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Hidden women of history: Australia’s first known female voter, the famous Mrs Fanny Finch



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Fanny Finch’s 1856 voting card.
Castlemaine Art Museum

Kacey Sinclair, La Trobe University

In this series, we look at under-acknowledged women through the ages.

On 22 January 1856, an extraordinary event in Australia’s history occurred. It is not part of our collective national identity, nor has it been mythologised over the decades through song, dance, or poetry. It doesn’t even have a hashtag. But on this day in the thriving gold rush town of Castlemaine, two women took to the polls and cast their votes in a democratic election.

Two days later, Melbourne newspaper The Argus unwittingly granted one of them posterity, writing “two women voted – one, the famous Mrs. Fanny Finch”. Fanny Finch was a London-born businesswoman of African heritage, a single mother of four and is the first known woman to cast a vote in an Australian election.

Victorian women over the age of 21 (excluding Indigenous women) would not receive full unconditional suffrage until 1908. (Victorian Indigenous women were not enfranchised until 1965.) But Fanny Finch, as a local business owner who paid rates, was able to exploit a loophole in suffrage law that was yet to discriminate against gender or race.

The Municipal Institutions Act of 1854 granted suffrage to ratepaying “persons”. The loophole was eventually closed in 1865 when “persons” became “men”.

Argus report excerpt, 24th January 1856.
Trove

Who was Fanny?

Frances Finch was born Frances Combe in London in 1815. At eight-weeks-old she was orphaned by her mother after a tryst with a footman ended in a pregnancy but no marriage proposal.

A cross-stitch sampler attributed to Frances Coombe (sic) in 1830 at the age of 15 suggests she understood both her parents to be free people of African racial heritage (although the UK did not free slaves unconditionally until 1838.) The London Foundling Hospital, where Fanny was accepted as an orphan, provided her with some protection against slavery as well as an otherwise inaccessible education and access to an apprenticeship scheme in “household duties”.

Sampler attributed to Frances Coombe (sic).
Author provided

By 1837, a 22-year-old Fanny was a free, literate, educated, and experienced domestic servant. In that year she was approved a labourer’s free passage to the new colony of South Australia.

In Adelaide, Fanny was a valued employee of Julia Wyatt, an author, artist, and wife of the surgeon and first Protector of Aborigines, Dr. William Wyatt. Over the course of the next decade Fanny left their employment, married a sailor, Joseph Finch, and started a family.

By 1850, for reasons unknown, Fanny had left her husband. With her four children in tow, she made her way to Victoria. She arrived in the colony 12 months before the start of the Victorian gold rush. By early 1852 she was operating a restaurant and lodging house on the Forest Creek goldfields, alongside approximately 25,000 gold digging men and a handful of women.

There, in the fledgling township of Forest Creek, Mrs Finch’s Board and Lodging House became “the only one in which any person could get respectable accommodation”. By 1854, she had moved to nearby Castlemaine where she ran a restaurant. She quickly became one of its most recognisable faces.

Fanny Finch’s Restaurant, Corner of Latimer’s Lane and Urquhart Street, Castlemaine, c1858.
Richard Daintree.

A successful businesswoman

Fanny was a successful businesswoman, known to dress in bright blue silk with her black hair adorned in artificial flowers. Strong and robust, with an even larger personality she was not one to shy away from attempting to remedy injustice when she saw it – be it with her words, her cooking or her fists. Evidently, she possessed visibility and power.

Her business acumen and conspicuity make it probable that her male contemporaries were unsurprised when they witnessed Fanny cast her vote at the Hall of Castlemaine (now the Theatre Royal). Did the men taunt her? Encourage her? Or were they complacent? We cannot know. We do know that no one stopped her. She selected her preference and signed her name.

Market Square, Castlemaine, c1855. By S.T Gill. The Hall of Castlemaine where Fanny Finch cast her vote can be seen to the right of centre.
Author provided

That afternoon, however, the two assessors of the day disallowed both Fanny and the other unknown woman’s votes. Their reasons were cited as: “they (the women) had no right to vote”. Further details were not divulged.

Still, Walter Smith, the man for whom Fanny voted, was elected to council. Smith was an agent and brewer who arrived at Forest Creek at around the same time as Fanny. Little is known about what motivated her to vote for him but no one else, despite being allowed to vote in seven councillors. She was clearly determined to elect him to council.

