The Artifacts of Lothal

Here is a photo of some pieces excavated from the Lothal site in northwest India during the 1950's-'60's. These pieces are often referred to online as from a "chesslike game", discovered at Lothal. It’s probably fair to say that some kind of board game(s) was played at Lothal, part of the Harrapan or Indus Valley civilization that thrived from about 2600 BCE to 1700 BCE. We know that the Indus Valley people had trade contacts with Mesopotamia, Egypt and the peoples of the Persian plateau and all of those people played board games. In Mesopotamia, there was the game of 20-squares, imported by Egypt, where the 20-squares boards (in somewhat modified form) were often on the other side of a 30-squares game called senet. In the Persian plateau stone game boards have been discovered at Jiroft – not all of which are frauds. And there was the magnificently carved wooden "serpent game board" discovered in excavations at Shar-i Sohktah – a variation of the 20-squares boards excavated by Woolley at Ur.

Trade contacts over a 900 year period would no doubt have led to the introduction of board games into the Indus region from any or all of these regions, even assuming their civilization had before then been unfamiliar with the concept and did not produce their own board games. As far as I am aware, however, no game boards were excavated in Lothal, or at any of the other Indus Valley sites. This does not mean that the people there did not play board games; it may simply mean that they made their boards out of materials that did not survive the ravages of time.

And so we are left with these pieces, many which resemble game pieces discovered in Egypt, Mesopotamia and Shar-I Sohktah. Did the Lothal residents play their own unique board game with them? We don’t know. Did the Lothal residents play 20-squares and senet? We don’t know. I also cannot tell you whether all of these pieces were found one at a time (such as the lonely Butrint piece, which was the kiss of death according to some chess historians because it could not be conclusively determined by other evidence that the Butrint piece was a chess piece) or whether some were found together. As some "experts" have said of the Butrint piece (it looks like a "finial"), these could all just be "finials."

It is tempting to assume that these pieces might be from a form of proto-chess. They were discovered, after all, in the area called Sindh (also called Hind in some 19th century literature on the subject of the origins of chess) and that is the area traditionally attributed by Murray as where chess first arose. I don’t know about you, but one of the Lothal pieces in the photo looks rather like a modern "knight" to me – very suggestive of a horse’s head. Rather like the Butrint piece looks like a modern "king" or "queen."

See here for some information about Lothal and the Indus Valley civilization.

For an analysis of the iconography embodied in the Butrint piece, see Don McLean’s "Butrint in Vivisection" Parts I and II. Here (and here) are some earlier blog entries where I talk about the Butrint piece.

Friday Night Miscellany

I'm tired tonight darlings, so this will be relatively short. Judit Polgar is one of the announced super-GMs who will be appearing in a stellar "A" Group line-up at the 2008 Corus in January. Corus, as you may (or may not) know, was bought out by the Indian Tata conglomerate. I'm glad to see the management is continuing the Corus Super-Tournament tradition. As far as I can tell from scanning news reports, Judit hasn't played in a tournament since she lost in the beginning rounds of the play-offs for spots in the World Chess Championship "Tournament" recently concluded in Mexico City. It will be good to see her in action again, and let's hope she's been doing some serious studying. It's a pain in the you-know-what to constantly keep to the grind of staying on top of the latest games and chess knowledge, but if you want to stay in the top, that's what you have to do. It's the same in many professions. Whew! Sure glad I'm not a top level chess player! Speaking of Tata brings to mind what I've been up to my ears in the past week - doing research for the investment club of which I'm President and chief, cook and bottlewasher. It's a grind when I'm doing research into potential "buys." Not only do I have to convince myself (not such an easy job), I have to also convince the members of the club that a particular company is a worthy "buy" candidate! I first heard about "investment clubs" in December, 2000 - yes, right around the time of the beginning of the tech stock crash (it took several months, if you'll recall). It was at the old "Officeworld" as I used to call it (where I work now, I just call it the office, because it's not near the soap-opera as was my former place of employment, my my my). I attended the January, 2001 club meeting at Officeworld and I was hooked. By March, 2001, I had opened up a brokerage account (my "play" account) and was regularly investing a fixed amount each month in addition to the amount I was contributing as a member of the Officeworld investment club. Theretofore, I was like millions of other Americans, convinced that investing and money management and such was something best left to the "experts" for which you paid fees every year. How wrong I was. I had "beginner's luck" - really - in my initial "on my own" investments. But - it also was not as easy as I thought at first. Shortly after I joined the Officeworld investment club, I took a good hard look at my 401(k) investments. Like millions of other Americans, I am not covered by a pension plan - there is only the 401(k) plan and - as I was lucky to have - a profit-sharing plan. From what I'd learned as an investment club member, I was able to insightfully analyze the investment returns of the various funds offered for investment through the 401(k) and profit-sharing plans, and made some adjustments - to my benefit. Before then, I'd been coasting along, just like millions of others do, "chasing" after prior returns instead of really grasping the essentials of fund returns. (Hint: It's not so hard to understand, when you know what to look for and what to look at). As I educated myself by extensive online reading as well as mass consumption of commercial investment magazines, I developed a real "feel" for picking stocks. I'm not a trader by any means. I invest for the long term - five years or more. And so, my criteria, and the criteria that I have since taught to several other fledgling investors, is different (a lot different) from the short-term or day-trader approach. Since that first paying of club dues in January, 2001, I've come a long way. I have invested every month in my club and individual account (I call it my "play" account) since 2001, even through the fear-inspiring drop in the market after 9/11. I've learned that, for the most part, commercial investment magazines aren't worth the paper they are written on. I learned how to spot winners and trends long before they're published in magazine articles, when the lemmings jump (positive or negative) and may make a price shift one way or the other - a temporary price shit. I have also learned the art of waiting - for a stock price to come down into my "buy" range, and for a stock price to go up after temporary market set-backs driven by the "lemmings" mentality. This is one of the most important things I have taught to my "pupils" - besides buying growing companies at a reasonable price. I have had good success - and some disasters along the way - but not so many disasters because I've been careful. I've also been overly cautious at times and sold out of positions where I've had a more than 100% gain, only to see the price continue upward to 200% and more. Oh well... Anyway, after I left Officeworld at the end of September, 2002, I continued with the investment club there for awhile, but eventually there was a parting of the ways. To make a long story short, it has been my pleasure to be the President of a very small investment club for the past couple of years, and we have had great success. Our returns to date are - bragging now - over 72% since May, 2005, when we made our initial investment. Our goal is to double our money every 5 years; looks like we're on-track to do that well before our five year "first investment date." Of course, as we continue to add to our portfolio, it will become harder to achieve the success we've had to date - although we'll certainly try! I couldn't be more pleased with how things have turned out. I continue to learn and learn more about investments and investing, and I'm pleased to be passing along to others what I've learned - and we all learn together. Yes, I know, that sounds sentimental and blah-blah. We're having fun while we're doing the blah-blah. We meet once a month, usually for breakfast on a Saturday or Sunday, for a couple of hours. Right from the beginning, we've had outings just for fun. For instance, we've held a meeting on the train to Chicago for a day-trip; we've met for breakfast at different locations and gone over reports over eggs and coffee and then spent hours attending fairs and festivals and shopping. In November we're doing a "spa" day. The goal is to get some of the young hairdressers and spa attendants interested in investing as we chat about our current buy prospects and the status of our portfolio :) Suffice to say - I was always one to say "pay someone else to do it." Now I know better. I can do it better myself and save money to boot by doing it myself. You can too.

