat are, respectively, most important to their survival. (For example, a hungry rat will explore before it eats even if food is placed in front of it.)

Role of Theta Rhythm

Furthermore, because the hippocampus is involved in memory processing, the presence of theta rhythm during REM sleep in that region of the brain might be related to that activity. I suggested that the theta rhythm reflected a neural process whereby information essential to the survival of a speciesâ�”gathered during the dayâ�”was reprocessed into memory during REM sleep.

In 1974, by recording signals from the hippocampus of freely moving rats and rabbits, I found the source from which theta rhythm was generated in the hippocampus. Together with the neocortex, the hippocampus is believed to provide the neural basis for memory storage. The hippocampus (from the Greek word for "seahorse," which it resembles in shape) is a sequential structure composed of three types of neurons. Information from all sensory and associational areas of the neocortex converges in a region called the entorhinal cortex; from there it is transmitted to the three successive neuronal populations of the hippocampus. The signal arrives first at the granule cells of the dentate gyrus, then at the CA3 pyramidal cells (so called because of their triangular shape) and finally at the pyramidal cells of CA1. After information is processed by this trio of cells, it is retransmitted to the entorhinal cortex and then back to the neocortex.

My studies showed that theta rhythm was produced in two regions within the hippocampus: the dentate gyrus and the CA1 neurons. The rhythms in these two areas were synchronous. Subsequently, Susan Mitchell and James B. Ranck, Jr., of the State University of New York Downstate Medical Center identified a third synchronous generator in the entorhinal cortex, and Robert Verdes of Wayne State University discovered the brain stem neurons that control theta rhythm. These neurons transmit signals to the septum (a forebrain structure) that activate theta rhythm in the hippocampus and the entorhinal cortex. Thus, the brain stem activates the hippocampus and the neocortexâ�”the core memory system of the brain.

To determine the relation between theta rhythm and memory, I made a lesion in the rat septum. Rats that had previously learned, using spatial cues, to locate a particular position in a maze were no longer able to do so after their septums were disabled. Without theta rhythm, spatial memory was destroyed.

Studies of the cellular changes that bring about memory illustrated the role of theta rhythm. In particular, the discovery in 1973 of long-term potentiation (LTP)â�”a change in neural behavior that reflects previous activityâ�”showed the means by which memory might be encoded. Timothy V. P. Bliss and A. R. Gardner-Medwin of the National Institute of Medical Research in London and Terje LÃ¸mo of the University of Oslo found changes in nerve cells that had been intensely stimulated with electrical pulses.

Long-Term Memory Storage

Earlier studies had shown that if one stimulated the pathway from the entorhinal cortex to the granule cells of the hippocampus, the response of these cells could be measured with a recording electrode. Using this technique, Bliss and his colleagues measured the normal response to a single electrical pulse. Then they applied a long series of high-frequency signalsâ�”called tetanic pulsesâ�”to this pathway. After the train of tetanic stimuli, a single electrical pulse caused much greater firing in the granule cells than had been observed prior to the experiment. The heightened effect persisted for as long as three days. This phenomenon of LTP was precisely the kind of increase in neuronal strength that could be capable of sustaining memory. LTP is now considered a model for learning and memory.

LTP is achieved by the activity of the NMDA (N-methyl-D-aspartate) receptor. This molecule is embedded in the dendrites of the granule cells and the CA1 cells of the hippocampus as well as in neurons throughout the neocortex. Like other neuronal receptors, the NMDA receptor is activated by a neurotransmitterâ�”glutamate in this case. Glutamate momentarily opens a non-NMDA channel in the granule cell dendrite, allowing sodium from the extra-cellular space to flow into the neuron. This influx causes the granule cell to become depolarized. If the depolarization is sufficient, the granule cell fires, transmitting information to other nerve cells.

Unlike other neuronal receptors, NMDA possesses an additional property. If a further activation of glutamate occurs while the granule cell is depolarized, a second channel opens up, allowing an influx of calcium. Calcium is thought to act as a second messenger, initiating a cascade of intracellular events that culminates in long-lasting synaptic changesâ�”or LTP. (The description given here has been necessarily simplified. LTP is the subject of extensive ongoing investigation.)

Because the tetanic impulses applied by Bliss and his colleagues did not occur naturally in the brain, the question remained as to how LTP was achieved under normal circumstances. In 1986 John Larson and Gary S. Lynch of the University of California at Irvine and Gregory Rose and Thomas V. Dunwiddie of the University of Colorado at Denver suggested that the occurrence of LTP in the hippocampus was linked to theta rhythm. They applied a small number of electrical pulses to CA1 cells in the rat hippocampus and produced LTP, but only when the pulses were separated by the normal time that elapses between two theta wavesâ�”approximately 200 milliseconds. Theta rhythm is apparently the natural means by which the NMDA receptor is activated in neurons in the hippocampus.

Work in my laboratory at the Rockefeller University duplicated Larson and Lynch's CA1 findings, but this time in the hippocampal granule cells. Constantine Pavlides, Yoram J. Greenstein and I then demonstrated that LTP was dependent on the presence and phase of theta rhythm. If electrical pulses were applied to the cells at the peak of the theta wave, LTP was induced. But if the same pulse were applied at the trough of the wavesâ�”or when theta rhythm was absentâ�”LTP was not induced.

A coherent picture of memory processing was emerging. As a rat explores, for example, brain stem neurons activate theta rhythm. Olfactory input (which in the rat is synchronized with theta rhythm, as is the twitching of whiskers) and other sensory information converge on the entorhinal cortex and the hippocampus. There they are partitioned into 200-millisecond "bites" by theta rhythm. The NMDA receptors, acting in conjunction with theta rhythm, allow for long-term storage of this information.

A similar process occurs during REM sleep. Although there is no incoming information or movement during REM sleep, the neocortical-hippocampal network is once again paced by theta rhythm. Theta rhythm might produce long-lasting changes in memory.

Storing Spatial Memory

The results of one of my further experiments served to show that spatial memory was indeed being stored in the rat hippocampus during sleep. John O'Keefe and J. Dostrovsky of the University College London had demonstrated that individual CA1 neurons in the rat hippocampus fired when the awake animal moved to a particular locationâ�”namely, the neuron's place field. The implication of this finding was that the CA1 neuron fired to map the environment, thereby committing it to memory.

In 1989 Pavlides and I located two CA1 neurons in the rat hippocampus that had different place fields. We recorded from both cells simultaneously. After determining the normal firing rates in awake and asleep animals, we positioned a rat in the place field of one of the neurons. The neuron fired vigorously, mapping that location. The second cell fired only sporadically because it was not coding space. We continued recording from the two pairs of neurons as the rat moved about and then entered several sleep cycles. Six pairs of neurons were studied in this manner.

We found that neurons that had coded space fired at a normal rate as the animal moved about prior to sleep. In sleep, however, they fired at a significantly higher rate than their previous sleeping baseline. There was no such increase in firing rate during sleep in neurons that had not mapped space. This experiment suggested that the reprocessing or strengthening of information encoded when the animal was awake occurred in sleep at the level of individual neurons.

Bruce L. McNaughton and his colleagues at the University of Arizona have developed a technique for simultaneously recording from a large number of neurons in the hippocampus that map locations. Their technique allows definitive patterns of firing to be identified. In animal studies, they found that ensembles of place-field neurons that code space in the waking state reprocess information during slow-wave sleep and then in REM sleep. These results suggest that sleep processing of memory may have two stagesâ�”a preliminary stage in slow-wave sleep and a later phase in REM sleep, when dreaming occurs.

Evolution of REM Sleep

Evidence that theta rhythm encodes memories during REM sleep may be derived not only from neuroscientific studies but also from evolution. The emergence of a neural mechanism to process memory in REM sleep suggests differences in brain anatomy between mammals that have that aspect of the sleep cycle and those that do not. And in fact, such differences clearly exist between the echidna and the marsupials and placentals.

The echidna has a large convoluted prefrontal cortex, larger in relation to the rest of the brain than that of any other mammal, even humans. I believe it needed this huge prefrontal cortex to perform a dual function: to react to incoming information in an appropriate manner based on past experience and to evaluate and store new information to aid in future survival. Without theta rhythm during REM sleep, the echidna would not be able to process information while it slept. (The echidna does, however, show theta rhythm when foraging for food.) For higher capabilities to develop, the prefrontal cortex would have to become increasingly largeâ�”beyond the capacity of the skullâ�”unless another brain mechanism evolved.

REM sleep could have provided this new mechanism, allowing memory processing to occur "off-line." Coincident with the apparent development of REM sleep in marsupial and placental mammals was a remarkable neuroanatomical change: the prefrontal cortex was dramatically reduced in size. Far less prefrontal cortex was required to process information. That area of the brain could develop to provide advanced perceptual abilities in higher species.

The nature of REM sleep supports this evolutionary argument. During the day, animals gather information that involves locomotion and eye movement. The reprocessing of this information during REM sleep would not be easily separated from the locomotion related to the experienceâ�”such disassociation might be expecting too great a revision of brain circuitry. So to maintain sleep, locomotion had to be suppressed by inhibiting motor neurons. Suppressing eye movement was unnecessary because this activity does not disturb sleep.

Eye movement potentials, similar to PGO spikes, accompany rapid eye movement in the waking state and also during REM sleep. The function of these signals has not yet been established, but they may serve to alert the visual cortex to incoming information when the animal is awake and may reflect the reprocessing of this information during REM sleep. In any case, PGO spikes do not disturb sleep and do not have to be suppressedâ�”unlike motor neurons.

