Ada Lovelace: Mathematics not Poetry.

The text from my talk at Skeptics in the Pub: Wednesday 5th June 2013. Thank you to everyone who was there, it was a very pleasant evening:

Rob Ives

Cartoons from the most excellent 2D Goggles by kind permission of Sydney Padua

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Ada Lovelace was born 10th December 1815 – almost exactly 200 years ago. Her father, Lord Byron, noted poet and philander had many other children by many other women but Ada was the only child born to a woman to whom he was married. However briefly.

A month after Ada was born Lord Byron and her Mother Anne Isabella Byron separated. Lord Byron left England shortly after and never met his daughter again He died when she was eight from the side effects of blood-letting.

Augusta Ada Byron was a sickly child. she suffered from a colourful variety of diseases and malaises from Measles to constant headaches and hysteria.In her early teens a year of enforced bed rest left her able to walk only with the aid of crutches. She was, however, prodigiously intelligent.

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Her mother, still bitter about the colourful Byron was determined that she should not grow up to be a poet. To that end she hired her a series of tutors and governesses who taught her mathematics. Ada spent much of her childhood living with her grandmother but was in constant touch with her mother through the post. Her mother, scared of loosing Ada to Lord Byron, took to adding covering letters with her correspondence asking that the letters be kept as proof of maternal interest.

Ada was a creative and inventive child. At the age of twelve she set about inventing a flying machine. She wrote to her mother.

“I am going to begin my paper wings tomorrow”

she planned to

“…bring the art of flying to great perfection. I think of writing a book of Flyology and illustrating it with plates”

For a time she signed her letter to her mother

“Your very affectionate carrier pigeon”

When Ada was 17 she had a brief affair with one of her tutors. They tried unsuccessfully to elope and as a consequence the tutor was dismissed. After this incident Ada was watched closely by several of her mother’s friends for signs of immoral behaviour. Ada called them The Furies and complained about their unwelcome attentions accusing them of making up stories about her.

ada19At age eighteen, as was the custom, Ada was presented in court. She made a positive impression on most people being able to dance well and having a ‘dainty’ appearance.

In July 1835 aged 21 she married William King (8th Baron King) gaining the title baroness King. They spent their time between their three homes, one in Ockham, Surrey, One in London and one in Loch Torridon.

The couple had three children Byron, Annabella and Ralph. In 1838 her husband was created Earl of Lovelace and she became The Right Honourable Countess of Lovelace.

Various scandal occured throughout Ada’s life, she had a relaxed relationships with men other than her husband leading to accusations of affairs. She also had a weakness for gambling. She set up a syndicate with some male friends and in 1851 attempted to create a mathematical system for large bets. It all went horribly wrong leaving her thousands o pounds in debt and when one of the syndicate tried to blackmail her she was forced to come clean to her husband who was not best pleased.

*Having put a framework round the life of Ada Lovelace lets go back to the interesting stuff.

ada11Ada first met Charles Babbage shortly after her right royal coming out party. She went, along with her mother, to see what she called his “thinking machine” a portion of his difference engine on display in his drawing room. An onlooker reported of the event

“While other visitors gazed on the workings of this beautiful instrument with the sort of expression, I dare say the sort feeling, that some savages are said to have shown on first seeing a looking glass or hearing a gun, Miss Byron, young as she was, understood its working, and saw the great beauty of the invention.”

This was the sort of mathematical adventure that Ada was looking for. She has quickly exhausted the expertise of her tutors and university was not open to women in those days. Babbage too, recognised the spark of enthusiasm in Ada’s eye. He wrote of her

“Forget this world and all its troubles and if possible its multitudinous Charlatans – every thing in short but the Enchantress of Numbers”

ada05Charles Babbage was the Brian Cox of his day, as famous and fair of face as our very own Coxy. Unlike Brian Cox though (so far as I know) Babbage had a hatred of street musicians saying of them

“It is difficult to estimate the misery inflicted upon thousands of persons, and the absolute pecuniary penalty imposed upon multitudes of intellectual workers by the loss of their time, destroyed by organ-grinders and other similar nuisances.”

He also campaigned against hoop-rolling, blaming the urchins involved for tripping horses and injuring their riders. In fact, the more you read of his campaigns against the irritations of Victorian city life the less Coxian he appears and the more Grumpy Old Man.

Babbage was a prolific polymath with many varied interests. He helped establish the original flat rate postage in the UK after realising that calculating the costs based on distance was more time consuming and expensive than simply delivering the letter. Babbage also had a hand in establishing universal time in the UK. Up until that period ada07different towns had their own time zone. Working with the uber-engineer Isumbard Kingdom Brunnel on the infrastructure of the railways he realised that time differences between places caused difficulties for timetabling. Indeed he and IKB narrowly avoided being involved in a train crash when the two trains they were travelling in stopped, just in time.

The project that Babbage is most remembered for now is his difference engine. In the 19th century complex mathematical calculations were carried out with the aid of log tables. As maths was an essential part of navigation is was literally the case that mistakes in the log tables could cause ships to be wrecked and crew to be lost. The tables were worked out manually by people known as calculators usually working from their own homes. The government was aware that the maintenance and supply of accurate number tables was vital. They commissioned multiple sets of tables to be produced by different people so that they could be cross checked but errors still appeared.

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Babbage, in his very own eureka moment said to William Hershall (of telescope fame)

“I wish to god these calculations could be carried out by steam!”

to which Hershal is said to have replied

“It is quite possible”

And so, was born the difference engine. The idea, at its core, is simple. Most mathematical progressions can be described by a difference. A difference between one number and the next. Take for example, the triangle numbers.

1, 3, 6, 10, 15 …

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The differences between these numbers is 1, 2, 3, 4 …

and the differences between the differences is 1, 1, 1, 1….

