Tau equals Two Pi

Open your mouth wide like a circle, now say "Tau", and no more Pi for you!

I'm not a good mathematician. But I did know how to work out the length of the circumference and the area of a circle, if given the diameter. You simply used an incredibly complex number represented by the Greek letter π which is the ratio of the circumference to the diameter of any circle.

I was very interested to read an article today that suggests, nay proves, that π would be better thrown out and we should really work with a constant that is based, not on the diameter, but the radius. The Tau Manifesto by Michael Hartl, proposes the use of a new constant that is twice π, called Tau () instead of Pi (π).

ie. τ = 2π

A seemingly simple change. Yet, having introduced circle functions to 8 - 12 year-olds, I can tell you, Tau would be so much easier for young people (and everyone!) to understand and use than Pi.

It seems astonishing that something that we have used for so many centuries might be improvable.

You might like to read the Manifesto and make up your own mind.

Miranda Floods and Fog

Very early last Friday morning I drove up to Miranda again.

Despite three days of torrential rain I was still unprepared for the extent of the flooding. And the thick fog was an unwelcome surprise which slowed me down considerably. But as dawn began to softly lighten the countryside, I stopped the car and got out and stood awhile. These two photos were taken from the same spot about 90 degrees and 30 seconds apart. The fog was slowly drifting to and fro and the quiet peace settled over me as it always does up on the Firth of the Thames.

The cows were less than impressed at their submerged grazing and stood around on the higher parts of their paddocks looking resigned. A tethered goat moaned about the wet.

But the wading birds were delighted at the vast sources of worms and bugs that were available for the taking, and, hooray! they didn't even have to wait for low tides. Flocks of Godwit and SIPO (South Island Pied Oystercatchers) chattered away on the edges of the temporary lakes behind the Miranda Shorebird Centre, and a lovely White Heron stalked systematically up and down the flooded drains enjoying a feast too.

The fog came and went all day, softening odd edges, removing hills and backdrops and making a strange, shifting, unfamiliar landscape.

By Sunday all the flooding had dried up and the sun came out, and all was back to normal.

Now it's hard to imagine 'Widgery Lake' in front of the Centre completely dried up, as it was in the drought this summer.

(Click on the images to enjoy them better.)

Beauty in Unexpected Places

Auckland - rushing through after our trip to Northland. I do have 'stiller' shots, but this one captures the feeling I had - 'let's get home and relax.'

Colton High School

My Vermeer Frog

The countdown to the end of term critique day is on again.

This fellow is about a metre across. I'm trying to work my scale up to the point when I can tackle an 8 x 4 mural on an outside wall next term. this will be a challenge! I usually work small, with small brushes.

S'cuse the light bounce in the top right.

The Droste Effect

Can you see the last visible The Last Visible Dog?

Escher explored a fantastical droste effect in some of his paintings. Here is a site I discovered that animates a loop so you can go on a 'journey' into an Escher painting... forever!

TLVD in Japanese

Today I had a visitor from Osaka to my blog who applied Google translator to it. This is how TLVD looks in Japanese. I wonder how accurate my words/ meanings are after translation.

Traditional Maori Carving

As part of our sculpture unit last term we visited the Rotorua Waiariki Institute of Technology (Mokoia Campus) just out of Rotorua.

As first-time visitors, we participated in the Powhiri (official welcome) onto the Tangatarua ("Two People") Marae grounds, and then were permitted to enter and view the wonderful carving works inside the Wharenui (meeting house). These are contemporary works and took three years to be completed under the instruction of master carver Lyonel Grant.

In the entrance I took some pics showing the detail and patterns. Each pattern has a traditional meaning, although these days many are adapted and recombined to reflect new ideas.

Now, don't laugh, here is my first attempt at carving. I know, pathetic really, but I was unbelievably proud of these little carvings. They are each about 3 cm square.

