Creativity and innovation, cornerstones of scientific and artistic progress

It’s World Creativity and Innovation Day today. In fact, the whole preceding week, 15-21 April, is celebrated as World Creativity and Innovation Week. To quote the website, “World Creativity and Innovation Week, April 15-21, celebrates the unlimited potential of people to be open to and generate new ideas, be open to and make new decisions, and to be open to and take new actions that make the world a better place and make your place in the world better too.”

The importance of creativity and innovation can hardly be overestimated. Throughout the history of science and art, progress was sparked by the innovations of those individuals who nurtured and positively exploited their creativity.

Creativity and innovation - weighty subjects that impact on every aspect of our lives, from art to science, from mathematics to literature. (© All Rights Reserved)
Creativity and innovation – weighty subjects that impact on every aspect of our lives, from art to science, from mathematics to literature.
(© All Rights Reserved)

Of course loads have been said about the art of innovation, and many clever people have devoted their lives to the study of creativity. Yet these remain elusive subjects, with much disagreement as to what constitutes creativity, and how you can increase/improve your own creative abilities.

I’ve featured many inspirational individuals, who have been responsible for amazing creativity and innovation, on this blog in the past, and hope to feature more in future. Rather than attempting to turn this post into a meaningful, comprehensive overview on the science of creativity (which would be pretty much impossible anyway), let me rather simply applaud all those innovators who have dazzled the world with their creative contributions, however big or small – may the river of human innovation never run dry, and may every day be a creativity and innovation day.

Celebrating complex knots and loops on International Tatting Day

It’s the 1st of April, and we all know what that means. It’s the day that every story you hear has to be taken with a bit of scepticism – you don’t want to be the fool falling for the crazy, almost-believable story on April Fool’s Day!

However, rather than spinning a yarn, or weaving a tall tale , I’ll focus on yarns and weaving of a different kind – today is International Tatting Day, the day we celebrate the age-old art of handcrafting lace-like edges using an intricate series of knots and loops. Tatting is usually done for decoration, for example to create fancy edges for doilies, collars, etc.

There's a thin line between tatting and crocheting, which also creates patterns with knotted yarn. Both these crafts are used to create patterns that are almost mathematical in their complexity. With apology to tatters everywhere, my illustration above is a piece of crochet work rather than tatting, but unfortunately I wasn't able to find a nice example of tatting to photograph.(© All Rights Reserved)
There’s a thin line between tatting and crocheting, which also creates patterns with knotted yarn. Both these crafts are used to create patterns that are almost mathematical in their complexity. With apology to tatters everywhere, I believe my illustration above is a piece of crochet work rather than tatting, but unfortunately I wasn’t able to find a nice example of tatting to photograph.
(© All Rights Reserved)

A range of different knots and loops can be used to create amazingly delicate and intricate patterns that have an almost mathematical complexity about them. In fact, with a little imagination the tatted patterns can almost resemble the beautiful fractal patterns created in mathematical topology.

Those engaged in the art of tatting are called ‘tatters’, and according to a number of sources, tatters celebrate International Tatting Day by “making tatted lace and eating chocolates”.

So, Happy Tatting Day, everyone! I don’t have the skill to join in on the tatting, but where did I leave that slab of chocolate?

Remembering Paul Erdős, collaborator, eccentric, lover of numbers

Today we celebrate the birthday of one of the most colourful and eccentric characters in the world of mathematics (a domain not short on eccentrics at the best of times)- the Hungarian Paul Erdős (26 March 1913 – 20 September 1996).

Erdős, a serial collaborator, was one of the most prolific publishers of mathematical papers in history. The volume of his output has been compared with the great Leonhard Euler, but while Euler published more pages (mostly as solo author), Erdős published more articles (more than 1500 in his lifetime), many in collaboration with other mathematicians.

