Happy Pi Day

It’s Pi Day again, and so there’s pie-eating contests, bickering over the merits of pi versus tau (pi times two), and throwdowns over who can recite more digits of π.

π does deserve a celebration, but for reasons that are rarely mentioned. In high school, we all learned that π is about circles. π is the ratio of a circle’s circumference (the distance around the circle, represented by the letter C) to its diameter (the distance across the circle at its widest point, represented by the letter d). That ratio, which is about 3.14, also appears in the formula for the area inside the circle, A = πr2, where π is the Greek letter “pi” and r is the circle’s radius (the distance from centre to rim).

Pi explained

The beauty of π is that it puts infinity within reach. The digits of π never end and never show a pattern. They go on forever, seemingly at random — except that they can’t possibly be random, because they embody the order inherent in a perfect circle. This tension between order and randomness is one of the most tantalizing aspects of π.

π touches infinity in other ways. For example, there are astonishing formulas in which an endless procession of smaller and smaller numbers adds up to π. One of the earliest such infinite series to be discovered says that π equals four times the sum 1 – 1/3 + 1/5 – 1/7 + 1/9 – 1/11 + ⋯. The appearance of this formula alone is cause for celebration. It connects all odd numbers to π, thereby also linking number theory to circles and geometry. In this way, π joins two seemingly separate mathematical universes, like a cosmic wormhole.

But wait, there’s more… After all, other famous irrational numbers, like e (the base of natural logarithms) and the square root of two, bridge different areas of mathematics, and they, too, have never-ending, seemingly random sequences of digits.

What distinguishes π from all other numbers is its connection to cycles. For those interested in the applications of mathematics to the real world, this makes π indispensable. Whenever we think about rhythms — processes that repeat periodically, with a fixed tempo, like a pulsing heart or a planet orbiting the sun — we inevitably encounter π. There it is in the formula for a Fourier series:

That series is an all-encompassing representation of any process, x(t), that repeats every T units of time. The building blocks of the formula are π and the sine and cosine functions from trigonometry. Through the Fourier series, π appears in the math that describes the gentle breathing of a baby and the circadian rhythms of sleep and wakefulness that govern our bodies. When structural engineers need to design buildings to withstand earthquakes, π always shows up in their calculations. π is inescapable because cycles are the temporal cousins of circles; they are to time as circles are to space. π is at the heart of both.

For this reason, π is intimately associated with waves, from the ebb and flow of the ocean’s tides to the electromagnetic waves that let us communicate wirelessly. At a deeper level, π appears in both the statement of Heisenberg’s uncertainty principle and the Schrödinger wave equation, which capture the fundamental behaviour of atoms and subatomic particles. In short, π is woven into our descriptions of the innermost workings of the universe.

So there is plenty to celebrate this Pi Day. With πe and πzza 🙂

Being rational is hard. Take the day off 🙂

Original article in The New Yorker.

Florentine Cherries

Yummy! Are Florentines from Florence?

They must be. They have cherries in the recipe. And Florence is a cherry place!

We found cherries at Solo A Firenze.

Cherry bounty in Florence – Puffles and Honey BC (Before Clothes 🙂 )
Solo A Firenze
Borgo Santissimi Apostoli, 37/r, Florence
Solo A Firenze
Borgo Santissimi Apostoli, 37/r, Florence

These cherries are made of alabaster. They are very pretty!

One of the many talents of the Florentine artisans is the stone inlay. Florence is the place where an amazing craftsmanship saw its birth in the 16th century thanks to the Medici family: the commesso fiorentino. It’s a very ancient job to transform the mosaic made up of tesseras into something more refined, that had to be closer to a painting out of stone. There are very few masters of this art left. They require a strong attitude to painting and design, a profound knowledge of materials, and a long-sightedness to see the final work from the very first stage. It’s a “puzzle” of colourful stones, made following the pattern of the design, so carefully that you don’t see the union of thousands of pieces. Artisans look for the stones on the river banks, in the country or in the mountains and they cut them into big slices. The big slices are then cut into many small pieces using a cherry bow and a clamp, in the same way the stone cutters did for centuries. Nothing has changed. The results are spectacular masterpieces, each is a unique piece, since it’s impossible to replicate them: paintings, table tops, little jewels. Every piece a different story.