A rare glimpse

During colonial times women were rarely identified by name in the press – particularly women of the working class. The 1856 Argus report now offers historians an unprecedented opportunity to identify an otherwise invisible minority – the 19th century Australian woman of colour – as an active participant in our political history.

Fanny was a woman, who, through relative privilege – wielded with her own blood, sweat and tears – refused to founder beneath the weight of a white, Anglo-male world of commerce. However, this came at a price. As a woman of colour occupying space in a white man’s world, assaults on her success were not uncommon. Yet she refused to disappear.

One of those assaults occurred in December 1855. Fanny Finch was fined £50 for the illicit sale of alcohol, known as “sly-grogging”. After a month-long trial, which involved scandalous cross-examinations of miners, policemen, and even her two young sons, she was charged and fined.

Despite the exorbitant fine and the public slandering of her character and commercial integrity, Fanny Finch was not defeated. Like many business people on the goldfields, she both owed money and was owed it by others, but over the following four months, she began an unprecedented campaign of self-representation.

The day following her conviction she published a letter in the local paper accusing the local authorities of injustice (a copy of this has not survived).
A month on, she cast that vote. Then a few months later in April, she published the following advertisement.

Mrs. Finch begs to inform the inhabitants of Castlemaine that henceforth she will carry on business for her children and would be happy to receive any outstanding debts … finding that the more she herself strives the more she is oppressed, although she can firmly state that if those who are in her debt would come forward each with one third, she will be relieved of all debt, have a good home for her family and about two thousand pounds in her pocket.

Fanny Finch also begs to state that as in her affluence she was so kindly trusted, they may be sure that she, from her own free will, may some day liquidate all, but she must have her time … and in spite of what enemies she may have, she intends to keep throughout the winter ready cooked Ham, Beef Soups (a la mode) from seven in the morning to seven in the night.

The vote of the famous Mrs. Fanny Finch adds a woman of colour’s voice to what Clare Wright has described as an unorganised movement for women’s rights during the 1850s.

Fanny died on the 15th October 1863, aged 48. She was remembered as “a strong minded woman” with “a genuine tenderness of heart, ever ready to serve another in distress … without the slightest ostentation”.

She was given a public burial in an unmarked grave at Castlemaine Cemetery.The Conversation

Kacey Sinclair, PhD Candidate in History, La Trobe University

This article is republished from The Conversation under a Creative Commons license. Read the original article.

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Who made Australia’s first ever bank deposit? Here’s our unsettling discovery



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The first kangaroo-leather bound ledgers of what became Westpac, photographed in the Westpac archives.
Westpac archives, Author provided

Nicole Sutton, University of Technology Sydney

One of Australia’s biggest banks, currently under scrutiny at the royal commission, has a long history.

The Bank of New South Wales, which later became Westpac, was established in 1817 under a charter of incorporation signed by Governor Lachlan Macquarie. It was Australia’s first bank and first public company.

But there’s something brushed over in the official history. Its first depositor, Sergeant Jeremiah Murphy, put in an unusually large sum of money (far more than his official salary) three days before the bank opened.

Just as the banking royal commission has been using ledgers, transaction accounts, remuneration reports and meeting minutes to try to get inside the behaviour of today’s banks, I and my colleagues Jason L’Ecuyer, Tom Allinson and Tamson Pietsch examined kangaroo-leather-bound ledgers and microfilm of military paymaster reports to understand how the bank started and how some people were making money in early colonial Australia.

The Bank, the Sergeant and his bonus.
2SER History Lab28.7 MB (download)

The results can be heard on the latest 2SER History Lab podcast. To many listeners, the findings will be unsettling.

Our investigation

Just like Antarctic ice core samples or ancient tree rings, financial documents capture and preserve events over time. Through them, we can grasp glimpses of the period in which they were created.

The bank’s ledgers show the growing wealth of early entrepreneurs, such as Mary Reiby, the convict-turned-merchant who appears on the Australian $20 bill.

In colonial accounts, we can also see the sale of liquor licences to Sydney’s first establishments, and infrastructure spending on bridges, wharves and hospitals.

