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The Man of Numbers: Fibonacci’s Arithmetic Revolution

Keith Devlin, Walker & Company, 2011.

Visitors to the Camposanto, the sacred burial ground of Pisa, so sadly damaged by Allied bombers in the Second World War, find all manner of monuments lining the walls, from Roman sarcophagi to statues of the illustrious citizens of later centuries. One of these, recently cleaned up and restored, dates from 1863 and it commemorates one of Pisa’s heroes, the mathematician Leonardo da Pisa, often known as Fibonacci (a corruption of Filius Bonacci, the son of Guiglielmo Bonacci). Although no contemporary depiction of him survives, he springs from the sculptor’s imagination with classical features, a cowled head and a long tunic. He lived from around 1170 to 1250.

Fibonacci is best known today for his famous mathematical puzzle of the breeding rabbits. Shut up a pair of rabbits in an enclosure, assume that the doe will give birth to a pair of baby rabbits every month and that these two will be up and breeding a pair a month within a month. Genetically impossible of course, but the numbers can be built up into a sequence of 1, 1, 2, 3, 5, 8, 13, 21, 34 and so on. These ‘Fibonacci’ numbers reappear in all kinds of strange places, not least as the typical number of petals in a flower.

Fibonacci was not the first to work out this sequence and Keith Devlin is not nearly as interested in it as in Fibonacci’s contribution to the commercial revolution of 13th and 14th century Italy. These years were the age of trading breakthroughs for the Italians as they captured new routes and filled them with finished grain in return for raw materials. The Venetians strengthened their position immensely after the Fourth Crusade of 1204 had allowed them to lay their hands on ports across the Mediterranean. Florence expanded fast after 1200. Yet there was a bottleneck in the commercial background. There were experts who could manipulate an abacus as quickly as one might operate a calculator today, but the final answers were always written in Roman numerals. As soon as complex issues arose, concerning how to divide profits or change money between coins of different alloys, the system just broke down. The Arab traders, on the other hand, were using a system they had adopted from India. It comprised nine numbers, each with a single-digit symbol, 8 for VIII, for instance, and, crucially, a zero, which was recognized as a number in its own right. The man who transferred the system into Italy was, Devlin argues in this entertaining book, none other than Fibonacci.

Fibonacci’s father had been posted by Pisa to the port of Bugia, in modern Algeria, where he acted as the Pisan go-between with the Berbers. Leonardo, still a boy, went with him. He must have picked up Arabic, as he tells how he talked to merchants from Egypt and Syria, and he soon grasped the superiority of their calculations and became obsessed by them. In 1202 he published a mammoth 600-page manuscript, the Liber Abaci, ‘The Book of Calculation’. It was the first time that the system had been spelled out fully and aimed directly at Italian merchants. Everything from how to divide profits and measure land to dealing in currency exchange was covered with a myriad examples to show how each kind of calculation could be made.

No copies of the 1202 manuscript survive but there are some of the second edition of 1228. By this time, Fibonacci was famous. He had been summoned to meet the formidable Holy Roman Emperor, Frederick II, who had set him three problems which he triumphantly solved. He wrote up the answers in his Liber quadratorum and this work has helped confirm him as the finest mathematician of the Middle Ages.

By the end of the 13th century there were a mass of simpler books of calculation and schools were teaching the system. In Florence in 1343, between 1,000 and 1,200 boys were working in abbaci schools. Until recently, however, historians have not been able to link Fibonacci directly to the introduction of the new system. The workbooks used by students and merchants did not appear to overlap with anything in Liber Abaci. Perhaps the system had come in at a less erudite level and slowly infiltrated the Italian cities. Yet later writers often named Fibonacci as the man who introduced arithmetic and algebra to Europe.

Devlin shows how the question has been resolved. Fibonacci must have realized that the huge manuscript of the Liber Abaci and another text he wrote for merchants on geometry, which was scarcely less large, were too much for the ordinary merchant to master. So he wrote a much shorter and simple text, now lost, and this can now be directly linked to the manuals to be found in the schools some decades later. Fibonacci was truly ‘the man of numbers’, both at a sophisticated level in algebra, but on the market floor.

