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One summer, in a beach house near San Diego, Malcolm Gladwell and Steven Covey worked on a book together. On a hot August night, after several weeks of tetchy collaboration, they had a big fight over whose name was going to appear first on the cover. The next morning, over a rather frosty breakfast, they agreed to go off and write separate books. And they never looked back. But now, the lost manuscript of that secret collaboration has come to light…. OK. Not true. But if there was a bastard love child of Malcolm “Outliers” Gladwell and Steven “7 Habits of Highly Effective People” Covey then this book might be it. On the one hand it takes something as seemingly impenetrable as “creativity” and then explains it with a mix of anecdote and simple maths to entertain and enchant the audience. But at the same time, by providing a formula for how “highly creative people” do it, the intent is to give the reader some simple steps to become more creative themselves. So let’s talk about the reader (who no doubt likes Gladwell and Covey). He or she will probably not work directly in the creative industries. But as a marketer, or accountant, or lawyer, or retailer, or general manager, they will bump into people that do. In fact, they may know that their role in some ways relies on the creativity of others. But their world is full of numbers, targets, spreadsheets and maths. And so they have often wondered exactly what goes on over there, on the wild shores of creativity? Is it - fashion, advertising, film, publishing - all about sex and drugs and rock and roll? What are they up to (and can I have some please)? This books explains what is going on “over there”, but in their terms : numbers. No bullshit, no self-serving myths, just a pragmatic analysis of the maths behind the magic. And The Mathematics of Creativity, Jon Leach, [email protected] , 07956 228 589, 17 Somerset Road, Brentford, TW8 8BT 1

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Page 1: Thriving in the Chaotic Zone - Pattern Recognition€¦ · Web viewBut now, the lost manuscript of that secret collaboration has come to light…. OK. Not true. But if there was a

One summer, in a beach house near San Diego, Malcolm Gladwell and Steven Covey worked on a book together. On a hot August night, after several weeks of tetchy collaboration, they had a big fight over whose name was going to appear first on the cover. The next morning, over a rather frosty breakfast, they agreed to go off and write separate books. And they never looked back.

But now, the lost manuscript of that secret collaboration has come to light….

OK. Not true. But if there was a bastard love child of Malcolm “Outliers” Gladwell and Steven “7 Habits of Highly Effective People” Covey then this book might be it.

On the one hand it takes something as seemingly impenetrable as “creativity” and then explains it with a mix of anecdote and simple maths to entertain and enchant the audience.

But at the same time, by providing a formula for how “highly creative people” do it, the intent is to give the reader some simple steps to become more creative themselves.

So let’s talk about the reader (who no doubt likes Gladwell and Covey).

He or she will probably not work directly in the creative industries. But as a marketer, or accountant, or lawyer, or retailer, or general manager, they will bump into people that do. In fact, they may know that their role in some ways relies on the creativity of others.

But their world is full of numbers, targets, spreadsheets and maths. And so they have often wondered exactly what goes on over there, on the wild shores of creativity? Is it - fashion, advertising, film, publishing - all about sex and drugs and rock and roll? What are they up to (and can I have some please)?

This books explains what is going on “over there”, but in their terms : numbers. No bullshit, no self-serving myths, just a pragmatic analysis of the maths behind the magic. And while this will really grab our creative-curious business folk I hope it will also appeal to the general reader.

Overall, how does this help the world?

Firstly, if we “understood a little more and condemned a little less” (to misquote Mrs Thatcher) then the creative people and business people would get along a whole lot better (indeed creative people may feel inclined to buy this book for their accountants, and other numerical tormentors).

Secondly, in a Google world where knowledge is common place, being an expert is becoming just a table stake. To be a real high roller you will have to add creativity to your playing style.

We all need to double our creativity (preferably in ten easy steps) and that’s why you must read the Mathematics of Creativity.

The Mathematics of Creativity, Jon Leach, [email protected], 07956 228 589, 17 Somerset Road, Brentford, TW8 8BT

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About the Author. Jon Leach

I have spend 25 years being a “creative strategist” flitting between the creative and commercial worlds. It would be wonderfully poetic to tag “never quite fitting into either” to the end of that first line, but I think both sides would claim me for their own.

I was trained in the advertising agency that created the Smash Martians, grew up in the agency that told us that “You Know When You’ve Been Tango’d” and currently work for the UK’s largest PR company.

Jasper Carrot once said of his granny’s car-driving history that she claims to have never had an accident in her life (pause for comic effect) but she’s seen thousands. And so with me and creativity : never had an original idea in my life but I’ve seen thousands.

Along the way, I have worked close up with the people that have created such great brands as Orange, First Direct, O2 and, ahem, Pot Noodle. I may not be a Lennon or a McCartney but George Harrison and I could usefully exchange notes.

Being an analytical kind of chap (my Dad was radio engineer at GCHQ, possibly a spy, but definitely good at maths) I have always tried to understand why things are the way they are, and then try to explain them to others.

Sometimes I use diagrams, occasionally analogies involving 70’s comedians but in this book maths.

Apart from the day job I also teach business people how to be more creative and creative people to more business like.

And at the weekends (apart from the books) I design board games for children. Current projects include “Knights of the Valley” (from humble farmhand to saving the Princess from the dragon in 90 minutes) and “Wannabee a Popstar?”. My children would really like these to be published so they can stop being my play testers.