Erdős lived his life on the road, moving regularly from one mathematical collaboration to the next.(© All Rights Reserved)
Erdős lived his life on the road, moving regularly from one mathematical collaboration to the next.
(© All Rights Reserved)

The British mathematician and author Timothy Gowers once wrote an essay entitled “The Two Cultures of Mathematics”, in which he classed mathematicians into two groups – the ‘problem solvers’ and the ‘theory developers’, with the latter often held in higher regard in the history of mathematics. Erdős, however, definitely fell into the former category – he was particularly fond of those problems that appeared simple to understand, yet notoriously difficult to solve. Most of his work focused on number theory, combinatorics, approximation theory, set theory and probability theory. However, thanks in part to his fondness for collaborating with other mathematicians, he also made contributions in completely unrelated fields such as topology.

As mentioned before, Erdős was known to be a bit of an eccentric. He had little interest in earthly possessions, giving most of what he had away to causes he considered worthy. Most of his life fit into a single suitcase, and since he first emigrated from Hungary (moving first to England, and later to America after accepting his first position at Princeton University), he lived a nomadic lifestyle, travelling between different mathematical colleagues and collaborators. It is said that he often arrived without warning, pitching up on a prospective collaborator’s doorstep with the words “My mind is open!”, to indicate his readiness to collaborate. After staying for a few weeks, he would move on to the next destination.

In recognition of his prolific collaborations, Erdős’ friends devised the ‘Erdős number’ – an indicator of a person’s degree of separation from Erdős himself (in terms of mathematical collaboration). Thus Erdős had a number of 0, while his immediate collaborators had an Erdős number of 1, his collaborators’ collaborators had an Erdős number of 2, and so on. Due to the extent of his mathematical collaborations, and the collaborations of these individuals with scientists from other fields, many physicists, engineers, biologists etc also have low Erdős numbers.

Despite the extent of his publications and collaborations, Erdős never received mathematics’ highest prize, the Fields Medal, nor did he co-author a paper with a recipient of this award. He similarly missed out on many other of the more illustrious mathematics awards, with the most significant award bestowed on him probably being the Israeli Wolf Prize.

Despite this lack of formal recognition, Erdős’ contribution to a wide range of mathematical topics have been acknowledged by his peers, and he is fondly remembered as someone with an unwavering passion for numbers, and one of the most colourful characters in mathematics.

Celebrating Einstein’s birthday on Pi Day

Besides today being World Kidney Day, which I incorrectly listed on the blog for yesterday, the 14th of March is also the celebration of Pi Day, commemorating the mathematical constant π (pi), which, to two decimal points, equals 3.14.

Enjoying 3.14 pies on Pi Day.(© All Rights Reserved)
Enjoying 3.14 pies on Pi Day.
(© All Rights Reserved)

OK, we’ve already celebrated Pi Approximation Day on the 22nd of July (22/7 is also used to approximate π), but surely this amazing number deserves another mention.

So bake yourself 3.14 pies and share in the celebrations!

Making today extra special, we also celebrate the birthday of Albert Einstein (14 March 1879 – 18 April 1955), the greatest scientist of the 20th century. What makes Einstein such an endearing figure is that, besides his numerous groundbreaking contributions to science (thermodynamics, relativity, quantum theory, wave-particle duality, statistics, cosmology, nuclear physics and much more), he has also made deeply profound contributions to secular subjects as diverse as war and peace, religion, human rights, economics and government.

The ideas and opinions of the great Albert Einstein - a continuous source of insight and inspiration. (© All Rights Reserved)
The ideas and opinions of the great Albert Einstein – a continuous source of insight and inspiration.
(© All Rights Reserved)

Many volumes have been written about the great man, so rather than trying (and no doubt failing) to adequately capture his contributions in a single blog post, I will rather leave you with one of his many, many wonderful quotes:

“Learn from yesterday, live for today, hope for tomorrow.
The important thing is not to stop questioning.”

Calculating the perfect pancake on Pancake Day

Today, 12 February 2013, is Shrove Tuesday, the day immediately preceding Lent – an observance in many Christian denominations, running for approximately 6 weeks from Ash Wednesday to Maundy Thursday (or Easter Eve). Lent is a period of religious preparation for Easter weekend.