New Rune Stone Discovered

See prior post mentioning runes. From Aftenposten.no Published 04 October 207 Ancient rune stone found Archeologists were very pleasantly surprised to discover an unknown rune stone under the floor of Hauskjeen church in Rennesøy, Rogaland in western Norway The rune stone likely stems from the 11th century, and tells of Halvard's powers or Halvard's magnificence. The stone slab has been broken off at both ends, and the text ("Mæktir haluar") is just a small part of the original inscription. Archeologists from the Archeological Museum in Stavanger thought at first that they had rediscovered a rune stone documented in 1639 and 1745, but closer examination revealed that the stone has not been reported before. The discovery site implies that the slab could have been a tombstone, but the text makes it more likely that it is the remains of a monument. The rune stone is now on exhibit at Stavanger's Archeological Museum. The runes are from the so-called medieval runes in use from the second half of the 11th century.

October 2007 "Chess Life"

Nice cover - it's IM Irina Krush on a beach, in the sun, with a king clutched in her hand and a "fierce" smirk on her face... No, she's not in a bikini, guys. There are, I think, better photos of her on page 4 and 23, in black and white, where she looks radiantly young and lovely (and yes, she is fully dressed). Krush is the cover story on page 22 with a review of the round by round action from the 2007 U.S. Women's Chess Championship. Yaaaayyyy! Goddesschess' Brilliancy Prize is mentioned on page 26 along with our url (www.goddesschess.com, ahem) and Liz Vicary's annotation of her brilliancy prize winning game behind the black pieces with Camilla Baginskaite. The cover story is 8 pages long - nice job, Chess Life. A bit of irony, the next article (beginning page 31) is "Ivanchuk Tops Montreal; Kamsky Disappoints." But flipping through the magazine I find on page 73 a "Special Notice!! GM Gata Kamsky (blah blah blah) will be playing BOARD #1 2008 National Open June 6-8, 2008 at the Riveria in Las Vegas." Of course, Gata is a draw, and a compelling story - but Chucky has been playing unconscious lately and winning just about everything in sight he's been invited to! Ivanchuk always has been brilliant, just has had problems with nerves at times (hey, darling, I can identify). On the October ratings list Ivanchuk has moved into the #2 position by virtue of his recent red-hot results. Way to go! Of more interest to me, though, is the photo that starts the article on page 31 - in the background are Pia Cramling and Iweta Rajlich waiting to face off against each other. The expressions on the ladies' faces is - well, priceless. The ladies were not playing in the 8th Montreal International but in a women-only event (without checking my notes, I believe it was the Monreal Grand Prix Finale that was running at the same time). I deduce from the photograph in question that the ladies and the gentlemen from both events (and maybe more events, for all I know) were playing at the same time, in the same venue. IM Irina Krush, who also played in the Ladies' Grand Prix in Montreal, was the author of the article that had to report on the rather disappointing finish for her main man GM Pascal Charbonneau, who still managed to score a point above GM Nigel Short, who finished in last place with 2.0! Paging through the mag now...interestingly, there are two reviews this month of books that aren't chess training manuals: a "letter" by J.C. Hallman containing a review of Michael Chabon's novel "The Yiddish Policemen's Union" and a review PLUS an article about Paul Hoffman's memoir "King's Gambit - A Son, a Father, and the World's Most Dangerous Game" AND an excerpt. Just curious - I wonder if Paul Hoffman made a generous contribution to USCF... This edition of Chess Life contains the USCF Sales Catalog for Winter 2008. Does anyone ever order anything from the USCF??? The catalog is 47 pages - and naive me, here I thought Chess Life was finally giving us a really meaty issue. An article worth a read - "Steroid Chess - How Computers, Tournaments & Etiquette Have Changed the Royal Game" by IM Danny Kopec, Ph.D.

Islamic Fascist Barbarians Target Women in Iraq

Oh yes, such an enlightened religion. Well, maybe they'll end up killing all their own women and end up self-genociding - and cleaning up the gene pool. In Basra, vigilantes wage deadly campaign against women By Jay Price and Ali Omar al Basri, McClatchy Newspapers 2 hours, 42 minutes ago BASRA, Iraq — Women in Basra have become the targets of a violent campaign by religious extremists, who leave more than 15 female bodies scattered around the city each month, police officers say. Maj. Gen. Abdel Jalil Khalaf , the commander of Basra's police, said Thursday that self-styled enforcers of religious law threatened, beat and sometimes shot women who they believed weren't sufficiently Muslim. "This is a new type of terror that Basra is not familiar with," he said. "These gangs represent only themselves, and they are far outside religious, forgiving instructions of Islam." Often, he said, the "crime" is no more than wearing Western clothes or not wearing a head scarf. Before the U.S.-led invasion in 2003, Iraqi women had had rights enshrined in the country's constitution since 1959 that were among the broadest of any Arab or Islamic nation. However, while the new constitution says that women are equal under the law, critics have condemned a provision that says no law can contradict the "established rulings" of Islam as weakening women's rights. The vigilantes patrol the streets of Basra on motorbikes or in cars with dark-tinted windows and no license plates. They accost women who aren't wearing the traditional robe and head scarf known as hijab. Religious extremists in the city also have been known to attack men for clothes or even haircuts deemed too Western. Like all of southern Iraq , Basra is populated mostly by Shiite Muslims, so sectarian violence isn't a major problem, but security has deteriorated as Shiite militias fight each other for power. British troops in the area pulled out last month. Khalaf, who has a reputation for outspokenness in a city where that can get you killed, scoffed at the groups, calling them no better than criminal gangs. He said he didn't care if some were affiliated with the militias, he planned to crack down on them. "If there is a red line related to the insurgents and militias, we will pass it over, because it's one of the factors that destroy the society," he said. The violence is displacing the few members of religious minorities in the area. Fuad Na'im , one of a handful of Christians left in the city, said Thursday that the way his wife dressed made the whole family a target. "I was with my wife few days ago when two young men driving a motorbike stopped me and asked her about her clothes and why she doesn't wear hijab," he said. "When I told them that we are Christians, they beat us badly, and I would be dead if some people nearby hadn't intervened." That was enough, he said. "I'm about to leave the city where I was born and where my father and grandfather were buried, because I can't live in a place where we're asked about our clothes, food and drink."

Sanchi

Sanchi, Madhya Pradesh, India

A UNESCO world heritage site in central India near the Betwa River. On a flat-topped sandstone hill, 90m above the countryside, stands the best-preserved group of Buddhist monuments in India. Most noteworthy is the Great Stupa, discovered in 1818. It was probably begun by the emperor Aśoka in the mid-3rd century BCE and later enlarged. Solid throughout, it is enclosed by a massive stone railing pierced by four gateways on which are elaborate carvings depicting the life of the Buddha. The stupa itself consists of a base bearing a hemispherical dome representing the dome of heaven enclosing the Earth; it is surmounted by a squared rail unit, the world mountain, from which rises a mast to symbolize the cosmic axis. The mast bears umbrellas that represent the various heavens. Other remains include several smaller stupas, an assembly hall (caitya), an Aśokan pillar with inscription, and several monasteries (4th–11th cent. CE). Several relic baskets and more than 400 epigraphical records have also been discovered.

