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Vince's Parable of the Sundial.

The Amateur Mathematician and the Brisbane Planetarium Sundial
- Vince Englart

The Sundial

"We must correct others, even if not rewarded, because of a natural revulsion at people doing wrong; especially when it involves a public good. Besides, who hasn't made mistakes?"

Vince Englart

(From the left) Keith Brooks, Ted Englart and Vince Englart, at the (unfinished) Sundial - 1982
Keith Brooks (left), Ted Englart (Vince's father) and Vince Englart (right) at the Sundial - 1982

Imagine the architect's busy office, Christopher Wren and Associates. The boss, Chris, asked the junior architect, Archie, if they had a drawing of a sundial on file. Archie soon found a small drawing done some years ago for the city of Newcastle. Chris was very pleased with Archie's initiative but Chris had a contract with the City of Brisbane for a much larger one at the Botanical Gardens.

"It doesn't matter a bugger how old it is!!", exclaimed Chris, "A sundial is a sundial. It tells the time by the sun, doesn't it? Just draw it to the scale that the City Council architects dimensions want."

The drawings were later delivered to the Council and were passed on to the construction carpenters and labourers to build the base of the sundial. The dial itself is 4.6 metres diameter standing on a 400 mm column 3 metres high. It was designed in expensive white cement instead of the normal, which is grey. The carpenter in charge was Bruno, like myself a political 'lefty'; of Italian origin, as was his mate, Joe.

My mate was Jem Browne, a highly skilled scaffolder, Dublin born, who would always deny he was blarney, but he has been a good mate of mine for years. The four of us successfully poured the concrete 400 mm diameter base. The carpenters then set about constructing the form work for the actual dial. Almost daily, the foreman, Alan Green, would call to check up on progress.

Then the surveyor, John Conway, arrived with his chainmen. He set up his theodolite to get the bearings for the sundial and indicated its orientation on a north-south line. He then indicated to the carpenters where the point of the 'fin' of the dial should be. He had it pointed south instead of north.

When Alan Green, called Greenie by the boys, arrived I protested to him that the orientation was 180 degrees out, but, naturally, he couldn't listen to me in front of those responsible, the surveying team. I remember my last words to Greenie as he drove away. "Allan, it won't work!!"

That evening, I rang the trump, the assistant clerk-of-works, John Buckley. I'd helped John out when he was a humble carpenter when he needed to pick my brains on matters mathematical. He invited me to make a model of a sundial and bring it to work the next morning. I did so and the surveyor, John, acknowledged his error.

That was on a Friday and I went home to enjoy the week end. On Saturday afternoon, Alan Green was on the phone. He had studied the drawings and noticed a discrepancy in the figures on the drawing. I must say that he was a most conscientious foreman, because it would be most unlikely for anyone just to pick such an error. "Vince, I've found a discrepancy on the drawings. Can you check the figures?"

A self educated man

I digress for a moment in order to explain how I happen to have knowledge that is mainly the province of astronomers, navigators, cartographers and surveyors - specialists on the globe and the sky.

During the war in New Guinea, when I wasn't sweating my guts out building roads and bridges, as well as being hassled by nightly storms, giant pythons, as well as the Japanese, I wrapped myself in my books; in particular 'Science for the Citizen' and 'Mathematics for the Million' by Lancelot Hogben. Hogben wrote in the spirit that if humanity had a future the ordinary citizen had to understand what scientists and mathematicians are on about.

While I had only a primary education I soon mastered not only plain (Euclidian) geometry and trigonometry, but also learnt spherical trigonometry. Such knowledge is necessary not only to plot the path of celestial bodies in the sky, but also to navigate on the surface of the earth. (For example, you have to appreciate the shortest distance between two points is not the Euclidean straight line, but the 'great' circle which passes through them.)

I worked all Saturday evening; worked out the correct figures for Brisbane; and it became obvious to me that the figures on the drawing were consistent but wrong for Brisbane's latitude; 27 degrees 25 minutes south. (That was in addition to the mistake that Alan had stumbled on). It became clear to me that they were for some place other than Brisbane.

