Thursday, 26 July 2012

Lessons from a geologist

From time to time, I come across a passage in a book or article that seems appropriate for O.R. scientists and the practice of O.R..  Recently, I have been reading a book about geology, "The Planet in a Pebble" by Jan Zalasiewicz which is a fascinating, readable, and - at times - humorous account of the geological history of our planet.  Thoroughly recommended!

On page 119, discussing the nature of graptolites (and you will have to read the book to find out what they are), and the presence of isotopes which help to date them, he writes:

Isotopes in geology can provide marvellous pictures of the past--but also mirages.  They need to be approached with care.  The trick, as ever, is to ask the right kind of question, tackle it by means of appropriate analysis, and to look at the answer one receives with due scepticism.  It's work in progress.

That highlighted sentence deserves to be inscribed at the start of many O.R. studies.  An O.R. training should prepare one for the three stages:
  • asking the right questions;
  • using appropriate analysis;
  • looking at the answer with care, even if scepticism is not always justified.

Thank you, Jan for that reminder!

A little later (page 183) he throws in another salutary reminder:

Ugly Facts [his capital letters] keep disturbing the symmetry of a neat explanation--but then the Ugly Facts, once understood and accommodated, can widen and deepen our understanding of how the Earth works, even in its smallest and most obscure corners.

Yes, we in Operational Research need to be reminded that there are often Ugly Facts which keep disturbing our neat O.R. models, but they can also make our models much better when we accommodate them.

Friday, 13 July 2012

The Puzzles Page of a newspaper

Once upon a time, daily newspapers were very serious publications.  Then, in the early decades of the 20th century, they gradually started to introduce crosswords, and these became very popular.  Crosswords have evolved in several different ways since then, with cryptic and simple, enigmatic and convoluted.  There are cross-number problems and general knowledge crosswords.

The last few years have seen many British newspapers offering a page (or more) of puzzles.  Sudoku logic is common, as are assorted crosswords.  Also extremely popular are word problems.  Enthusiasts will tell you that it is proven that regularly tackling such puzzles is good for one's mental health.

The "Independent" newspaper which Tina and I read, normally has the following:
a quick crossword, where the first two/three/four across solutions run together to make a pun
a cryptic crossword
three sudoku puzzles

a codeword, which is a crossword without clues, but each letter of the alphabet is represented in the grid by a number from 1 to 26, with two or three given; the object is to fill in the grid by logically deducing the code for each letter
two word ladders - convert MOON into STAR using intermediate words which differ by one letter from the previous one
a word wheel with nine letters, one highlighted, with the object of finding as many words which use the highlighted letter and some of the others
two maths puzzles, described below

In the paper today, there is a letter about the word ladders, asking if a slang word is allowed.  The leeter goes on to criticise the text that accompanies the word wheel.  "We have found XX words, including one nine-letter word"  The writer points out that the setters clearly start with a nine-letter word, check that it has no anagrams, and make the word wheel.

The maths puzzles are interesting.  The digits 1 to 9 are arranged in three rows of three columns.  In each row and column, the digits are separated by one of the basic arithmetic operations, +, -, *, /.  Ignoring the priority rules of mathematics, the result at the right hand side of the rows and at the base of the columns is given.  The aim is to find the arrangement of the digits.  In the elementary puzzle, two digits are given.  In the advanced puzzle, only one is given.  For example:

A- B* C=-21
+  -  -
8+ D/ E=3
+  -  +
9- F* G=12
=  =  =
19 -2 8

To a mathematician/O.R. person, the puzzle is to solve six simultaneous equations for the unknowns, with the side condition that the unknowns are all different single digit integers.  However, it is not necessary to use combinatorial optimisation to solve them.