Strategy for Survival

With the evolution of REM sleep, each species could process the information most important for its survival, such as the location of food or the means of predation or escapeâ�”those activities during which theta rhythm is present. In REM sleep this information may be accessed again and integrated with past experience to provide an ongoing strategy for behavior. Although theta rhythm has not yet been demonstrated in primates, including humans, the brain signal provides a clue to the origin of dreaming in humans. Dreams may reflect a memory-processing mechanism inherited from lower species, in which information important for survival is reprocessed during REM sleep. This information may constitute the core of the unconscious.

Because animals do not possess language, the information they process during REM sleep is necessarily sensory. Consistent with our early mammalian origins, dreams in humans are sensory, primarily visual. Dreams do not take the form of verbal narration.

Also in keeping with the role REM sleep played in processing memories in animals, there is no functional necessity for this material to become conscious. Consciousness arose later in evolution in humans. But neither is there any reason for the material of dreams not to reach consciousness. Therefore, dreams can be rememberedâ�”most readily if awakening occurs during or shortly after a REM sleep period.

Consistent with evolution and evidence derived from neuroscience and reports of dreams, I suggest that dreams reflect an individual's strategy for survival. The subjects of dreams are broad-ranging and complex, incorporating self-image, fears, insecurities, strengths, grandiose ideas, sexual orientation, desire, jealousy and love.

Dreams clearly have a deep psychological core. This observation has been reported by psychoanalysts since Freud and is strikingly illustrated by the work of Rosalind Cartwright of Rush-Presbyterian-St. Luke's Hospital in Chicago. Cartwright is studying a series of 90 subjects who are undergoing marital separation and divorce. All the subjects are clinically evaluated and psychologically tested to ascertain their attitudes and responses to their personal crisis. Cartwright's subjects are also awakened from REM sleep to report their dreams, which are then interpreted by the subjects themselves without questions that might influence their interpretation. In the 70 individuals studied to date, the dream content conveys the person's unconscious thoughts and is strongly correlated with the manner in which he or she is coping with the crisis while awake.

Although the topic "chosen" for consideration during a night's sleep is unpredictable, certain of life's difficultiesâ�”as in the case of Cartwright's subjectsâ�”so engage psychological survival that they are selected for REM sleep processing. In the ordinary course of events, depending on the individual's personality, the themes of dreams may be freewheeling. Moreover, when joined with the intricate associations that are an intrinsic part of REM sleep processing, the dream's statement may be rather obscure.

Nevertheless, there is every reason to believe that the cognitive process taking place in Cartwright's subjects occurs in every individual. Interpretation of the coherent statement that is being made depends on the individual's tracing of relevant or similar events. These associations are strongly biased toward early childhood experience.

My hypothesis also offers an explanation for the large amount of REM sleep in infants and children. Newborns spend eight hours a day in REM sleep. The sleep cycle is disorganized at this age. Sleep occurs in 50- to 60-minute bouts and begins with REM rather than with slow-wave sleep. By the age of two, REM sleep is reduced to three hours a day, and the adult pattern has been established. Thereafter, the time spent in REM sleep gradually diminishes to a little less than two hours.

REM sleep may perform a special function in infants. A leading theory proposes that it stimulates nerve growth. Whatever the purpose in infants may be, I suggest that at about the age of two, when the hippocampus, which continues to develop after birth, becomes functional, REM sleep takes on its interpretive memory function. The waking information to be integrated at this point in development constitutes the basic cognitive substrate for memoryâ�”the concept of the real world against which later experiences must be compared and interpreted. The organization in memory of this extensive infrastructure requires the additional REM sleep time.

For reasons he could not possibly have known, Freud set forth a profound truth in his work. There is an unconscious, and dreams are indeed the "royal road" to its understanding. The characteristics of the unconscious and associated processes of brain functioning, however, are very different from what Freud thought. Rather than being a cauldron of untamed passions and destructive wishes, I propose that the unconscious is a cohesive, continually active mental structure that takes note of life's experiences and reacts according to its own scheme of interpretation. Dreams are not disguised as a consequence of repression. Their unusual character is a result of the complex associations that are culled from memory.

Memory Consolidation

Research on REM sleep suggests that there is a biologically relevant reason for dreaming. The revised version of the Hobson-McCarley activation synthesis hypothesis acknowledges the deep psychological core of dreams. In its present truncated form, the hypothesis of random brain stem activation has little explanatory or predictive power.

The Crick-Mitchison hypothesis provides a function for REM sleepâ�”reverse learningâ�”but it does not apply to narrative, only to the bizarre elements of the dream. What this implies with regard to REM processing in lower species must be defined before the theory can be evaluated further. In addition, the Crick-Mitchison hypothesis as applied to the hippocampus would suggest that neurons fire randomly during REM sleep, providing reverse learning. Instead, in my experiment on the neurons that coded space, these neurons fired selectively, implying an orderly processing of memory.

Recently Avi Karni and his colleagues at the Weizmann Institute of Science in Israel were able to show that memory processing occurs in humans during REM sleep. In their experiment, individuals learned to identify particular patterns on a screen. The memory of this skill improved after a night with REM sleep. When the subjects were deprived of REM sleep, memory consolidation did not occur. This study is an important breakthrough and opens a particularly promising field for exploration.

Further study will continue to elucidate the meaning of dreams. In particular, an experiment is needed to determine whether eliminating theta rhythm during REM sleep alone results in a memory deficit. Because theta rhythm has not been demonstrated in primates, it may have disappeared as vision replaced olfaction as the dominant sense. An equivalent neural mechanism may exist in the hippocampus that periodically activates the NMDA receptor. These studies in animals and others to come in humans will probe fundamental aspects of memory processing and the neuroscientific basis of human psychological structure.

About the author: Jonathan Winson started his career as an aeronautical engineer, graduating with an engineering degree from the California Institute of Technology in 1946. He completed his Ph.D. in mathematics at Columbia University and then turned to business for 15 years. Because of his keen interest in neuroscience, however, Winson started to do research at the Rockefeller University on memory processing during waking and sleeping states. In 1979 he became an associate professor there and as professor emeritus continues his work on memory and dreaming. His research has been supported by the National Institute of Mental Health, the National Science Foundation and the Harry F. Guggenheim Foundation.

The Haemoglobin Molecule

The haemoglobin molecule in red blood cells transports oxygen from the lungs to cells throughout the body. In the late 1930s Austrian-born British biochemist Max F. Perutz began examining the structure of this complex protein molecule by using a technique known as X-ray crystallography. By 1960 he had determined the three-dimensional structure of the protein. For this work, Perutz shared the 1962 Nobel Prize in chemistry. Perutz describes his study of the haemoglobin molecule in a 1964 Scientific American article.

The Haemoglobin Molecule

Its 10,000 atoms are assembled into four chains, each a helix with several bends. The molecule has one shape when ferrying oxygen molecules and a slightly different shape when it is not

By M. F. Perutz

In 1937, a year after I entered the University of Cambridge as a graduate student, I chose the X-ray analysis of haemoglobin, the oxygen-bearing protein of the blood, as the subject of my research. Fortunately the examiners of my doctoral thesis did not insist on a determination of the structure, otherwise I should have had to remain a graduate student for 23 years. In fact, the complete solution of the problem, down to the location of each atom in this giant molecule, is still outstanding, but the structure has now been mapped in enough detail to reveal the intricate three-dimensional folding of each of its four component chains of amino acid units, and the positions of the four pigment groups that carry the oxygen-combining sites.

The folding of the four chains in haemoglobin turns out to be closely similar to that of the single chain of myoglobin, an oxygen-bearing protein in muscle whose structure has been elucidated in atomic detail by my colleague John C. Kendrew and his collaborators. Correlation of the structure of the two proteins allows us to specify quite accurately, by purely physical methods, where each amino acid unit in haemoglobin lies with respect to the twists and turns of its chains.

Physical methods alone, however, do not yet permit us to decide which of the 20 different kinds of amino acid units occupies any particular site. This knowledge has been supplied by chemical analysis; workers in the U.S. and in Germany have determined the sequence of the 140-odd amino acid units along each of the haemoglobin chains. The combined results of the two different methods of approach now provide an accurate picture of many facets of the haemoglobin molecule.

In its behaviour haemoglobin does not resemble an oxygen tank so much as a molecular lung. Two of its four chains shift back and forth, so that the gap between them becomes narrower when oxygen molecules are bound to the haemoglobin and wider when the oxygen is released. Evidence that the chemical activities of haemoglobin and other proteins are accompanied by structural changes had been discovered before, but this is the first time that the nature of such a change has been directly demonstrated.

Haemoglobin's change of shape makes me think of it as a breathing molecule, but paradoxically it expands, not when oxygen is taken up but when it is released.

When I began my postgraduate work in 1936 I was influenced by three inspiring teachers. Sir Frederick Gowland Hopkins, who had received a Nobel Prize in 1929 for discovering the growth-stimulating effect of vitamins, drew our attention to the central role played by enzymes in catalyzing chemical reactions in the living cell. The few enzymes isolated at that time had all proved to be proteins. David Keilin, the discoverer of several of the enzymes that catalyze the processes of respiration, told us how the chemical affinities and catalytic properties of iron atoms were altered when the iron combined with different proteins. J. D. Bernal, the X-ray crystallographer, was my research supervisor. He and Dorothy Crowfoot Hodgkin had taken the first X-ray diffraction pictures of crystals of protein a year or two before I arrived, and they had discovered that protein molecules, in spite of their large size, have highly ordered structures. The wealth of sharp X-ray diffraction spots produced by a single crystal of an enzyme such as pepsin could be explained only if every one, or almost every one, of the 5,000 atoms in the pepsin molecule occupied a definite position that was repeated in every one of the myriad of pepsin molecules packed in the crystal. The notion is commonplace now, but it caused a sensation at a time when proteins were still widely regarded as "colloids" of indefinite structure.