This is the eastern gateway to the giant stupa. It is particularly interesting because one row shows elephants with riders atop (bishop) and on the row above that are calvary riders (knight). The stupa dates to the mid 3rd century BCE; it seems unlikely that armies of this period didn't also have foot soldiers (pawns) and chariots (rooks). We know, of course, that there were plenty of kings to go around - just about one for each city-state - and where there are kings, there are counselors (queen). The dating of Asoka's Sanchi definitely supports Ferlito's and Sanvito's proposition that all elements for chess were in place in India well before Murray's hypothetical date of invention of the 5th to 6th centuries CE.

No Rest for the Champion

This is a fine article from the New York Times.

In the Major League of Chess, Next Year Comes So Soon
By DYLAN LOEB McCLAIN
Published: October 3, 2007

Hours after winning the World Chess Championship, Viswanathan Anand, an Indian grandmaster, sat in his hotel in Mexico City on Saturday and groped for words to explain how he felt.

“You can imagine,” he said by telephone. “I don’t know how on an emotional level it affects me.”

Mr. Anand’s victory was not a surprise — he is ranked No.1 in the world — but it was a milestone. He is the first Asian to be the undisputed champion and only the second player from outside Eastern Europe in the last 60 years. (The other was the American Bobby Fischer, who held the title from 1972 to 1975.)

Mr. Anand will not have a lot of time to rest on his laurels. Under rules of the World Chess Federation, the organizers of the championship, he will have to play a match early next year against the Russian Vladimir Kramnik, the previous champion.

While they are facing off, Veselin Topalov of Bulgaria, another former champion, will play the winner of a tournament to be held later this year in Russia.

The winners of those two matches will play a final match to determine a new champion.

Mr. Anand’s strength has always been his speed and computational ability. He quickly sees deeply into positions, rarely spending much time on his moves or using anywhere near his allotted time for a game. For many years, he has widely been acknowledged to be the best rapid chess player in the world.

Mr. Anand, 37, took a long time to win the championship. He broke into the elite in 1991 by winning a strong tournament that included Garry Kasparov, then the world champion, and the former champion Anatoly Karpov.

Since then he has won all the top tournaments at least once, but he has always struggled to win matches. In a match, the historical format for determining a champion, two players face each other repeatedly, while in a tournament, many face one another just once or twice.

Some observers and fellow competitors have ascribed Mr. Anand’s struggles in matches to nerves. In 1995 he lost an 18-game match at the top of the World Trade Center to Mr. Kasparov. In 1998, he won a tournament to select a challenger to Mr. Karpov for the World Chess Federation championship; they played to a tie in a six-game match, but Mr. Karpov prevailed in a playoff.

Technically, Mr. Anand’s victory in Mexico City is his second world title. In 2000, he won the federation’s championship tournament held in Tehran and New Delhi. But at the time, the title was split and many people recognized Mr. Kramnik, the Russian, as the legitimate champion, a situation that Mr. Anand acknowledged tainted his victory.

“Anytime you have two titles, it hangs over you,” Mr. Anand said.

Last year Mr. Kramnik became the undisputed champion after he beat Mr. Topalov in a match in Elista, Kalmykia, a remote Russian republic.

In the Mexico City championship, a tournament, Mr. Anand outdistanced 7 of the world’s top 14 players, including Mr. Kramnik, emerging as the only undefeated player.

He is now the undisputed champion, acknowledged even by Mr. Kramnik, but since his victory some fans have said on the Internet that he cannot be considered a true champion until he proves his mettle in a match. So the match against Mr. Kramnik will be important.

In the phone interview, Mr. Anand said that Mr. Kramnik and Mr. Topalov, who did not play in Mexico City, should not have been given “special privileges” to try to reclaim the championship in the coming matches, but, he added, “It is water under the bridge.”

In the modern era, it is unusual for a champion to be so old — in his late 30s — raising the possibility that Mr. Anand’s reign may be short. He said that while the top players are getting younger, he also noted that the top three in Mexico City — himself and the two who tied for second and third, Boris Gelfand, 39, of Israel, and Mr. Kramnik, 32 — were also the oldest. “Maybe a bit of experience didn’t hurt,” he said.

Mr. Anand said he did not know how long he would play competitively, but he drew a clear line. Referring to Viktor Korchnoi, a former world championship challenger, who is 76 and continues to play regularly in tournaments, Mr. Anand said, “You can rest assured that I won’t be doing a Korchnoi.”

Worshipping the Goddess Lands King in Hot Soup

From The Times of India online Nepal king visits goddess, lands in soup 2 Oct 2007, 0054 hrs IST,TNN KATHMANDU: A traditional visit to receive the blessings of a goddess said to be the patron deity of the royal dynasty has landed Gyanendra in a fresh controversy with PM G P Koirala construing it as a challenge to his authority. Koirala, who till recently had championed giving “space” to the kingdom’s two-century old ruling family and had advocated that Gyanendra should abdicate in favour of his five-year-old grandson, on Monday trained his sights on the monarch, warning that the government would take action if Gyanendra tried to challenge his authority. The warning came a day after both Koirala and Gyanendra went to the site of a traditional Hindu festival that ends with the Kumari- Nepal’s living goddess - blessing the head of state. Though Nepal is now officially a secular state, the multi-party government however still continues to patronise traditional Hindu festivals to the exclusion of Muslim and Christian celebrations. After the end of Gyanendra’s government last year, Nepal’s parliament, in a bid to make Gyanendra powerless, took away all his official functions, including attending religious ceremonies. With the king’s functions as head of state being given to the PM, Koirala has also stepped into Gyanendra’s religious shoes. Despite his erratic health and mounting crises, Koirala has been revelling in his newly acquired role, attending various festivals. Last week, it was he who kicked off the Indrajatra festival but did not have the stamina to see it through. On Sunday, it was a reversal of roles at the festival where the PM went in pomp and the king came as a commoner after him. When the king was all powerful, protesters shouted slogans against him and showed him black flags. This time, it was the all-powerful prime minister who faced the wrath of protesters. At the earlier religious festivals, the king had expressed his desire to attend though stripped of his prominent role. However, the government stopped him. ********************************************************************************* Well, I know that some folks out there may snicker at the King asking the blessing of the embodiment of the Living Goddess, but these things are taken deadly seriously in Nepal, and they have political consequences, where right now a war-by-proxy is going on behind the Chinese-backed "democratic" forces and those who support the traditional monarchy. It's pretty damned pissy to me when the King can't visit the Living Goddess (embodied in a girl child - I've posted about here earlier in the year here) without permission from the fricking government. Suddenly worship in the traditional way has to be sanctioned by the government. Do you get it now, folks? Hey?

Run, Run for the Hills Grey Squirrels!

Can you believe this?

From the Telegraph.co.uk

Sterilisation plan for grey squirrels
By Graham Tibbetts
Last Updated: 6:01pm BST 02/10/2007

EEK! RUN FOR THE HILLS, GREY SQUIRRELS - RUN, RUN FOR YOUR NUTS!