This piece tells a story from Florence. We found it at the Uffizi Gallery shop.

Then we found a cherry at Pitti Mosaici. Located across the Arno from the Ponte Vecchio, and directly across from the Pitti Palace, Pitti Mosaici houses magnificent treasures of “painting” using multicolored stones. The results are three-dimensional masterpieces.

Pitti Mosaici Showroom
Sdrucciolo de’ Pitti, 5R, Florence
Photo Courtesy of Pitti Mosaici
Photo courtesy of Pitti Mosaici

The artistic tradition of Florentine de Filippis family started back in the 19th century. Grandfather Emilio I specialised in marble sculpture in Paris, and the tradition was carried forward by his son Ernesto in monumental, religious and residential architecture. Ernesto’s son, Emilio II, known as Ilio, moved to Florence to learn the technique of semi-precious stones inlay or pietre dure, allowing him to express his own versatile creativity in jewellery, mosaics, as well as architecture and design, thanks to the savoir-faire his family passed down to him.

Today, Pitti Mosaici is an internationally active art studio, carrying out bespoke residential projects recalling a Renaissance style and atmosphere, and creating with the same passion commesso fiorentino mosaics of astounding beauty.

That cherry was yellow and we like red cherries! So we got in touch with Anna and Isse from Pitti Mosaici after we got home and started designing together an inlaid pietre dure mosaic panel with hard and semi-precious stones – Cherries. They sent us several design options and we took the bits we liked from each of them and put them together like this!

Final Cherry Design – Pitti Mosaici

The sketch functioned as a kind of jigsaw puzzle and the artisan had to find stones with the right colours and natural markings to reproduce the design, and then trim them to fit their particular niches in the cherry puzzle.

There it is!

The mighty stone façade of the Pitti Palace is one of Florence’s landmarks, and the rooms of the palace resound with the voices of tour guides extolling the glorious paintings by Raphael, Rubens and Titian that cover the walls. In the excitement, visitors all too often overlook another glory of the Renaissance, the palace’s rich collection of mosaics made with semiprecious stones.

More than four centuries ago, the art of shaping fragments of jasper, lapis lazuli and the like into stone “paintings” was nurtured in Florence by the Medici princes, the Pitti’s owners. The city became the leading center for the manufacture of pietre dure, and its elegant mosaic tabletops and wall panels decorated homes and churches throughout Europe. The most expensive piece of furniture ever sold in auction is a pietre dure cabinet made in Florence around 1730 for a British nobleman.

Badminton cabinet

An item like this really ties the room together — with money… When the 18th century Florentine ebony chest inlaid with amethyst quartz, agate, lapis lazuli and other stones sold for $36 million at a 2004 Christie’s auction, it broke its own record as the most expensive piece of furniture sold at auction. The Badminton Cabinet, so named because it remained in Badminton, England, for over two centuries, had set the previous record in 1990 when Christie’s sold it to billionaire Barbara Piasecka Johnson (of the Johnson & Johnson fortune) for $16.59 million. Johnson put it up for sale in 2004, when it was bought by Prince Hans Adam II of Liechtenstein, who donated it to the Liechtenstein Museum in Austria.

Pietre dure masterpieces are still to be found in Florence, not only at the Pitti but at museums and public sites – notably the Chapel of the Princes in San Lorenzo, the Medici family mausoleum, a huge octagonal chamber whose floors and walls are a made-in-marble rainbow of rich color and elaborate design.