But back to the book…

The Mathematics of Creativity, Jon Leach, [email protected], 07956 228 589, 17 Somerset Road, Brentford, TW8 8BT

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The Mathematics of Creativity

(and how to double yours)

By Jon Leach

A visualisation of a statistical analysis of the creative content of this book

The Mathematics of Creativity, Jon Leach, [email protected], 07956 228 589, 17 Somerset Road, Brentford, TW8 8BT

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The Mathematics of Creativity

(and how to double yours)

By Jon Leach

Section One : the maths of individual creativity

1. The Mathematics of Novelty

2. The Geometry of Good Ideas

3. The Statistical Perils of a Creative Partnership

Section Two : the maths of group creativity

4. A Formula for Creative Meetings

5. Calculating the Ideal Size of a Creative Meeting

6. The Predictable Nature of Breakthrough Meetings

Section Three : the maths of the creative business

7. The Hard Sums of Commercial Creativity

8. Thriving in the Chaotic Zone : Why Creative Agencies Exist

9. The Maths of Being a Good Client

10. Summary : how to be 100% more creative in ten easy steps

The Mathematics of Creativity, Jon Leach, [email protected], 07956 228 589, 17 Somerset Road, Brentford, TW8 8BT

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Section One : the maths of individual creativity Introduction : The Maths of Novelty

How does creativity work on the brain. What is the mathematical difference between the ideas that stick and the ideas that fade away (or don’t even get noticed in the first place)? And how come so little sticks?

Various studies have suggested that we are on the receiving end of literally thousands of commercial messages a day. Other studies (or a brief self-examination by the reader) suggests that only a tiny fraction of those ideas stick. What is going on here?

Many stimuli may impinge on our short term memory but few ideas (or adverts, or images, or tunes) are good enough to get into the long term memory and become permanent.

Part of the explanation may be to do with decay rates.

The Mathematics of Creativity, Jon Leach, [email protected], 07956 228 589, 17 Somerset Road, Brentford, TW8 8BT

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If we say that the most powerful idea possible is one that we think about every day with 100% probability, for ever, and the worst idea is one that doesn’t even register day one (nul points, Norwege), then we have a spectrum of ideas with a “memory chance” of 0 to 100%.

The first thing we notice is that mediocre ideas rapidly get forgotten. The statistical Mr Average who sits right on the 50% mark has only a 25% chance of still being amongst the apples of our eye on the second day (0.5 x 0.5 = 0.25) and a one in eight chance on the third day. A full week after Mr Average came into our lives there is only a 0.4% chance that we are still thinking about him, a tragic one in 250 chance.

But what is less immediately obvious is that those ideas that initially seem to be highly memorable also suffer the degradations of time and get forgotten. So a strapping young buck of an idea with 90% memorability does quite well on the second day (81%) but is becoming quite tiresome and dull by the end of the week (43%).

Given enough time, even pretty good ideas can start to fade in our minds. Mr 90% is down to 21% after two weeks, 10% by three and a washed out 4% by the end of the month.

One thousand pennies

So what we find is that only a few rare ideas are robust enough to cling on within our careless, fitful brains. A 99% idea is still doing pretty well after a month at 74 % while the “one in a thousand” idea that is 99.9%, even after a month is virtually unchanged at 97%.

The Mathematics of Creativity, Jon Leach, [email protected], 07956 228 589, 17 Somerset Road, Brentford, TW8 8BT

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But, as one economist put it, in the long term we are all dead. And so, using this mathematical model, all ideas that are less than 100% will decay into mediocrity given enough time.

As at least some ideas do become permanent, perhaps after a certain period of time a select few ideas acquire “squatters rights” and - less metaphorically - become a permanent set of neurones firing in a predictable sequence in our minds.

Now if we are to believe the social scientists and assume that (in round numbers) we are on the receiving end of about 1000 ideas a day, does that mean that every day a real charmer starts worming its way into our mind and takes up permanent residence?

Probably not, due to another piece of maths known as the normal distribution or the bell curve. This theory suggests that most biological populations arrange themselves with a lot of people around the middle and increasingly less numbers toward the edges.

So if the average man is 5’10” tall then there are loads of men who are 5’8” or 6’, quite a lot (but not so many) who are 5’6” or 6’2” but not many at all at 5’0” or 6’8”. And when we get to 4’6” and 7’2” then these are rare flowers indeed.

And so with creative artefacts which are, after all, just a product of the biological phenomenon that is mental innovation. Many more ideas are in the

The Mathematics of Creativity, Jon Leach, [email protected], 07956 228 589, 17 Somerset Road, Brentford, TW8 8BT

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40% to 60% range than in the 80-100% range. And so encountering an idea that has 99.9% memorability power is not a one in a thousand (or daily) event but something much rarer than that.

This is arguably the core challenge for the creative industries : if “natural” creativity is clustered around the 50% mark then it will decay rapidly (to 0.4% within week) and not be memorable or useful. Even 90% creativity isn’t that much better.

So the job of the creative professional and indeed the creative organization is to deliver creativity that is way up in the high nineties, for only then will it have real commercial power

Perhaps it is worth exploring how creativity works mathematically and in understanding the “formula” what we as individuals can do about it?

As a starter, one of the most basic things creative people do is generate a lot of creative ideas; dozen, hundreds even. The explanation for this (although this is not how they would put it) is just basic probability theory.