There is even a schedule of prices for Australia’s first toll road out to Parramatta.



But the records also contain sobering evidence of darker aspects of Australia’s past.

Disturbingly, we can see financial payments to settlers and the military for punitive expeditions against Aboriginal Australians.

Why trust the accounts?

Financial records can shed light on what happened because of the meticulous manner in which they were prepared.

Military payslips were cross-referenced against muster sheets. Colonial payments were reviewed by committees.

Customer withdrawals were matched against signatures. Ledgers were periodically balanced. The bank’s own clerks ran the risk of having their pay docked for errors or poor penmanship.


One fo the first banknotes issued by the Bank of New South Wales. April 8, 1817.
© Australian Museum

These records also make for compelling sources because, ironically, most were never intended for outsider eyes.

They lack the vague, self-conscious or euphemistic language often found in public proclamations.

Instead, they were working documents.

They served particular functions, such as keeping track of a bank’s funds, maintaining fiscal control over regiments spread across an empire or managing the revenue and expenditure of an emerging colony.

To be effective they had to be accurate, comprehensive, and complete.

Holding to account

In the year before his mysterious deposit Sergeant Jeremiah Murphy was sent out by Governor Macquarie “in pursuit of natives”.

It is highly doubtful that Jeremiah Murphy ever anticipated that some 200 years later, a team of researchers and radio producers would pore over his financial dealings to piece together an account of his movements and decisions.

Yet since his time, there has been an enormous expansion in both the legal and regulatory compliance requirements to maintain and preserve internal records, as well as avenues for public scrutiny, media attention and inquiry.




Read more:
So what’s a secretary to do? Banking Royal Commission raises questions about what’s in minutes


Bankers, like all of those who work in organisations and colonial institutions, should be mindful of the traces their actions leave behind in mere administrative records.

Sooner or later someone might look at their books.

The Bank, The Sargent and His Bonus is a collaboration between 2SER 107.3, the Australian Centre for Public History and the UTS Business School. It is available for download through the Think Business Futures and History Lab podcasts.The Conversation

Nicole Sutton, Lecturer in Accounting, University of Technology Sydney

This article is republished from The Conversation under a Creative Commons license. Read the original article.


Why New Zealand was the first country where women won the right to vote



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A memorial by sculptor Margriet Windhausen depicts the life-size figures of Kate Sheppard and other leaders of the Aotearoa New Zealand suffrage movement.
Bernard Spragg/Wikimedia Commons, CC BY-ND

Katie Pickles

125 years ago today Aotearoa New Zealand became the first country in the world to grant all women the right to vote.

The event was part of an ongoing international movement for women to exit from an inferior position in society and to enjoy equal rights with men.

But why did this global first happen in a small and isolated corner of the South Pacific?




Read more:
Women’s votes: six amazing facts from around the world


Setting the stage

In the late 19th century, Aotearoa New Zealand was a volatile and rapidly changing contact zone where British settlers confidently introduced systematic colonisation, often at the expense of the indigenous Māori population. Settlers were keen to create a new world society that adapted the best of Britain and left behind behind the negative aspects of the industrial revolution – Britain’s dark satanic mills.

Many supported universal male suffrage and a less rigid class structure, enlightened race relations and humanitarianism that also extended to improving women’s lives. These liberal aspirations towards societal equality contributed to the 1893 women’s suffrage victory.

At the end of the 19th century, feminists in New Zealand had a long list of demands. It included equal pay, prevention of violence against women, economic independence for women, old age pensions and reform of marriage, divorce, health and education – and peace and justice for all.

The women’s suffrage cause captured widespread support and emerged as the uniting right for women’s equality in society. As suffragist Christina Henderson later summed up, 1893 captured “the mental and spiritual uplift” women experienced upon release “from their age-long inferiority complex”.

Two other factors assisted New Zealand’s global first for women: a relatively small size and population and the lack of an entrenched conservative tradition. In Britain, John Stuart Mill presented a first petition for women’s suffrage to the British Parliament in 1866, but it took until wartime 1918 for limited women’s suffrage there.

Women as moral citizens

As a “colonial frontier”, New Zealand had a surplus of men, especially in resource towns. Pragmatically, this placed a premium on women for their part as wives, mothers and moral compasses.

