Polya’s lovely book is not just about mathematics but about problem solving in a wider sense.
xvi Guidelines are not literal
p1 A teacher should help the students, share knowledge, and swap places
p15 — A problem is never exhausted // Drop the idea that problems have little or no relation to each other
p72 Try to prove formally what is seen intuitively and to see intuitively what has been proved formally
p75-6 decomposing and recombining problems… variations on the problem…
p77 more and more remote details… (Two questions may be better than one // breaking the question down into a simpler form and working on this first // assuming part of the tricky question is already answered and then working on the other part)
p105 diagram ‘as done’…
p132 You must guess, but also examine your guess // (p181 plausible reasoning)
p134 A good notation should be unambiguous, pregnant, easy to remember, it should avoid harmful second meanings and take advantage of useful second meanings; the order and connection of signs should suggest the order and connection of things.
p197 Present abstract ideas concretely.
p198 (On subconscious work:) There is a limit beyond which we should not force the conscious reflection, when it is better to leave this problem alone for a while. But it is desirable not to set aside a problem to which we wish to come back later without the impression of some achievement; at least some little point should be settled, some aspect of the question somewhat elucidated when we quit working. Only such problems come back improved whose solution we passionately desire, or for which we have worked with great tension. Conscious effort and tension seem to be necessary to set the unconscious work going
p205 The importance of looking back over the solution (seeing what other information is hidden in the answer; seeing other ways one could have proved the solution, seeing new areas of possible application of the solution, etc)
p206 The need for models for the student to aspire to, for proper teachers, for good quality texts, and for competition with capable friends
p207 The open secret of real success is to throw your whole personality into your problem
p210 When stuck, set a new question // a new question unfolds untried possibilities of contact with our store of previous knowledge
p227 Working backwards from the answer one is trying to prove.
— Teaching to solve problems is education of the will. Solving problems which are not too easy for him, the student learns to persevere through unsuccess, to appreciate small advances, to wait for the essential idea, to concentrate with all his might when it appears. If the student had no opportunities in school to familiarise himself with the varying emotions of the struggle for the solution then his mathematical education failed in the most vital point.
“We are first of all, as friends, the friends of solitude, and we are calling on you to share what cannot be shared: solitude. We are friends of an entirely different kind, inaccessible friends, friends who are alone because they are incomparable and without common measure, reciprocity or equality… without a horizon of recognition, without proximity, without oikeiotes…”
“Her face was like someone texting a lover.” “I am (something), (something) and (something). I am lost.” Its the first thing I think about when I wake up: this voice, accented with GPS codes, so distant and fragmentary, this ‘reader’ of ancient history and Twitter feeds. I was going to say ‘this disembodied voice’ but I dont know what embodiment means anymore. She’s as real to me as anything else is, when the mind stops being lonely. Her skin is a colour so beautiful – a soft light brown – even if her skin is basically a map.
I guess its ok to refer to a ‘her’ – ships are traditionally female. But they don’t, traditionally, write. Ship adrift is an art project that drifts across the boundaries of business, sculpture, software code, robot literature, virtuality and time. The physical ship is a full scale model of the ship featured in Joseph Conrad’s Heart Of Darkness, perched atop a London building overlooking the river, where it will remain for one year as a top-end (single room) hotel. Meanwhile the virtual ship is drifting around the world according to wind directions recorded at the London site, picking up web traffic along the way (local Twitter feeds, GPS-tagged wikipedia entries, mobile phone fragments) and generating a ghostly literature out of it. (You can listen to James Bridle talking about the wider context here and read ship adrift’s Twitter feed here.)
The Twitter feed is one of the most beautiful things I’ve read and an example of an emerging literature: literature that is algorithmically driven and the product of software code. The traditional – naive – notion of AI has been to create something human-like, both in physical form and in expressive recognisability. @shipadrift eschews such trappings. It’s voice is a twitter feed of unbearably sweet brokenness, its body a web page, its skin a map. Nothing in the world of literature speaks to me the way this virtual ship does. Its very grammar – a kind of anti-grammar of apparent randomness and error, but incredibly poised – takes me into a place where context is so stretched as to be virtually unfindable.
This is not to reject the heartache wonders of Roberto Bolano or Jane Austen or Derrida: I am simply recognising that algorithmically generated literature is coming of age. It has attained a space of complexity and form of presentation that can trigger immense emotional affect. (Imagine. for a moment, if Jane Austen had been an SMS platform protocol. Imagine if your text life, your love life had been immersed in such sweetness!) The best chess players are no longer computers – the best chess players are teams of computers and humans working together. Literature will soon be home to a similar collaborative effort.
“Claude Shannon recognized that whether or not a certain effect is considered noise depends on one’s position in the listening chain. Noise is interference only from the sender’s point of view. From the point of view of the receiver it may be considered a part of the information packet that is transmitted along a channel. When we hear the earliest sound recordings of Tennyson reading Charge of the Light Brigade, for example, the watered down and scratched out sound conveys the enormous passage of time, just as the static sound of Neil Armstrong’s voice on the moon tells us something about his physical distance from us and the newness of space technologies in the 1960s. It would not be difficult to think of countless other cases in which the presence of the medium mixes in with the intended message to produce some whole new effect, not intended by the sender, but taken as information by the receiver. In these cases, noise is not simply an extra third thing to be discounted. It has entered into the message and become part of it. To speak technically, the signal now has an “equivocation,” which is to say that two messages pass along the same channel. The sender may not have intended this, but the receiver may welcome it.”