Scientists are planning a mass sterilisation programme to halt the growth of Britain's grey squirrel population which is now feared to have reached five million.

Teams in Britain and America are working against the clock to develop a method of rendering the pests infertile using treated bait.

Some estimates put the number of greys in Britain at five million and it is feared the local red population could die out within two decades unless dramatic steps are taken to curb their bigger, stronger rivals.

As well as forcing out red squirrels, greys destroy trees by stripping bark and have taken their toll on songbird populations by taking eggs. They also steal food from garden bird tables and infest loft spaces.

The problem of the burgeoning grey population was highlighted by the Daily Telegraph in an article by associate editor Simon Heffer which prompted a flood of letters and emails from readers. He called for a cull to stop them damaging the countryside.

Government scientists are working on a two-year programme commissioned by the Department for Environment, Food and Rural Affairs to find an effective oral contraceptive for grey squirrels.

They are also trying to pinpoint the best way of giving it to the rodents without affecting other animals. If successful, the treatment could be adopted in around five to 10 years.

Brenda Mayle, who is leading the research, said sterilisation injections had already proved successful in horses and deer in the US.

"If it eats part of the bait and leaves the rest it is a risk to non-target species. We are looking for a food package that the squirrel will eat in its entirety and not cache, which it does with acorns," said Ms Mayle, who is research programme manager for Forest Research – part of the Forestry Commission – in Surrey.

The contraceptive would work by attacking the immune system of the squirrel, suppressing its fertility. Scientists are desperate to find ways of tackling the grey squirrel threat before it causes more damage to the red population.

Greys have been found to carry a disease called squirrelpox virus (SQPV) which does not harm them but kills reds.

It is spreading through Britain and has recently been found as far north as Lowland Scotland.

Ms Mayle said: "It's very important that we do find something to reduce the rate of their spread, particularly because we are seeing the squirrelpox virus spreading north in Scotland now."

But she added: "It's not an alternative to culling. It will become another tool in our ability to manage wildlife populations but it's not an alternative to lethal methods."

A spokesman for Defra ruled out a national cull, saying it had been considered but would be too expensive with no guarantee of success.

"The Government is committed to preventing the further spread of grey squirrels, however, eradication is considered impracticable at national level. Some local programmes of control are under way, particularly in areas where grey squirrels are threatening remaining populations of reds or to protect forestry," she said.

Grey squirrels were introduced to Britain from America in the Victorian era but swiftly pushed out red squirrels, which are now only found in the Isle of Wight, Brownsea Island, western Wales, northern England and parts of Scotland.

********************************************************************************
Well, well, well. Isn't this ironic. The land of Charles Darwin, who introduced the concept of "survival of the fittest" into the world in the "Age of Enlightenment" (cough cough cough) is now trying to wipe out the fittest species (grey squirrels) in order to keep an inferior species (red squirrels) alive. Hey, Darwin, are you spinning in your grave?

Gee, when it's put like this - up close and personal - it really sucks to believe in such baloney sausage as "survival of the fittest", doesn't it. But if the scientists (the "experts", after all) believe in this B.S. theory, then it behooves them to being committed to allowing the red squirrel population to die out, except perhaps for a few specimens in zoos. Otherwise, they're speaking out of both sides of their mouth at the same time. THERE ARE NO "BUTS" IN DARWIN'S WORLD OF EVOLUTION - NATURAL SELECTION AND SURVIVAL OF THE FITTEST. NO EXCEPTIONS. THE WEAK DIE. THE FIT LIVE. BYE BYE SUCKA.

And you know the scientists, they're just going to really screw up the ecology EVEN MORE if they try and "cull" the grey squirrels using treated bait for birth control. Anyone other than those scientists can predict right now what will happen. There will be tons more "unintended consequences" than what happened some 100 years ago when some frigging idiot introduced an invasive species (the grey squirrels) into the British Isles, and the scientists really have no clue as to what most of those new unintended consequences will be! And yet they're discussing doing this - finding the right "magic bullet." GEEZ!

Chess Stuff

As you all no doubt know by know, Anand is the new world chess championship, to some of us at least :) Congratulations to Anand for playing fine chess to win the Mexican tournament. Guess chess isn't such a young man's game after all, heh heh heh. This is really big news in India, of course, and I expect the game will surge even more there now in popularity. There is an interview with Susan Polgar published in the International Herald Tribune yesterday. The October, 2007 FIDE Ratings List came out today. Anand is #1 on the list with 2803, the second time he has achieved a rating of 2800 or better. Ivanchuk, who was chewing up every chess board in sight, or so it seemed, during the past three or four months, increased his rating by 25 points, to 2787, and takes over the #2 spot. Not to be outdone, Koneru Humpy pushed her rating to 2606 by adding 28 points over the past 3 months. Well done, Humpy! Only Judit Polgar exceeds her ELO on the Women's List.

Even a Goddess Gets Hit with Inflation...

From The Telegraph Calcutta, India September 30, 2007 The goddess Durga will also notice that the banks have increased their rates of interest on loans this time. For the idol-makers at Kumartuli, beset by many problems, trouble started this year even before work began, when the banks they usually took loans from suddenly hiked the rate of interest. “We have been taking loans for our work from the State Bank of India (SBI) and the United Bank of India. Last year the rate of interest was 9.5 per cent per annum. But this year when we went for a loan, the SBI officials told us that the rate of interest has been increased to 12 per cent per annum. It is impossible for us to pay such a high rate of interest,” says Nemai Pal, president of the Kumartuli Mritshilpi Sanskritik Samity. The artisans were forced to change their bank. “We have been banking with the SBI for eight years. We spoke to many senior officials of the bank, but to no avail. Finally the Bank of India agreed to lend us money at 9-9.5 per cent per annum. We are getting a special concession on the usual rate. We also took loans from the United Bank at the same rate,” says a thankful Babu Pal, the secretary of the union. Looking for another bank has taken its toll on the work. “Our work was delayed by at least two months,” says Nemai. The SBI authorities try to explain their point. “The SBI Advanced Rate has gone up to 12 per cent. The artisans had asked for a concession that would have meant bringing down the rate to 2 per cent below the rate. We had sent an appeal to the higher authorities, but I was transferred at that point so I don’t know what happened after that,” says Arunava Aich, assistant general manager (IBD), SBI. However, Swapan Sengupta, assistant regional manager (region II), SBI, says: “Some artists have taken a loan from us. They have asked for a concession, but we haven’t heard from the higher authorities yet.” Kumartuli is not new to problems — both financial and practical. The price that Puja committees pay for the idols is never enough to cover the increase in the price of raw materials. “The committees at the most are ready to increase rates by 10 per cent, but the prices of raw materials, like clay, bamboo and hay, go up much more,” says Babu. There is little electricity. “The power cuts often continue for two hours or more,” complains Nemai. The idols need to be dried with oil lamps. And then came the rains. “For three days we couldn’t work. Especially those who had kept their idols along the roads. The rain washed away the colours and melted the idols. Not only is it a monetary loss to us because we will have to redo it, but we are also worried about how we will manage to finish work in time,” says Babu. The rains have been a problem for Puja committees too. “The bamboos and planks that we had brought for our work was washed away. Some Plaster of Paris art-work we had finished will also have to repainted. We could start work again only on Thursday because the area was so waterlogged,” says Anjan Ukil, the secretary of the Ballygunge Cultural Association puja committee. Other committees who had not yet started work on the outside of the pandal fared slightly better. “All administrative work was thrown out of gear. No one could reach us,” says Neelanjan Deb, the joint secretary of the Deshapriya Park puja committee. Adds Suman Chatterjee, the president of the Babubagan puja committee: “We have constructed a huge pagoda at the entrance and we were scared that it might collapse. Thankfully that did not happen.” POULOMI BANERJEE