There was a fear of a chaotic frontier full of marauding single men. This colonial context saw conservative men who supported family values supporting suffrage. During the 1880s, depression and its accompanying poverty, sexual licence and drunken disorder further enhanced women’s value as settling maternal figures. Women voters promised a stabilising effect on society.

New Zealand gained much strength from an international feminist movement. Women were riding a first feminist wave that, most often grounded in their biological difference as life givers and carers, cast them as moral citizens.

Local feminists eagerly drew upon and circulated the best knowledge from Britain, America and Europe. When Mary Leavitt, the leader of the US-based Women’s Christian Temperance Union (WCTU) visited New Zealand in 1885, her goal was to set up local branches. This had a direct impact, leading to the country’s first national women’s organisation and providing a platform for women to secure the vote in order to affect their colonial feminist concerns.

Other places early to grant women’s suffrage shared the presence of liberal and egalitarian beliefs, a surplus of men over women, and less entrenched conservatism. The four frontier US western mountain states led the way with Wyoming (1869), Utah (1870), Colorado (1893) and Idaho (1895). South Australia (1894) and Western Australia (1899) made the 19th century and, before the first world war, were joined by other western US states, Australia, Finland and Scandinavia.

Local agency

Social reformer and suffragist Kate Sheppard, around 1905.
Wikimedia Commons, CC BY-ND

New Zealand was fortunate to have many effective women leaders. Most prominent among them was Kate Sheppard. In 1887, Sheppard became head of the WCTU’s Christchurch branch and led the campaign for the vote.

The campaign leaders were well organised and hard working. Their tactics were petitions, pamphlets, letters, public talks and lobbying politicians – this was a peaceful era before the suffragette militancy during the early 20th century elsewhere.




Read more:
Adela Pankhurst: the forgotten sister who doesn’t fit neatly into suffragette history


The women were persistent and overcame setbacks. It took multiple attempts in parliament before the Electoral Act 1893 was passed. Importantly, the suffragists got public opinion behind the cause. Mass support was demonstrated through petitions between 1891 and 1893, in total garnering 31,872 signatures, amounting to a quarter of Aotearoa’s adult women.

Pragmatically, the women worked in allegiance with men in parliament who could introduce the bills. In particular, veteran conservative Sir John Hall viewed women’s suffrage as a way to a more moral and civil society.

The Suffrage 125 celebratory slogan “whakatū wāhine – women stand up!” captures the intention of continuing progressive and egalitarian traditions. Recognising diverse cultural backgrounds is now important. With hindsight, the feminist movement can be implicated as an agent of colonisation, but it did support votes for Māori women. Meri Te Tai Mangakāhia presented a motion to the newly formed Māori parliament to allow women to vote and sit in it.

New Zealand remains a small country that can experience rapid social and economic change. Evoking its colonial past, however, it retains both a reputation as a tough and masculine place of beer-swilling, rugby-playing blokes and a tradition of staunch, tea drinking, domesticated women.The Conversation

Katie Pickles, Professor of History at the University of Canterbury and current Royal Society of New Zealand Te Apārangi James Cook Research Fellow

This article is republished from The Conversation under a Creative Commons license. Read the original article.


How our discovery of Julius Caesar’s first landing point in Britain could change history



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Wellcome Trust/Wikimedia Commons, CC BY-SA

Andrew Fitzpatrick, University of Leicester

During the nine-year-long Battle for Gaul, Julius Caesar fought his way across northwest Europe. He invaded Britain twice; in 55BC, and again in 54BC. But while archaeologists have found evidence of the war in France, there has been very little discovered in Britain – until now.

At a site called Ebbsfleet, in northeast Kent, my colleagues from the University of Leicester and I finally uncovered the site where Julius Caesar’s fleet landed in 54BC. A series of surveys and excavations, spanning from 2015 to 2017, revealed a large enclosure, defended by a ditch five metres wide and two metres deep.

What a find: pilum tip from Ebbsfleet.
University of Leicester, Author provided

We dated the ditch all the way back to the first century BC, by examining the pottery and using radiocarbon dating techniques.