This is a short book on a man about whom almost nothing is known. Fibonacci sometimes called himself Bigallo, perhaps a Tuscan dialect word for traveller, and he certainly knew his way around the cosmopolitan Mediterranean world of the 13th century. It was perhaps inevitable that the Hindu-Arabic system would have come to Italy in time—it was simply too useful in a complex trading world—but Devlin has certainly shown that Fibonacci deserves the credit for setting in all in motion. This is a readable and enjoyable book and I actually understood the maths!

Reviewed by Charles Freeman, historical consultant to the Blue Guides and author of Sites of Antiquity: 50 Sites that Explain the Classical World. For more on Fibonacci, see here.

To see more details about this book, check the Amazon links below.

11.11.2011
16:46

Comments on Blue Guide India

All new first edition, all India in one volume.  The result of four years’ work by Delhi-based Sam Miller, head of the BBC Trust in India.

See the contents, index and sample pages, and buy online direct from the publisher.

The author’s Facebook page is here with quizzes, comments and questions answered.

Available in print and as an e-book by chapter.

 

The Roman Forum

By David Watkin (Profile Books, hardback 2009; paperback June 2011)

‘Archaeology often brings to light relics—mysterious foundations, tumbled blocks, a charred sacrificial pit, the decaying stumps of dead houses—fascinating to the scholar but a stunning bore to the simple visitor.’ So wrote Dilys Powell in The Villa Ariadne. Archaeologists can be monomaniacs and their interests are often distressingly narrow. So it was with some anticipation that I took up David Watkin’s The Roman Forum, whose contentions are very clear: ‘Archaeologists have eliminated much evidence of the fascinating post-antique life of the Forum,’ and their labours have made ‘visiting parts of the Forum about as attractive as looking into the hole made in New York on 9/11.’ Ouch! These accusations run like leitmotifs throughout the book, together with the curious conspiracy theory that guidebooks are complicit; that there are things they ‘do not want us to see’.

If one works night and day to produce guidebooks, it is difficult not to get on the defensive. The Portico of the Dii Consentes doesn’t ‘turn out’ to be a modern reconstruction. Pay attention to your Blue Guide! It clearly says that it dates from 1858. There is no plot to keep visitors in the dark about the churches of San Lorenzo in Miranda or Santi Luca e Martina. They are just never, ever open. But for Watkin, everything was better in the time of Piranesi. Piranesi, he tells us, with the authority of one who knew him in a former life, recorded the Forum ‘at the last time when it was still a place of poetry, capable of inspiring great painters, writers and thinkers.’ Glum stuff, but the threnody does begin to strike a chord and the aimiable style in which the bad news is delivered soon reels you in. Watkin laments the fact that the Forum has been turned inside out: its surviving churches open away from it, no longer into it; it has been severed from the life of the city and turned into a visitors’ theme park. Up until a very few years ago, entry was free and one could use the Forum as a thoroughfare; Romans going about their daily business could loiter and linger in it. Now you have to queue to be admitted through a turnstile, custodians are bossy and offhand, and no one who is not a tourist (or an archaeologist) ever goes there. The magnificent ‘challenge of the relationship between ancient and modern’ has been obscured.

Despite the underlying crotchetiness, the book is immensely enjoyable. Watkin’s love for the Forum, his breadth of knowledge, and his wistfulness about what might have been (in a Peter Pan world) are ingenuous, impressive and infectious—a beguiling combination. The chapter on the despoliation of the Forum’s monuments in the service of the new St Peter’s is a superb read. No visitor should ever again imagine that the mere march of time had anything to do with it. What Watkin cannot admit, though, is that if archaeologists hadn’t got their hands on the Forum when they did (in the late 19th century), the urban planners certainly would have. And the challenging relationship between ancient and modern would now be as desperate a tussle there as it is at Largo Argentina.

Nevertheless, if you’re travelling to Rome—either for the first or the fiftieth time—I recommend that you get this book. Not only will it add whole layers of meaning to your visit, but it will also force to you answer the following testing questions: if archaeologists are to be banished, who will take their place (and who will pay for it)? What is the point of a desert like the Forum in the centre of a busy and increasingly cramped-feeling capital city? And whose opinion was nearer to the mark: Palladio’s, for whom the Forum offered ‘not the spectacle of ancient glory but rather the possibility of recreating it’; or Pevsner’s, for whom the Forum belongs ‘to the civilisation of Antiquity, not to what we usually mean when we speak of European civilisation’? Watkin loves the Baroque churches that were built over the ancient ruins in the 17th century. But did their architects believe they were ‘recreating’, or did they believe they were moving forward into a ‘modern’ era?