Matsu Islands to Host Summit on Marine Goddess

From the Taipei Times STAFF WRITER, WITH CNA Friday, Sep 28, 2007, Page 4 Academia Sinica is organizing an international conference next month to discuss belief in the goddess Matsu and her connection with the Matsu Islands, officials with the Lienchiang County Government's Cultural Affairs Bureau said yesterday. The officials said that Academia Sinica's Institute of Ethnology would invite 40 academics from Taiwan and abroad to participate in the conference on Oct. 17 and Oct. 18 at the Matsu Folklore Culture Museum in Nangan (南竿), one of five major islands in the Matsu archipelago. Altogether, 15 papers will be presented at the conference on different aspects of the belief in the "Goddess of the Sea" and the historical relationship with the Matsu Islands. Matsu was born in 960AD to a fisherman's family in China's Fujian Province during the Sung dynasty and was given the name Lin Mo-niang (林默娘). Legend has it she was a genius with supernatural powers, including the ability to calm storms at sea. The numerous miracles ascribed to her include rescuing sailors in distress and curing the sick with her vast knowledge of Chinese medicine. One day, at the age of 28, she told her parents it was time for her to leave them. After reaching the top of a mountain near her home, she was encircled by clouds and carried into the heavens in a golden glow amid enchanting celestial music. She was deified and referred to as Matsu. Emperors in the Ming and Ching dynasties referred to her as the "Heavenly Empress." Residents on the Matsu Islands, however, have a different version of the story. They believe that Lin Mo-niang drowned while trying to rescue her father from a storm at sea, and that her body was washed ashore on the island of Nangan. A temple named the Palace of the Heavenly Empress was built on Nangan. The temple is said to contain her sarcophagus. The local people also named the archipelago Matsu in memory of the goddess, but the first character in the name was later changed to give it a different tone so as to make it sound more masculine. Today, Matsu has become the most widely worshipped deity in Taiwan, with temples dedicated to her seen in almost every township and city. Academia Sinica is the nation's most prominent academic institution, with more than 1,000 full-time research fellows undertaking in-depth academic research on various subjects.

Weinreb Review of "King's Gambit"

In yesterday's New York Times Magazine, Michael Weinreb reviews Paul Hoffman's book "King's Gambit - A Son, A Father, and the World's Most Dangerous Game." Sounds like another book to add to my never-ending reading list!

Hunting Relics Modern Style

When I'm retired, one of the things on my "to do" list is signing up with an overseas archaeological dig as a grunt worker. Yes, these people have got it - the lure of discovering "hidden treasure" calls to us all...

Couple turns relic-hunting hobby into business

By BILL HENDRICK
The Atlanta Journal-Constitution
Published on: 09/17/07

looks around and quickly points to what looks like a very old brass bugle, priced at $45.

"How old is that?" the man asks. "I've got one from the Crimean War that looks just like it."

19th century, but I think it's more likely World War I, or it could be just a plain old fake."

The aging baby boomer lifts it to his lips and starts tooting, squeezing out a few wheezy bugle calls. And he's hooked, offering $30, which the Holcombes accept, knowing it could be worth a lot more — or less.

That's the way it goes in the antiques business, which Butch and Anita Holcombe went into a few years ago when he decided to quit his job as a machinist and his wife got laid off from an administrative position.

But it's not their little Greybird Relics shop in the Big Shanty Antique Market in Kennesaw that pays their bills, or the Victorian jewelry, 19th-century dominoes, ancient coins or Civil War bullets they sell on their Web site. It's the slick-covered American Digger magazine they started "on a wing and a prayer" in January 2005.

They felt publishing might produce a more predictable income than selling relics.

What's more, Butch was tired of 10-hour days, and she'd lost her job.  So far, she says, "the magazine has struck a chord out there, with 1,600 subscribers around the world already."

Bigger and thicker than the average Newsweek, the magazine is filled with pictures of artifacts, such as patent medicine "miracle cure" bottles, 15th-century coins from Eastern Europe, Victorian jewelry and all sorts of relics dating from the War of 1812 to the Civil War.

It's also full of advertisements from companies that sell metal detectors and books for history buffs.

"We're not getting rich, but we're doing well," Butch says. "We've tapped into something out there."

The magazine's most popular feature is called "Just Dug," several pages of pictures of relics unearthed around the world, including stuff dug up around Marietta.

Much of it, such as a folding mirror found by Ed Travis of Cobb County, dates from the Civil War era, dug up by members of the North Georgia Relic Hunters Association or the Georgia Research & Recovery Club.  Butch says most people think "the relics hobby it's just Southerners looking for Civil War stuff, but there are relic hunters all over this country, and the world, too."

Janet Levy, an anthropology professor at the University of North Carolina-Charlotte, says artifact hunting as a hobby goes back at least to the days of a Babylonian king 2,500 years ago.

But the hobby is exploding now in popularity in part because technology has made it easier for buried metallic objects to be found, says Randall Miller, a history professor at Saint Joseph's University in Philadelphia.

"The Internet has changed the hobby," he says. "People are digging and hunting for relics not just on battlefields, but in old cisterns and privies, which can be gold mines for very old bottles."

Miller and other academics say the magazine is tapping into the same phenomenon that has made "Antiques Roadshow" such a hit on PBS.  Avid relic hunters for years, the Holcombes went to Virginia in 2004 to try to find how to turn "the hobby we love into a magazine to cater to people like us."

Butch learned to use graphic design software to lay out the pages, Anita began pitching ads to metal detector companies, and they took the finished product to Star Printing in Acworth.

"It's even surprised us," Butch says. "We have subscribers in 48 states."

They send copies to U.S. warships and artifact clubs and organizations such as the Federation of Metal Detector and Archaeological Clubs, the Authentic Artifact Collectors Association and the Smithsonian Institution.

"We got a Web site up right away for the magazine so other groups could link to it," Anita says. "Payment for articles includes three comp copies and a free ad, if the author desires. Artifact hunters like to show off their finds."

Miller says most people interested in hunting for artifacts are in their 50s and 60s.

In New Mexico and Arizona, people look for pottery and Native American artifacts. Some folks walk beaches with metal detectors, looking for jewelry lost by bathers. And in the West, people hunt for gold and items from cowboy days, says Jerry Smith of Boom Town & Relic Hunters in northeastern Washington.

"We have unearthed rare saloon tokens, gold nuggets and solid gold $1 pieces worth thousands of dollars," he says.

"There are magazines out there for all sorts of things," Butch Holcombe says. "Ours concentrates on things that are newly dug up. The real interest is in seeing what's just been found because it says a lot about what's still out there. And there's an awful lot."