At the bottom of the ditch, we found the tip of an iron weapon, which was later identified as a Roman spear, or “pilum”. Similar weapons were discovered at the site of Alésia in France, where the decisive encounter in the Battle for Gaul took place. What’s more, the defensive ditches at Alésia are the same size and shape as those we discovered at Ebbsfleet.

In Caesar’s own words

Our dig was situated next to Pegwell Bay, a large, sandy beach with chalk cliffs at its northern end. This striking landscape also helps to confirm that we really have found the location of Caesar’s base. Most of what is known about Caesar’s voyage comes from his own written accounts, based on his annual reports to the Roman senate.

When the Roman fleet set sail from France, they intended to use the wind to help them cross the Channel to find a large, safe place to lay anchor and prepare for battle. But the wind dropped, and the fleet was carried too far northeast by the tide.

We came, we saw, we excavated.
University of Leicester., Author provided

At sunrise, Caesar saw Britain “left afar on the port side”. Only high land would have been visible from a small ship far out at sea. And the only such land in northeast Kent are the cliffs near Ebbsfleet. Caesar also describes how he left the ships riding at anchor next to a “sandy, open shore” – a perfect description of Pegwell Bay.

Given Caesar’s own words seem so clear, it’s surprising that Pegwell Bay has never been considered as a possible landing site before. Instead, Caesar was long thought to have landed at Walmer, 15 kilometres to the south. One reason might be that, until the Middle Ages, Thanet was an island.

The Isle of Thanet was separated from the mainland by the Wantsum Channel. But no one knows how big the channel was 2,000 years ago; it could be that whatever disadvantages it presented were offset by the presence of a large and safe beach, where 800 ships could land and disembark 20,000 men and 2,000 horses in one day.

Peace by force

Despite the imposing size of Caesar’s fleet, it was long thought that his landing had little lasting impact on Britain. Caesar himself returned to France immediately after the two campaigns, without leaving a garrison. Yet the discovery of the landing site gives us cause to question this assumption.

Making history at Ebbsfleet.
Andrew Fitzpatrick/University of Leicester, Author provided

Historical sources, royal burials and ancient coins indicate that from about 20BC, the kings of southeast England had strong links to Rome. But historians have found it hard to explain how these alliances came into existence. The suggestion that they sprung from diplomatic ties forged by the emperor Augustus at that time has never been convincing.

But Caesar tells us that he reached a peace accord with the Britons in 54BC, even taking hostages from the ruling families to ensure the agreement was respected. Perhaps the alliances which came to light in the 20s BC were originally established by Caesar, a generation before emperor Augustus asserted his authority over the Roman Empire.

The close ties between Rome and the kings of southeast England assured emperor Claudius of a relatively easy military victory, when he first set out to conquer England in 43 AD. So it seems Caesar’s earlier conquest could have laid the foundations for the Roman occupation of Britain, which lasted more than 300 years.

The ConversationFor Caesar, the consequences of his invasions were clear. In his day, Britain lay beyond the known world. By crossing the ocean and conquering Britain, Caesar caused a sensation in his homeland. He was awarded the longest public thanksgiving in Rome, winning great acclaim and glory in the process. Mission accomplished.

Andrew Fitzpatrick, Research Associate, University of Leicester

This article was originally published on The Conversation. Read the original article.


Written in stone: the world’s first trigonometry revealed in an ancient Babylonian tablet



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The Plimpton 322 tablet.
UNSW/Andrew Kelly, CC BY-SA

Daniel Mansfield, UNSW and Norman Wildberger, UNSW

The ancient Babylonians – who lived from about 4,000BCE in what is now Iraq – had a long forgotten understanding of right-angled triangles that was much simpler and more accurate than the conventional trigonometry we are taught in schools.

Our new research, published in Historia Mathematica, shows that the Babylonians were able to construct a trigonometric table using only the exact ratios of sides of a right-angled triangle. This is a completely different form of trigonometry that does not need the familiar modern concept of angles.

At school we are told that the shape of a right-angled triangle depends upon the other two angles. The angle is related to the circumference of a circle, which is divided into 360 parts or degrees. This angle is then used to describe the ratios of the sides of the right-angled triangle through sin, cos and tan.


Read more: Your guide to solving the next online viral maths problem


But circles and right-angled triangles are very different, and the price of having simple values for the angle is borne by the ratios, which are very complicated and must be approximated.