In the late 1930's the importance of the nucleic acids had yet to be discovered; according to everything I had learned the "secret of life" appeared to be concealed in the structure of proteins. Of all the methods available in chemistry and physics, X-ray crystallography seemed to offer the only chance, albeit an extremely remote one, of determining that structure.

The number of crystalline proteins then available was probably not more than a dozen, and haemoglobin was an obvious candidate for study because of its supreme physiological importance, its ample supply and the ease with which it could be crystallized. All the same, when I chose the X-ray analysis of haemoglobin as the subject of my Ph.D. thesis, my fellow students regarded me with a pitying smile. The most complex organic substance whose structure had yet been determined by X-ray analysis was the molecule of the dye phthalocyanin, which contains 58 atoms. How could I hope to locate the thousands of atoms in the molecule of haemoglobin?

The Function of Haemoglobin

Haemoglobin is the main component of the red blood cells, which carry oxygen from the lungs through the arteries to the tissues and help to carry carbon dioxide through the veins back to the lungs. A single red blood cell contains about 280 million molecules of haemoglobin. Each molecule has 64,500 times the weight of a hydrogen atom and is made up of about 10,000 atoms of hydrogen, carbon, nitrogen, oxygen and sulphur, plus four atoms of iron, which are more important than all the rest. Each iron atom lies at the centre of the group of atoms that form the pigment called heme, which gives blood its red colour and its ability to combine with oxygen. Each heme group is enfolded in one of the four chains of amino acid units that collectively constitute the protein part of the molecule, which is called globin. The four chains of globin consist of two identical pairs. The members of one pair are known as alpha chains and those of the other as beta chains. Together the four chains contain a total of 574 amino acid units.

In the absence of an oxygen carrier a litre of arterial blood at body temperature could dissolve and transport no more than three millilitres of oxygen. The presence of haemoglobin increases this quantity 70 times. Without haemoglobin large animals could not get enough oxygen to exist. Similarly, haemoglobin is responsible for carrying more than 90 percent of the carbon dioxide transported by venous blood.

Each of the four atoms of iron in the haemoglobin molecule can take up one molecule (two atoms) of oxygen. The reaction is reversible in the sense that oxygen is taken up where it is plentiful, as in the lungs, and released where it is scarce, as in the tissues. The reaction is accompanied by a change in colour: haemoglobin containing oxygen, known as oxyhaemoglobin, makes arterial blood look scarlet; reduced, or oxygen-free, haemoglobin makes venous blood look purple. The term "reduced" for the oxygen-free form is really a misnomer because "reduced" means to the chemist that electrons have been added to an atom or a group of atoms. Actually, as James B. Conant of Harvard University demonstrated in 1923, the iron atoms in both reduced haemoglobin and oxyhaemoglobin are in the same electronic condition: the divalent, or ferrous, state.

They become oxidized to the trivalent, or ferric, state if haemoglobin is treated with a ferricyanide or removed from the red cells and exposed to the air for a considerable time; oxidation also occurs in certain blood diseases. Under these conditions haemoglobin turns brown and is known as methemoglobin, or ferrihemoglobin.

Ferrous iron acquires its capacity for binding molecular oxygen only through its combination with heme and globin. Heme alone will not bind oxygen, but the specific chemical environment of the globin makes the combination possible. In association with other proteins, such as those of the enzymes peroxidase and catalase, the same heme group can exhibit quite different chemical characteristics.

The function of the globin, however, goes further. It enables the four iron atoms within each molecule to interact in a physiologically advantageous manner. The combination of any three of the iron atoms with oxygen accelerates the combination with oxygen of the fourth; similarly, the release of oxygen by three of the iron atoms makes the fourth cast off its oxygen faster. By tending to make each haemoglobin molecule carry either four molecules of oxygen or none, this interaction ensures efficient oxygen transport.

I have mentioned that haemoglobin also plays an important part in bearing carbon dioxide from the tissues back to the lungs. This gas is not borne by the iron atoms, and only part of it is bound directly to the globin; most of it is taken up by the red cells and the noncellular fluid of the blood in the form of bicarbonate. The transport of bicarbonate is facilitated by the disappearance of an acid group from haemoglobin for each molecule of oxygen discharged. The reappearance of the acid group when oxygen is taken up again in the lungs sets in motion a series of chemical reactions that leads to the discharge of carbon dioxide. Conversely, the presence of bicarbonate and lactic acid in the tissues accelerates the liberation of oxygen.

Breathing seems so simple, yet it appears as if this elementary manifestation of life owes its existence to the interplay of many kinds of atoms in a giant molecule of vast complexity. Elucidating the structure of the molecule should tell us not only what the molecule looks like but also how it works.

The Principles of X-Ray Analysis

The X-ray study of proteins is sometimes regarded as an abstruse subject comprehensible only to specialists, but the basic ideas underlying our work are so simple that some physicists find them boring. Crystals of haemoglobin and other proteins contain much water and, like living tissues, they tend to lose their regularly ordered structure on drying. To preserve this order during X-ray analysis crystals are mounted wet in small glass capillaries. A single crystal is then illuminated by a narrow beam of X rays that are essentially all of one wavelength. If the crystal is kept stationary, a photographic film placed behind it will often exhibit a pattern of spots lying on ellipses, but if the crystal is rotated in certain ways, the spots can be made to appear at the corners of a regular lattice that is related to the arrangement of the molecules in the crystal. Moreover, each spot has a characteristic intensity that is determined in part by the arrangement of atoms inside the molecules. The reason for the different intensities is best explained in the words of W. L. Bragg, who founded X-ray analysis in 1913â�”the year after Max von Laue had discovered that X rays are diffracted by crystalsâ�”and who later succeeded Lord Rutherford as Cavendish Professor of Physics at Cambridge:

"It is well known that the form of the lines ruled on a [diffraction] grating has an influence on the relative intensity of the spectra which it yields. Some spectra may be enhanced, or reduced, in intensity as compared with others. Indeed, gratings are sometimes ruled in such a way that most of the energy is thrown into those spectra which it is most desirable to examine. The form of the line on the grating does not influence the positions of the spectra, which depend on the number of lines to the centimetre, but the individual lines scatter more light in some directions than others, and this enhances the spectra which lie in those directions.

"The structure of the group of atoms which composes the unit of the crystal grating influences the strength of the various reflexions in exactly the same way. The rays are diffracted by the electrons grouped around the centre of each atom. In some directions the atoms conspire to give a strong scattered beam, in others their effects almost annul each other by interference. The exact arrangement of the atoms is to be deduced by comparing the strength of the reflexions from different faces and in different orders."

Thus there should be a way of reversing the process of diffraction, of proceeding backward from the diffraction pattern to an image of the arrangement of atoms in the crystal. Such an image can actually be produced, somewhat laboriously, as follows. It will be noted that spots on opposite sides of the centre of an X-ray picture have the same degree of intensity. With the aid of a simple optical device each symmetrically related pair of spots can be made to generate a set of diffraction fringes, with amplitude proportional to the square root of the intensity of the spots. The device, which was invented by Bragg and later developed by H. Lipson and C. A. Taylor at the Manchester College of Science and Technology, consists of a point source of monochromatic light, a pair of plane-convex lenses and a microscope. The pair of spots in the diffraction pattern is represented by a pair of holes in a black mask that is placed between the two lenses. If the point source is placed at the focus of one of the lenses, the waves of parallel light emerging from the two holes will interfere with one another at the focus of the second lens, and their interference pattern, or diffraction pattern, can be observed or photographed through the microscope.

Imagine that each pair of symmetrically related spots in the X-ray picture is in turn represented by a pair of holes in a mask, and that its diffraction fringes are photographed. Each set of fringes will then be at right angles to the line joining the two holes, and the distance between the fringes will be inversely proportional to the distance between the holes.â�¦

The Phase Problem

An image of the atomic structure of the crystal can be generated by printing each set of fringes in turn on the same sheet of photographic paper, or by superposing all the fringes and making a print of the light transmitted through them. At this point, however, a fatal complication arises. In order to obtain the right image one would have to place each set of fringes correctly with respect to some arbitrarily chosen common origin. At this origin the amplitude of any particular set of fringes may show a crest or trough or some intermediate value. The distance of the wave crest from the origin is called the phase. It is almost true to say that by superposing sets of fringes of given amplitude one can generate an infinite number of different images, depending on the choice of phase for each set of fringes. By itself the X-ray picture tells us only about the amplitudes and nothing about the phases of the fringes to be generated by each pair of spots, which means that half the information needed for the production of the image is missing.

The missing information makes the diffraction pattern of a crystal like a hieroglyphic without a key. Having spent years hopefully measuring the intensities of several thousand spots in the diffraction pattern of haemoglobin, I found myself in the tantalizing position of an explorer with a collection of tablets engraved in an unknown script. For some time Bragg and I tried to develop methods for deciphering the phases, but with only limited success. The solution finally came in 1953, when I discovered that a method that had been developed by crystallographers for solving the phase problem in simpler structures could also be applied to proteins.