If you have one idea, then on average, it will be, err, average. As above let’s call it 50%. If you have three ideas, then one of them will probably be bit above average (say 66%), and one a bit dodgy (33%). If you keep adding in ideas then they will tend to spread out into a “normal” distribution much like human heights do or as if you were dropping grains of sand on the same spot.

Now as discussed above, if we are looking for ideas that will stick, then we need to get out to the 99% or even 99.9% mark. Creative people are not so arrogant to think that all their ideas will naturally be at that end of the scale so they systematically generate far more ideas than they will ever need.

This may seem wasteful for those who don’t create ideas for a living. Why not just think of the good ideas first? Unfortunately, much like extracting gold from low grade ore, you need to churn through a lot of stuff to find the value.

The Mathematics of Creativity, Jon Leach, [email protected], 07956 228 589, 17 Somerset Road, Brentford, TW8 8BT

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(As an aside, they will often re-cycle some of this “waste” into other projects. In the trade it is known as the “bottom draw”.)

But at least this idea explains why the creative process can take a bit of time. If you need to generate a 1000 ideas to find one great one (as Thomas Edison is alleged to have done with is light bulb), then even the hardest task master will agree that you need to be cut some slack (one and a half years in Edison’s case).

However, this idea of trying to find a highly impactful, one in a thousand, 99.9%-er assumes that creativity works only in one way. A lot of professional creative people do believe this and subscribe to what some call the “active processing” theory of creativity. The (vaguely) scientific idea here is that an idea needs to be consciously thought about in the “higher parts” of out brains, and actively processed to be remembered (and hence acted upon). There is a rival theory though.

This is called the Low Involvement Processing Theory of communication. This argues that ideas that gently or lightly brush against your brain, often at an unconscious or emotional level can, especially over time, have an effect on your behaviour, even if you are not really “thinking” about them in a way you are aware of. You (or perhaps your brain) are processing them in a low involvement way, hence the name.

A way of modelling this is the reverse of the decay rate : compound interest (once described as the most powerful force in nature). Active processing advocates are fans of ideas that are very slow to erode from a high of 100; low involvement processing advocates value ideas that very consistently accumulate from a low start point.

The Mathematics of Creativity, Jon Leach, [email protected], 07956 228 589, 17 Somerset Road, Brentford, TW8 8BT

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As Douglas Adams in the Hitchhikers Guide to the Galaxy pointed out, if you could go back 2000 years in time to Rome and invest one pound (or whatever Romans were using back then) in a bank offering just 1% over the rate of inflation, then in the year 2000 you could have withdrawn £439 million (assuming your bank didn’t get pillaged in the Dark Ages).

To personalise this, think about a brand that you have never purchased or thought about that much, but often pops up in the periphery of your vision due to the sheer persistence and consistency of their marketing.

For me it could be Chanel. I probably see it in the duty free shops, I have vague awareness of posters in airports or at Xmas time, or maybe a moody but vacuous TV ad. Its probably one of the double paged ads I flick through at the front of glossy mags, it’s certainly one of several Haute Couture brands that crop up in news stories occasionally. All very “low involvement”, but also a very consistent presence in my life. But not something I actively “buy”.

But, when I examine my feelings, if I found myself, perhaps due to some crisis at the airport, buying some Chanel or maybe receiving a gift, I’d feel pretty good about the brand. I could probably even rationalise in some detail why Chanel was such a good thing, even though I have no recollection of ever consciously deciding that Chanel was fine by me. How have the Chanel creatives done this?

The answer is to do with consistency and patience.

Let’s say that every year Chanel has been investing “love points” into my mind. And let’s say that when those love points approach 100 then I’m officially beguiled.

The Mathematics of Creativity, Jon Leach, [email protected], 07956 228 589, 17 Somerset Road, Brentford, TW8 8BT

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Now rather than go for the big clinch straight away, with one of those “high-impact”, actively processed, 99.9%-er ideas, their strategy has been to gently woo me each and every year.

If this has been going on for about 20 years then we could imagine that they have been wooing me with 5 love points a year to get to the 100. The danger of this approach is that how many of these meagre fivers will I notice and pick up, especially when other noisier brand are offering instant win £99.90-ers? So they may have been doing something more subtle than that.

Perhaps they started quite subtly with just a simple “10 love-pointer” many years ago. I would have barely noticed it, for I was young, foolish and head strong. But then each and every year they used their consistent, low-processing seductions to add 10% compound interest to my Chanel account.

After 10 years they were up to 26 love points, well beneath my threshold and, if I were to consciously think about it, a pretty mediocre candidate for my affections. But they were patient and had a plan….

After 17 years they were half way there but more importantly things were starting to accelerate. For then in a rush of compounding interest, in just 7 more years, 24 years after they had started the process they had got me to 98.5 love points. With our (rather one-sided) silver anniversary approaching I was poised to consummate my relationship with Chanel.

Now the advantage of this strategy is that it avoids the risk associated with trying to conjure up a one in a thousand creative idea. If you fall short – and the odds say you probably will – then your idea will decay in people’s minds and leave no trace.

The Mathematics of Creativity, Jon Leach, [email protected], 07956 228 589, 17 Somerset Road, Brentford, TW8 8BT

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On the other hand, the low processing strategy is not much use if you are in a hurry.