Reviewed by Annabel Barber

Blue Guide Rome (10th edition) has extensive coverage of the Forum, with a map of the site and detailed notes on all its monuments, past, present and conjectural.

To see more details about this book, check the Amazon links below.

Whispering City: Rome and its Histories

R.J.B. Bosworth, Yale University Press, 2011

I first arrived in Rome in January 1966 when I was eighteen. I had had a long journey by train from London but I have never forgotten the emotional impact as my taxi sped by the Forum. All the hours I had spent trying to construe the speeches of Cicero and the odes of Horace gained meaning and since then I have never been able completely to separate ancient texts from the places they were created.

I still know of no other city where the histories and myths intermingle quite so powerfully as they do in Rome, for any period of its past one chooses. Even the traditional founders of the city, Romulus and Remus, were heirs to the myth of Aeneas. What Bosworth achieves in this sophisticated and penetrating history is to show how the Roman pasts have pervaded the political and religious life of the city since 1800. The revolutionary French, the austere and embittered popes, the leaders of the new secular government after 1870, Mussolini with his bombast of a rediscovered empire, none of these could never escape from or fail to manipulate some precedent. Every leader sought to find the ‘right’ Roman past—republican, imperial, Christian or nationalist—to use for political resonance whatever the cost. Mussolini blindly destroyed large parts of medieval Rome to claw out the imperial ruins that lay buried beneath it.

What I loved about this book was Bosworth’s acute sensitivity to every nuance of Rome’s past. Symbols were refashioned to meet each contemporary need, however transient it might prove. I warmed to the story of how, during the ‘revolution’ of 1848–49, the cross on St Peter’s was, in the absence of the fugitive pope, painted in republican colours, while in the 1948 elections, the Italian communists linked Giuseppe (Joseph) Garibaldi, to another Josef, Stalin. (The Church responded with ‘At the urn, God sees you but Stalin does not’.) And I never knew that the last surviving ship of the papal navy was a paddle-boat called the Immaculate Conception.

The perpetual game-playing between popes, outraged at the loss of their patrimony in 1870, and city rulers achieved high levels of drama. When in 1889 the Roman government launched a grand unveiling of the statue of Giordano Bruno, burned by the Inquisition in 1600, Pope Leo XIII retaliated by spending the day prostrate before a statue of St Peter. When the Fascists commemorated the anniversary of the March on Rome on 28th October, Pope Pius XI countered with the institution of a new feast day, of Christ the King, for the last Sunday of October. In the great public ceremonies, blackshirts offered no competition to a pope clothed, as Pius was on one occasion, ‘in a huge silver mantle interwoven with gold’. Whatever Il Duce’s ambitions, no one knelt when Mussolini passed by. They did in their thousands when the pope did. Well might Pius XII reassert Rome’s primacy as the universal Christian centre of civilisation when the Fascist regime collapsed ignominiously in 1943. One of his successes was to secure the placing of figleaves on the virile genitalia of Fascist heroic statuary during the Holy Year of 1950.

Assiduously researched and always absorbing, this book should have an appeal far beyond lovers of Rome. Anyone sensitive to history is aware of how easily the past becomes mythical and /or fugitive. Sniff the air in Rome and, above the traffic fumes, you can sense the currents of nostalgia merging, separating, remingling, swirling around the ruins of past and present. Bosworth shows how even the most determined rewriters of history, Mussolini prominent among them, were out-manoeuvred by the insistent presence of alternative myths which subverted their proclamations of the revival of an ‘eternal city’. Rome is indeed ‘eternal’ but primarily, perhaps, in its ability to eternally manipulate its past.

Reviewed by Charles Freeman, historical consultant to the Blue Guides and author of Sites of Antiquity: 50 Sites that Explain the Classical World. His Holy Bones Holy Dust, a study of the medieval cult of relics, is reviewed here.

To see more details about this book, check the Amazon links below.