"The Hidden Ones"

This book review speaks for itself, quite eloquently. We're No Angels By KATHRYN HARRISONPublished: September 30, 2007 New York Times, Book Review "The pervasive theme is rebellion." Laurel Thatcher Ulrich begins her new book, "Well-Behaved Women Seldom Make History," struggling to explain — understand — the appeal of an aside she made in the spring 1976 issue of an academic journal, a comment that has become a popular slogan printed on T-shirts and coffee mugs and bumper stickers, usually without her permission and often without attribution. It was in an article for "American Quarterly," about the pious and extremely well-behaved colonial women described by Cotton Mather as "the hidden ones," that Ulrich made her now familiar observation . Her study of wives and mothers and daughters as they were remembered in funeral eulogies, the sole record of women who lived and labored in silent obscurity, illustrates a critical point. Much of what is characterized as female "misbehavior" is a matter of voice — of a woman insisting she be heard, paid not only attention, but also the respect due a being as fully human and necessary as a man. Given millenniums of patriarchy, the issue of women speaking out is necessarily that of their speaking out of turn. The mostly male forums of public life may patronize women with token attention and even, sometimes, take their words seriously, but they rarely if ever pay attention to a woman as they would to a man, without consciously taking her sex into account. Is it an accident of fate that "Well- Behaved Women Seldom Make History" is published as we look ahead to what may become the historic first of a major political party nominating a female candidate for president? Has Hillary Clinton arrived at the forefront by misbehaving? Ulrich, a Harvard historian whose "Midwife’s Tale" won the 1991 Pulitzer Prize for history, uses "three classic works in Western feminism" as a springboard for examining the theme of "bad" behavior. Could the popularity of her slogan, she wondered, be explained by "feminism, postfeminism or something much older?" The answer emerges in Ulrich’s choice of texts: Christine de Pizan’s "Book of the City of Ladies," written in 1405; Elizabeth Cady Stanton’s "Eighty Years and More," published in 1898; and "A Room of One’s Own," based on two lectures Virginia Woolf gave in 1928 — all works by women who "turned to history as a way of making sense of their own lives." History, Ulrich reminds us, "isn’t just what happens in the past," but what we choose to remember. As much invention as discovery, history attempts to make the chaotic present into a coherent picture by comparing it to images, equally artificial, fashioned from events long past. Pizan, Stanton, Woolf: three women with "intellectual fathers" and "domestic mothers," who were "raised in settings that simultaneously encouraged and thwarted their love of learning" and "married men who supported their intellectual ambitions." For each, her "moment of illumination came through an encounter with an odious book" expressing man’s "disdain" for women. Pizan responded to a 15th- century satire containing "diatribes" against her sex, Stanton to law tomes that set forth the rights of husbands and fathers over their wives and daughters, Woolf to "The Mental, Moral and Physical Inferiority of the Female Sex," an imagined history representing what she discovered in the reading room of the British Museum. Ulrich’s new book is a work of selection and synthesis; she finds common archetypes in far-flung sources, making connections that are sometimes distant but never tenuous. The "Amazons" chapter is illustrated by examples from archaeological digs in Kazakhstan, South American folk tales and her own cultural backyard, which yields "an Olympic athlete, a female soldier, a lesbian separatist, a comic-book heroine." Her associative logic reveals how A prefigures Q or even Z rather than ordering A before B before C, and brings a female sensibility to what is more typically the linear, cause-and-effect formula of history, a majority of which, Ulrich points out, is written by men. Defined broadly by Ulrich as "women warriors," Amazons make history because they misbehave; they assert their presence in a world that instructs women to remain silent, submissive. Hillary Clinton, who famously refused to "bake cookies" in the background of her husband’s career, is an Amazon, destined to be as much the property of myth as of history, between which lies a vast and unfixed common ground. The celebrated Rosa Parks didn’t happen onto the stage of American history but was cast for her myth-ready appeal. The president of the Montgomery, Ala., N.A.A.C.P. interviewed women arrested for refusing to give up their bus seats, rejecting unusable candidates — an unwed mother, for example — before he found Parks, whose stainless reputation made her suitable for championing a cause. Parks’s good behavior was as necessary as her "bad," itself confined to voicing her refusal to comply with segregation. As Hillary Clinton well knows, to claim an audience is to submit to muckraking, and while an exposé can enhance the career of an Amy Winehouse or a Paris Hilton, it can halt political aspirations. It behooves an ambitious woman to be judicious in her misbehavior. Women have long perceived their status, at least in the United States, as analogous to that of blacks (and, by extension, other people of color). Here we’ve arrived at the 21st century yet to become citizens first and women second, our successes still the exception and never the rule in any career that isn’t inherently decorative, or doesn’t require changing sheets or bandages, or taking off clothing. That women don’t have voices but female voices is obvious from the way our vote is courted, our leanings studied as if influenced by whim or superstition or, heaven forbid, hormones (never a problem for men, of course). ULRICH considers the women’s suffrage movement in the chapter titled "Slaves in the Attic," addressing the subjugation of race and gender as twin forms of slavery, a stance taken by anti-abolitionists themselves, who legitimized it with biblical discussions of who was to serve whom. Her portraits of four 19th-century women named Harriet, three runaway slaves — Powell, Tubman and Jacobs — and the novelist Beecher Stowe, provide a surfeit of answers to the question Ulrich frames at the end of "Amazons," of where women’s "fury comes from and why it will not go away." Because Ulrich’s extensive research allows her to make imaginative leaps, spanning centuries and continents, the reader accepts that she occasionally forces coherence onto unwieldy material, resorting to the overly careful formula of academic papers, rehearsing established connections before introducing new ones. Pizan, Stanton and Woolf appear throughout to reorient us, their interruption more welcome in some contexts than in others. Whether scripted as "angels in the house" or slandered as whores for the sexual freedom that enhances a man’s prowess, women continue to struggle against the restrictions of patriarchy. If it feels like a leap of faith to look forward to when we will be citizens first and women second, Christine de Pizan offers a plan for the meantime. "Redefining the boundaries of womanhood" through a highly selective review of the past, she wrote a history of her sex that she could accept — a recipe for shoring up female sanity if ever there was one.

"The Hidden Ones"