My interest in the puzzle page is to consider how the puzzles on a particular page might be created.  There is an extensive literature about crosswords and sudokus, and computer programmes to help create a crossword with selected words included, and sudokus which range from easy to fiendish.  Word ladders have been studied by graph theorists, representing each word as a node and connecting a pair of nodes if they are "adjacent".  Donald Knuth's Stanford GrephBase does this, and Donald Knuth is also a fan of puzzles, as he writes:

I believe that the creation of a great puzzle or a great pattern is a scholarly achievement of great merit, an important contribution to world culture, even though the author of such a breakthrough is often an amateur who has no academic credentials. Therefore I'm proud to follow in the footsteps of the pioneers who have come up with significant new “mind-benders” as civilization developed. 

Word wheels -- well, anyone with a word list and elementary UNIX commands can find the words in them.

Codewords are more intriguing.  They are crossword grids with extra constraints.  First, every letter must occur at least once).  Second, there must be at least one word which can be deduced from its pattern, possibly with the help of one or other of the given letters.   Thus, yesterday we had the pattern 1 2 3 3 4 3 4 with no clues.  (we also had Z 5 6 7 A 1 with two clues)  Third, rule 2 must continue to apply as the solver progresses.  Fourth, rules 2 and 3 may possibly lead to a choice of letters, which further study will reveal.  Finally, the words must be everyday ones.  A friend observed that the vocabulary of the setters includes a large range of words using the infrequently used letters of the alphabet, J, K, Q, Z

But those maths puzzles.  I have a theory about the ones that appear in the daily paper.   It is that they do not need any given digits to be solvable.  I have looked at many of them, ignoring the given one or two digits, and by logic have been able to solve each one.  So I reckon that they are created without human intervention.  All that happens is that a random grid is created using the digits, with added arithmetic operation and the six results are recorded.  Then the digits are removed, and a computer program runs through the 9! (nine factorial = 362880) arrangements to see if there is a unique solution.  Then one or two digits are added at random.  As a result, the puzzles are generally very simple.  I am sure that there is scope for developing a set of construction rules which would be more challenging for the puzzler.  Any takers?  Did you spot cheeses and zodiac?

Saturday, 7 July 2012

Plymouth Hoe Bollards

A few weeks ago, Tina and I went for a walk along Plymouth's sea-front.  As we walked along the Hoe, we spotted that there was a sort of art installation.  Polished vertical bollards marked the edge of the pavement and barred vehicles from going onto it.  Each one was inscribed with a name.  We didn't examine each one, but we recognised several of the names as belonging to famous people with some association with Plymouth.  Sir Francis Drake, famous for his naval exploits and for playing bowls on the Hoe itself.  Captain John MacArthur, a pioneer settler in Australia, and a rogue.  And many others.  We were curious about the bollards, so enquired at the Tourist Information Centre (TIC).  Surely such an interesting piece of art should be publicised?  The TIC didn't know much  - but from a file of odd information from behind the desk they produced a typed list, and said that they thought it might be on the internet.  Well, I searched, and found nothing.  Maybe Google hasn't found the page?  So, having scanned the list, and corrected a few omissions and errors, here is that list.  Perhaps Google will find this for other curious people?  And this post has very little to do with operational research ... though I suppose that if you do a piece of interesting work, which someone else might like to know about, in whatever sphere it is, get it out there!  (And if there are errors, please comment ...)