The three ratios of a modern trigonometric table, rounded to six decimal places, with auxiliary angle Θ in degrees.
Daniel Mansfield, Author provided

This approach can be traced back to the Greek astronomer and mathematician Hipparchus of Nicaea (who died after 127 BCE). He is said to be the father of trigonometry because he used his table of chords to calculate orbits of the Moon and Sun.

But our new research shows this was not the first, or only, or best approach to trigonometry.

Babylonian trigonometry

The Babylonians discovered their own unique form of trigonometry during the Old Babylonian period (1900-1600BCE), more than 1,500 years earlier than the Greek form.

Remarkably, their trigonometry contains none of the hallmarks of our modern trigonometry – it does not use angles and it does not use approximation.

The Babylonians had a completely different conceptualisation of a right triangle. They saw it as half of a rectangle, and due to their sophisticated sexagesimal (base 60) number system they were able to construct a wide variety of right triangles using only exact ratios.

The Greek (left) and Babylonian (right) conceptualisation of a right triangle. Notably the Babylonians did not use angles to describe a right triangle.
Daniel Mansfield, Author provided

The sexagesimal system is better suited for exact calculation. For example, if you divide one hour by three then you get exactly 20 minutes. But if you divide one dollar by three then you get 33 cents, with 1 cent left over. The fundamental difference is the convention to treat hours and dollars in different number systems: time is sexagesimal and dollars are decimal.

The Babylonians knew that their sexagesmial number system allowed for many more exact divisions. For a more sophisticated example, 1 hour divided by 48 is 1 minute and 15 seconds.

This precise arithmetic of the Babylonians also influenced their geometry, which they preferred to be exact. They were able to generate a wide variety of right-angled triangles within exact ratios b/l and d/l, where b, l and d are the short side, long side and diagonal of a rectangle.

The ratio b/l was particularly important to the ancient Babylonians and Egyptians because they used this ratio to measure steepness.

The Plimpton 322 tablet

We now know that the Babylonians studied trigonometry because we have a fragment of a one of their trigonometric tables.

Plimpton 322 is a broken clay tablet from the ancient city of Larsa, which was located near Tell as-Senkereh in modern day Iraq. The tablet was written between 1822-1762BCE.

In the 1920s the archaeologist, academic and adventurer Edgar J Banks sold the tablet to the American publisher and philanthropist George Arthur Plimpton.

Plimpton bequeathed his entire collection of mathematical artefacts to Columbia University in 1936, and it resides there today in the Rare Book and Manuscript Library. It’s available online through the Cuneiform Digital Library Initiative.

In 1945 the tablet was revealed to contain a highly sophisticated sequence of integer numbers that satisfy the Pythagorean equation a2+b2=c2, known as Pythagorean triples.

This is the fundamental relationship of the three sides of a right-angled triangle, and this discovery proved that the Babylonians knew this relationship more than 1,000 years before the Greek mathematician Pythagoras was born.

The fundamental relation between the side lengths of a right triangle. In modern times this is called Pythagoras’ theorem, but it was known to the Babylonians more than 1,000 years before Pythagoras was born.

Plimpton 322 has ruled space on the reverse which indicates that additional rows were intended. In 1964, the Yale based science historian Derek J de Solla Price discovered the pattern behind the complex sequence of Pythagorean triples and we now know that it was originally intended to contain 38 rows in total.

The other side of the Plimpton 322 tablet.
UNSW/Andrew Kelly, Author provided

The tablet also has missing columns, and in 1981 the Swedish mathematics historian Jöran Friberg conjectured that the missing columns should be the ratios b/l and d/l. But the tablet’s purpose remained elusive.

The first five rows of Plimpton 322, with reconstructed columns and numbers written in decimal.

The surviving fragment of Plimpton 322 starts with the Pythagorean triple 119, 120, 169. The next triple is 3367, 3456, 4825. This makes sense when you realise that the first triple is almost a square (which is an extreme kind of rectangle), and the next is slightly flatter. In fact the right-angled triangles are slowly but steadily getting flatter throughout the entire sequence.

Watch the triangles change shape as we go down the list.

So the trigonometric nature of this table is suggested by the information on the surviving fragment alone, but it is even more apparent from the reconstructed tablet.