Indeed one of the attractions of the high impact, actively processed style of creativity is that it not only affects minds rapidly, it can also affect populations rapidly too. For if you are “excited” by an idea then you are likely to talk to some other people about it and perhaps “excite” them too. They then can pass this idea on to others and a potent idea can cascade through a population, much like a virus.

This phenomenon has attracted a lot of interest from the advertising industry who frequently deploy ideas that they hope will “go viral” or spread via “word of mouth”. Sometimes they will design ideas that are naturally shareable and sometimes they will try to seed ideas into social influencers or connectors.

Cascades can be very powerful mathematically speaking. Rather than fighting the natural decay rates of creativity or having to wait patiently for the compound interest to kick in, a cascade can create a mathematical avalanche.

Studies amongst populations have shown that if the right idea encounters the right person (this is not easy to do, by the way) then they will typically spread it to 15 other people. They will then on average pass the idea on to about 3 other people (notice the rapid decay here) each who in turn will pass it on to one more each. On average the avalanche stops there, although clearly with more exceptional crazes the thing keeps running until it has reached the whole population.

Looking at this as a formula we can see the power of creative ideas that people want to share:

1 idea : 1 initiator : 15 recipients : 45 recipients : 45 recipients = 106 minds reached.

The Mathematics of Creativity, Jon Leach, [email protected], 07956 228 589, 17 Somerset Road, Brentford, TW8 8BT

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This explains the industries excitement with famous, talk-worthy ideas. By contrast low processed, subconsciously received ideas by definition are not available at the conscious level to be talked about and hence passed on. But we should not be so quick to side line this approach.

Perhaps, it is those people who already have an affinity or appreciation of (to come back to our previous example) Chanel who are the ones who listen to this new message arriving over the bush telegraph. Perhaps it is they, and only they, who feel its value and pass it on.

This pincer movement upon people’s brains may be what is occurring today. Advertisers seem to be obsessed with two things - brand consistency in all their communications and striving for famous, highly talked about interventions. The former makes sure that marketing is a genuine investment that keep compounding away, while the latter will occasionally deliver an idea that not only sticks in individuals mind but also grows of its own accord in the populations collective mind.

******************************

Highly impactful and highly talked are not the same thing as being lovable or popular. Indeed some of the most instantly impactful advertising is intrusive and notorious. How does that sort of creativity work on the human mind?

Let us think about puppies for a moment, in particular Labrador puppies. Most people like, even love, puppies (they feel +2 for puppies) and Andrex regularly show puppies doing lovable things (they show +2 for puppies).

What the adverts do is multiply the two together to generate a +2 x +2 = + 4 feeling for Andrex.

The Mathematics of Creativity, Jon Leach, [email protected], 07956 228 589, 17 Somerset Road, Brentford, TW8 8BT

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If Andrex (stupidly) showed nasty things happening to puppies (showing a minus 2 thing) they would have the opposite effect : +2 x -2 = -4 for Andrex. This is not a major insight, of course.

But what are we to make of the self parodying of Michael Winner in the e-sure ads (or indeed any other ad where they seem to be deliberately trying to rub us up the wrong way)? Why do they use this intrusive, notorious forms of creativity? It seems so negative.

The negativity is the source of their power. If you remember your secondary school maths then -2 times -2 is actually +4 (this is the equivalent of facing the wrong way on a set of stairs and then walking backwards – you end up higher. Or in other words, mathematically, two wrongs do make a right).

So, perhaps how it works is that many people dislike Michael Winner ( feel -2) and the advertisers are showing him in a rather unpleasant mode (show -2). Then with a -2 x -2 = +4 result, we find the name of e-sure firmly embedded in our mind.

Following the maths through, anyone who likes Michael (+2) will end up feeling -4 (+2 x -2) for E-sure as a result of the depiction of their hero. Similarly, if they showed us a kind, sympathetic depiction of the real Winner perhaps many people would also end up feeling -4 for E-sure (no one wants their villains to disappoint in real life).

However the serious point of this is that there is a price to pay for this highly intrusive, non-decaying, highly memorable but ultimately negative style of advertising. And it comes back to the low processing theory.

Chanel will be scrupulous in making sure that all there creative materials have positive, if subtle, associations built in. E-sure, and those who use the -2 x -2 style of advertising, in their determination to be so intrusive are leaving a small but growing trail of negativity behind them. Each (negative) use of the

The Mathematics of Creativity, Jon Leach, [email protected], 07956 228 589, 17 Somerset Road, Brentford, TW8 8BT

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(negative) character leaves a small subconscious stain on our brains even while we have the E-sure brand dancing brightly in our conscious, insurance buying mind. There is a low-processing cost.

Think of it as running an overdraught and never worrying about paying it back. Although the amount of goodwill you withdraw may be small on each occasion, the remorseless power of compound interest will mean that one day when they want to dip into a well of public goodwill they may find that the public has foreclosed on them.

So although the maths of memory suggests that “toxic” advertising is effective in the short term, at some point, some one is going to have to pay for the clean up.

But regardless of how ideas work on the brain, where do ideas come from in the first place…

The Mathematics of Creativity, Jon Leach, [email protected], 07956 228 589, 17 Somerset Road, Brentford, TW8 8BT

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CHAPTER 2

The Geometry of Good Ideas : Ley Lines in the Creative Mind

Ley lines are the geographical phenomenon whereby certain “places of power” like standing circles, ancient churches or cross roads line up in straight lines when examined from the air. For some, these reveal strange mystical and magical lines radiating across the landscape; lines that our ancient forebears could sense and thus mark them with their most sacred constructions.