Rotorua - Roar - tore - roo - ah

Waiariki - Why - ah - ree - kee

Mokoia - More - koy - ee - ah

Powhiri - Poor - fee - ree

Tangatarua - Taa - ngaa - taa - roo - ah

Marae - Maa - rye - ee

Wharenui - Far - ray - noo - ee

Te Reo Maori - Tay Ray - or Mar - or -ree

Note: there is no emphasis on any one syllable over any other.

Disclaimer: These are as close as I can get to the pronunciation, as far as I know it. I'm not a fluent Te Reo (the language of) Maori speaker.

Colours

What an amazing complex world it is. My interests, and therefore my blog posts, just scratch the surface.

And even if I take just one bit; say, colours, and how we perceive them, it doesn't seem to get any simpler!

Take the patterns above. Each contains only four colours and a dark background. Yet each interests me for a different reason. Some feel more serene and calming, and others definitely catch my eye more. Some individual colours predispose me to react, like red (blood). Of course Emergency signage and advertising makes use of these colours like red and orange that we find more alerting.

Then there's the placement of colours next to others. Highly contrasting colours like red and white or yellow and black, draw my eye. I once saw a white and black striped sea-snake while skindiving over a coral reef in Vanuatu, and although I had never seen one before it made me instinctively curl up my toes and swim away.

And of course the concentric bull's eye shapes draw me in to the centres. They are like a whole lot of predator eyes looking at me. The old OXO boxes are perfect examples of 'eyes' plus a good, bright red. It's hard not to look at circles, especially red ones, as you pass them on the supermarket shelf.

And then there's plain ol' personal preference. Everyone seems to have a favourite colour or two. Mine's green.

Beauty in Unexpected Places

Entangled

My Grandfather was a keen trout fisherman. I often remember him sitting at the kitchen table painstakingly unravelling a seemingly impossible mess of pale translucent fishing line. "Never pull at an end' he would say to me. Always push, tease, and follow your line back until it almost undoes itself. If you pull, you'll make the nylon kink or knot and then your job will be so much harder."

There's no big metaphor here for life. Well, none that springs to my mind at this point. But I did learn from watching him that patience and thought usually solves problems and gets jobs done both quicker and better than the 'rip shit and bust' method.

Here's a nice little game that reminds me of that nest of fishing line of Poppa's.

My Eye.

Under about ten years old, I was an extremely shy and retiring sort of person. I mean, really. You have no idea. When I was ten, my English-born parents had saved up enough for them and my sister and I to take a trip to England - big ships each way - and we travelled around in a campervan, visiting relatives for six months. The trip was wonderful, and just what I needed to give me a bit of confidence, which continued to develop until now I am the woman you see before you.

But even in my Very Shy years, I was always rather vain about my eyes. I remember looking at myself in the mirror for the first time (as one does) and thinking the colours were wonderful. Sort of a greeny-gold with burnt sienna specks. (I knew about burnt sienna from my paint-box). I learnt in due course that other people had interesting eye colours too. Gazing into men's eyes has always been an interest of mine.

However when it came time to get my first passport, and I had to write down the colour of my eyes, I was surprised to find that you couldn't describe your eyes in detail. There was a very limited choice, and I felt quite cheated that mine were just put into the category 'hazel'. What kind of a one-size-fits-all type of thing is that? Hrumph! You could be green, blue, brown or hazel. And worse still, 'hazel' wasn't a particular colour, it just meant 'a mixture of colours'. So I was lumped in with 'blue with specks of brown', 'greyish-blue', and all the other flotsam and jetsam. Sigh.

It's so very hard to be humble when you have beautiful eyes.