26.09.2011
11:05

The 15th-century Health Museum at Edirne

The hospital complex with its mosque (image © Nevit Dilmen)

Edirne, which stands on the Turkish border with Greece and Bulgaria, has seen extraordinary highs and lows during its history. As the Roman Adrianople, it stood close to the site of one of the most disastrous battles in history, when the Roman emperor Valens and most of his army was annihilated in AD 378. In 1205, just after they had taken Constantinople, the Crusaders were defeated here by the Bulgarians. In 1365 the Ottoman Sultan Murat I captured the city and made it the capital of his empire—until his successors finally took Constantinople itself in 1453. Edirne suffered appallingly in the Balkan Wars of the early 20th century. At one point, 20,000 Ottoman troops were marooned on an island and starved to death while thousands of civilians died in the city itself.

Times are quieter now. The Treaty of Lausanne of 1922 ensured that the city remained firmly inside Turkey. Today Edirne is worth visiting for its two 15th-century mosques and the wonderful Selimiye Mosque, built in the 1570s by Sinan (1489–1588), the greatest Ottoman architect of them all. It was completed when Sinan was in his eighties and is now a World Heritage Centre, even though, at three hours driving from Istanbul, it is still little visited. The city is also famous for its special fried liver—the main dish at any restaurant and apparently impossible to recreate anywhere else!

Almost as impressive as the Selimiye Mosque is the Medical Complex built by Sultan Beyazit II, the son of Murat I, just outside the city. It was completed in 1484 and was still functioning as a hospital until as late as 1916. Now beautifully restored to its original state and resplendent with its multiple domes and its mosque, the complex was opened to the public in 2008. Even before this it had won awards from the Council of Europe.

The hospital could take 32 patients at a time, housed in ten rooms, but in the first courtyard were treatment rooms for outpatients. The central room of the hospital has a fine dome: the treatment of mental cases in particular placed great emphasis on soothing surroundings. The hospital had a ten-piece orchestra with a repertoire designed to calm or stimulate according to the patients’ state of mind of the patients. Water, too, was considered to be calming, so the fountains were an important part of the ambience.

Alongside the hospital was the Medical School, with room for eighteen students. The hospital was well endowed with income from the local market dues, which meant that treatment was free and that the students were even paid for their attendance. The exhibit includes re-created displays of teaching and treatment sessions with illustrations of some of the procedures. Resolving back pain seems to have been a priority, as patients are shown tied up and being yanked about by 15th-century physios. Other treatments, one of them involving a cockerel, were perhaps less likely to succeed.

Until I had seen this wonderful museum I had been hesitant about bringing a group three hours out of Istanbul across a dull stretch of countryside. The Selimiye Mosque was perhaps enough of a draw in itself, but it is the Health Museum that made it a must. Adding the resplendent 19th-century Railway Station, now home of the History of Art Faculty of Edirne University—you approach the porter’s lodge through the original glass front of the booking office—and the recent, impressive, monument to the Treaty of Lausanne, plus a concluding cup of tea by the 16th-century bridge makes an excellent day out. Who knows, I may even get my group to tuck into the fried liver!

by Charles Freeman. Charles will be leading a tour of Istanbul and Edirne for Ciceroni Tours from 2nd–8th October.

City of Fortune, How Venice Won and Lost a Naval Empire

Roger Crowley, Faber, 2011.

The struggle by the city-states of Italy to dominate the medieval Mediterranean trade routes was a ruthless one and Venice was the key player. The famous account of Venetian merchants stealing the body of St Mark from Alexandria in 828, whether the stuff of legend or not, shows that Venetian merchants were trading in the East as early as the ninth century. Roger Crowley begins his own lively study of Venice’s fortunes in the eleventh century, but he is soon off to his first great set-piece, the notorious Fourth Crusade of 1204.

The crusaders who had answered the call from Pope Innocent III to free the Holy Land had booked a fleet of Venetian galleys to take them there. Crowley tells the tale of what actually happened when they could not pay up: a free-booting enterprise which ends with the sacking of Constantinople, the greatest Christian city of the Mediterranean, by the crusaders.  Whether or not this shocking diversion was manipulated by the aged, and blind, Venetian doge, Enrico Dandolo, who led the expedition, the Venetians were quick to ensure that harbours and trading posts of the shattered Byzantine Empire along the routes back to Venice now became theirs. Booty, including the fine copper horses that were placed on St Mark’s and a mass of sacred relics, looted from the heretical Greeks, flowed back into Europe.