In this method the molecule of the compound under study is modified slightly by attaching heavy atoms such as those of mercury to definite positions in its structure. The presence of a heavy atom produces marked changes in the intensities of the diffraction pattern, and this makes it possible to gather information about the phases. From the difference in amplitude in the absence or presence of a heavy atom, the distance of the wave crest from the heavy atom can be determined for each set of fringes. Thus with the heavy atom serving as a common origin the magnitude of the phase can be measured. â�¦[T]he phase of a single set of fringes, represented by a sinusoidal wave that is supposedly scattered by the oversimplified protein molecule, can be measured from the increase in amplitude produced by the heavy atom H1.

Unfortunately this still leaves an ambiguity of sign; the experiment does not tell us whether the phase is to be measured from the heavy atom in the forward or the backward direction. If n is the number of diffracted spots, an ambiguity of sign in each set of fringes would lead to 2n alternative images of the structure. The Dutch crystallographer J. M. Bijvoet had pointed out some years earlier in another context that the ambiguity could be resolved by examining the diffraction pattern from a second heavy-atom compound.

â�¦[T]he heavy atom H2, which is attached to the protein in a position different from that of H1, diminishes the amplitude of the wave scattered by the protein. The degree of attenuation allows us to measure the distance of the wave crest from H2. It can now be seen that the wave crest must be in front of H1; otherwise its distance from H1 could not be reconciled with its distance from H2. The final answer depends on knowing the length and direction of the line joining H2 to H1. These quantities are best calculated by a method that does not easily lend itself to exposition in nonmathematical language. It was devised by my colleague Michael G. Rossmann.

The heavy-atom method can be applied to haemoglobin by attaching mercury atoms to the sulphur atoms of the amino acid cysteine. The method works, however, only if this attachment leaves the structure of the haemoglobin molecules and their arrangement in the crystal unaltered. When I first tried it, I was not at all sure that these stringent demands would be fulfilled, and as I developed my first X-ray photograph of mercury haemoglobin my mood alternated between sanguine hopes of immediate success and desperate forebodings of all the possible causes of failure. When the diffraction spots appeared in exactly the same position as in the mercury-free protein but with slightly altered intensities, just as I had hoped, I rushed off to Bragg's room in jubilant excitement, expecting that the structure of haemoglobin and of many other proteins would soon be determined. Bragg shared my excitement, and luckily neither of us anticipated the formidable technical difficulties that were to hold us up for another five years.

Resolution of the Image

Having solved the phase problem, at least in principle, we were confronted with the task of building up a structural image from our X-ray data. In simpler structures atomic positions can often be found from representations of the structure projected on two mutually perpendicular planes, but in proteins a three-dimensional image is essential. This can be attained by making use of the three-dimensional nature of the diffraction pattern. The X-ray diffraction pattern â�¦ can be regarded as a section through a sphere that is filled with layer after layer of diffraction spots. Each pair of spots can be made to generate a set of three-dimensional fringes.â�¦ When their phases have been measured, they can be superposed by calculation to build up a three-dimensional image of the protein. The final image is represented by a series of sections through the molecule, rather like a set of microtome sections through a piece of tissue, only on a scale 1,000 times smaller.

The resolution of the image is roughly equal to the shortest wavelength of the fringes used in building it up. This means that the resolution increases with the number of diffracted spots included in the calculation. If the image is built up from part of the diffraction pattern only, the resolution is impaired.

In the X-ray diffraction patterns of protein crystals the number of spots runs into tens of thousands. In order to determine the phase of each spot accurately, its intensity (or blackness) must be measured accurately several times over: in the diffraction pattern from a crystal of the pure protein and in the patterns from crystals of several compounds of the protein, each with heavy atoms attached to different positions in the molecule. Then the results have to be corrected by various geometric factors before they are finally used to build up an image through the superposition of tens of thousands of fringes. In the final calculation tens of millions of numbers may have to be added or subtracted. Such a task would have been quite impossible before the advent of high-speed computers, and we have been fortunate in that the development of computers has kept pace with the expanding needs of our X-ray analyses.

While I battled with technical difficulties of various sorts, my colleague John Kendrew successfully applied the heavy-atom method to myoglobin, a protein closely related to haemoglobin. Myoglobin is simpler than haemoglobin because it consists of only one chain of amino acid units and one heme group, which binds a single molecule of oxygen. The complex interaction phenomena involved in haemoglobin's dual function as a carrier of oxygen and of carbon dioxide do not occur in myoglobin, which acts simply as an oxygen store.

Together with Howard M. Dintzis and G. Bodo, Kendrew was brilliantly successful in managing to prepare as many as five different crystalline heavy-atom compounds of myoglobin, which meant that the phases of the diffraction spots could be established very accurately. He also pioneered the use of high-speed computers in X-ray analysis. In 1957 he and his colleagues obtained the first three-dimensional representation of myoglobin.

It was a triumph, and yet it brought a tinge of disappointment. Could the search for ultimate truth really have revealed so hideous and visceral-looking an object? Was the nugget of gold a lump of lead? Fortunately, like many other things in nature, myoglobin gains in beauty the closer you look at it. As Kendrew and his colleagues increased the resolution of their X-ray analysis in the years that followed, some of the intrinsic reasons for the molecule's strange shape began to reveal themselves. This shape was found to be not a freak but a fundamental pattern of nature, probably common to myoglobins and haemoglobins throughout the vertebrate kingdom.

In the summer of 1959, nearly 22 years after I had taken the first X-ray pictures of haemoglobin, its structure emerged at last. Michael Rossmann, Ann F. Cullis, Hilary Muirhead, Tony C. T. North and I were able to prepare a three-dimensional electron-density map of haemoglobin at a resolution of 5.5 angstrom units, about the same as that obtained for the first structure of myoglobin two years earlier. This resolution is sufficient to reveal the shape of the chain forming the backbone of a protein molecule but not to show the position of individual amino acids.

As soon as the numbers printed by the computer had been plotted on contour maps we realized that each of the four chains of haemoglobin had a shape closely resembling that of the single chain of myoglobin. The beta chain and myoglobin look like identical twins, and the alpha chains differ from them merely by a shortcut across one small loop.

Kendrew's myoglobin had been extracted from the muscle of the sperm whale; the haemoglobin we used came from the blood of horses. More recent observations indicate that the myoglobins of the seal and the horse, and the haemoglobins of man and cattle, all have the same structure. It seems as though the apparently haphazard and irregular folding of the chain is a pattern specifically devised for holding a heme group in place and for enabling it to carry oxygen.

What is it that makes the chain take up this strange configuration? The extension of Kendrew's analysis to a higher resolution shows that the chain of myoglobin consists of a succession of helical segments interrupted by corners and irregular regions. The helical segments have the geometry of the alpha helix predicted in 1951 by Linus Pauling and Robert B. Corey of the California Institute of Technology. The heme group lies embedded in a fold of the chain, so that only its two acid groups protrude at the surface and are in contact with the surrounding water. Its iron atom is linked to a nitrogen atom of the amino acid histidine.

I have recently built models of the alpha and beta chains of haemoglobin and found that they follow an atomic pattern very similar to that of myoglobin. If two protein chains look the same, one would expect them to have much the same composition. In the language of protein chemistry this implies that in the myoglobins and haemoglobins of all vertebrates the 20 different kinds of amino acid should be present in about the same proportion and arranged in similar sequence.

Enough chemical analyses have been done by now to test whether or not this is true. Starting at the Rockefeller Institute and continuing in our laboratory, Allen B. Edmundson has determined the sequence of amino acid units in the molecule of sperm-whale myoglobin. The sequences of the alpha and beta chains of adult human haemoglobin have been analyzed independently by Gerhardt Braunitzer and his colleagues at the Max Planck Institute for Biochemistry in Munich, and by William H. Konigsberg, Robert J. Hill and their associates at the Rockefeller Institute. Fetal haemoglobin, a variant of the human adult form, contains a chain known as gamma, which is closely related to the beta chain. Its complete sequence has been analyzed by Walter A. Schroeder and his colleagues at the California Institute of Technology. The sequences of several other species of haemoglobin and that of human myoglobin have been partially elucidated.

The sequence of amino acid units in proteins is genetically determined, and changes arise as a result of mutation. Sickle-cell anaemia, for instance, is an inherited disease due to a mutation in one of the haemoglobin genes. The mutation causes the replacement of a single amino acid unit in each of the beta chains. (The glutamic acid unit normally present at position No. 6 is replaced by a valine unit.) On the molecular scale evolution is thought to involve a succession of such mutations, altering the structure of protein molecules one amino acid unit at a time. Consequently when the haemoglobins of different species are compared, we should expect the sequences in man and apes, which are close together on the evolutionary scale, to be very similar, and those of mammals and fishes, say, to differ more widely. Broadly speaking, this is what is found. What was quite unexpected was the degree of chemical diversity among the amino acid sequences of proteins of similar three-dimensional structure and closely related function. Comparison of the known haemoglobin and myoglobin sequences shows only 15 positionsâ�”no more than one in 10â�”where the same amino acid unit is present in all species. In all the other positions one or more replacements have occurred in the course of evolution.

What mechanism makes these diverse chains fold up in exactly the same way? Does a template force them to take up this configuration, like a mold that forces a car body into shape? Apart from the topological improbability of such a template, all the genetic and physicochemical evidence speaks against it, suggesting instead that the chain folds up spontaneously to assume one specific structure as the most stable of all possible alternatives.