I'm going to buy "Well-Behaved Women Seldom Make History. " It's fascinating to reflect on some of the themes raised in the New York Times book review. For instance, "bad behavior" is most often relative, subject to time, place, culture and, sometimes, motivation. Murder, for instance, is universally proscribed by law, and yet there have been and always will be exceptions to our condemnation of such behavior. In the Bible, Rahab, a Canaanite prostitute, aids and abets the invading Israelites to kill her own townspeople of Jericho. For her assistance, Rahab and her family are spared after victory by the invading army of Joshua, the leader of the Israelite tribes. Rahab later marries a prominent Israelite, Salmon, and becomes an ancestress in the line of Christ through her son, Boaz. Boaz married Ruth (another "foreigner"), who becomes mother to Obed; Obed is the father of Jesse; and Jesse is the father of David, who is the founder of the Davidic line of Iraelite kings. During the times of the Judges (after Joshua but before Saul was annointed as the first King of Israel), Jael, "the wife of Heber the Kenite," commits an atrocious murder and is hailed for it in a song that praises the suffering of the dead man's mother. There is war between a Canaanite king, Jabin, and the Israelites. An Israelite prophetess, Deborah, who also acts a female Judge (in the days before the kings of Israel were established), calls upon Barak to lead an army against Jabin's forces, which are led by Jabin's general, Sisera. Interestingly, Barak says he will lead the fight, but only if Deborah accompanies him and the troops. Deborah then says yes, she will accompany him, but - perhaps as a result of his doubting the word of God as delivered through Deborah that victory against Sisera would be his - she tells Barak that the death of General Sisera will be at the hands of a woman: Judges 4:9: "Without fail I shall go with you. Just the same, the beautifying thing will not become yours on the way that you are going, for it will be into the hand of a woman that Jehovah will sell Sisera." With that Deborah got up and went with Barak to Kedesh. The Israelite forces are victorious, and Sisera runs for his life, seeking shelter in the tent of Jael. While he sleeps Jael takes a tent spike and strikes it through his temple with a hammer, driving the spike all the way through into the ground below. When the pursuing Israelite forces, led by Barak, arrive at her camp, she comes out to meet him and says "Come and I shall show you the man you are looking for." Judges 4:22: So in he went to her, and look! there was Sistera fallen dead, with the pin in his temples. Jael is hailed as a heroine. Here are parts of the victory song of Deborah and Barak: Judges 5:24: Jael, the wife of Heber the Kenite, will be most blessed among women, Among women in the tent she will be most blessed. (25) Water he asked, milk she gave; In the large banquet bowl of majestic ones she presented curdled milk. (26) Her hand to the tent pin she then thrust out, And her right hand to the mallet of hard workers. And she hammered Sisera, she pierced his head through, And she broke apart his temples. (27) Between her feet he collapsed, he fell, he lay down; Between her feet he collasped, he fell; Where he collasped, there he fell overcome. (28) From the window a woman looked out and kept watching for him. The mother of Sisera from the lattice, 'Why has his war chariot delayed in coming? Why must the hoofbeats of his chariots be so late?' (29) The wise ones of her noble ladies would answer her. Yes, she too would talk back to herself with her own sayings, (30) 'Ought they not to find, out they not to distribute spoil, A womb - two wombs to every able-bodied man, Spoil of dyed stuffs for Sisera, spoil of dyed stuffs, An embroidered garment, dyed stuff, two embroidered garments For the necks of men of spoil?' But there would be no ransom demand made for the life of Sisera, for which his mother could contribute finely embroidered and dyed garments made with her own hands. Sisera was already dead, at the hands of another woman, who gave him milk - ironically described as "curdled milk," so that rather than being the sustenance of life, as milk from a mother's breast, its curdled form was a precursor of death. Three thousand years later, Susan Smith and Andrea Yates, among others, serve up "curdled milk" to their own children. Their names will live forever in the case-histories of psychiatric tomes. Yes, I think Ulrich is correct. It's the bad girls of history that have gotten publicity - not the good girls.