Plymouth Hoe Bollards -- famous people with associations in Plymouth

Hoe colonnade bollards
Order from east to west: 
Admiral Sir John Hawkins 1532-1595, Naval commissioner
Sir Martin Frobisher c1535-1594, Navigator
Sir Humphrey Gilbert,1539-1584, Navigator
Sir Francis Drake,1540-1596, English sea captain, privateer, navigator, slaver, and politician
Sir Richard Grenville,1541-1591, Sailor
Captain Philip Amadas,1550-1618, Navigator
Sir Walter Raleigh,1552-1618, Navigator
William Kemple,c1563-1601, Headmaster
Sir Ferdinand Georges,1565-1647, Soldier
Captain John Oxenham,d1580, Navigator
John Endecott,1588-1665, Colonizer
Admiral Albert Blake,1599-1657, Naval commander
King Charles II,1630-1655, Monarch
Elize Hele,d c1635, Benefactor
Henry Winstanley,1644-1703, Engineer
James Yonge,1647-1721, Surgeon?
Captain John Avery,b c1665, pirate
Alexander Selkirk,1675-1721, Sailor
Mary Read,1695-1720, Pirate
William Cookworthy 1705-1780, Chemist
Samuel Northcote,1703-1781, Clockmaker
Sir Joshua Reynolds,1723-1792, Artist
John Smeaton,1724-1792, Engineer
Rev Andrew Kinsmon,1724-1793, Preacher
Capt. James Cook,1723-1779, Explorer
Capt. Tobias Furneaux,1725-1781, Explorer
Thomas Northcote,1736-?, Artist
Robert Hawker,1753-1827, Preacher
Captain William Bligh,1754-1817, Navigator
Capt. John MacArthur,1757-1834, Australian Pioneer
Napoleon,1769-1821,French emperor
John Collier,1769-1849, Politician
Zachary Mudge,1770-1852, Admiral,-
John Foulston,1772-1841,Architect
Nicholas Toms Carrinton,1777-?, Poet
Sir John Colbornne,1778-1863, Battle of Waterloo hero
Samuel Prout,1783-1852,painter
Colonel Sir George Arthur 1784-1854, Colonizer
Major Edmund Lockyer,1784-1860, Colonizer
Benjamin R Hayden,1786-1846, Painter
Sir William Harris,1791-1867, Inventor
Jonathan Hearder,1791-1876, Scientist
Thomas Byrth,1793-1849, Theologian
Sir Charles Eastlake,1793- 1865, Artist
Thomas Holloway,1800-,1883, Medicine manufacturer
Sir John Kitto,1804-1854, Scholar
Samuel Phelps, 1804-1878, Actor
Isambard K Brunel,1806-1859, Engineer
Charles Darwin, 1809-1882, Naturalist
Captain William Mogg, 1811-1870, Explorer
John Yeo, 1813-1884, Businessman
William Derry, 1817-1903, Businessman
Able Seaman Hinckley, 1819-1904, Tai Ping Rebellion hero
Augustus Bampton, 1823-1857, Engineer
Mortimer Collins, 1827-1876, Writer
Francis Balkwill, 1837-1921, Dentist
Emma L Gifford, 1840-1912, wife of Thomas Hardy
Agnes Weston, 1840-1915, Philanthropist
Cora Pearl, 1842-1886, Courtesan
Stanley Gibbon, 1842-1913, Postage stamp collector
Lt. Sir Hohn Chard VC, 1847-1897, Rorkes Drift hero
Sir John Jackson, 1851-1919, Engineer
Marshall Stevens, 1852-1936, Engineer
William Greene, 1855-1921, Photographer
Sir Arthur Conan Doyle,1859-1930 , Author
Sir Harry Moreton, 1864-1961, Musician
Albert Ballard, d 1969, Philanthropist
Robert F Scott, 1863-1912, Adventurer
Charles Brittan, 1870-1949, Painter
Sir Patrick Abercrombie,1879-1957, Architect / town planner
Lady Nancy Astor,1879-1964, Politican
Isaac Foot, 1880-1960, Politician
Thomas E Lawrence, 1888-1935, Arabist
Leslie Hawe Belisha, 1893-1957, Politician
Capt. Frederick J Walter, 1895-1944, Naval hero
James P Watson, 1898-1979, Engineer
Sir Francis Chichester,1901-1972, Adventurer
Harry `Bugler' Lake, 1902-1970, Boxer
Sir Dingle Foot, 1905-1978, Politician
Lord Caradon, 1907-1990, Diplomat
Baroness Vickers, 1907-1994, Politician
Stanley Bate, 1911-1959, Composer
Victor Canning, 1911-86, Novelist
Michael Foot, 1913-2010, Politician
Prof John Lawlor, 1918-1999, Scholar
Richard Greene, 1918-1985, Actor
Sir Herchel Smith, 1925-2001, Chemist
Beryl Cook, 1926-2008, Artist
Angela Mortimer, 1932-, Wimbledon champion
Baroness Fookes, 1936-, Politician
Lord Owen, 1938-, Politician
Robert Lenkiewicz, 1948-2002, Painter
Wayne Sleep, 1948-, Dancer
John Childs, 1951-, Cricketer
Paul Mariner, 1963-, Footballer
Trevor Francis,1954-, Footballer
Dawn French,1957- , Actress
Chris Maddocks, 1957-, Racewalker
Peter Goss, 1961-, Yachtsman
Sharon Davies, 1962-, Olympic swimmer
Ian Ward, 1972-, Cricketer
Gareth Jones, 1984-, Highboard diver
Admiral Sir Charles Napier 1780-1860, Naval reformer