This argument must be made carefully because modern notions such as angle were not present at the time Plimpton 322 was written. How then might it be a trigonometric table?

Fundamentally a trigonometric table must describe three ratios of a right triangle. So we throw away sin and cos and instead start with the ratios b/l and d/l. The ratio which replaces tan would then be b/d or d/b, but neither can be expressed exactly in sexagesimal.

Instead, information about this ratio is split into three columns of exact numbers. A squared index and simplified values of b and d to help the scribe make their own approximation to b/d or d/b.

No approximation

The most remarkable aspect of Babylonian trigonometry is its precision. Babylonian trigonometry is exact, whereas we are accustomed to approximate trigonometry.


Read more: Curious Kids: Why do we count to 10?


The Babylonian approach is also much simpler because it only uses exact ratios. There are no irrational numbers and no angles, and this means that there is also no sin, cos or tan or approximation.

It is difficult to say why this approach to trigonometry has not survived. Perhaps it went out of fashion because the Greek approach using angles is more suitable for astronomical calculations. Perhaps this understanding was lost in 1762BCE when Larsa was captured by Hammurabi of Babylon. Without evidence, we can only speculate.

The ConversationWe are only beginning to understand this ancient civilisation, which is likely to hold many more secrets waiting to be discovered.

Daniel Mansfield, Associate Lecturer in Mathematics, UNSW and Norman Wildberger, Associate Professor in Mathematics, UNSW

This article was originally published on The Conversation. Read the original article.


How Australia played the world’s first music on a computer


Paul Doornbusch, University of Melbourne

We don’t think twice about playing music via a computer – we have them in our pockets, and in our homes and offices, with music on tap. But playing music on a computer was once an almost unthinkable leap of the imagination and the most devilishly difficult programming challenge.

The world’s fourth digital computer was designed and built in Australia by the Council for Scientific and Industrial Research (CSIR, the precursor of the CSIRO). It started life as a dream in 1947, ran its first test program in 1949 and played music in 1950 or 1951.

Initially known as the CSIR Mark 1 – later renamed CSIRAC (the CSIR Automatic Computer) – it was built at the CSIR’s radiophysics division in Sydney.

CSIRAC was a very primitive computer by today’s standards. It was very slow (1,000 cycles per second); it did not have very much memory (about 2KB of RAM and 3KB of disk memory); it filled a room and; it had no display like a modern computer.

Out of the hooter

Most output from CSIRAC was via punched paper tape that was later converted to text on another machine. The only familiar output device was a speaker (called the hooter), and it was used to track the progress of a program.

Programmers would place a sound at the end of their program so they knew it had ended (this was known as a blurt), or they would program progress-indicator blurts into a program.

Despite being primitive, CSIRAC performed groundbreaking work, including running the calculations to find the centre of our galaxy in 1953, and for the engineering of our first skyscraper building.

CSIRAC before it was put on display at Museum Victoria.
Paul Doornbusch

CSIRAC was a serial computer, it passed digital bits around one at a time unlike the 32 or 64 bits passed around in parallel in modern computers.

The memory on the CSIRAC was mercury acoustic delay lines. That means a pulse would be put into the memory tube, it would travel to the other end of the tube and be recycled back to the front. In this way, many bits and digital words could be stored in one tube of mercury. There were about 20 memory tubes functional at any time.

A consequence of using mercury acoustic delay time memory was that each memory access took a different time. This would prove problematic for any time-critical application, such as playing music in real time.

The music maker

The first software engineer or programmer was the mathematician Geoff Hill, who is something of an unsung hero of Australian computing.

Hill came from a very musical family; his mother was a music teacher, his sister a performer and he had perfect pitch. This is crucial, as the way CSIRAC created sounds was by sending raw pulses from the computer data bus to the speaker.

If casually programmed, these pulses would arrive at the speaker at somewhat random times, resulting in the blurting type of sound used by programmers to indicate points in the program’s execution.

Hill would have quickly realised that if he could get the pulses to arrive at a regular time, then he would get a steady pitch. Then, perhaps he could program the notes of a musical scale.

This was an exceedingly difficult task because each memory access took a different time, and the overall clock frequency was only 1,000 cycles a second.