“Vortices appear to be points of power or energy on the Earth, and ley lines are the relationships between those points. An analogy might be that the vortices are accupressure

points. and the ley lines between them are meridians on the skin of the body of Mother”

For others Ley Lines are no more than statistical co-incidences that occur naturally. These kill joys say they can be created with no more than standard human endeavour and do not require you to get in touch with your Inner Druid.

Now creative ideas can also have an intimidating and rather mystical nature. Are they a rather magical thing; the product of a mysterious alchemy only knowable by a few mystical savants? Do creative people have in built neuronal Ley Lines in their brains where upon magical ideas alight?

Or can any educated person turn base metal into gold if they understand the chemical engineering of the human creative brain?

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I suspect it is the latter. And – apart from overly secretive keepers of the sacred creative brain – this is probably a Good Thing.

But first let us come back to Ley Lines and what we might term the Hippy vs Statistician dispute.

Sceptics have noted that human beings are inveterate pattern spotters and will ascribe “agency” to what may just be a random occurrence : just because three things have formed a straight line doesn’t mean that someone or something planned it this way.

Now there is a spectrum here. Most modern humans won’t ascribe agency to “Cloud Gods” when they see faces in the sky; only the most religious will regard a piece of toast with the face of Jesus as being divinely carbonised; but all of us may be struck by the co-incidence of being phoned by someone “just when I was thinking of you”.

So Ley Lines with their spooky straightness and the clear significance of the objects lining up do seem to resonate with most of us. Sometimes you even get four or five artefacts in a row!

But statisticians have observed that if you throw enough beans on a tray (say about 20) at least three of them will line up just by chance, especially if you are not over fussy about what counts as “straight”.

Now this is just the sort of party pooper-ish comment that you would expect from a soul-less statistician (similar to the question “and how many people did you think of today who didn’t call you at that moment?”). And to drive the point home a young statistican who went on to become a famous name in advertising Simon Broadbent found a way of proving that Ley Lines were extremely likely to be natural co-incidences not mystical artefacts.

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The way he did it is by observing that straight lines made up of three points were really just a sub-set of triangles, namely very flat triangles.

He argued that on a flat surface, whether a mystical Celtic landscape or a tray for bean chucking, when you scatter objects across it (obelisks or beans) by definition, when you draw in the lines, they produce triangles of various shapes and sizes.

So, he observed, given your view on how flat those triangles have to be in order to count as a “straight” line, it was only a matter of adding more and more obelisks/dots (and hence creating more and more triangles) before a Ley Line emerged.

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For the average bean chucker (or obelisk mapper) it was very long odds that just three points would make one of those rare ultra-flat triangles.

Think of it this way: with two points awaiting in the landing zone, the new one has a narrow zone to land in to create a flat triangle.

But suppose the first new stone (the 3rd in total) drops in and misses but suddenly there are now three lines for the next stone to drop in on and make that flat triangle:

The Mathematics of Creativity, Jon Leach, [email protected], 07956 228 589, 17 Somerset Road, Brentford, TW8 8BT

Likely landing zone

Unlikely“Flat triangle” zone

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Put another way, as the fourth stone arrives it creates four possible triangles the original one and the three potential new ones. As more and more stones arrive from the heavens they generate more and more potential triangles to try their luck with the Ley Line Gods.

With five points on the map there are now 8 triangles, six points gives us 13 triangles and so on…

PointsPrior Triangles

New triangles

Total triangles

123 0 1 14 1 3 45 4 4 86 8 5 137 13 6 198 19 7 269 26 8 34

10 34 9 4311 43 10 5312 53 11 6413 64 12 7614 76 13 8915 89 14 10316 103 15 118

So in the county of Cornwall, which Broadbent used as his real life study example, there were dozens of standing stones that you could use as reference points. Now there is obviously a debate about where definite Obelisks stop and random-debris-in-a-vertical-position starts but if you take a relatively low cut off at 30 you still find that there are 433 triangles. And depending on how hard you squint, an awful lot of those are flat. Or Ley Lines if you still insist.

As the table above shows, even 16 stones will give you more than 100 triangles.

The point here – and the one that is important for creativity - is that the more objects you are playing with the greater the chance that they will form a meaningful pattern. What this means is that people who are interested in lots of different things tend to have interesting ideas.

But first we need to tidy up the question of how flat does a triangle have to be in order for it to appear flat/straight?

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Let’s show that a deviation of less than 1 part in 50 (or 2%) is pretty invisible to the human eye. Here is what that looks like. Put a straight line along to see that it does in fact deviate

This is, of course, our mystical very flat triangle:

Then we need to allow for the fact that sometimes, when the third point lands closer to one or other of the two reference dots, kinks will be easier to spot, so we need to draw a splash zone that represents a less than 1 part in 50 deviation wherever the dot lands (the diagram below is not completely to scale)

Finally we have to add in the possible landing zones for our dots that form skewed triangles off to the side (and while we’re at it, limit the dot to landing “in sight” of at least one of the other two dots, otherwise we will have Brittany obelisks lining up with Cornish ones, and that seems like cheating).

If you then divide the area of the splash zone by the total landing zone you discover that it represents about 1% of the total area.