Possible Folding Mechanisms

What is it, then, that makes one particular configuration more stable than all others? The only generalization to emerge so far, mainly from the work of Kendrew, Herman C. Watson and myself, concerns the distribution of the so-called polar and nonpolar amino acid units between the surface and the interior of the molecule.

Some of the amino acids, such as glutamic acid and lysine, have side groups of atoms with positive or negative electric charge, which strongly attract the surrounding water. Amino acid side groups such as glutamine or tyrosine, although electrically neutral as a whole, contain atoms of nitrogen or oxygen in which positive and negative charges are sufficiently separated to form dipoles; these also attract water, but not so strongly as the charged groups do. The attraction is due to a separation of charges in the water molecule itself, making it dipolar. By attaching themselves to electrically charged groups, or to other dipolar groups, the water molecules minimize the strength of the electric fields surrounding these groups and stabilize the entire structure by lowering the quantity known as free energy.

The side groups of amino acids such as leucine and phenylalanine, on the other hand, consist only of carbon and hydrogen atoms. Being electrically neutral and only very weakly dipolar, these groups repel water as wax does. The reason for the repulsion is strange and intriguing. Such hydrocarbon groups, as they are called, tend to disturb the haphazard arrangement of the liquid water molecules around them, making it ordered as it is in ice. The increase in order makes the system less stable; in physical terms it leads to a reduction of the quantity known as entropy, which is the measure of the disorder in a system. Thus it is the water molecules' anarchic distaste for the orderly regimentation imposed on them by the hydrocarbon side groups that forces these side groups to turn away from water and to stick to one another.

Our models have taught us that most electrically charged or dipolar side groups lie at the surface of the protein molecule, in contact with water. Nonpolar side groups, in general, are either confined to the interior of the molecule or so wedged into crevices on its surface as to have the least contact with water. In the language of physics, the distribution of side groups is of the kind leading to the lowest free energy and the highest entropy of the protein molecules and the water around them. (There is a reduction of entropy due to the orderly folding of the protein chain itself, which makes the system less stable, but this is balanced, at moderate temperatures, by the stabilizing contributions of the other effects just described.) It is too early to say whether these are the only generalizations to be made about the forces that stabilize one particular configuration of the protein chain in preference to all others.

At least one amino acid is known to be a misfit in an alpha helix, forcing the chain to turn a corner wherever the unit occurs. This is proline. There is, however, only one corner in all the haemoglobins and myoglobins where a proline is always found in the same position: position No. 36 in the beta chain and No. 37 in the myoglobin chain. At other corners the appearance of prolines is haphazard and changes from species to species. Elkan R. Blout of the Harvard Medical School finds that certain amino acids such as valine or threonine, if present in large numbers, inhibit the formation of alpha helices, but these do not seem to have a decisive influence in myoglobin and haemoglobin.

Since it is easier to determine the sequence of amino acid units in proteins than to unravel their three-dimensional structure by X rays, it would be useful to be able to predict the structure from the sequence. In principle enough is probably known about the forces between atoms and about the way they tend to arrange themselves to make such predictions feasible. In practice the enormous number of different ways in which a long chain can be twisted still makes the problem one of baffling complexity.

Assembling the Four Chains

If haemoglobin consisted of four identical chains, a crystallographer would expect them to lie at the corners of a regular tetrahedron. In such an arrangement each chain can be brought into congruence with any of its three neighbours by a rotation of 180 degrees about one of three mutually perpendicular axes of symmetry. Since the alpha and beta chains are chemically different, such perfect symmetry is unattainable, but the actual arrangement comes very close to it. As a first step in the assembly of the molecule two alpha chains are placed near a twofold symmetry axis, so that a rotation of 180 degrees brings one chain into congruence with its partner.

Next the same is done with the two beta chains. One pair, say the alpha chains, is then inverted and placed over the top of the other pair so that the four chains lie at the corners of a tetrahedron. A true twofold symmetry axis now passes vertically through the molecule, and "pseudo-axes" in two directions perpendicular to the first relate the alpha to the beta chains. Thus the arrangement is tetrahedral, but because of the chemical differences between the alpha and beta chains the tetrahedron is not quite regular.

The result is an almost spherical molecule whose exact dimensions are 64 Ã— 55 Ã— 50 angstrom units. It is astonishing to find that four objects as irregular as the alpha and beta chains can fit together so neatly. On formal grounds one would expect a hole to pass through the centre of the molecule because chains of amino acid units, being asymmetrical, cannot cross any symmetry axis. Such a hole is in fact found.

The most unexpected feature of the oxyhaemoglobin molecule is the way the four heme groups are arranged. On the basis of their chemical interaction one would have expected them to lie close together. Instead each heme group lies in a separate pocket on the surface of the molecule, apparently unaware of the existence of its partners. Seen at the present resolution, therefore, the structure fails to explain one of the most important physiological properties of haemoglobin.

In 1937 Felix Haurowitz, then at the German University of Prague, discovered an important clue to the molecular explanation of haemoglobin's physiological action. He put a suspension of needle-shaped oxyhaemoglobin crystals away in the refrigerator. When he took the suspension out some weeks later, the oxygen had been used up by bacterial infection and the scarlet needles had been replaced by hexagonal plates of purple reduced haemoglobin. While Haurowitz observed the crystals under the microscope, oxygen penetrated between the slide and the cover slip, causing the purple plates to dissolve and the scarlet needles of haemoglobin to re-form. This transformation convinced Haurowitz that the reaction of haemoglobin with oxygen must be accompanied by a change in the structure of the haemoglobin molecule. In myoglobin, on the other hand, no evidence for such a change has been detected.

Haurowitz' observation and the enigma posed by the structure of oxyhaemoglobin caused me to persuade a graduate student, Hilary Muirhead, to attempt an X-ray analysis at low resolution of the reduced form. For technical reasons human rather than horse haemoglobin was used at first, but we have now found that the reduced haemoglobins of man and the horse have very similar structures, so that the species does not matter here.

Unlike me, Miss Muirhead succeeded in solving the structure of her protein in time for her Ph.D. thesis. When we examined her first electron-density maps, we looked for two kinds of structural change: alterations in the folding of the individual chains and displacements of the chains with respect to each other. We could detect no changes in folding large enough to be sure that they were not due to experimental error. We did discover, however, that a striking displacement of the beta chains had taken place. The gap between them had widened and they had been shifted sideways, increasing the distance between their respective iron atoms from 33.4 to 40.3 angstrom units. The arrangement of the two alpha chains had remained unaltered, as far as we could judge, and the distance between the iron atoms in the beta chains and their nearest neighbours in the alpha chains had also remained the same. It looked as though the two beta chains had slid apart, losing contact with each other and somewhat changing their points of contact with the alpha chains.

F. J. W. Roughton and others at the University of Cambridge suggest that the change to the oxygenated form of haemoglobin takes place after three of the four iron atoms have combined with oxygen. When the change has occurred, the rate of combination of the fourth iron atom with oxygen is speeded up several hundred times. Nothing is known as yet about the atomic mechanism that sets off the displacement of the beta chains, but there is one interesting observation that allows us at least to be sure that the interaction of the iron atoms and the change of structure do not take place unless alpha and beta chains are both present.

Certain anaemia patients suffer from a shortage of alpha chains; the beta chains, robbed of their usual partners, group themselves into independent assemblages of four chains. These are known as haemoglobin H and resemble normal haemoglobin in many of their properties. Reinhold Benesch and Ruth E. Benesch of the Columbia University College of Physicians and Surgeons have discovered, however, that the four iron atoms in haemoglobin H do not interact, which led them to predict that the combination of haemoglobin H with oxygen should not be accompanied by a change of structure. Using crystals grown by Helen M. Ranney of the Albert Einstein College of Medicine, Lelio Mazzarella and I verified this prediction. Oxygenated and reduced haemoglobin H both resemble normal human reduced haemoglobin in the arrangement of the four chains.

The rearrangement of the beta chains must be set in motion by a series of atomic displacements starting at or near the iron atoms when they combine with oxygen. Our X-ray analysis has not yet reached the resolution needed to discern these, and it seems that a deeper understanding of this intriguing phenomenon may have to wait until we succeed in working out the structures of reduced haemoglobin and oxyhaemoglobin at atomic resolution.

Allosteric Enzymes

There are many analogies between the chemical activities of haemoglobin and those of enzymes catalyzing chemical reactions in living cells. These analogies lead one to expect that some enzymes may undergo changes of structure on coming into contact with the substances whose reactions they catalyze. One can imagine that the active sites of these enzymes are moving mechanisms rather than static surfaces magically endowed with catalytic properties.

Indirect and tentative evidence suggests that changes of structure involving a rearrangement of subunits like that of the alpha and beta chains of haemoglobin do indeed occur and that they may form the basis of a control mechanism known as feedback inhibition. This is a piece of jargon that biochemistry has borrowed from electrical engineering, meaning nothing more complicated than that you stop being hungry when you have had enough to eat.

Constituents of living matter such as amino acids are built up from simpler substances in a series of small steps, each step being catalyzed by an enzyme that exists specifically for that purpose. Thus a whole series of different enzymes may be needed to make one amino acid. Such a series of enzymes appears to have built-in devices for ensuring the right balance of supply and demand. For example, in the colon bacillus the amino acid isoleucine is made from the amino acid threonine in several steps. The first enzyme in the series has an affinity for threonine: it catalyzes the removal of an amino group from it. H. Edwin Umbarger of the Long Island Biological Association in Cold Spring Harbor, N.Y., discovered that the action of the enzyme is inhibited by isoleucine, the end product of the last enzyme in the series. Jean-Pierre Changeux of the Pasteur Institute later showed that isoleucine acts not, as one might have expected, by blocking the site on the enzyme molecule that would otherwise combine with threonine but probably by combining with a different site on the molecule.

