The Fibonacci Framework

Unlocking the unknowable

August 3, 2011
by Ian
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Maths, Music, Chartres and Me

Having had a week to reflect on the BBC2 programme ‘The Code’, there is one thought that has stood out for me. It is a thought that ties into much of the thinking we have been doing around the Fibonacci Framework and it is a thought that is capable of keeping me thinking for some time to come.

In episode 1 of The Code, Marcus du Sautoy pointed out a connection between harmony in music and architecture. The ratio between the frequencies of two notes an octave apart is 2:1. The ratio between the two notes of a perfect 5th is 3:2. A perfect 4th has a frequency ratio of 4:3 and finally the two notes of a minor 6th is 8:5. It turns out that sounds we think of as pleasant are always made up of sounds with frequencies that relate to one  another in simple ratios. At the same time, the more complex the ratios the more dissonant the sound. Nature adopts these sounds as alarm calls.

In Chartres Cathedral, and in many other buildings, these harmonic ratios are translated into the architecture of a magnificent structure. It appears that not only do these ratios define the sounds we find pleasing but also the physical proportions of beauty.

Whether you see this ‘code’ as evidence of a creator God or simply the maths underpinning the universe it raises some fascinating questions about us. Given that these proportions exist in nature and are hard wired into our brains as defining beauty and harmony what other proportions have this effect on us?

In his work on the neuro-science of leadership David Rock has proposed a model that consists of 5 characteristics that each of us looks for in life. If any of these five characteristics of life are challenged our brains are hard wired to respond at a instinctive level of ‘fight or flight’. The five elements of the model are Status, Certainty, Autonomy, Relatedness and Fairness. In other words, it is built into us to recognise that these elements are among the essential ingredients of a fulfilling life. All five of these ingredients relate to the way we, as unique individuals, understand ourselves to be interacting with the world.

In the Fibonacci framework this interface with the world is explored in stages 2 and 3 where the following topics are considered:

Stage 1: VALUES – PURPOSE – PASSION

Stage 2: PERSONALITY – STRENGTHS – SKILLS

We are not suggesting that these 6 ingredients are the only ingredients to a successful and satisfying life/ business. We simply propose them as places to begin the exploration. What does seem to become more and more apparent is that life has a set of basic proportions and ratios that define success, beauty, joy and fulfilment. The detailed application of these proportions in the architecture of a life or business will be unique to the individual but the raw proportions may yet turn out to be common to all.

July 29, 2011
by Ian
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A comfortable interface with the world – 1. Values

The recent scandal over phone hacking is a fascinating insight into our society. Perhaps more chilling than the hacking itself is the cycle that becomes visible within the media and our appetite for scandal. In order to satisfy our insatiable appetite for scandal and gossip the News of the World engaged in illegal behaviour. Now the source of the gossip and scandal that was so eagerly consumed has been revealed it has itself become the object of those self-same desires that gave it birth. Whilst there are clearly questions that need to be asked about the extent of this behaviour (was it confined to News of the World?), the whole issue of values is now in open discussion. On the surface this must be a good thing but there is always the possibility that the focus on the values in one organisation distracts us from the question over our own values in our society.

In his latest blog article Umair Haque raises a penetrating question: is the excess of the super-rich merely a reflection of our own “monstrous appetites.” We have been outraged by the values that led to the banking crisis. We are outraged by the values that lead journalists to hack people’s phones. So we should be, but sometimes outrage can distract us from self-reflection.

Values are one of the most fundamental interfaces between the unique individual and the world. Alongside our individual sense of purpose and our passions, our values are a profound expression of the self. Values are the expression of those things that we hold to be fundamentally important. They are often expressed in single words. Values are not moral statements, though morality may be a value. You may have fun, adventure or family as a value. As Laura Whitworth put it: “Values are the qualities of a life lived fully from the inside out.” Whatever your values are, life will be uncomfortable if you are living in opposition to them. Understanding your values will both add to your understanding of your unique individuality and enable you to be who you are in the world you occupy.

July 27, 2011
by Ian
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Uniqueness and individuality at the core of an organisation

There is a view of society or of organisations that sees the individual as its antithesis. Cohesion is understood to rely on conformity and conformity is understood to be absolute. Some years ago talking to a friend they mentioned the view that in order to work for a certain soft-drinks manufacturer you had to have a transfusion in which your blood was replaced with their headline product. Dictatorships around the world often seek to impose absolute conformity of thought and action but in doing so they store up the ingredients of their own downfall. Suppressing individual uniqueness is like trying to contain a gas under ever increasing pressure. An explosion is an inevitability. The unique individuality expressed in the human race is irrepressible.