So – using this particular degree of visual acuity - a random comet-like asteroid falling from the sky onto a double dotted patch of land has about a 1 in 100 chance of landing in our splash zone and purely by chance forming a very flat triangle (aka a line). Or to turn it around, there is a 99% chance of it forming a discernibly triangular shape of no interest to hippies or statisticians.

Now at this point non-statisticians go – “oh I get it, with four triangles there would be a 4% chance (1/100 + 1/100 + 1/100 + 1/100). And looking at the

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above table when there are 11 points there is an about an even chance (53%%) of a Ley Line appearing and with 15 points it’s a racing certainty!”

This is an admirable use of mathematics but is not quite right.

Because the more important probability is the stat. of how likely the falling stone misses all the drop zones and fails to form a line.

So we know the probability of the first new point not having a made a line : 99% . But this now with four zones, this leaves a more crowded splash zone for our second new stone (the 5th stone) to land in : it needs to avoid three new splash zones and so this happens only 97% of the time).

Now the game was over if the first new stone aligned up, so for the purpose of our second (no.4) stone we can calculate that there will still be no lines when both the first stone missed (99% chance) AND the second one flunked it (97%). This gives us an incidence of 0.99 x 0.97 or 96.04% of the time.

Or if we turn it round, four random points will make a line only 3.96% of the time. (Incidentally, if you are trying this at home and your four magic beans all align in perfect four point line then don’t be too freaked out – this happens one time in 10,000. Do take a photo though).

Now this 3.96% may look like a trivial distinction from the earlier calculation of 4%.

But what we find when we think about it is that the more and more stones arrive the more crowded it is and the harder each one has to try (excuse me assigning “agency” to them here) to find triangular shapes with ALL the other stones. (The same maths as “Not having the same birthdays in class” applies here). After a while there aren’t enough empty spaces to land in.

This is a bit like trying to find a place to put your towel on a crowded South of France beach. At first it is really easy. Then as the beach fills up you have to boldly insert yourself between families. But at some point, you have to decide if placing your self in a gap that would leave you 10cm away from the topless beauty next door is acceptable.

So to return to our obelisks, for five stones falling at random they have a probability of avoiding creating any straight lines of 91.23% (c.9% chance of a Ley Line), 6 stones make Ley lines about 15% of the time and so on as the table below shows..Points Triangles Probability

1 of no lines23 1 99.00%4 4 96.03%5 9 91.23%6 16 84.84%7 25 77.21%

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8 36 68.71%9 49 59.78%

10 64 50.81%11 81 42.18%12 100 34.16%

This means that a more precise (pedantic?) answer to the enthusiast’s first offering is that it is when there are 10 stones lying around that there is roughly an even chance of them forming a Ley Line.

We can also extend the table to see that there is always a chance that the latest stone to arrive will form a triangle and avoid forming a Ley Line (this is not the case with some French beaches at peak season, by the way). But with the 22nd stone there is less than a 1 in a 100 chance of this happening and with the 29th stone there is less than 1 in 10,000 chance of there being no Ley Lines. Or put the other way round, if you have 30 or so objects lying around it would be extremely unlikely that no “Ley Lines” were found..

Points TrianglesProbability of no line

10 64 50.81%11 81 42.18%12 100 34.16%13 121 26.99%14 144 20.78%15 169 15.59%16 196 11.38%17 225 8.08%18 256 5.57%19 289 3.73%20 324 2.43%21 361 1.53%22 400 0.93%23 441 0.55%24 484 0.31%25 529 0.17%26 576 0.09%27 625 0.05%28 676 0.02%29 729 0.01%

With a bit more maths you can also show that 4 and or 5 point Ley Lines also crop up if you put enough points in your circle of land. So on the whole, Statisticians 1, Hippies Nil.

But what of the Ley Lines of the Creative Mind?

There is a parallel here in that a creative idea can be defined as the point of connection in one person’s mind of two previously unrelated ideas in a way that is recognized and valued by other people.

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So for example, Damien Hirst combines 1) human skulls with 2) diamond encrusted bling and we get 3) the Diamond Skull and an object that is much discussed and photographed (and as proof of its creativity is more valuable than the sum of its two components).

Now the trick here is not just to put together any random ideas to create a third; that just gives you a common or garden triangle.

It’s a bit like with jokes. Linking two things together is the core trick with humour. But it depends how you do it. For example if you combine “Reindeer” with the use of the homophone word “Dear” as a term of affection, you get the following.

The reason you may not have seen that cartoon before is that it isn’t very funny. It’s a triangle. It doesn’t line up. It hasn’t been passed around much. Better ideas are more famous….

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So just as a good Ley Line stops being just three random points, so a good creative idea, (or joke or piece of art) occurs when a new “line” is formed in the creators mind and then in other peoples. The new thing aligns perfectly with the two other things to make a very flat triangle – a line.

But what do we mean by “a line in a mind”? Certainly this is more of a metaphor than a neurological claim (although neurones do form lines). So an idea “feels right” in the sense that it feels aligned and proper. Or shoots off into the distance in a clear purposeful direction (watch people’s eyes as they grasp an idea : as they look away are they seeing it stretch off into the distance).

For those of you of a more musical disposition a good idea may “resonate” or “sound right”. The analogy here is with a musical chord where the frequencies of the three notes have clear and simple mathematical relationships to each other like 2 to 1 or 3 to 2.

Just as human hairs in the cochlea resonate when the right frequency touches them so a great creative idea makes the hair on the back of your neck stand up : it just feels right.