But Hill managed this, and his musical knowledge was invaluable, although on at least one occasion he telephoned his mother late at night and asked her if some notes were in tune while holding the telephone receiver to the computer speaker.

Her response on the first occasion was to scold Hill for playing silly buggers with a comb and a piece of paper and annoying her late and night when his dinner was in the oven! She didn’t understand what was going on.

A simple tune

Hill programmed CSIRAC to play various popular tunes of the day, such as Colonel Bogey, Girl with Flaxen Hair and so on. This was natural as the programmers were not musical specialists and were not interested in what using a computer meant for the potential composition and performance of music.

The music was one of CSIRAC’s parlour tricks. Dick McGee remembers it playing music when he started at the CSIRO in April 1951. At Australia’s first computing conference, on August 7-9, 1951, everyone was talking about it afterwards and it caused quite a stir.

The late Trevor Pearcey led the team that created CSIRAC and he remembers its musical performances well, as recalls in the video interview from 1996, a couple of years before he died.

CSIRAC was thus the first computer in the world to play music. Sadly, none of the music it played was ever recorded.

Change of plan at CSIRO

There was some internal refocusing within the CSIRO and it was decided to concentrate on weather science and primary production rather than computation, leaving that to others and the commercial sector.

So it is not surprising that the CSIRO resisted the music being recorded at the time. However, it has now been faithfully reconstructed and can be heard again.

A reconstructed valve amplifier built to the original CSIRAC design to generate the correct pulse shapes.
Paul Doornbusch, Author provided

A team at The University of Melbourne, led by myself, built (valve) hardware to faithfully reconstruct CSIRAC’s pulse shapes, and software to be able to run the old programs.

After hand reading and entering the data from the old punched-paper program tapes, the programs were run with the reconstructed pulses and the music regenerated accurately.

The team even went to the trouble of sourcing a new speaker made within a few weeks of the original to play the music through. Museum Victoria very kindly let us put the speaker in the old cabinets to record the music being played so that it is as authentic as possible.

CSIRAC plays a music scale.
Paul Doornbusch, Author provided116 KB (download)

CSIRAC plays Colonel Bogey.
Paul Doornbusch, Author provided270 KB (download)

CSIRAC plays The Bonnie Banks o’ Loch Lomond.
Paul Doornbusch, Author provided289 KB (download)

CSIRAC plays Auld Lang Syne.
Paul Doornbusch, Author provided287 KB (download)

Shortly after CSIRAC first played music, in 1951 the BBC recorded a Ferranti Mark 1 computer playing music in Manchester, England. That is the oldest recording of a computer playing music.

When CSIRAC moved to the University of Melbourne in 1956, it continued to play music. The university’s mathematics professor Tom Cherry wrote a program so that anyone could punch a “score” or “pianola” tape for the computer to play without the intricacies of knowing how to program the hooter.

Professor Cherry’s instructions on how to use the music program still exist.

CSIRAC music instructions.
Paul Doornbusch

A lost opportunity

The most significant early developments in computer music and digital audio happened in the United States from the late 1950s at Bell Labs.

In 1957, the acoustic researcher Max Mathews had the foresight to see the potential of this technology. He wrote a program that allowed an IBM 704 mainframe computer to play a 17-second composition.

Despite the earlier musical work with CSIRAC in Sydney, it is Matthews who is often referred to as the father of computer music.

But the developments started in the 1950s have led to the most exciting musical adventure we have ever embarked on – the application of digital technology to the creation, making, listening and distribution of music.

When discussing the CSIRAC music reconstruction project with the original engineers who had worked on CSIRAC in Melbourne, I lamented that the then Melbourne-based composer Percy Grainger had not been introduced to CSIRAC.

Peter Thorne, a former CSIRAC computer technician, told me:

We used to see him walk past the computation laboratory, we’d say, ‘There goes Percy Grainger’.

I sighed. Grainger was Australia’s most adventurous composer of the day was a few metres away from a machine that could have realised some of his musical dreams. If he had met CSIRAC, some of the remarkable developments of combining computers and music could have been another Australian first.

The Conversation

Paul Doornbusch, Adjunct professor of computer science at The University of Melbourne and Associate Dean, Australian College of the Arts., University of Melbourne

This article was originally published on The Conversation. Read the original article.


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