So I worked backward to establish that the figures on the drawing were for a latitude of 32 degrees 52 minutes south. But where?? So I scanned the home atlas and the only Australian city with such a latitude was the city of Newcastle, New South Wales.

On sunday evening I rung John Buckley and told him of my discovery and he told me, your humble labourer, to tell Bruno not to go ahead with the work until he arrived on the job in the morning. When John came on the job early on Monday morning he, with Alan and myself, went straight to the phone in the office of the curator, Jeff Ryder, of the newly constructed Planetarium and rang the Brisbane City Architect.

The City Architect referred John to the contract architect. John tactfully told the contract architect of Alan Green's discovery, and suggested that they look over all the figures. John silenced my mutterings, "They're all wrong!!".

While I didn't have a computer and worked with mathematical tables, the computers whirled away on Monday evening. On Tuesday morning I was the hero of the job! John Conway, the surveyor, confirmed my figures; Jeff Ryder also not only confirmed my work but expressed his disappointment that the authorities hadn't discussed the sundial with him. After all, the sundial was an integral part of the planetarium complex.

We stood around for some days, doing nothing (on full pay) but waiting on the response from the contract architects. They didn't have time to redraw the original drawings, but had written over the original figures on the blue-prints. I enjoyed myself with mind stretching discussions with the surveyor, John, and the curator, Jeff, on the nature of sundials.

On hearing me tell of my initiative in this story, a few, very few, said, "Why did you correct the mistakes, Vince? Why not let the 'experts' responsible make fools of themselves?". But most, including myself, think I did the right thing. We must correct others, even if not rewarded, because of a natural revulsion at people doing wrong; especially when it involves a public good. Besides, who hasn't made mistakes?

Casualty of the Cold War

Like so many other Australians, I was also a casualty of the Cold War. While U.S. citizens; intellectuals, actors, writors, and civil rights workers, would be 'honoured' by being called to the Un-American Affairs Committee by Senator Joseph McCarthy, we had no such honour bestowed on those of us who opposed the status quo in Australia. Many thousands of loyal Australians, battlers for a better life, were subjected to witch hunts - blacklisted - without finding a single spy.

If I hadn't been on Australian Security Intelligence Organisation's (ASIO) blacklist and denied employment in some other field to use my mathematical skills, such as they are, perhaps I wouldn't have been employed by the Brisbane City Council as a labourer, then who could say what would be the eventual history of the Planetarium Sundial. It is the nature of human history to be contingent; what if I wasn't there??

If we had gone ahead with the original drawings and orientation the city's landmark would have been a joke and it would have cost a fortune to bulldoze the structure and rebuild it in white cement and stainless steel. I've fictionalised the name of the contract architect to save any embarrassment to the people involved.

It stands as an example to a most unlikely chain of events - not only because citizens, like myself who can master spherical trigonometry, are rare; with a conscientious foreman like Alan Green; and a boss like John Buckley who is modest enough to listen to a humble labourer. Such is the nature of serendipity!

I was also proud of my help on other jobs. One challenge was the stage at the concert shell in Albert Park. It is in the form of a quadrant, providing not only the stage but also dressing and other backstage rooms. The quadrant was designed to suit the open air amphitheatre audience.

The columns supporting the shell are not set out in a rectilinear fashion as in a regular building but on radii from a central point. It was difficult for the tradesman in charge, Howard Kirby, to be sure that the columns were correctly placed. I worked out the equivalent points on a rectilinear grid using trigonometry.

Many tradesmen use the three, four, five rule in order to construct a right angle. They now have the benefit of hand held electronic calculators. When setting out a job to ensure that the building is square they measure the diagonals which must be equal to be square.

They will move the string lines a few millimetres to the right or left, backward or forward, by trial and error, to be square. I would show them, by calculation using Pythagoras theorem, exactly what length the diagonals will be. I've always got a lot of intellectual satisfaction as well as the pleasure of a job well done.

I retired from the Brisbane City Council aged sixty in October, 1983. Besides devoting time to contribute to the welfare of my sons, daughters-in-law and grandchildren, I applied myself to using a computer to generate pattern developments for boilermakers and sheet metal workers. I'm pleased to say that, while I'm falling to bits physically, I still have my marbles.

I remain your amateur mathematician.

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