In many parts of the Commonwealth, including the UK, Ireland, New Zealand, Australia and Canada, Shrove Tuesday is commonly known as Pancake Day, based on the tradition of eating pancakes on the day.

Pancakes became associated with this day because it was traditionally considered a good way to consume a range of rich foods – eggs, milk, sugar, butter, fat, cream – before Lent’s period of self-denial. Of course, as with gift-giving during Christmas, the original religious association has moved somewhat into the background, with Pancake Day now being about pancakes and little more.

Sadly I am not doing much to reverse this tradition, as the rest of my post is pretty much only about pancakes…

A stack of American style pancakes with bananas and strawberries, topped with a generous helping of ice-cream and drizzled with liquidised strawberries - so fresh and fruity, it almost feels healthy! (© All Rights Reserved)
A stack of American style pancakes with bananas and strawberries, topped with a generous helping of ice-cream and drizzled with liquidised strawberries – so fresh and fruity, it almost feels healthy!
(© All Rights Reserved)

Just a quick point of clarification – pancakes in Europe (thin, flat pancakes, usually rolled up and eaten with sweet or savoury filling – also called crêpes) aren’t exactly the same as pancakes in the US and Canada (smaller, thicker ‘cakes’ that are often stacked on top of each other, dusted with icing sugar and eaten with syrup – also known as Scotch pancakes, pikelets or flapjacks).

Now you may be curious about the link between pancakes and science. While I don’t know how much science there is in a pancake, I can report that it has apparently been the subject of some rather rigorous scientific scrutiny. A mathematics professor from Wolverhampton University, Dr Ruth Fairclough, has developed what has been reported as “a complicated formula for the perfect pancake”.

Dr Fairclough’s full pancake ‘recipe’ is:

100 – [10L – 7F + C(k – C) + T(m – T)]/(S – E)

where
L = number of lumps in the batter
F = flipping score
C = consistency of the batter
k = ideal consistency
T = pan temperature
m = ideal pan temperature
S = standing time of batter before cooking
E = time the pancake stands before eating

The closer a pancake gets to the perfect score of 100, the better.

I’ve played around with the formula, and while most of it makes sense, it doesn’t always stand up to scrutiny. My main concern relates to the 1/(S-E) factor – if the standing time of the batter before cooking is equal to the time the pancake stands before being eaten, you end up dividing by zero. But perhaps I misunderstand the way these variables should be measured…

The bottom line, however, is that Dr Fairclough’s formula agrees that batter with perfect consistency and no lumps, stood to rest for a while, and then cooked at the perfect temperature and eaten piping hot off the pan, should give you a pretty perfect pancake.

But then you don’t need a PhD in maths to know that, do you? 😉

Enjoy some mental gymnastics on Card Playing Day

Today, 28 December, is Card Playing Day – the day to celebrate all games involving your classic deck of cards.

When you think about it, a deck of cards is a pretty impressive creation – the diversity and complexity covered in all the games using a card deck is quite staggering. From games testing cunning and deception (poker), to games teaching teamwork and planning (bridge), to those based on statistical probability and counting skills (blackjack), to visual pattern-matching games (rummy), to the single-player solitaire/patience type games, and hundreds more in-between, the options are almost limitless. And all this based on a simple collection of 52 playing cards, involving four different ‘suits’ of 13 cards each.

Playing cards - a world of complexity lurking in a deck of 52 cards.(© All Rights Reserved)
Playing cards – a world of complexity lurking in a deck of 52 cards.
(© All Rights Reserved)

Playing cards have a long history – they were first found in China as early as the 9th century, and appeared in Europe around the 14th century. The first card decks containing the now-standard 52 cards consisted of suits with themes like polo sticks, coins, swords and cups. The famous suits of spades, hearts, diamonds and clubs, as we still use today, was first introduced in France around 1480. The Kings, Queens and Knaves (Jacks) in the different suits were based on English and French history, and referred to different historical characters such as King David, Julius Caesar, Alexander the Great, and others.