Thursday, 5 July 2012

When Exeter got rid of its trams

In September 1929, the newspaper for Exeter reported that there was "Pandemonium in the High Street" of the city.  The problem was that there was too much traffic trying to get through the narrow medieval streets.  According to the chief constable, who took a census of traffic every five years, the daily flows of different types of vehicles were:
  • 1920: 1386 horse-drawn vehicles, 1314 motor vehicles and 2340 bicycles
  • 1925: 1296 horse-drawn vehicles, 3403 motor vehicles and 3252 bicycles
The High Street was also used by the city's public transport, electric trams, which ran up to eight times per hour in each direction on each of three routes.  Deliveries to the shops in the High Street were made through the shops' front doors, adding to the congestion.  By 1929, the number of motor vehicles had risen further.  Holiday through traffic had to go through the city, because there was no by-pass.  The city council faced a decision, and identified four types of action:
  1. Take some of the traffic away from the High Street by building new roads.
  2. Launch some drastic traffic control measures - traffic lights were not in widespread use.
  3. Make some streets one-way
  4. Get cooperation from the High Street shop owners about deliveries.
However, many people saw that the trams were the problem.  The city council was proud of its tram system, which was profitable (partly because there had not been much investment in maintenance!).  In April 1929, it was reported that the working expenses were 16.35(old) pence per passenger mile, and earnings were 19.08 pence.  The trams ran at a profit, but for how long?  Eventually, the council agreed to add a fifth action to the list of possibles,
  • Replace trams by buses or trolley buses
Other cities were doing that - it was seen to be the fashionable thing to do; would the city be left behind?   So the council commissioned a study, which would be called a cost-benefit study these days.  It was a kind of Operational Research, asking the question "What happens if ...?"
One scenario was to modernise the system, and it was costed.
The alternative was to replace the trams by buses
The report was discussed, and the council procrastinated, voting to put off a decision for five years.  However, the chief constable (who seems to have liked statistics) presented an analysis of traffic delays in the High Street.  At one stop, in one hour (12 noon to 1pm) 27 trams stopped, and traffic was held up for over 29 minutes.  The figures frightened the council, but there was still procrastination.  However, there were council elections in late 1929, and after these, there was more decisive action.  By August 1930, the decision to scrap the trams had been taken.  By then, the survey of traffic in the High Street showed that:
  • 1930: 522 horse-drawn vehicles, 5901 motor vehicles and 3000 bicycles (the last is suspiciously like an estimate)
Not long afterwards, a by-pass was built, which took the Plymouth and Torquay through traffic away from the city centre, but it was many years before the Okehampton through traffic was able to avoid the city centre.
Today, there is one surviving tram from Exeter, running on the holiday attraction of Seaton Tramways.   For thirty years, Exeter had been well served by electric trams, which had opened up the city for expansion, and stimulated the economy of the city.
And the lessons for O.R today?
  • Should the council have collected more traffic statistics?  (More than every 5 years)
  • Should they have been more decisive, and not procrastinated?
  • What were the limits of the system being studied?  The High Street, the city's street network, the region, the local economy?

Thanks to Julia Neville's book (2010) "Exeter and the Trams 1992-1931" [ISBN 978-0-9544343-1-1] for the facts.  The interpretation is mine