The two sites on the molecule must therefore interact, and Jacques Monod, Changeux and FranÃ§ois Jacob have suggested that this is brought about by a rearrangement of subunits similar to that which accompanies the reaction of haemoglobin with oxygen. The enzyme is thought to exist in two alternative structural states: a reactive one when the supply of isoleucine has run out and an unreactive one when the supply exceeds demand. The discoverers have coined the name "allosteric" for enzymes of this kind.

The molecules of the enzymes suspected of having allosteric properties are all large ones, as one would expect them to be if they are made up of several subunits. This makes their X-ray analysis difficult. It may not be too hard to find out, however, whether or not a change of structure occurs, even if it takes a long time to unravel it in detail. In the meantime haemoglobin will serve as a useful model for the behaviour of more complex enzyme systems.

GlÃ¼hwein

I always loved GlÃ¼hwein and first tasted it when I was in Germany... Many of you must have tried it... but if you haven't, or if you are willing to make it yourself, here's the recipe! Hope you like it!!

Hot Apple Wine "Heisse Ebbelwein"
(Traditional Frankfurt Recipe)

US visitors, please see note below

Ingredients:
1 Liter Apple Wine
1/8 Liter water
60 grams sugar (approx 2oz)
1/4 stick cinnamon
3 cloves
Peelings of half a lemon or two lemon slices

Preparation

Bring the sugar, spices and water to a boil. (instead of the water experts say that you really should use apple wine for a better flavor) Then let this mixture steep for 30 minutes.
finally, mix in the remainder of the apple wine and carefully reheat to just under the boiling point.

Gluehwein (Traditional Glow Wine)

Use the same ingredients and methods, but substitute a good red wine for apple wine.
If desired, flavor with lemon or orange juice to taste.
GlÃ¼hwein is sometimes also made from raspberry, blueberry and blackberry wines.

Below are Variations of Gluehwein (but never of Heisse Ebbelwei!!!):

1. French Glow Wine: Use Bordeaux with cinnamon, rubbed nutmeg and bay leaves as the spices.

2. Seehund (Sea Dog): Substitute white wine for the red, and prepare as traditional glow wine. Depending on the acidity of the wine, a little lemon juice can be added to taste.

3. Negus: Prepare with port wine (1/2 wine, 1/2 water) and use rubbed nutmeg and lemon peelings for the spices.4. Honig Gluehwein (Honey Glow wine): prepare with red wine, 150gm honey (5oz), some cinnamon stick and two lemon slices. Heat to just under boiling.

The following is a special sort of Gluehwein. It is popular in alpine regions, especially after skiing.

Jagertee (Hunter's Tea)

1/4 Liter black tea
1/4 Liter red wine
1/4 Liter orange juice
1/4 Liter Obstler (Schnapps - not the sweet American versions, but something like Kirschwasser or dry plum brandy)
60 - 80 grams sugar (2-3 oz)
1/4 stick cinnamon
3 cloves
peelings of 1/2 lemon or two lemon slices.

Heat all the ingredients until they simmer gently for about 5 minutes. Add sugar to taste...

NOTE: for those unfamiliar with the Frankfurt and Sachsenhausen versions of apple wine. Most Americans may associate apple wine with a heavily sweetened cinnamon flavored concoction. This has no resemblance the Frankfurt version, which may be likened loosely to an apple version of Chablis or Rhine wine. It's flavor is dry and crisp, and slightly tart. We have not been able to find a good source for the Frankfurt variety in the US, or one with a similar flavor. Using the recipes above, if you are using a spiced version (standard American) of wine, you may try skipping the cinnamon and extra sugar, and adding some tartness with some lemon juice. It will not taste at all like the genuine version, but still may be quite tasty.

For the adventurous among you, you might try making your own Frankfurter Ebbelwei using the method found at Kaisers-online.de. The recipe is in German.

On the Generalized Theory of Gravitation

After presenting his general theory of relativity in 1915, German-born American physicist Albert Einstein tried in vain to unify his theory of gravitation with one that would include all the fundamental forces in nature. Einstein discussed his special and general theories of relativity and his work toward a unified field theory in a 1950 Scientific American article. At the time, he was not convinced that he had discovered a valid solution capable of extending his general theory of relativity to other forces. He died in 1955, leaving this problem unsolved.

On the Generalized Theory of Gravitation

An account of the newly published extension of the general theory of relativity against its historical and philosophical background

By Albert Einstein

The editors of Scientific American have asked me to write about my recent work which has just been published. It is a mathematical investigation concerning the foundations of field physics.

Some readers may be puzzled: Didn't we learn all about the foundations of physics when we were still at school? The answer is "yes" or "no," depending on the interpretation. We have become acquainted with concepts and general relations that enable us to comprehend an immense range of experiences and make them accessible to mathematical treatment. In a certain sense these concepts and relations are probably even final. This is true, for example, of the laws of light refraction, of the relations of classical thermodynamics as far as it is based on the concepts of pressure, volume, temperature, heat and work, and of the hypothesis of the non-existence of a perpetual motion machine.

What, then, impels us to devise theory after theory? Why do we devise theories at all? The answer to the latter question is simply: Because we enjoy "comprehending," i.e., reducing phenomena by the process of logic to something already known or (apparently) evident. New theories are first of all necessary when we encounter new facts which cannot be "explained" by existing theories. But this motivation for setting up new theories is, so to speak, trivial, imposed from without. There is another, more subtle motive of no less importance. This is the striving toward unification and simplification of the premises of the theory as a whole (i.e., Mach's principle of economy, interpreted as a logical principle).

There exists a passion for comprehension, just as there exists a passion for music. That passion is rather common in children, but gets lost in most people later on. Without this passion, there would be neither mathematics nor natural science. Time and again the passion for understanding has led to the illusion that man is able to comprehend the objective world rationally, by pure thought, without any empirical foundationsâ�”in short, by metaphysics. I believe that every true theorist is a kind of tamed metaphysicist, no matter how pure a "positivist" he may fancy himself. The metaphysicist believes that the logically simple is also the real. The tamed metaphysicist believes that not all that is logically simple is embodied in experienced reality, but that the totality of all sensory experience can be "comprehended" on the basis of a conceptual system built on premises of great simplicity. The skeptic will say that this is a "miracle creed." Admittedly so, but it is a miracle creed which has been borne out to an amazing extent by the development of science.

The rise of atomism is a good example. How may Leucippus have conceived this bold idea? When water freezes and becomes iceâ�”apparently something entirely different from waterâ�”why is it that the thawing of the ice forms something which seems indistinguishable from the original water? Leucippus is puzzled and looks for an "explanation." He is driven to the conclusion that in these transitions the "essence" of the thing has not changed at all. Maybe the thing consists of immutable particles and the change is only a change in their spatial arrangement. Could it not be that the same is true of all material objects which emerge again and again with nearly identical qualities?

This idea is not entirely lost during the long hibernation of occidental thought. Two thousand years after Leucippus, Bernoulli wonders why gas exerts pressure on the walls of a container. Should this be "explained" by mutual repulsion of the parts of the gas, in the sense of Newtonian mechanics? This hypothesis appears absurd, for the gas pressure depends on the temperature, all other things being equal. To assume that the Newtonian forces of interaction depend on temperature is contrary to the spirit of Newtonian mechanics. Since Bernoulli is aware of the concept of atomism, he is bound to conclude that the atoms (or molecules) collide with the walls of the container and in doing so exert pressure. After all, one has to assume that atoms are in motion; how else can one account for the varying temperature of gases?

A simple mechanical consideration shows that this pressure depends only on the kinetic energy of the particles and on their density in space. This should have led the physicists of that age to the conclusion that heat consists in random motion of the atoms. Had they taken this consideration as seriously as it deserved to be taken, the development of the theory of heatâ�”in particular the discovery of the equivalence of heat and mechanical energyâ�”would have been considerably facilitated.

This example is meant to illustrate two things. The theoretical idea (atomism in this case) does not arise apart from and independent of experience; nor can it be derived from experience by a purely logical procedure. It is produced by a creative act. Once a theoretical idea has been acquired, one does well to hold fast to it until it leads to an untenable conclusion.

As for my latest theoretical work, I do not feel justified in giving a detailed account of it before a wide group of readers interested in science. That should be done only with theories which have been adequately confirmed by experience. So far it is primarily the simplicity of its premises and its intimate connection with what is already known (viz., the laws of the pure gravitational field) that speak in favor of the theory to be discussed here. It may, however, be of interest to a wide group of readers to become acquainted with the train of thought which can lead to endeavors of such an extremely speculative nature. Moreover, it will be shown what kinds of difficulties are encountered and in what sense they have been overcome.

In Newtonian physics the elementary theoretical concept on which the theoretical description of material bodies is based is the material point, or particle. Thus matter is considered a priori to be discontinuous. This makes it necessary to consider the action of material points on one another as "action at a distance." Since the latter concept seems quite contrary to everyday experience, it is only natural that the contemporaries of Newtonâ�”and indeed Newton himselfâ�”found it difficult to accept. Owing to the almost miraculous success of the Newtonian system, however, the succeeding generations of physicists became used to the idea of action at a distance. Any doubt was buried for a long time to come.