Beyond the historical connotations, a range of symbolic meanings are attached to the deck of cards as we know it. The 13 cards in each suit is said to refer to the 13 months of the lunar year; the 52 cards corresponds to the 52 weeks in a year; the Ace, which is both the lowest and highest card in each suit, is symbolic of the beginning and end, alpha and omega.

From a scientific point of view, playing cards represent an invaluable demonstration and teaching aid in fields such as mathematical logic, probability and statistics.

Whether you enjoy playing cards for the thrill and uncertainty of games of chance, or because of the complex mathematics they represent, or simply because of the social interaction inherent in many card games, today is the day to celebrate all facets of card playing. So while you’re enjoying that pleasant lull between Christmas and New Year, why not pull out a deck of cards –  play an old game, learn a new one, and lose yourself in the mathematical complexities hidden in your standard card deck.

Sir Isaac Newton, a saint among the scientists

Today is Christmas Day. No surprises there. But to add a slightly more scientific flavour to 25 December, did you know that today is also the birthday of arguably the greatest scientist that ever lived – Sir Isaac Newton (25 Dec 1642 – 20 Mar 1727).

Mery Christmas, and a happy birthday to Sir Isaac Newton.(© All Rights Reserved)
Merry Christmas, and a happy birthday to Sir Isaac Newton.
(© All Rights Reserved)

A physicist, mathematician, astronomer, natural philosopher, alchemist and theologian, the importance and influence of Newton on science as we know it can hardly be overstated. Newton provided the foundation of mechanics with his description of universal gravitation and his three laws of motion. He shares the credit (with Gottfried Leibnitz) for developing the mathematical field of differential and integral calculus. He published, in 1687, one of the most important books in science, Philosophiae Naturalis Principia Mathematica (‘Mathematical Principles of Natural Philosophy’) – a book not only fundamental because of its content, but also because of the clear style it was written in; a style still setting the standards for scientific publication today.

Beyond the above, he also made fundamental contributions to a disparate range of fields  including astronomy, optics and many more – too much to even consider covering with a single blog post.

Newton was also a deeply religious man, so I’m sure he must have considered being born on Christmas day a most amusing coincidence. If ever there was a scientist deserving of some form of sainthood, surely it must be him.

So, on this day, I wish you a Merry Christmas, and lots of good science – theoretically robust and ethically sound, according to the example of Sir Isaac Newton.

Sophus Lie and the secret mathematical code

Today we celebrate the birthday of one of the great names in mathematics, Norwegian Sophus Lie (17 Dec 1842 – 18 Feb 1899). Lie made fundamental contributions to the theories of algebraic invariants, continuous groups of transformations and differential equations. Two concepts, Lie groups and Lie algebras, have been named after him.

Beyond being a great mathematician, Lie was, for a short while, also mistakenly considered to be a great spy. He was in Paris during the outbreak of the 1870 French-German war, and decided to leave France for Italy. Before he made it to the Italian border, however, the French arrested him as a German spy.  Reason being, they found his mathematics notes, and thought these were secret, coded messages.

A stack of papers with weird notes and symbols - can you blame military security for thinking they just arrested a super spy!?(© All Rights Reserved)
A stack of papers with weird notes and symbols – can you blame military security for thinking they just arrested a super spy!?
(© All Rights Reserved)

It was only after the French mathematician, Gaston Darboux, intervened and confirmed that the notes was in fact legitimate mathematics, that Lie was released.

Based on this experience, Lie decided that perhaps it was safer to return home and continue his work in the Norwegian town of Christiania, where he had originally studied mathematics.

The moral of the story, I guess, is that if you plan on travelling through a war zone with your math notes, keep them plain and simple, or keep them very well hidden!