Chapel of the Princes
Mausoleum of the Medici Family
Chapel of the Princes
Mausoleum of the Medici Family
Chapel of the Princes
Mausoleum of the Medici Family

And the art form lives on at private workshops and stores in and around the city, where visitors can sometimes watch artisans at their trade.

Properly executed, the Florentine mosaic is extraordinary, an image made of hundreds or thousands of fragments of rock so carefully selected, cut and glued together that it presents an apparently unbroken surface, as though it had been painted. Subjects range from traditional bird-and-flower designs and still life to portraits and landscapes. Materials include not only such hard stones as malachite but also softer rocks such as marble and alabaster.

The task is daunting, and the quality of the mosaics for sale ranges widely – as do the prices. A small, ill-wrought version may sell for $25, while more finished pieces cost hundreds or even thousands of dollars.

One place to start your research is the museum of the Opificio delle Pietre Dure, “the workshop of the hard stones,” at 78 Via degli Alfani. The workshop, housed in an 18th century palace, grew out of the original Medici mosaic factories, but has become a government art restoration conglomerate. In the museum, one finds mosaics of every variety, including a contemporary portrait-in-stone of Cosimo de Medici and some remarkable floral tables and wall hangings. A special insight into pietre dure is provided by the pairing of two oil paintings with their mosaic copies. One shows milkmaids on a farm, the other an ancient marketplace. From a few feet away, the copies and originals look identical.

As much as anything, the Florentine mosaic requires extraordinary patience. A piece may take artisans weeks to complete. They work with slices often less than an inch thick, looking for just the right shade or marking in the rock to fill in a section of the jigsaw puzzle – a tiny flower petal here, a rosy cheek there. The greater the number of pieces, the more subtle the finished work can be.

Before any cutting, the artisans use a mixture of beeswax and resin to attach a section of the sketch to the appropriate spot on the rock slice; the paper serves as their pattern. The actual cutting is done with a type of saw that has not changed over the last four centuries. Essentially it is a bow, a bent branch of chestnut with a string made of metal wire. As the artisans move the bow over the stone, they constantly add an abrasive, muddy mixture of water and emery dust, known as smeriglio, to the wire. This slow process keeps the surrounding rock intact and makes possible great precision.

No matter how skilled the cutter, though, the pieces of the puzzle require endless filing for the fragments to fit together so exactly that the seams between them all but vanish. The finished product is polished until it takes on a high gloss.

Many gift shops and antique stores carry one form or another of pietre dure. The price of a mosaic is determined not only by the level of workmanship but also by the materials. The softer stones such as marble are easier to work than hard stones like lapis, so mosaics made primarily of marble are apt to be less expensive.

The proportion of hard stones to marble in pietre dure has changed over the years, depending in part on public taste. The vivid colors found in semi-precious stones were ideal for the geometric patterns of the classical style and for the stylized birds and flowers of the Mannerist school. But even in those early days, marble and other soft stones were used to enlarge the artist’s palette. That became more important as pietre dure works began to reflect such newer schools as Impressionism.

On the roof terrace of Hotel Torre Guelfa, Florence
Cherry picnic on the roof terrace of Hotel Torre Guelfa, Florence

We love cherries!

Mark Twain himself was suitably impressed with the pietre dure mosaics. He mentioned them in the Innocents Abroad.

Magnanimous Florence! Her jewelry marts are filled with artists in mosaic. Florentine mosaics are the choicest in all the world. Florence loves to have that said. Florence is proud of it. Florence would foster this specialty of hers. She is grateful to the artists that bring to her this high credit and fill her coffers with foreign money, and so she encourages them with pensions. With pensions! Think of the lavishness of it. She knows that people who piece together the beautiful trifles die early, because the labor is so confining, and so exhausting to hand and brain, and so she has decreed that all these people who reach the age of sixty shall have a pension after that! I have not heard that any of them have called for their dividends yet. One man did fight along till he was sixty, and started after his pension, but it appeared that there had been a mistake of a year in his family record, and so he gave it up and died.

