Calendar

Several calendars are in use in Tibet. In this chapter we discuss the official Phuglugs (or Phug-pa or Phukluk) version of the Kālacakra (“Wheel of Time”) calendar, derived from the Kālacakra Tantra, translated into Tibetan from the Sanskrit in the eleventh century, used by the majority of Tibetans today, and sanctioned by the Dalai Lama. (The other widely used version is the Tsurphu.) The calendar is similar to the Hindu lunisolar calendars, somewhere between the arithmetic simplicity of the old Hindu version, and the astronomical complexity of the modern Hindu. There are also regional variants, because the calculated astronomical events are in terms of local time. The Bhutan, Mongolian, and Sherpa calendars are very similar.

Months are lunar; their length is based on an approximation to the varying length of the true synodic month, and can be 29 or 30 civil days long. Months are numbered consecutively, except for leap months, which precede their ordinary counterparts, as on the Hindu lunisolar calendar, and are named and numbered the same. The month names in Tibetan are:

Weekdays are named in Tibetan as follows:

There are several conventions for naming years. The most common is to use a 60-year cycle, naming them either like the Hindu Jovian years (Section 10.1), or using simultaneous 12-totem and 5-element cycles, in the fashion of the Chinese calendar (Section 19.4).

This book has developed over a more than 30-year period during which the calendrical algorithms and our presentation of them have continually evolved. Our initial motivation was an effort by one of us (E.M.R.) to create Emacs-Lisp code that would provide calendar and diary features for GNU Emacs [15]; this version of the code included the Gregorian, Islamic, and Hebrew calendars (the Hebrew implemented by N.D.). A deluge of inquiries from around the globe soon made it clear to us that there was keen interest in an explanation that would go beyond the code itself, leading to our article [3] and encouraging us to rewrite the code completely, this time in Common Lisp [16]. The subsequent addition—by popular demand—of the Mayan and French Revolutionary calendars to GNU Emacs prompted a second article [13]. We received many hundreds of reprint requests for these articles. This response far exceeded our expectations and provided the impetus to write a book in which we could more fully address the multifaceted subject of calendars and their implementation.

The subject of calendars has always fascinated us with its cultural, historical, and mathematical wealth, and we have occasionally employed calendars as accessible examples in introductory programming courses. Once the book's plan took shape, our curiosity turned into obsession. We began by extending our programs to include other calendars such as the Chinese, Coptic, modern Hindu, and arithmetic Persian. Then, of course, the code for these newly added calendars needed to be rewritten, in some cases several times, to bring it up to the standards of the earlier material. We have long since lost track of the number of revisions, and, needless to say, we could undoubtedly devote another decade to polishing what we have, tracking down minutiæ, and implementing and refining additional interesting calendars. As much as we might be tempted to, circumstances do not allow us to follow Maimonides’ dictum quoted above.

The following description of the presentation of the annual calendar in China is taken from Peter (Pierre) Hoang (A Notice of the Chinese Calendar and a Concordance with the European Calendar, 2nd edn., Catholic Mission Press, Shanghai, 1904):

Numerous calendars are used in India for different purposes. The Gregorian calendar is used by the government for civil matters; the Islamic calendar is used by Muslims; the Hindus employ both solar and lunisolar calendars. Indeed, there are over 30 variations of the Hindu calendar in active use. In March 1957, an attempt was made to revise the traditional calendar to follow the pattern of the Gregorian leap-year structure [1]. The proposed reform has not, however, been widely accepted, though the new National Calendar dates appear in published calendars. An excellent description of many Indian calendars, together with extensive tables, is given in [6].

The best known of several related systems used on the Indian subcontinent is the classical Hindu calendar of the (present) Sūrya-Siddhānta (circa 1000), said to have been revealed to Asura Maya the Assyrian at the end of the last “Golden Age,” in the year 2163154 b.c.e. al-Bīrūnī attributes the book to Lata. This work introduced a calendar based on approximations to the true times of astronomical events rather than the mean values used in the earlier, simpler, calendar described in Chapter 10. This calendar is somewhat similar to the Chinese, beginning its months according to the actual time of new moon; however, the Chinese calendar today uses modern astronomical methods to determine these times whereas the Hindu calendar applies fixed, ancient methods to approximate the true positions of the sun and moon.

Alan Turing's short life ran from 1912 to 1954. The inspiration for this volume lay in the centenary of his birth. But Barry Cooper and I, as editors, wanted the word ‘future’ in our title, as well as a reference to the past. We chose the provocative title The Once and Future Turing, alluding to the legend of King Arthur's tomb. We invited a range of distinguished contributors to give us snapshots of scientific work which rest upon Turing's original discoveries, and share the spirit of his thought, but which also give a glimpse of something lying beyond the present. The result is a volume of 15 papers, whose authors responded to our prompting in utterly different ways.

Turing himself was not reticent about advancing visions of the future. Famously, he did so in his classic 1950 paper ‘Computing machinery and intelligence’. He was not always right. Few people would claim that his 50-year prediction for machine intelligence, cautiously phrased as it was, has been fulfilled. On the other hand, he underestimated the potential for fast, cheap, huge-scale computing. His 1948 picture of the future of computer hardware correctly identified the speed of light as the critical constraint governing computing speed. But his assumption of centimetre-scale electronic components overlooked the enormous potential for miniaturisation. Turing's foresight was more strikingly demonstrated by his 1946 observations about the power of the universal machine and the future of what would now be called the software industry; ‘every known process has got to be translated into instruction table form … ’

In 1946 he could speak with the confidence of being the mastermind of the Anglo-American crypto war – with its own legacy for the future of international relations, which, to say the least, has not yet been evaluated. In 1939 he and Gordon Welchman had pulled off the feat of persuading the British authorities to make a huge investment in the untried technology of the Turing Bombe, on the conviction, correct as it turned out, that its logical brilliance would transform British fortunes. This vision was not his alone. To beat Hitler, Bletchley Park seems to have borrowed from the future, scientifically, organisationally and socially, as if the sixties had arrived before the forties.