About clip-on ties, real ties and mathematics

Rumor has it that today, 84 years ago in 1928, some clever folk came up with the concept of the clip-on tie. You know, those ties that look like the real deal, but instead of being tied around your neck just consist of the hanging bit with a permanent knot at the top, which can be attached to your shirt via a little metal clip stuck to the back of the knot.

Try as you might, but a clip-on tie will never have the 'oomph' of a classy, properly tied tie.(© All Rights Reserved)
Try as you might, but a clip-on tie will never have the ‘oomph’ of a classy, properly tied tie.
(© All Rights Reserved)

I’m not sure if it was originally designed for people too lazy to tie a tie, or for people who had difficulty mastering the skill, but it proved to be quite a useful invention. Disabled people can use it without trouble. So can kids. Cops and security personnel wear clip-on ties as a safety precaution – it negates the potential risk of being strangled by your conventional necktie. Similarly, people in factory environments who wear ties are also advised to wear clip-ons – in the unfortunate event that the tie gets caught in a piece of machinery, it will simply clip off, rather than pulling its owner into the machine as well. (Then again, why people in factories would wear ties I have no idea.)

On the downside, clip-ons aren’t exactly haute couture – you are unlikely to get a designer-styled, silk clip-on tie. And a clip-on tie pretty much looks like a clip-on tie – the unique individuality of a slightly unsymmetrical knot is not an option. And of course you cannot go for the cool chic of the ‘loosened tie look’ with your clip-on tie – well, I guess you can clip it on to one side of your loosened collar, but somehow it just ain’t going to have the same effect!

So what does a clip-on tie have to do with science, you may ask? Well, very little, but it did bring to mind a mathematics book by Thomas Fink and Yong Mao, called ‘The 85 ways to tie a tie’ – a book where the authors use concepts from topology and a mathematical representation of knots to prove that a conventional neck tie can be tied in exactly 85 possible ways. The 85 ways are pretty theoretical – apparently only a dozen or so are sufficiently unique and handsome to be sensible candidates for an actual tie knot.

Yes, today is about ties, but as is often the case, the maths are lurking just below the surface!

John Backus and the development of high-level computer programming languages

Today we’re celebrating the birthday of John Backus (3 Dec 1924 – 28 Oct 1988), American computer scientist and the leader of the team who invented the Fortran programming language (at the time called FORTRAN) while working at IBM in the mid 1950s.

Fortran was the first so-called ‘high-level computer language’, which means it was capable of converting standard mathematical formulas and English-based expressions into binary code used by computers. The language is particularly suited to scientific computing and numeric computation. Over the years, many improvements were made to the original Fortran language, with versions known by a sometimes strange series of numeric identifiers – FORTRAN, FORTRAN II, FORTRAN III, FORTRAN IV, FORTRAN 66, FORTRAN 77, Fortran 90, Fortran 2003 and Fortran 2008.

FORTRAN was the first widely used high-level computer language, providing an interface between equations and expressions understandable to humans,  and binary code used by computers.(© All Rights Reserved)
FORTRAN was the first widely used high-level computer language, providing an interface between equations and expressions understandable to humans, and binary code used by computers.
(© All Rights Reserved)

Despite being one of the oldest computer languages, it has been one of the most enduring, and after more than half a century it is still a preferred language for computationally intensive applications such as weather prediction, computational fluid dynamics and finite element analysis. One of the reasons for Fortran’s longevity is that some of the later Fortran compilers in particular are capable of generating very fast and efficient code, which can make a big difference when solving large, complex mathematical computations. It is still the primary language for used on many supercomputers, and many of the floating-point benchmarks to test the performance of new processors are still written in Fortran.

As a high-level language, Fortran has also provided an impetus for the development of numerous subsequent computer languages such as ALGOL, COBOL and BASIC.

The IEEE awarded John Backus the W.W. McDowell Award in 1967 for the development of FORTRAN. He also received the National Medal of Science in 1975 and the ACM Turing Award in 1977 for his contributions to the design of high-level computer programming systems.