All (I think) number sequences (polynomials) have these underlying difference patterns, it might be a second order difference like with the triangle numbers where the second set of differences is same number or a third order difference like the cube numbers:

1, 8, 27, 64, 125, 216 …

7, 19, 37, 61, 91…

12, 18, 24, 30…

6, 6, 6 …

Babbage proposed to use his difference engine to reverse engineer the number sequences in log tables outputting the result directly to paper with no errors. Genius!

In 1822 (when Lovelace was only 7) the government began funding Babbage to produce the difference engine. They funded him for almost nineteen years but he never produced a finished machine prefering instead to move onto the next development then the next without ever finishing any one project.The government, who were interested in receiving accurate tables and not an ever improving vapour-ware device eventually pulled the plug. Much, as you can imagine, to Babbage’s chagrin. By the time the government had abandoned the project Babbage too had moved on. He was now working on the far more flexible and capable (and, ultimately, ethereal) Analytical Engine.

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After being shunned by the British establishment Babbage headed for a more receptive audience in Italy and Greece along with his plans for the analytical engine. On his journey he called in to see a Jacquard loom, the programmable loom capable of amazingly intricate weaving using punch cards. In Turin he made his first and last presentation about the Analytical Engine to a group of engineers and mathematicians.

Present at the meeting was mathematician and future prime minister of Italy Luigi Menabrea. He later prepared a paper on Babbage’s work “Notions sur la machine analytique” and so we return after filling in the background, to Ada Lovelace.

ada04She received a copy of the paper, written in French by an Italian and translated it into English. As she did that she made some corrections using her understanding of mathematics. She also added her own notes which amounted in the end, to more in length than the original document. The analytical engine was a step change from the differential engine. It was designed from the start to be programmable. Central to the device were two main parts; the store, equivalent to memory which could hold 1000 numbers each of 40 decimal digits making a total memory of just over 16k and “the mill” an kind of mechanical central processing unit. Her appendix contained a complete section describing how Bernoulli numbers could be calculated with the Engine. Had the engine ever been built computer scientist have determined that it would have worked correctly. Based on this work Ada Lovelace is often credited as the first computer programmer.

Lovelace made the leap of understanding that the Analytical Engine could act on more than just numbers, in this sense her work was a precursor to the work on computers by Alan Turin. She wrote:

“The Analytical Engine might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine…

Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.”

Lovelace expanded on the work of Babbage producing a programming language similar to assembler which would be capable of operating as a Turing type machine.

Lovelace and Babbage worked together over the next few years sending many letters back and forth across London sometimes working right through the night.

Babbage never constructed a complete difference engine though he did have various parts in working condition. The analytical engine, however, was purely theoretical. Various versions of the difference engine have been constructed over the years including some working sections constructed by other people during Babbage’s life time. In 1991 London Science Museum unveiled a fully working difference engine which is still on display to this day.

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If you search online there are also various sections of difference engine constructed from that universal maker material, Lego. Check out YouTube for some fine examples.

In 1852 Ada became very ill with Uterine cancer. A lifelong materialist, Ada had a death bed conversion at the bidding of her mother. Her husband abandoned her on her death bed after she confessed something to him of 30th August. It is not known what she said but a confession of adultery has been suggested. Ada Lovelace died aged thirty six on 27th November 1852 from a mix of cancer and the side effects of blood letting.

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Since her death Ada Lovelace’s contribution to mathematics and computing continues to be recognised. The computer language Ada, used in defence systems, is named after her. From last year a day in mid October has been put aside to celebrate the achievements of women in science and technology. The second Ada Lovelace Day is on 15th October this year.

* * * *

Recommended Reading

urlThe Information by James Gleik:

Fascinating book about the information revolution from talking drums to the internet age. Chapter 4 is about Ada Lovelace and Charles Babbage.

Amazon UK

The-Difference-Engine-Swade-Doron-9780670910205The Difference Engine: Doron Swade

Charles Babbage and the quest to build the first computer.

Mainly from the view point of Babbage but does have information about the contribution of Ada Lovelace.

Amazon UK

imgres-1The Cogwheel Brain; Doron Swade.

Weirdly – this is the same book as The Difference Engine but with a different name. There”s 1p +£2.80 shipping I’m not getting back.

Amazon UK

booksJacquard’s Web : James Essinger

How the hand loom led to the birth of the information age.

Starting with the Jacquard Loom, the first automated weaving machine programmed by punch cards the book follows the rise and rise of the information age with an extensive section on the contributions of Ada Lovelace and Charles Babbage.

Amazon UK

imgresThe Difference Engine: William Gibson & Bruce Sterling

Alternate Steampunk fiction where steam powered Babbage Engines power the Industrial Revolution. I’ve only just started reading it but it’s looking promising!

Amazon UK

CharlesBabbageAdaLovelace1 2D Goggles: Sydney Padua

Brilliant alternative history Web Comic where Ada Lovelace and Charles Babbage fight crime and organ grinders!

2DGoggles

Last but not least: Wikipedia has all sorts of articles.

Ada Lovelace | Charles Babbage | Difference Engine | Analytical Engine 

4 thoughts on “Ada Lovelace: Mathematics not Poetry.

  1. Thanks! October? 4 months of prevarication followed by 2 days panic? – Yep that should be do-able. I’ll think up a topic and let you know.

    • We could all get dressed up in Steampunk gear and engage in stimulating palaver whilst imbibing copious quantities of hydro-ethanolic beverages in a licensed public house.
      Perhaps, if I’m good, I could persaude my beloved marital partner to deliver me forthwith to the grand gem town of Cockermouth via petroleum-powered pneumo-dynamic vehicular contrivance.

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