Crowley tells this story with great panache. Then he turns his attention to the problems of control of the Stato da Mar, the Venetian Empire, that followed. Crete was vital as a staging post but with its people tenaciously clinging to their Greek Orthodoxy and resentful of the Venetian settlers, there were continual revolts. The Venetians never pretended that they ruled in the interests of their subjects and suppression was harsh, especially when a revolt of 1363 was crushed with the help of mercenaries. Everyone in Venice knew how vital the Cretan harbours were to their prosperity and the city exploded with flamboyant celebrations in St Mark’s Square as soon as the galleys brought home the news of a successful repression.

The fourteenth century also saw the culmination of centuries of struggle with Genoa. The Genoese had been masters of the sea almost as early as the Venetians. Yet Venice’s success in the Fourth Crusade had edged them out and they were determined on revenge. The wars were debilitating and in 1379 nearly ended in utter disaster for Venice when the Genoese captured Chioggia, just a few miles south of the city. Venice was isolated and the Genoese stranglehold began to suffocate her.  The charismatic Venetian naval commander, Vettor Pisani, who had been brought back and imprisoned in the city after an earlier defeat, was the Venetians’ last hope and by popular acclaim he was released. Crowley regales us with the story of how Pisani, with a revitalised fleet behind him,  finally out-manoeuvred the resilient enemy.

After these dramatic events, Crowley pauses to draw breath and there are more reflective chapters on the Venetian state and empire in the fifteenth century, the intricacies of diplomacy and the management of the fleets, with the lucrative pilgrimage trade to the East among the sources of new income. Yet by the fifteenth century there is a new threat after the Ottoman empire begins its inexorable expansion over the eastern Mediterranean. Crowley makes another set-piece of the fall of Negroponte, the island of Euboea, in 1470, and then there is the devastating loss of nerve by the Venetians at the battle of Zonchio in the Ionian Sea in August 1499, when Venice failed to engage the Ottoman fleet and so lost the initiative for ever.

This is a fast-paced and enjoyable book. Perhaps Crowley concentrates too much on the big moments when all seemed lost or won and the blood flows freely—but read City of Fortune and you will understand with what trepidation the arrival of a galley from the East was greeted. Did it bear news of a defeat that could put all in jeopardy or of another conquest which would keep the fabulous riches of the Orient flooding into the city? Each was equally possible and Crowley vividly reminds us that the survival of Venice was as precarious in the fourteenth century as it is today.

Reviewed by Charles Freeman, historical consultant to the Blue Guides and author of Sites of Antiquity: 50 Sites that Explain the Classical World. His Holy Bones Holy Dust, a study of the medieval cult of relics, is reviewed here.

To see more details about this book, check the Amazon links below.

Books about Istanbul

Some suggestions from Blue Guides’ historical consultant Charles Freeman

I haven’t been to Istanbul for some years, so it is good to be going back at last, to set up a tour I shall be leading in October. Of course, I shall be keen to put the new Blue Guide to Istanbul to the test and I have already been browsing. John Freely has alerted me to several smaller mosques that I have never visited so my appetite is already whetted. All my group will have their copies of the Guide but I need to offer them other recommendations.

I was depressed by Orhan Pamuk’s novel Snow, which I read last summer, but have preserved much warmer memories of his Istanbul, Memories of a City, a bittersweet account of his growing up in the city in the 1960s and 1970s (Faber, 2005). Pamuk brilliantly describes the complex and brooding relationships of a family that is trapped between traditional life and the pseudo-western alternative that is replacing it. He mourns the wooden buildings of the old town but in his adolescence he gradually found his own way into the complex and transient cultures that were being erased. So here too is an introduction to the literature of the city, the writers who visited it with their preconceptions and desires. Over the city, for Pamuk, rests huzun, a blanket of melancholia, heavy with the memories of those who have passed through. Has anyone really found a permanent home in a city of such transience? Pamuk suggests not. This haunting and beautifully-written book will certainly be on the list.