So the art (or craft) of being creative is to create straight lines between disparate ideas. In a world full of unremarkable triangles, it is the very flat ones that stand out.

Now as Steve Martin has observed, “some people have a way with words, and some people not have way”. So a writer like Nabokov can give us this creative metaphor

Shadow of the waxwing slain by the false azure of the window pane.

… where clumsier talents will give us…

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The ballerina rose gracefully en pointe and extended one slender leg behind her, like a dog at a fire hydrant.

Two metaphors, one ugly and misshapen the other perfectly, achingly straight.

Clearly great artists have the ability to pluck Ley Lines out of their minds. Where does this leave the rest of us?

The first skill we can hone is the recognition of straight lines i.e. good creative ideas. For some this may be an innate skill but is also one that can be acquired with practice.

However the practice may be more like sexing chickens than learning how to do long multiplication.

Chicken sexing is the craft of dividing one day old chicken hatchlings into males and females. This is done by examining the rear end of a chicken and from some very subtle clues intuiting which sex it is. Allegedly, the only way to become a chicken sexer is to watch someone else do it for days on end until you just kind of get it. The experts can’t actually describe what it is they are seeing - you just have to let your subconscious tune in to their wave length.

Creative directors in advertising or design agencies (the “editors” of an agencies output) will often review a hundred creative concepts a day. Even allowing for a few days down at Cannes they may well see 10,000 triangles year and must get very good at spotting the straight lines amongst the crooked chaff.

Similarly a young creative team will be generating 100’s of lumpen triangles a week and be told which of them might just be straight enough to work. And so they learn their craft.

So apart from working in a creative agency the advice would be to see and consume a lot, a huge amount of creative work (on TV, in annuals, in galleries, on shelves) and rather than force them to explain “why” something is good/straight/a male chick let the experts give you the benefit of their intuition. Just let it wash over you until you pick it up.

So while it may seem annoying that creative directors often divide creative ideas into “brilliant” and “crap” with nothing in between, perhaps there is something to be said in a world of multiple triangles to have a culture where straight lines are worshipped and anything that is slightly bent is despised. It’s part of the craft culture.

But there is one other thing you can do that relates to how many standing stones you have in your geographical area.

To stick with the analogy that creative ideas are like Ley Lines, in that they are very flat triangles, you may recall that adding in more and more

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points/obelisks increases the chances of a Ley Line appearing. Indeed, if you keep adding in points it becomes increasingly hard not to form a Ley Line.

And that would be a nice situation to be in: really hard not to have a good idea.

So what you often find with creative people is that they are interested in many, many things. Often quite obscure, unrelated topics. And more to the point they are always filling up their brains with new ideas that are unrelated to their immediate creative challenge. I once had lunch with a Creative Director of a top advertising agency and ended up discussing his interests in unreconstructed Tory philosophy, midnight blogging, statistics in Direct Marketing, the merits of German Camper vans over USA ones, and the secret of good Indian food.

This lack of structure and focus can be annoying to more mechanical minds. But to the hunters of the Ley Lines of the human mind, being told to stay focussed on the problem at hand is like asking them to move heavy obelisks around to make straight lines: too much like hard work. They would rather wander off into the glades, find a few new obelisks and conjure up a new line of thinking that way.

What can the rest of us learn from this?

Well firstly as organisations, more mechanically-minded companies should continue to employ outside agencies to work on their creative problems. Not only will a creative agency bring fresh pairs of eyes it also brings people who work on problems outside the category. Applying lessons from seeming unrelated categories can often solve the problem. In fact it makes it hard not to.

And on a personal level the task is to be an interesting person. The best advice on how to be interesting is to be interested. So by all means become a specialist in your industry or category. But also move around a bit. Change companies, or at least projects regularly. Live in a different country.

And finally, also nurture and develop interests in other things in the world however un-commercial or lateral.

These are not just your hobbies or indulgences but valuable personal obelisks you can place upon your own mental plain. And perhaps one day, when you get that mystical feeling of a strange power coursing through you, three of them will have aligned and you too will have a perfect Ley Line in your mind.

Indeed, it’s a statistical inevitability.

But what do you do with this idea once you’ve got it…?

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3. The bonus effect of a thinking partner

Lennon and McCartney*, Dolce and Gabbanna, Saatchi and Saatchi; a regular feature of the creative world is the creative duo. And even us lesser talents often find it easier to work with a good partner when trying to crack a brief. What’s the maths behind working with a partner?

(*Analyzing their collaboration is hard to do as some songs were written “nose to nose”, some were originated by one partner with the other adding and tweaking, and some, while completely attributed to Lennon or McCartney are very much Beatles songs. What the stats do tell us is that as Solo artists Lennon and McCartney created 17 No.1s either side of the Atlantic. Working as a team they created 46. Were they three times more potent together?).

Fairly trivially, on a “1+1 = 2” basis, more would seem to be better. And also fairly clearly, someone who you like working with is more productive than someone you don’t (1 -1 = 0).

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Indeed ideas are not like money (even if they are valuable); when I give you £10 I have £10 less. But when I gift you an idea, I still have it too. So sharing ideas is an instant win for both of us.

But more important is the way ideas don’t just add up when you share them but the way they multiply when they encounter another mind.

Let’s say I have ten ideas and you have ten ideas. If I give you all of mine then you don’t just have twenty ideas but (at least in principle) 100 ideas.