These artists will take particles of stone or glass no larger than a mustard seed, and piece them together on a sleeve button or a shirt stud, so smoothly and with such nice adjustment of the delicate shades of color the pieces bear, as to form a pigmy rose with stem, thorn, leaves, petals complete, and all as softly and as truthfully tinted as though Nature had builded it herself. They will counterfeit a fly, or a high-toned bug, or the ruined Coliseum, within the cramped circle of a breastpin, and do it so deftly and so neatly that any man might think a master painted it. I saw a little table in the great mosaic school in Florence–a little trifle of a centre table–whose top was made of some sort of precious polished stone, and in the stone was inlaid the figure of a flute, with bell-mouth and a mazy complication of keys. No painting in the world could have been softer or richer; no shading out of one tint into another could have been more perfect; no work of art of any kind could have been more faultless than this flute, and yet to count the multitude of little fragments of stone of which they swore it was formed would bankrupt any man’s arithmetic! I do not think one could have seen where two particles joined each other with eyes of ordinary shrewdness. Certainly we could detect no such blemish. This table-top cost the labor of one man for ten long years, so they said, and it was for sale for thirty-five thousand dollars.

Pirates Island

Very pretty, but no treasure anywhere!

Little bears are on Penguin Island.

There are more than 1200 little penguins that call Penguin Island home, but they leave the island before sunrise to go fish hunting at sea and they return to the island approximately one hour after sunset. Some penguins will stay on the island, however, they stay hidden in their burrows or other secluded places.

Little bears got to see little penguins at the island Discovery Centre. The centre is home to 10 little penguins who were injured or orphaned and were unable to be released back into the colony.

Little Kevin was abandoned as a chick, but is the life of the party now! He very helpfully translates into penguin squeaks the entire presentation given by the penguin keeper 🙂

Little Sedge and Nemo are a lovely penguin couple who have been together for over ten years.

Yet in that time they never produced an egg. It might have something to do with the fact that they are both males! One year all their Christmases came at once when they found an egg in their burrow. Another very young penguin couple had abandoned their eggs, and the penguin keepers decided to give an egg to Sedge and Nemo. They took turns taking care of the egg (as little penguins do, they share the chick rearing duties) and a miracle happened. The egg hatched! The penguin keepers never expected that to happen and were not sure what to do with the little chick, return her to her egg parents or leave her with her adopted parents. Happy to say that adopted parents won! Instinct took over and Sedge and Nemo did a fantastic job taking care of the little chick. When she was ready, she was microchiped and released into the colony on the island.

Cape Naturaliste Lighthouse

Only 13 kilometres from Dunsborough, Cape Naturaliste Lighthouse is one of the most popular attractions in the Geographe Bay and Margaret River region.

Cape Naturaliste Lighthouse was the last manned lighthouse on mainland Australia and is one of the few operational lighthouses the public can access.

Built from limestone quarried from nearby Bunker Bay, and standing on a 100m bluff overlooking Geographe Bay, at its highest point the lighthouse is 123 metres above sea level.

Last year, Cape Naturaliste Lighthouse received some much needed TLC, including a bright red door 🙂

Cape Naturaliste Lighthouse is one of the 56 heritage-listed lighthouses in Australia. The Australian continent has more than 37,600 kilometres of coastline and countless potential hazards for ships approaching landfall.

Tales of shipwrecks abound through Australia’s history, and many lighthouses were built as a result of numerous fatal shipwrecks. Areas such as Bass Strait and the south-western point of Western Australia have proved especially treacherous for ships.

Cape Naturaliste is the northernmost point of the Leeuwin-Naturaliste Ridge and separates the relatively sheltered waters of Geographe Bay from the southern Indian Ocean. At least 12 ships have come to grief in the strong currents and dangerous reefs which lie off Cape Naturaliste’s sharp point. The list includes Governor Endicott (1840), Halycon (1844), Geffrard (1875), Ella Gladstone (1878), Mary (1879), Day Dawn (1886), Dato (1893), Electra (1904). A number of other ships run aground in the area.