Recently out is Peter Clark’s Istanbul, A Cultural History in The Cities of the Imagination series (Signal Books, Oxford, 2010). Clark has never lived in Istanbul but he has family there and a long experience of viewing, as a British Council employee, its impact as the capital of the empire on its former provinces. He has amassed a large repertoire of stories and impressions, of his and others, and writes with a pleasing style. The bulk of the book comes after the Ottoman conquest of 1453; only 45 pages are on the Byzantine Empire and much of this on the empire rather than the city (although this could be justified by his title). As the book continues, it gradually becomes more of an anthology, a pastiche of the stories Clark has picked up in his wide reading or gleaned from his wanderings in the city. While never dull, it really needed to be brought into better order. Chapter Four, on the nineteenth century, jumped from subject to subject, often without any relationship between them. Another chapter is a wander through Belle Epoque Istanbul. I would happily sign Peter Clark as a real guide here but in print, and with few illustrations, the details of each building overwhelm. The chapter ‘Sailing to Istanbul’ is simply a series of vignettes of nineteenth-century travellers who left some memories of their visits. With good editing, however, there is a valuable second edition waiting to emerge from the present text.

So I have gone back to rereading Philip Mansel’s superb Constantinople: City of the World’s Desire, 1453–1924 (John Murray, 1995). I finished it the first time as I was on a boat going up the Bosphorus in the late 1990s and found it magnificently detailed and absorbing. It brilliantly captures the atmosphere and tensions of the city. Much of my work on Istanbul is on its Christian Byzantine past and I have forgotten most of what I learned about the sultans the first time around, so it will be a treat to meet them again in Mansel’s vivid account. He reminds us too just how much Istanbul was part of a wider Mediterranean commercial and political world in the nineteenth century as the European powers tried to fit it into their strategic plans. It remains a great and relevant read nearly twenty years on and so will certainly be on my recommendations list.

To see more details about this book, check the Amazon links below.

Comments on Blue Guide Istanbul

Fully updated new edition to this ever-more-popular destination.

View details, look inside and order securely on line direct from the publisher.

 

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St Augustine and his mother at Ostia
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Cividale del Friuli and the Lombards
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Hitherto unknown language discovered in east Anatolia
Painting of the Day
Museo Barracco: a little-visited gem
Santo Stefano Rotondo in Rome
Staten Island: Upcoming Exhibition …
International Gothic at the Uffizi
Celebrating Santa Rosalia, patron of Palermo
Delhi Ghost Trail
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The Roman Villa at Balácapuszta (Baláca, Nemesvámos,...
The Bard of….Messina? Was Shakespeare Sicilian?
Rereading Ruskin
Sicily’s emblem: the Trinacria
Luca Signorelli on exhibition in Umbria
The Tribuna of the Uffizi reopens
The Venice equivalent of the anonymous Tweet?
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Sicilian Holiday Reading
Attila the Hun and the Foundation of Venice
Death in Venice cocktail a hit
The Gentry: Stories of the English
381 years ago this June
Brooklyn Bridge: a New York landmark
A Venetian Update
Sixth-century church to reopen
Roman Aquileia
Springtime in Friuli
Northern Italy dining and accommodation recommendations
Al Dente: Madness, Beauty & the Food of Rome
A celebration of Lucca
Romantic music in a Baroque setting
Blue Guide India Delhi Launch
Nikolaus Pevsner: The Life
The Man of Numbers: Fibonacci’s Arithmetic Revolution
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The Roman Forum
Whispering City: Rome and its Histories
The 15th-century Health Museum at Edirne
City of Fortune, How Venice Won and Lost a Naval Empire
Books about Istanbul
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Constantine: Unconquered Emperor, Christian Victor
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The 54th Venice Biennale stars Tintoretto
Holy Bones, Holy Dust
RECOMMENDED PLACES TO STAY AND EAT ON CRETE
Delhi: Adventures in a Megacity
Full Circle: How the Classical World Came Back to Us
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Familiar face
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Blue Guide Northern Italy
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A day trip to Ostia Antica from Rome - highly recommended
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A day trip from Venice up the Brenta Canal
A day trip to Murano from Venice
Pietrasanta, Pisa: in search of Stagi
Reading list for Venice
Reading list for Florence and Tuscany
The Best Credit / Debit Card for Travel
Ruskin on Venice
Reading list for Rome
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