Bacon Bone Soup

Bacon bone soup has to be one of the nicest winter soups. Well, pumpkin is a close second. But nothing really beats the aroma of onions and bacon steaming up the windows on a cold and rainy Sunday morning. It's so easy! Pop a bacon hock in the biggest saucepan half full of water (say two litres?), three chopped onions, a couple of handfuls of pearl barley, three sliced carrots, some leftover pumpkin and spuds, and simmer for four hours or so. You can take the bone out and cut the meat into chunks if you like. No salt usually needed, there's plenty in the bacon. (If you want to leave it overnight to cool and skim the fat off in the morning, that's a good idea.) At the last minute I like to add a cup of frozen peas. It just needs to be returned to the boil to cook them. Add some hot buttered toast, and here they come in to wash their hands after raking up the leaves.

Smokin'

One of the special things that characterise High Renaissance paintings is a smoky appearance - as if a drift of thin, fine, net curtain had been drawn across the paintings. The darks seem slightly lighter and the lightest places somewhat duller. The master of this (and almost everything else!) was of course Leonardo da Vinci.

The Italian word for this effect is Sfumato, from the word sfumare, 'to smoke'. Look at those wonderful soft corners of her mouth - that subtle shading that, from a distance is partly the reason it is difficult to tell if she is smiling or not. I once read that she was an intelligent woman. The mouth would suggest that she found da Vinci interesting. Or at least, that what I'd like to think. That he was propounding something enthusiastically to her as she sat, and he was challenged to capture that gentle amusement at his excitement.

Anyway, sfumato - the smoky look. Not that hard to do, actually. Very thin titanium white is the secret. And lots of glazing in layers.

Da Vinci himself described the effect as 'without lines or borders'. But of course he would have said it in Italian.

It's

... that people who want to spend all their day painting and making art shouldn't live in 120-year old houses set on large sections with lots of trees. In autumn.

A Jungley Breakfast

Up in Kerikeri we breakfasted each morning on the sunny verandah overlooking the tropical lushness of the 'Wharepuke' gardens.

A tame jungle fowl arrived early and waited while the coffee brewed and we set the table with our tropical fruits.

Feijoas, mandarins, gold kiwifruit, and, straight from the tree nearby, those green things that look like unripe apples are Casimiroa edulis, or white sapote. I had never tasted one before and it was absolutely heavenly! A soft, custardy, creamy texture, not too sweet, with a flavour somewhere between a musky peach and vanilla ice-cream. My mouth is watering at the memory even now as I look at the photo I took.

I've saved the seeds. I hope they germinate.

Next morning, guess who was waiting politely on the doorstep for some more breakfast crusts.

Goodness Gracious Me

This song came up in conversation the other day. I thought it was Bridget Bardot, but it was Sophia Loren, of course. Apparently she is working this year on a biopic of her early life, based on her sister Maria's diary. That should be interesting, given that her story is of growing up fatherless and poor in wartime Italy.

That Prickly-Trunked Tree

Well, here's me all excited by a strange, rare and exotic tree that I met in the flesh bark for the first time a couple of weeks ago, and Judy has had one in her back garden!

Here are the rest of the images I took of Ceiba speciosa, also known as palo borracho in Spanish. It's one of the kapok family, and also related to the baobab. The green patterns and spikes on the trunk reminds me of some kind of chameleon or one of those spiky lizards that the Australian outback seems to spontaneously generate.

The flowers are very pretty as you can see. They look a lot like hibiscus or mallow flowers, and, not surprisingly, are the same family. But obviously this branch (ha ha) of the family is not vertically challenged at all. Ceiba speciosa can grow to 25 metres (75 feet) if they get enough water.

The pods contain a fluff, like kapok. Unlike cotton it isn't suitable for spinning but used to be used for stuffing. Remember those old kapok mattresses? And I'm sure my old Teddy bear had kapok insides.

This specimen was growing in 'Wharepuke' - a 5 acre private jungle-like garden in Kerikeri, New Zealand, where we stayed a couple of nights recently. The owners told us that Northland's summer drought seems to have especially increased the number of flowers, as the tree looks particularly flamboyant this year.

Mystery

Guess what this is.

Another clue tomorrow.

Winner of the closest answer gets a pat on the back and a big cyber-huzzah.

Eye Candy Day 22