The 1890s gold rush enabled the Western Australian government to undertake several capital works programs, including the construction of lighthouses such as Cape Naturaliste Lighthouse. Before the lighthouse was built most mariners depended on ‘The Tub’ as a landmark. This was a barrel on top of a 9 metre pole erected in Busselton, to mark the best landing place for passengers and stores.

Twenty metres high, the Cape Naturaliste Lighthouse was built over 10 months in 1903-04, at an estimated cost of 4,800 pounds, with limestone carted by bullock wagon from a quarry at Bunker Bay, about 1.5 km away.

Like most Australian lighthouses in the late 1800s, Cape Naturaliste Lighthouse used kerosene to power the light and a mercury bath to assist in the rotation of the large glass lens assembly. The lighthouse was fitted with a Chance Brothers lantern and First Order lens, which are still in place today. Chance Brothers of Birmingham, England supplied the equipment for most of Australia’s early lighthouses.

Each day before dusk, men across Australia left their cottages to ascend a familiar spiral staircase, set the light going by winding it up and pumping the kerosene, maintaining it and watching it throughout their watch. This occurred night after night, in still weather and in the midst of the worst storms that the sea could throw against the nearby shores. The lighthouse prisms also had to be cleaned at least once a fortnight; it took two men the best part of a day to clean and polish both sides.

Life was hard for light keepers and their families. With no paid annual leave or travel assistance, light keepers remained at their isolated stations for many years.

Friendly tour guides provide a fascinating insight into the functions of this working lighthouse and take visitors to the lighthouse observation platform to enjoy panoramic views across the Indian Ocean, the beautiful Geographe Bay coastline and the Leeuwin-Naturaliste National Park. The balcony offers the perfect vantage point to observe whales and their young during the annual migratory period, from September to December.

View from the lighthouse observation platform
Hold on tight! The wind is trying to bearnap us!
This is much safer… Thank you Jack!

Three light keepers and their families originally lived and worked at Cape Naturaliste Lighthouse. Life revolved around night watches which were divided into three periods, one for each man. During each watch the keeper had to wind the clockwork, carry and then pump kerosene to the burner.

Once a fortnight, stores and supplies were delivered from Busselton, including classwork for the children who were home schooled. The nearest school was 20 kilometres away at Quindalup.

The original light produced 755,000 candelas, which was increased to 1.2 million candelas in 1924, and subsequently converted to electric illumination. The light was converted to automatic operation in July 1978, with its white beam visible for 26 nautical miles (48 km), and it identifies itself to mariners by flashing twice every 10 seconds with a 2.5 and 7.5 second interval.

Cape Naturaliste Lighthouse seen from Sugarloaf Rock

The last lighthouse keeper, Max Nethery, left in 1996. Cape Naturaliste Lighthouse was the last manned lighthouse on mainland Australia.

The Lloyds signal station at the lighthouse was connected by telephone with the main telegraph system.

The steps leading up inside the tower are made from blocks of Burmese teak, dowelled together and set end-grain up for long wearing. This remarkable method of joinery has successfully withstood the test of time, and of course, thousands of tramping feet. And paws 🙂

The three stands (painted green) inside the base of the tower were originally tank stands for fresh water.

The light keepers went up and down the stairs every hour. Originally a clockwork mechanism rotated the lens and the clockwork had to be wound every hour. At least Cape Naturaliste Lighthouse has only 59 steps, compared to 176 at Cape Leeuwin Lighthouse.

The lighthouse’s apparatus consists of the original Fresnel lens, made of lead crystal, driven by an electric motor. Originally a clockwork mechanism rotated the lens which, including the turntable, weighs about 12.5 tons. The turntable is hollow and contains 156.5kg of mercury (less than 12 litres) on which the lens floats. The original shipment of mercury for the Cape Naturaliste Lighthouse arrived safely from England, only to be lost overboard while being unloaded at Quindalup jetty!