But when, in the second half of the 19th century, the laws of electrodynamics became known, it turned out that these laws could not be satisfactorily incorporated into the Newtonian system. It is fascinating to muse: Would Faraday have discovered the law of electromagnetic induction if he had received a regular college education? Unencumbered by the traditional way of thinking, he felt that the introduction of the "field" as an independent element of reality helped him to coordinate the experimental facts. It was Maxwell who fully comprehended the significance of the field concept; he made the fundamental discovery that the laws of electrodynamics found their natural expression in the differential equations for the electric and magnetic fields. These equations implied the existence of waves, whose properties corresponded to those of light as far as they were known at that time.

This incorporation of optics into the theory of electromagnetism represents one of the greatest triumphs in the striving toward unification of the foundations of physics; Maxwell achieved this unification by purely theoretical arguments, long before it was corroborated by Hertz' experimental work. The new insight made it possible to dispense with the hypothesis of action at a distance, at least in the realm of electromagnetic phenomena; the intermediary field now appeared as the only carrier of electromagnetic interaction between bodies, and the field's behavior was completely determined by contiguous processes, expressed by differential equations.

Now a question arose: Since the field exists even in a vacuum, should one conceive of the field as a state of a "carrier," or should it rather be endowed with an independent existence not reducible to anything else? In other words, is there an "ether" which carries the field; the ether being considered in the undulatory state, for example, when it carries light waves?

The question has a natural answer: Because one cannot dispense with the field concept, it is preferable not to introduce in addition a carrier with hypothetical properties. However, the pathfinders who first recognized the indispensability of the field concept were still too strongly imbued with the mechanistic tradition of thought to accept unhesitatingly this simple point of view. But in the course of the following decades this view imperceptibly took hold.

The introduction of the field as an elementary concept gave rise to an inconsistency of the theory as a whole. Maxwell's theory, although adequately describing the behavior of electrically charged particles in their interaction with one another, does not explain the behavior of electrical densities, i.e., it does not provide a theory of the particles themselves. They must therefore be treated as mass points on the basis of the old theory. The combination of the idea of a continuous field with that of material points discontinuous in space appears inconsistent. A consistent field theory requires continuity of all elements of the theory, not only in time but also in space, and in all points of space. Hence the material particle has no place as a fundamental concept in a field theory. Thus even apart from the fact that gravitation is not included, Maxwell's electrodynamics cannot be considered a complete theory.

Maxwell's equations for empty space remain unchanged if the spatial coordinates and the time are subjected to a particular kind of linear transformationsâ�”the Lorentz transformations ("covariance" with respect to Lorentz transformations). Covariance also holds, of course, for a transformation which is composed of two or more such transformations; this is called the "group" property of Lorentz transformations.

Maxwell's equations imply the "Lorentz group," but the Lorentz group does not imply Maxwell's equations. The Lorentz group may indeed be defined independently of Maxwell's equations as a group of linear transformations which leave a particular value of the velocityâ�”the velocity of lightâ�”invariant. These transformations hold for the transition from one "inertial system" to another which is in uniform motion relative to the first. The most conspicuous novel property of this transformation group is that it does away with the absolute character of the concept of simultaneity of events distant from each other in space. On this account it is to be expected that all equations of physics are covariant with respect to Lorentz transformations (special theory of relativity). Thus it came about that Maxwell's equations led to a heuristic principle valid far beyond the range of the applicability or even validity of the equations themselves.

Special relativity has this in common with Newtonian mechanics: The laws of both theories are supposed to hold only with respect to certain coordinate systems: those known as "inertial systems." An inertial system is a system in a state of motion such that "force-free" material points within it are not accelerated with respect to the coordinate system. However, this definition is empty if there is no independent means for recognizing the absence of forces. But such a means of recognition does not exist if gravitation is considered as a "field."

Let A be a system uniformly accelerated with respect to an "inertial system" I. Material points, not accelerated with respect to I, are accelerated with respect to A, the acceleration of all the points being equal in magnitude and direction. They behave as if a gravitational field exists with respect to A, for it is a characteristic property of the gravitational field that the acceleration is independent of the particular nature of the body. There is no reason to exclude the possibility of interpreting this behavior as the effect of a "true" gravitational field (principle of equivalence). This interpretation implies that A is an "inertial system," even though it is accelerated with respect to another inertial system. (It is essential for this argument that the introduction of independent gravitational fields is considered justified even though no masses generating the field are defined. Therefore, to Newton such an argument would not have appeared convincing.) Thus the concepts of inertial system, the law of inertia and the law of motion are deprived of their concrete meaningâ�”not only in classical mechanics but also in special relativity. Moreover, following up this train of thought, it turns out that with respect to A time cannot be measured by identical clocks; indeed, even the immediate physical significance of coordinate differences is generally lost. In view of all these difficulties, should one not try, after all, to hold on to the concept of the inertial system, relinquishing the attempt to explain the fundamental character of the gravitational phenomena which manifest themselves in the Newtonian system as the equivalence of inert and gravitational mass? Those who trust in the comprehensibility of nature must answer: No.

This is the gist of the principle of equivalence: In order to account for the equality of inert and gravitational mass within the theory it is necessary to admit non-linear transformations of the four coordinates. That is, the group of Lorentz transformations and hence the set of the "permissible" coordinate systems has to be extended.

What group of coordinate transformations can then be substituted for the group of Lorentz transformations? Mathematics suggests an answer which is based on the fundamental investigations of Gauss and Riemann: namely, that the appropriate substitute is the group of all continuous (analytical) transformations of the coordinates. Under these transformations the only thing that remains invariant is the fact that neighboring points have nearly the same coordinates; the coordinate system expresses only the topological order of the points in space (including its four-dimensional character). The equations expressing the laws of nature must be covariant with respect to all continuous transformations of the coordinates. This is the principle of general relativity.

The procedure just described overcomes a deficiency in the foundations of mechanics which had already been noticed by Newton and was criticized by Leibnitz and, two centuries later, by Mach: Inertia resists acceleration, but acceleration relative to what? Within the frame of classical mechanics the only answer is: Inertia resists acceleration relative to space. This is a physical property of spaceâ�”space acts on objects, but objects do not act on space. Such is probably the deeper meaning of Newton's assertion spatium est absolutum (space is absolute). But the idea disturbed some, in particular Leibnitz, who did not ascribe an independent existence to space but considered it merely a property of "things" (contiguity of physical objects). Had his justified doubts won out at that time, it hardly would have been a boon to physics, for the empirical and theoretical foundations necessary to follow up his idea were not available in the 17th century.

According to general relativity, the concept of space detached from any physical content does not exist. The physical reality of space is represented by a field whose components are continuous functions of four independent variablesâ�”the coordinates of space and time. It is just this particular kind of dependence that expresses the spatial character of physical reality.

Since the theory of general relativity implies the representation of physical reality by a continuous field, the concept of particles or material points cannot play a fundamental part, nor can the concept of motion. The particle can only appear as a limited region in space in which the field strength or the energy density are particularly high.

A relativistic theory has to answer two questions: 1) What is the mathematical character of the field? 2) What equations hold for this field?

Concerning the first question: From the mathematical point of view the field is essentially characterized by the way its components transform if a coordinate transformation is applied. Concerning the second question: The equations must determine the field to a sufficient extent while satisfying the postulates of general relativity. Whether or not this requirement can be satisfied depends on the choice of the field-type.

The attempt to comprehend the correlations among the empirical data on the basis of such a highly abstract program may at first appear almost hopeless. The procedure amounts, in fact, to putting the question: What most simple property can be required from what most simple object (field) while preserving the principle of general relativity? Viewed from the standpoint of formal logic, the dual character of the question appears calamitous, quite apart from the vagueness of the concept "simple." Moreover, from the standpoint of physics there is nothing to warrant the assumption that a theory which is "logically simple" should also be "true."

Yet every theory is speculative. When the basic concepts of a theory are comparatively "close to experience" (e.g., the concepts of force, pressure, mass), its speculative character is not so easily discernible. If, however, a theory is such as to require the application of complicated logical processes in order to reach conclusions from the premises that can be confronted with observation, everybody becomes conscious of the speculative nature of the theory. In such a case an almost irresistible feeling of aversion arises in people who are inexperienced in epistemological analysis and who are unaware of the precarious nature of theoretical thinking in those fields with which they are familiar.

On the other hand, it must be conceded that a theory has an important advantage if its basic concepts and fundamental hypotheses are "close to experience," and greater confidence in such a theory is certainly justified. There is less danger of going completely astray, particularly since it takes so much less time and effort to disprove such theories by experience. Yet more and more, as the depth of our knowledge increases, we must give up this advantage in our quest for logical simplicity and uniformity in the foundations of physical theory. It has to be admitted that general relativity has gone further than previous physical theories in relinquishing "closeness to experience" of fundamental concepts in order to attain logical simplicity. This holds already for the theory of gravitation, and it is even more true of the new generalization, which is an attempt to comprise the properties of the total field. In the generalized theory the procedure of deriving from the premises of the theory conclusions that can be confronted with empirical data is so difficult that so far no such result has been obtained. In favor of this theory are, at this point, its logical simplicity and its "rigidity." Rigidity means here that the theory is either true or false, but not modifiable.

