22 posts tagged “mathematics”

The video in my last post, and Christopher Richards's blog from which I nicked it, have really got me thinking about creativity, inspiration, and analytical thinking. My own creativity is woeful and worsening. Is this a common feeling amongst adults? Why do most of us stop painting as we grow up? Is it because we learn, or adopt social conventions, of what is a "good" or "bad" painting? Why do we stop writing stories (pace Christopher) and poems, playing make-believe with our friends, and having wild daydreams?

I wish I could remember where, but I once read that 90% of mathematicians think in images during the creative stages, and only in symbols and logical manipulations when they are tidying things up for presentation to others. I'm one of the other 10%. Why? Did I unlearn an image-based way of thought as I progressed through school and its exams? Can I (re)learn to be in touch with the wellspring of vivid imaginal inspiration apparently gushing within us all?

One of Christopher's other blogs mentioned the book Hare Brain Tortoise Mind by Guy Claxton which I promptly borrowed and am reading through (slowly, yay me). The book is a wonder. It gathers together a welter of scientific studies which reveal the bubbling, brilliant, and bizarre unconscious which underpins true creativity as outlined in anecdotes from the arts and sciences. It seems that not only can our unconscious be more "intelligent" than our consciousness, outperforming it under all sorts of circumstances, but that it acts independently of our consicous cognition. In this way, unconscious intelligence outperforms and overrides conscious cognition without our consicous perception of it, and consciously-held facts and beliefs seem not to influence it. A strange world indeed. I haven't begun to do the book justice, but I strongly recommend you to read it.

I would like to tag Christopher for a post on messiness and creativity. For motivation, here's a photo of Einstein's office on the day he died:

(downloaded from http://faculty.rmwc.edu/tmichalik/einstein.htm). Einstein is widely regarded as being an individual of fabulous imagination. His revolutionary breakthroughs in physics came largely from strong pictorial imaginings while staring into space (literally and figuratively). He also is quoted as saying "If a cluttered desk signs a cluttered mind, of what, then, is an empty desk a sign?" I keep my own desk scrupulously tidy, but am in a tiny minority amongst my colleagues in doing so, as well as being in the minority who don't think in images. Is there a link? What about in other areas of life? What does messiness speak of creativity?

Here is an article from Scientific American which struck a chord with me for two reasons. Firstly, it explains the rapid increase in the vocabulary of toddlers, a breathtaking phase my son is currently blossoming through. Secondly, it does so without any fancy hypothetical linguistic white elephants, but merely with a common statistical entity: the bell curve.

Finally, after six months, I've got my website up and running at work. Check it out!

There are two excellent new mathematical articles on the Scientific American website.

The first rather bravely and lucidly takes the reader through Cantor's proof that there are more numbers between 0 and 1 than there are positive whole numbers. Like the author, I remember being blown away by this result when I first saw it. The proof is so short and elegant, understandable even by those who normally quail at mathematics, and yet opens up vistas of astonishing scope. Think about it: there are different sizes of infinity. There are not only more numbers between 0 and 1 than there are positive whole numbers, but there are more numbers between any two numbers you care to pick than there are positive whole numbers, even if your chosen two numbers differ first at the billionth decimal place. In fact, there are an infinite number of sizes of infinity - how big is the set of "infinities", though?

The second article details work done by scientists at my alma mater, University College London, to describe the Mobius strip (descriptions: technical, non-technical), that mind-bending object which has only one side and one edge. You can make one by taking a strip of paper, giving it a half-twist, and gluing the ends together. For the first time, we can now determine the exact shape of a physical realisation of this object given certain facts about the material from which it is to be made. The proof uses minimisation techniques - minimising energy or another quantity seems to be an ubiquitous law of the universe of mysterious and powerful beauty. I will shortly be writing an article about this for the magazine Plus. I'll be sure to post a link when it appears.

Where did those three months just go? They vanished in a vortex of introspection and general existential angst that consumes me from time to time, and during which blogging seemed risibly inane. I think my posts are still inane, if not risibly so, but here we go again. Maybe I should try to concentrate more on the maths.

Recent cool things:

• The final Harry Potter book, Harry Potter and the Deathly Hallows. The reason I think these books are wonderful is that their evolving narrative structure mirrors the changes in perception of the world that we go through in adolescence. The books therefore not only provide an heroic tale of coming of age, from which the reader learns lessons for her own life, but embodies these lessons into the composition of each book, and the series as a whole. A younger reader might consider the magic, magical creatures and hidden world to be the best parts, but I think older readers recognise that the two worlds are alike, and that the key magical ideas are the power of love, friendship, and courage.
• Facebook and LinkedIn. Alright, I'm slow on the uptake. Nuff said; come and join me!
• ZenHabits - some excellent life hacking tips.
• Asymptotia - one of the better science blogs.
  

An interesting article in Scientific American (linking in nicely to an earlier post)reveals that there is more to success in mathematics than a high IQ. It seems that the ability to hold information in your working memory, while simultaneously being able to control your impulse to automatically follow a well-trodden path leads to success. The authors of the quoted study suggest that training a child's "executive function" and "impulse control" should be a core part of the math curriculum. Suggested training includes listening to and then repeating in reverse order a sequence of numbers.

Math makes it onto the BBC!

Another tip-off from Scientific American - the long-awaited mathematical proof of how to stop a table wobbling. Read the preprint here. (Quite by coincidence, the first author of this paper occupies the office next to mine - an office I only moved to when I came to this country two weeks ago.)

Physicsweb has a great little article about a peer-reviewed study showing how "[t]he rise and fall in the popularity of major religions can be described using the same mathematics that is used to model crystallization processes . . . The researchers have modelled the time evolution of the numbers of adherents to religions and claim that their work sheds light on an important social phenomenon – how a religion such as Christianity can grow rapidly from very small beginnings (Europhysics Letters to be published)."