To accommodate the massive lens, the lantern had an internal diameter of 4.2 metres, one of the largest ever installed in an Australian lighthouse. The weight of the optic was almost five tonnes, however could be turned with just one finger due to the mercury pedestal.

A notable event in the lighthouse’s history occurred in 1907 when the Carnarvon Castle caught fire on her way from Liverpool to Melbourne. The crew transferred to lifeboats and were stuck in gales and high seas during a gruelling 24 day journey to find land. For the victims of this wreck the Cape Naturaliste light was a beacon of salvation which guided them finally to land, suffering from dehydration and exposure. Using ropes the light keepers pulled fourteen survivors from the bottom of the cliffs to safety, where they were then cared for at the lighthouse station for ten days until they could travel.

The tour was very interesting!

The original three quarters for light keepers are still on site. They were included in the refurbishment project last year, along with extensive landscaping of the site.

Cottage 1 has been remodelled for ticket office, retail souvenirs and guides station.

Cottage 3 is now a café with external decking, featuring old wooden pylons from the Busselton Jetty, overlooking the natural materials themed playground. Nestled in the playground’s sandpit is a 1930’s wooden clipper boat, restored with the assistance of the Dunsborough Men’s Shed. The Lighthouse Keeper’s Cottage Café is operated by Busselton’s popular restaurant The Goose and allows you to step back in time and enjoy a cup of coffee and a bite to eat in one of three charming rooms fitted out with vintage furniture and ornaments. Each room also features rotating art displays from local artists.

Lighthouse Keeper’s Cottage Café
Lighthouse Keeper’s Cottage Café
Playground with the wooden clipper boat

A new interactive interpretive centre, with local Cape Naturaliste stories, housed in the remaining light keepers’ cottage (2), is scheduled to open July 2018.

The original workshops/storage have been converted to classrooms & meeting place for schools & groups.

Dunsborough Sculpture by the Bay

For three days each March long weekend, the Dunsborough Foreshore at the end of Dunn Bay Road is transformed into an outdoor display of sculptural works for all to enjoy. The event commenced in 2010 with 12 artworks on display, while this year there were 28 artworks.

Some of our favourites…

Boudica’s Bicycle, by Lesley Barrett
All famous people have their toys, and Boudica had her bike… and it turned into a chariot for a warrrior
My New Life Blossoms, by Greg Gelmi
I Am Not A Fox, by Lily Mercer
The numbat (myrmecobius fasciatus) is the faunal emblem of Western Australia. Sculpture made of buff raku and porcelain
River of Rock Fish, by Dunsborough Primary School
Two Views, by Trish Waters
‘Two Views’ displays iconic vistas from the drive down Yallingup Beach Road, painted on a broken surfboard which was snapped in half by the power of the waves.
Wren’s Reflection, by Dennis Wilson

Hiking Goes With Glamping

There is only one place to find little bears after a hiking Expotition 🙂

This time they are at Mile End Glamping in one of the two luxurious light-filled geodesic domes that include a king bed, kitchen (the domes are self-catering), bathroom and adjacent deck with private spa bath and BBQ.

There is no WiFi but there is mobile reception if you need your daily electronic media fix. There is no TV reception, but there is a TV / DVD player that plays DVDs and USB media. There are a few movies provided on DVD, but best to take your own favourites along if you need to watch TV. Apart from that, the attention to detail and the many luxury touches are perfect.

The domes are in an idyllic location and we can imagine they can be particularly cosy in winter with the gas fire and the electric blankets. In summer they might get a bit hot during the day despite the reverse-cycle air conditioning and the netted windows to assist with cooling.

Content little bears 🙂

You can watch the sunrise from the deck…

Sunrise at Mile End Glamping
Sunrise at Mile End Glamping

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