The Magic of Phi

Hola darlings! It's another beautiful day here. I am sore from raking - I spent hours yesterday raking out the backyard, picking up the branches from several strong-wind days that had blown through during the past month (when, I confess, I was lazy and on good weather days I sat on the deck and read rather than doing yardwork) and also raking out the mysterious patches all over the backyard like a damn checkerboard pattern where the grass has turned brown and brittle and comes out one blade at a time as I rake. Damn! Anyway, I have about 1/3rd of the yard still to rake up before I pull out the mower for what will probably be its second-last cut. I came across this intersting article about the number 1.618... - the "divine proportion" or "golden ratio." Trying to understand the formula makes my eyes cross and puts me to sleep, but I understand the "practical" applications as far how the proportion is expressed in architecture, art and in nature. Many years ago I tried plotting out the Fibonnaci sequence on a chessboard, and came up with an interesting graphic that Don colorized and turned into a rather "fractal" looking piece of art that we used at Goddesschess for awhile. I'll see if I can find that graphic and post it here if I do. In the meantime, here is the article. It gives credit where credit is due - to the ancient Egyptians. Al-Ahram September 27 - October 3, 2007 Issue 864 The amazing Golden Ratio Artists reckon that the "Golden Ratio", also called the "Golden Section Phi" and nature's most astonishing number, is the ratio that controls the proportions of all beautiful objects, writes Assem Deif* [* The writer is a professor of mathematics at Cairo University and Misr University for Science and Technology] It is said that a well-proportioned face must lie in what is called a "golden rectangle" of dimensions in the ratio of approximately 1 to 1.6. Not only living forms, but also works of art and buildings, including the splendid domes of Persia and the Athens Parthenon, are found to adhere to this rule. The ratio became even more pronounced during the European Renaissance, when Leonardo Da Vinci studied the physical proportions of man and portrayed them in his unfinished canvas of St Jerome along with other works such as the "Mona Lisa" and the "Vitruvian Man". So, quite apart from the other mathematical constants, Pi = 3.14, e = 2.718 (Euler Number), Gamma = 0.577 (Euler Constant), and i = sqrt(- 1) which possess mathematical properties only, the Golden Ratio Phi = 1.618... has an additional aesthetic feature. Since mathematicians in ancient times were often poets and philosophers who believed in the uniformity of nature, mathematics served to satisfy their need to understand the world around them and to resolve its secrets. Hence, they started tracking this constant in everyday objects such as plants and animals, and discovered that the proportions of many conformed with this ratio. This was why, by the time of the Renaissance, it had become known as the "Divine Proportion". Mathematically, the Golden Ratio appears as the limit of several sequences, the most important of which are those that satisfy the recurrence relation s(n+1) = s(n) + s(n-1) where s (n) is the nth term of the sequence, whereas s(n- 1) and s(n+1) are respectively the preceding and succeeding terms, as in the famous Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, .... in which any term is the additive sum of its two preceding terms, or in any other sequence satisfying the above recurrence, even if we start with any two numbers such as 5 and 2; that is 5, 2, 7, 9, 16, 25... We always have that the quotient of two successive terms s(n+1)/s(n) approaches a certain number called Phi. To calculate the value of Phi from the above recurrence relation written as s(n+1)/s(n) = 1 + s(n-1)/s(n), it turns out, in the limiting situation, that Phi = 1 + 1/phi, or that Phi equals half of the quantity 1+sqrt(5) = 1.618... Historians trace the Golden Ratio back to Euclid, yet it appears that even before him it was governing the dimensions of monuments in ancient Egypt. The most pronounced of these is the Great Pyramid. The dimensions of the inner triangle (the so-called "Egyptian triangle") of Khufu's Pyramid, for instance, in Royal cubits (one cubit equalling roughly 0.524 metres), are (220c, 280c, 356c) i.e. in the ratios 1 : sqrt(Phi) : Phi. That the foregoing relation is not a matter of coincidence is discussed elsewhere. However, the Great Pyramid is not the only structure from ancient Egypt that complies with constants like Pi or Phi; Schwaller De Lubicz, who studied the temples of Upper Egypt from 1937 to 1952, collected massive amounts of evidence to show that the Egyptians used the Golden Ratio in many ways both in the architecture of their temples and in their drawings. So whereas, prior to De Lubicz's research, the discovery of the "golden rule" was generally credited to the Greeks (although some historians denied this), the findings of such Egyptologists as De Lubicz and Fliders Petrie produced irrefutable proof that the Egyptians had a mathematical understanding of these constants, the ratios, not the symbol, 1000 earlier. Petrie, for example, noticed that the dimensions of many Egyptian tombs, especially those of a parallelepiped structure, adhered to the ratios 1 : Phi : Phi square. The same ratio also appears in a grid surrounding a human body depicted in the royal tomb of Amenhotep III in the Valley of the Kings. There was much cross-culture between the Egyptian and Greek civilisations in the cities of the north coast during the Hellenistic era, particularly in Alexandria where Egyptian and Greek scientists studied together at the Mouseion. Among them, in the third century BC, was one who was considered, par excellence, the most reputed scientist in antiquity, the great Euclid. Historians call him Euclid of Alexandria without precluding the possibility he might have been Egyptian. It was in Alexandria that Euclid wrote his opus The Elements, still the most famous mathematical work ever written. Since the invention of the Gutenberg machine this work, compiled in 13 volumes, has been printed more than any book apart from the Bible. (Euclid introduced the ratio, obtained from extreme and mean ratio of three collinear points, in volume VI). The Arab mathematician Al-Haggag produced the first translation of The Elements into Arabic, and as the original Greek work was subsequently lost it was only through the Arabic translation that the book became known to the rest of the world. Euclid was only one of the scientists who performed research at the Mouseion. The great intellects of the day flocked to Alexandria, and among them we encounter such names as Eratosthenes, Archimedes, Apollonius, Menelaus, Heron, Nicomachus, Ptolemy, Diophantus, Pappus, Galen, Theon and his daughter Hypatia. Greek scholars were visiting Egypt even before the Mouseion was founded, including Thales, Socrates, Plato and Aristotle, and above all Pythagoras who spent 22 years in Egypt about 600 BC and announced his theory only after leaving. Records tell us that the Egyptians were aware of the triangle 3:4:5 which Pythagoras himself called the "Holy Triangle". Eight pyramids from the fourth and fifth dynasties have their inner triangle conforming to these ratios. There are many applications for the Golden Ratio varying from mathematical optimisation to architecture. We find it in other sciences too. In biology it controls the distribution of the leaves around the stem of a plant such that they receive the maximum amount of light. It was found that the distribution of their angle of rotation or distances from one another followed terms as in the sequence 1/2, 1/3, 2/5, 3/8, 5/13, 8/21, 13/34, in which the numerator a(n) of the quotients represents the number of turns we climb, say, around the stem in such that any one leaf returns to a position exactly above the point where it started, whereas the denominator b(n) represents the number of leaves in between. This ratio differs from plant to plant, yet it varies on average between 1/2 and 1/3. The reader will notice that in the sequence both the numerators and denominators are terms in the Fibonacci sequence, in which a(n) and b(n) satisfy b(n+1) = b(n) + a(n+1). Since both a(n+1)/a(n) and b(n+1)/b(n) tend to Phi, it follows that a(n+1)/b(n) tends to Phi-1 = 1/Phi. As to the distribution of the leaves around the stem b (n)/a(n), it tends to Phi square for at each turn the leaves organise themselves on the stem. We can elaborate further to calculate the divergence angle of any one leaf such that no two leaves would be above one another; allowing for maximum light exposure. Having that each complete turn of any one leaf in order to return to its original position travels an angle of a(n)x360 while passing by b(n) leaves in between, it follows that each leaf occupies an angle of a(n)x360/ b(n) = 360/(Phi square) almost 137 degrees. Thus, if there are Phi square leaves per turn (or equivalently 1/Phi square turns per leaf), then each leaf gets the maximum exposure to light while casting the least shadow on the others. This also gives the best possible area exposed to falling rain, or, in the case of flowers, the best possible exposure to attract insects for pollination. Still in biology, the Fibonacci sequence, of which the ratio of two successive terms tend in the limit to Phi, often appears in the reproduction of animals and plants. The figure depicts the increase in the number of leaves in some plants from row to row. Likewise, in rabbit reproduction, say, starting with one pair of rabbits, at the end of the first month they will have mated but there is still one only pair. At the end of the second month they produce a new pair, so now there are two pairs of rabbits. At the end of the third month the original pair produces a second pair, making three pairs. At the end of the fourth month the original pair has produced yet another new pair, while the pair born two months before produces their first pair, making five pairs. And so on (assuming that each pair born consists of a male and a female rabbit). A fascinating phenomenon associated with the Golden Ratio is its regular appearance in such objects of nature as nautili and other shells. Such shells imitate a curve called in mathematics the "logarithmic spiral", first investigated by Jacob Bernoulli in the 18th century. This was the second curve in history, next to the circle, to have its length calculated, since although it has an infinite number of loops, its length approaches a finite value. One extremely amazing appearance of the logarithmic spiral in nature is associated with raptors. Since these predatory birds must keep the prey in sight all the time, and since their eyes are on the side of the head, a hawk or eagle swivels its head to one side at an angle of about 40 degrees and fixes its prey in this eye. Keeping its head fixed at that 40-degree angle, the bird then dives in a way which keeps the prey in sight in that one eye. The fixed angle of the head results in the bird's following a logarithmic spiral path that converges on its prey. A special case of the logarithmic spiral is the "golden spiral". This is drawn either from the outside or the inside. In the first option, we start from a square of unit side-length, then extend it into a "golden rectangle" of base unity and height 1.618. Then we draw a quarter of a circle inside the square, and another one in the extension of radius 0.618 = 1/Phi, etc... making sure that each time we isolate a square from a golden rectangle. An interesting feature that I found with this spiral is that its inner area can almost be filled up (I said almost) by a set of adjacent Egyptian triangles. As to the mathematical properties of Phi, we summarise them as follows: Phi = 1.618..., 1/ Phi = 0.618, Phi square = 2.618... and so on. For instance, Phi raised to the 11th power equals 199.00502... and 1/Phi raised also to the 11th power equals 0.00502. Also Phi has the peculiar continued fraction representation [seems to be something missing here, but this is how it is in the article] Again, in terms of nested radicals: Also, by writing Phi square = 1 + Phi, Phi cube = 1 + 2Phi, Phi power 4 = 2 + 3Phi, Phi power 5 = 3 + 5Phi, Phi power 6 = 5 + 8Phi, etc... we notice that the coefficients represent two Fibonacci sequences. The interesting properties of the golden ratio led the academic circle to issue a regular periodical called the Fibonacci Quarterly. We can still deduce further properties: Phi power 10 = Phi power 9 + Phi power 8 = Phi power 8 + 2Phi power 7 + Phi power 6 = Phi power 7 + 3Phi power 6 + 3Phi power 5 + Phi power 4 = Phi power 6 + 4Phi power 5 + 6Phi power 4 + 4Phi power 3 + Phi power 2 = .... in which the coefficients in the polynomial represent successively rows of a "Pascal Triangle" , known to the Arabs and which represent the coefficients of a binomial expansion of any two numbers raised to a positive integer n. The applications of the Golden Ratio in the physical sciences are endless, so we have restricted ourselves in this short article to a few of the most famous which yet have no complicated mathematical features. © Copyright Al-Ahram Weekly. All rights reserved