Top-down versus bottom-up design

The design of modern products commonly follows a well-defined path, such as for example the human-centered approach used by the famous IDEO design consultancy, Kelley (2001). Design has turned into a process that can be studied, formalized, learned, and improved. As Tom Kelley (2001) explains, IDEO uses a methodology that has the following five basic steps: understand, observe, visualize, evaluate and refine, implement. Two things are important to notice in this process. First, there is an implicit “loop” for the evaluation and refinement process. No product is perfect from the beginning and most of them will need to be refined and re-evaluated over and over again. Second, the process is organized in a very top-down manner, i.e., it is a step-wise process that starts with a high-level goal, target, or vision and then gradually follows down in the hierarchy by specifying, evaluating, and implementing the lower-level (sub)systems. That is the way engineers design cars, airplanes, computers, and whatnot. The most important reason why top-down design has been so successful in the engineering world is divide et impera, or in more contemporary words, divide and conquer. Top-down design allows us to handle complex problems and to treat subsystems as abstract black boxes. While this generally works well in the engineering world, an entirely different design process can be observed in nature. Nature proceeds in a bottom-up way by simple trial and error. The process is called evolution and has led to amazing, albeit by no means perfect, ‘designs. ’ As the name says, bottom-up design proceeds from the bottom up by piecing subsystems into something bigger. Often, the functionality of the resulting system is greater than the sum of its parts. In that context, the term emergence (Holland, 1999) comes up frequently. Loosely speaking, emergence means that the interactions of the subsystem components do not necessarily allow us to predict the behavior at the next level. There is an element of surprise (Ronald et al., 1999) involved, which describes that non-predictibility nicely.

Today, the computing disciplines face difficult challenges from extending CMOS technology to and beyond dimensional scaling. One solution path is to use an innovative combination of novel manufacturing techniques, devices, compute paradigms, and architectures to create new information processing technology that may be radically different from what we currently know.

When we look back at the twentieth century, I have no doubt that the single most important idea that we will see to have emerged there is the idea of computation. And already that idea has transformed our technology and many aspects of our world. But there is, I believe, still much more to come.

Although he certainly did not realize the magnitude of what he was starting, Alan Turing in 1936 laid the single most critical foundation for the idea of computation when he invented the universal Turing machine.

By the time Turing died in 1954, this idea had come by a circuitous route (through neural networks and the like) to inform early practical electronic computers. And it had also led Turing himself to think in a real way about the creation of artificial intelligence.

But that was about as far as it got. And in his last years, when Turing thought, for example, about theories of biology, he did not realize that his ideas of computation might be relevant to them.

Through the rest of the 1950s and into the 1960s and 1970s, practical computers became more and more powerful, and more and more common. And, at least among the small community of theoretical computer scientists, universal computing took its place as a foundational concept.

Meanwhile, however, the rest of science continued its development, based in some cases on experiment and in some cases on mathematical analysis. Computers were occasionally used to support these existing methods. But there was no real idea that computation as an abstract concept might be centrally relevant.

And indeed, in a sense, as computer technology advanced, computation as a concept seemed to recede more and more – as something to be mentioned for background but not something to be made the core of what should be studied.

If Turing had lived longer, I rather suspect he might not have left it that way –instead he might have begun to realize the much broader significance of the concept of computation, the foundations of which he was so instrumental in laying.

I was born five years after Alan Turing died. And in my half-century of life so far, I have launched three large projects, all fundamentally based on the idea of computation and all, strangely enough, pointing in directions that I suspect Alan Turing might have followed had he lived longer.

The world is open for fresh ideas about fundamentals of mind, matter, information, space and time. Turing made just such a plunge in 1936, undeterred by being young and new to the field. Compared with the carefully delineated and trained trajectory expected of modern research students, his d ébut seems amazing. It was extraordinary even then, being without precursor papers or collaborators. But, of course, the young Turing was not alone: Einstein and Eddington, von Neumann and Russell, had spoken volumes to his receptive mind, and he had worked hard through Cambridge mathematics. He was justifiably proud of his breakthrough as a 24-year-old, and correspondingly interested in spotting new youthful talent. His highly unconventional running with young Garner had a parallel: a wish to hand on scientific inspiration to a young person, perhaps in a way quite outside the standard academic framework. This Alan Turing indeed achieved, to some extent, but maybe he has still more to do.

These essays themselves, with their unusual connections and incomplete conclusions, might stimulate new minds with new thoughts. Miguel Walsh, winner of the 2014 Ramanujan Prize, explains how he learned about outstanding problems in mathematics from the Internet, while otherwise isolated in Argentina. We are reminded of how Srinivasa Ramanujan himself emerged from isolation, in the very India where Alan Turing was conceived, through the old mechanism of print and post offices. In the last century, the universal machine has greatly accelerated and amplified such global interaction. Who knows! The history of science depends on the strangest encounters of human brains. The once and future Turing both take their life from the unpredictable and sometimes highly inconvenient magic of human thought.