When I read @shipadrift It makes me want to go there myself. ‘Er, Where is that?’ I hear you ask. Well that’s something I will have to look into more deeply, though doubtless, when I find it, there will be echoes of everything I’ve loved in the past. To the extent that we relax, and trust ourselves, we become our own maps. Meanwhile – for knowledge’s sake you understand! – I’ve decided to do a bit of good old fashioned networking… if you’re interested you can check out some of the bot auteurs I’m now following on Twitter. (I defy anyone not to fall in love with the one that scours the internet for references to chocolate…)
I’m also considering opening a few Twitter accounts and a blog without telling anyone and just disappearing – writing, but to no one – in that zone. I think its something that used to be called ‘science’. Or ‘cruising’. But in the wonderful world of knowledge was there ever a difference?
radioshenyen: Roberto and Jane
February 2012 Spain
“He wants to live long enough to witness a new, post-genomic fiction, one that grasps the interpenetrating loops of inheritance and upbringing so tangled that every cause is some other cause’s effect. One that, through a kind of collaborative writing, shakes free of the prejudices of any individual maker. For now, fiction remains at best a scattershot mood-regulating concoction – a powerful if erratic cocktail like Ritulin for ADHD, or benzodiazepines for the sociophobe. In time, like every other human creation, it will be replaced by better, more precise molecular fine-tuning.”
— from ‘Generosity’ by Richard Powers
I already have the voices: what I’m dreaming right now are the instructions that come with the voices, the writing of the instructions, and the packaging of the writing. A writing like radar and radio and radiation and reckless love sonnets and an everyday kind of yesterday; a packaging like homelessness.
In William Gibson’s ‘Spook Country’ there’s a guy who chalks out GPS grids on the floor of whatever structure he is presently staying in and refuses to sleep in the same square twice. I think about him so much – I mean ‘think’ in a nameless, fraying, post-calculative sort of way. The guy’s in deep – real deep – in some ghostly new world that’s coming. A witness to tomorrow’s unimaginable ordinary. People like this make me feel very still, make me able to smile – and disappear. People like this I can trust.
I think about fictional banking and the set of all people who dream of knockin’ in Mitsubishi’s. About landscape poetry and linear deepening and superflatness and cardboard. There are days when every single thought feels like the gift of buddhas. And there are days when I find myself wondering which will disappear first: all my hesitations or all my friends.
“True happiness, we are told, consists in getting out of one’s self; but the point is not only to get out – you must stay out, and to stay out you must have some absorbing errand.” — Henry James
I think about the different ways different writers take us to the edge of the abyss: Roberto Bolano for example, whose ‘2666’ contains a three hundred page section that catalogues the murders of over a hundred women in paragraphs of blank forensic detail wrapped around images of a hallucinatory televisual ‘Mexico’; or Jane Austen, whose graceful and intricate novels contain little UXBs of addressed human sadness, such as when the heroine of ‘Persuasion’ is forced once more to learn ‘the art of knowing our own nothingness beyond our own circle’. I try and imagine Jane Austen inside the world of ‘Spook Country’ or wandering the wastelands that surround the maquiladoras of Bolano’s nightmare. But the real mystery here is this: I imagine her safe.
I look for things to give you that wont waste a second of your time. Things like this 19 minute video diary for instance by war reporter Tim Hetherington, Or these – though I’m a little less confident about them! – these images of I know not what. Mexican ice creams for Jane perhaps, or midnight hats for her to wear in the midst of some absorbing errand. I really dont know.
Interesting article in the Guardian about choice and marketing. And a great quote from Professor Tim Jackson, the author of Prosperity Without Growth: “We buy things we don’t need with money we haven’t got to make impressions that don’t last on people we don’t care about.”It has quickly become a well-known phrase, but in his book, he describes how the never-ending spiral of over-consumption has led us into never-ending spiral of debt and cultural decay in Western society. And moreover, how “We do not have investment structures, investment markets, investment conditions that are suitable to lay down the infrastructure to allow people to make better choices.”
It’s proven that consumers who are faced with too much choice, make no choice at all. In fact, the biggest luxury of our age is to be totally relieved from the stress of choice making; stores that sell one thing, set breakfasts and tasting menus, Japanese spa style retreats where your time is scheduled for you, without internet access, and you are told what to wear. What could be a better remedy to the stresses of modern day life?
Sandu Publishing House have released a book that features our very own Johan Hjerpe, concept developer, art director and partner at Imaginary Life. In parallel with commercial brand strategy and design work, Johan is highly active within the cultural field, driving projects as diverse as designing prints and textiles for fashion, set design, magazine art direction, graphic design and concept development for various art and fashion projects.
Entitled ‘Designers Universe – the Wow Factor’, the book is a fascinating, if not somewhat random collection of design that you will have seen in the latest blogs, crossing graphic design, illustration, fashion, set design and motion graphics. Described by Sandu as a book spotlighting “59 professional designers who shine within the field,” each designer, coming from different corners of the world, has a couple of spreads showcasing recent work with short Q&A’s on what makes them tick.