The greatest inner difficulty impeding the development of the theory of relativity is the dual nature of the problem, indicated by the two questions we have asked. This duality is the reason why the development of the theory has taken place in two steps so widely separated in time. The first of these steps, the theory of gravitation, is based on the principle of equivalence discussed above and rests on the following consideration: According to the theory of special relativity, light has a constant velocity of propagation. If a light ray in a vacuum starts from a point, designated by the coordinates x1, x2 and x3 in a three dimensional coordinate system, at the time x4, it spreads as a spherical wave and reaches a neighboring point (x1 + dx1, x2 + dx2, x3 + dx3) at the time x4 + dx4. Introducing the velocity of light, c, we write the expression:

âˆš(dx12+dx22+dx32)=cdx4

This can also be written in the form:

dx12+dx22+dx32-c2 dx42=0

This expression represents an objective relation between neighboring space-time points in four dimensions, and it holds for all inertial systems, provided the coordinate transformations are restricted to those of special relativity. The relation loses this form, however, if arbitrary continuous transformations of the coordinates are admitted in accordance with the principle of general relativity. The relation then assumes the more general form:

Î£ik gik dxi dxk=0

The gik are certain functions of the coordinates which transform in a definite way if a continuous coordinate transformation is applied. According to the principle of equivalence, these gik functions describe a particular kind of gravitational field: a field which can be obtained by transformation of "field-free" space. The gik satisfy a particular law of transformation. Mathematically speaking, they are the components of a "tensor" with a property of symmetry which is preserved in all transformations; the symmetrical property is expressed as follows:

gik=gki

The idea suggests itself: May we not ascribe objective meaning to such a symmetrical tensor, even though the field cannot be obtained from the empty space of special relativity by a mere coordinate transformation? Although we cannot expect that such a symmetrical tensor will describe the most general field, it may well describe the particular case of the "pure gravitational field." Thus it is evident what kind of field, at least for a special case, general relativity has to postulate: a symmetrical tensor field.

Hence only the second question is left: What kind of general covariant field law can be postulated for a symmetrical tensor field?

This question has not been difficult to answer in our time, since the necessary mathematical conceptions were already at hand in the form of the metric theory of surfaces, created a century ago by Gauss and extended by Riemann to manifolds of an arbitrary number of dimensions. The result of this purely formal investigation has been amazing in many respects. The differential equations which can be postulated as field law for gik cannot be of lower than second order, i.e., they must at least contain the second derivatives of the gik with respect to the coordinates. Assuming that no higher than second derivatives appear in the field law, it is mathematically determined by the principle of general relativity. The system of equations can be written in the form:

Rik=0

The Rik transform in the same manner as the gik, i.e., they too form a symmetrical tensor.

These differential equations completely replace the Newtonian theory of the motion of celestial bodies provided the masses are represented as singularities of the field. In other words, they contain the law of force as well as the law of motion while eliminating "inertial systems."

The fact that the masses appear as singularities indicates that these masses themselves cannot be explained by symmetrical gik fields, or "gravitational fields." Not even the fact that only positive gravitating masses exist can be deduced from this theory. Evidently a complete relativistic field theory must be based on a field of more complex nature, that is, a generalization of the symmetrical tensor field.

Before considering such a generalization, two remarks pertaining to gravitational theory are essential for the explanation to follow.

The first observation is that the principle of general relativity imposes exceedingly strong restrictions on the theoretical possibilities. Without this restrictive principle it would be practically impossible for anybody to hit on the gravitational equations, not even by using the principle of special relativity, even though one knows that the field has to be described by a symmetrical tensor. No amount of collection of facts could lead to these equations unless the principle of general relativity were used. This is the reason why all attempts to obtain a deeper knowledge of the foundations of physics seem doomed to me unless the basic concepts are in accordance with general relativity from the beginning. This situation makes it difficult to use our empirical knowledge, however comprehensive, in looking for the fundamental concepts and relations of physics, and it forces us to apply free speculation to a much greater extent than is presently assumed by most physicists. I do not see any reason to assume that the heuristic significance of the principle of general relativity is restricted to gravitation and that the rest of physics can be dealt with separately on the basis of special relativity, with the hope that later on the whole may be fitted consistently into a general relativistic scheme. I do not think that such an attitude, although historically understandable, can be objectively justified. The comparative smallness of what we know today as gravitational effects is not a conclusive reason for ignoring the principle of general relativity in theoretical investigations of a fundamental character. In other words, I do not believe that it is justifiable to ask: What would physics look like without gravitation?

The second point we must note is that the equations of gravitation are 10 differential equations for the 10 components of the symmetrical tensor gik. In the case of a non-general relativistic theory, a system is ordinarily not overdetermined if the number of equations is equal to the number of unknown functions. The manifold of solutions is such that within the general solution a certain number of functions of three variables can be chosen arbitrarily. For a general relativistic theory this cannot be expected as a matter of course. Free choice with respect to the coordinate system implies that out of the 10 functions of a solution, or components of the field, four can be made to assume prescribed values by a suitable choice of the coordinate system. In other words, the principle of general relativity implies that the number of functions to be determined by differential equations is not 10 but 10-4=6. For these six functions only six independent differential equations may be postulated. Only six out of the 10 differential equations of the gravitational field ought to be independent of each other, while the remaining four must be connected to those six by means of four relations (identities). And indeed there exist among the left-hand sides, Rik, of the 10 gravitational equations four identitiesâ�”â�œBianchi's identities"â�”which assure their "compatibility."

In a case like thisâ�”when the number of field variables is equal to the number of differential equationsâ�”compatibility is always assured if the equations can be obtained from a variational principle. This is indeed the case for the gravitational equations.

However, the 10 differential equations cannot be entirely replaced by six. The system of equations is indeed "overdetermined," but due to the existence of the identities it is overdetermined in such a way that its compatibility is not lost, i.e., the manifold of solutions is not critically restricted. The fact that the equations of gravitation imply the law of motion for the masses is intimately connected with this (permissible) overdetermination.

After this preparation it is now easy to understand the nature of the present investigation without entering into the details of its mathematics. The problem is to set up a relativistic theory for the total field. The most important clue to its solution is that there exists already the solution for the special case of the pure gravitational field. The theory we are looking for must therefore be a generalization of the theory of the gravitational field. The first question is: What is the natural generalization of the symmetrical tensor field?

This question cannot be answered by itself, but only in connection with the other question: What generalization of the field is going to provide the most natural theoretical system? The answer on which the theory under discussion is based is that the symmetrical tensor field must be replaced by a non-symmetrical one. This means that the condition gik=gki for the field components must be dropped. In that case the field has 16 instead of 10 independent components.

There remains the task of setting up the relativistic differential equations for a non-symmetrical tensor field. In the attempt to solve this problem one meets with a difficulty which does not arise in the case of the symmetrical field. The principle of general relativity does not suffice to determine completely the field equations, mainly because the transformation law of the symmetrical part of the field alone does not involve the components of the antisymmetrical part or vice versa. Probably this is the reason why this kind of generalization of the field has hardly ever been tried before. The combination of the two parts of the field can only be shown to be a natural procedure if in the formalism of the theory only the total field plays a role, and not the symmetrical and antisymmetrical parts separately.

It turned out that this requirement can indeed be satisfied in a natural way. But even this requirement, together with the principle of general relativity, is still not sufficient to determine uniquely the field equations. Let us remember that the system of equations must satisfy a further condition: the equations must be compatible. It has been mentioned above that this condition is satisfied if the equations can be derived from a variational principle.

This has indeed been achieved, although not in so natural a way as in the case of the symmetrical field. It has been disturbing to find that it can be achieved in two different ways. These variational principles furnished two systems of equationsâ�”let us denote them by E1 and E2â�”which were different from each other (although only slightly so), each of them exhibiting specific imperfections. Consequently even the condition of compatibility was insufficient to determine the system of equations uniquely.

It was, in fact, the formal defects of the systems E1 and E2 that indicated a possible way out. There exists a third system of equations, E3, which is free of the formal defects of the systems E1 and E2 and represents a combination of them in the sense that every solution of E3 is a solution of E1 as well as of E2. This suggests that E3 may be the system we have been looking for. Why not postulate E3, then, as the system of equations? Such a procedure is not justified without further analysis, since the compatibility of E1 and that of E2 do not imply compatibility of the stronger system E3, where the number of equations exceeds the number of field components by four.

An independent consideration shows that irrespective of the question of compatibility the stronger system, E3, is the only really natural generalization of the equations of gravitation.

But E3 is not a compatible system in the same sense as are the systems E1 and E2, whose compatibility is assured by a sufficient number of identities, which means that every field that satisfies the equations for a definite value of the time has a continuous extension representing a solution in four-dimensional space. The system E3, however, is not extensible in the same way. Using the language of classical mechanics we might say: In the case of the system E3 the "initial condition" cannot be freely chosen. What really matters is the answer to the question: Is the manifold of solutions for the system E3 as extensive as must be required for a physical theory? This purely mathematical problem is as yet unsolved.

The skeptic will say: "It may well be true that this system of equations is reasonable from a logical standpoint. But this does not prove that it corresponds to nature." You are right, dear skeptic. Experience alone can decide on truth. Yet we have achieved something if we have succeeded in formulating a meaningful and precise question. Affirmation or refutation will not be easy, in spite of an abundance of known empirical facts. The derivation, from the equations, of conclusions which can be confronted with experience will require painstaking efforts and probably new mathematical methods.

Sami5001's Journals

The Book of Mozilla

The Book of Mozilla

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Contents

About The Book of Mozilla

The Book of Mozilla, 12:10

The Book of Mozilla, 3:31

The Book of Mozilla, 7:15

See also

External links

Changes to about:mozilla page

Book of Mozilla on Mozilla.org

Articles about The Book of Mozilla

Collections of passages

The Meaning of Dreams

The Haemoglobin Molecule

GlÃ¼hwein

On the Generalized Theory of Gravitation