Assuming that you reciprocate, then as a pair we have gone from 10+10 = 20 ideas to 100 + 100 = 200.

This we can take as a theoretical maximum quantity of ideas. Whether the pair can work together to nurture and develop all these ideas depends on how good as a team they are a topic we will get to in a moment. But given the importance of quantity in the creative process (see chapter One) , then working in pairs does seem to increase the chances of producing something good by a large amount.

As an aside, another thing that is going on here is the phenomenon of “creative tension”. If two people are committed to working together then it doesn’t matter if the initial reaction is negative. Here’s how that works:

Lennon : here’s my idea “+2”

McCartney : I don’t like XYZ about that idea +2 x -2 = -4

Lennon: you’re wrong about that because of ABC -4 x -2 = +8

McCartney: I love what you did there because now I can see PQR +8 x +2 = +16

Lennon : we’ve cracked it!

(note the “we”)

Now all of this is not to encourage people to be routinely negative about ideas; the phenomenon of creative tension is best seen in high trust, highly

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committed partnerships where honesty is helpful and is delivered with “positive intent”.

But this does highlight the second aspect of a successful creative partnership: working with someone who is good at nurturing your creative ideas.

Ideas are incredibly vulnerable entities when they first appear. Like pre-mature babies, if not rapidly incubated then they will expire. However, if they can survive those first critical minutes then even the oddest, ugliest, scrawniest idea can grow up to be a Nobel Prize winner.

Similarly, in the middle of World War One, young officers had extremely high mortality rates when serving in the front line. But rather than there being a steady attrition rate for all front line officers, it was the newest arrivals that tended to get killed. Indeed, if you could survive the critical first few days and learn your trench warfare survival skills (which could not be taught at Sandhurst) then you had a fair chance of surviving your tour of duty.

And so it is with your creative ideas, as they stagger out into the hostile landscape of other people’s opinions. What they really need is a friendly NCO who can stop them getting blown up in those first, most deadly moments.

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In creative terms you need a partner who is sufficiently positive and “gets what you really mean” as your naïve, fresh faced ideas present themselves at the front line. Perhaps as a rule of thumb, you need someone who can talk about any of your ideas for five minutes without you losing your nerve and killing the idea your self.

Now no one has a 100% confidence in their ideas so let’s say you send one of your ideas over the top with 90% confidence that it’s a contender for greatness.

If you have a good partner who can talk about this idea with the same degree of support as you, then it will have a survival rating of .9 x .9 or 81% after the first minute. But even if this continues with the same degree of positivity and empathy then as it crosses this dangerous conversational no mans land it’s survival chances drop as follows

After one minute 81%Two minutes 73%Three minutes 65%Four minutes 59%Five minutes 53%

At this point, we don’t know if the idea is going to be a great one (this will only be revealed in the long term), but it still being above the 50:50 line after five minutes can be taken as it being more alive than dead and so it lives to fight another day.

But, contrast this with working with a partner who, while very positive perhaps they don’t quite “get” you. Let’s say they are just 10% less good at nurturing your ideas. Tragically, with Sergeant 80% your ideas are a lot less likely to survive:

After one minute 72%Two minutes 58% Three minutes 46%Four minutes 37%Five minutes 29%

Using the 50% survival line notion, in the third minute the idea is fatally wounded : you’ve lost confidence in it and so has your partner. You might spend two more minutes thrashing about in the mud but it’s a goner.

Just for the record anyone who is less than 50% supportive can kill an idea instantly (50% of 90% is 45%). But even working with Mr 70% or Mr 60% you will see your ideas die in 2 minutes or less.

All of this is about believing in ideas.

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(I once worked with a Creative Director who had three responses to creative work “yeah”, “yeah, yeah!” and “yeah, yeah, yeah!!!”. He kept many young whipper snapper of an idea alive in the bloody warfare of 90’s advertising).

You, if no one else, needs to believe that your (crazy) idea might just work. Even better is to have a creative partner who can suspend their disbelief for long enough to walk along beside you and see where your new idea goes.

In cartoons, characters can walk off the edge of a cliff and defy gravity AS LONG AS THEY DON’T LOOK DOWN. If you (or your partner) start doubting an idea and “look down” then it will fall out of the sky. What you need is a partner who will take a few steps with you across the “Suspension Bridge of Disbelief” because if you take enough steps you may just find that you have got to the other side of the chasm.

Good creative partners are those who can look into the distance (“share your creative vision”) with you and help you skip gleefully towards it, ignoring the insanity of what you are both doing. It’s a magical feeling when it happens and as such, when you look back, you can’t quite remember how you did it.

You just know that “we” did.

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(Link to next chapter)

As with sex, generating ideas in pairs is usually more fun (and ultimately more productive) than doing it on your own. But it does not follow that doing it in threes (or more) is even better. In fact, as we shall see in the following chapters, it tends to complicates things….

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(note to reader : the other chapters are avilable in a similar form as above)

Section Two : the maths of group creativity

4. A Formula for Creative Meetings

5. Calculating the Ideal Size of a Creative Meeting

6. The Predictable Nature of Breakthrough Meetings

Section Three : the maths of the creative business

7. The Hard Sums of Commercial Creativity

8. Thriving in the Chaotic Zone : Why Creative Agencies Exist

9. The Maths of Being a Good Client

10. Summary : how to be 100% more creative in ten easy steps

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