The question then is how can you allow people to be themselves in such a way that brings you success? The answer requires courage and faith.

It is possible that you may have to allow people to express their uniqueness by leaving you. This is not a loss to you or to them. These people will not have been engaged in their work and it is better for you and for them that they be allowed to go. The key is to think of your employees as willing followers rather than as bond-slaves. This, in turn, requires that you see yourself as a leader.

1n 1943 Abraham Maslow published a paper entitled: “A Theory of Human Motivation” in which he postulated his, now well known, hierarchy of human needs. Whilst monetary reward can permeate as far up the hierarchy as ‘Esteem Needs’, by the time it gets there it is a very flimsy platform. In a modern society income will enable us to meet our physiological needs. Income may contribute to a sense of safety and it may enable our social interaction. It is clear that income rapidly declines in its significance as a motivator. More recent research has suggested that human needs ought to be thought of in terms of a network as opposed to a hierarchy but the basic conclusions regarding the limitations of income as a motivator remain valid.

For years our system of recruitment has centred on financial reward. We have thought generically and have focused on financial reward. Rather than look for people who are in tune with our vision we have assumed that anyone with the right skills will thrive if given enough of a financial incentive. The problem is that we end up with drones whose individual uniqueness is suppressed in favour of financial wealth.

What if you revolutionised your recruitment. What if you prioritised passion? What if you looked for people who believed in what you are trying to achieve and whose personal uniqueness aligns with uniqueness of your organisation? What if you recruited people who would have followed you even if they couldn’t get a job with you?

Consider the books you have read that were written by successful business people. They will fall into two categories. Some will have been interesting, you will have learned from them but they left you cold. You took the lessons learned and moved on. Some, probably only a few, will have left you longing to work for the author. I could list two or three books that have left me ready to drop everything for the right opportunity. The opportunities never came and I did not pursue them and yet I remain an admirer of the businesses concerned. They are on my list of organisations I would like to work with. My motivation is not financial reward but belief and a sense of empathy with the organisational values and objectives.

What if the unique individuals at the heart of your organisation felt the same way? How would that change the levels of engagement and commitment? How would productivity be improved? How would staff retention be affected?

At the centre of the Fibonacci Framework are two considerations for any organisation. The first is a consideration of the uniqueness of the organisation. The second is an understanding of the value of the uniqueness of every individual within the organisation.

Imagine for a moment you could stand back from your organisation and in one glance take in its entire shape. At first it may appear to have some regularity, you may even be tempted to caricature it as being like a regular geometric shape. As you look more closely the shape is irregular and hard to describe. In fact, your initial representation is seen to skew certain aspects.

When mapmakers tried to map the coastline of Britain they ran into a problem. Different scales of map rendered significantly different lengths for the coastline. They realised that the closer they looked, the more detailed and longer the coastline became.

Returning to your image of your organisation, it is worth noting the way closer examination changes the proportions and shapes of its outline.

Imagine now that you could put your organisation under a microscope in order to view its internal structures. What do you see?

It is now recognised that throughout nature there are irregular shapes that do not conform to the shapes of regular geometry. As useful as are the squares, rectangles, triangles and polygons that we learned to draw and measure in school, they rarely occur in nature. What is fascinating is that group of irregular shapes whose parts reflect the whole. The closer one examines these shapes the more evident this self-similarity becomes. The whole is to the parts as the parts are to the whole. These shapes are referred to as ‘fractals.’

As we journey out along the Fibonacci Framework we will discover the explanations for this self-similarity in a healthy organisation. In doing so we will be enabled to explore the proportionality that makes an organisation a thing of beauty. For now, it is enough to note that the relationship between the organisation and the unique individuals within it can be profound.

When the right individuals form the parts of an organisation then their uniqueness will bear a similarity to the uniqueness of the business. The organisation will reflect its constituent individuals and the individuals will reflect the uniqueness of the business. This ‘fractal’ quality will enhance productivity and profitability. Rather than employing people whose commitment is bought with a salary the organisation will be made up of people who believe in the essence of the organisation. Such employees will find greater levels of fulfilment which will express itself in higher levels of engagement and productivity.

July 26, 2011
by Ian
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Personal individuality and uniqueness

Having previously stated that the centre of everything must be the unique one we must begin our exploration of the Fibonacci Framework with the individual. The framework has applications for both personal and organisational development but in both cases the starting point  is the uniqueness of the individual.

How does one begin to define uniqueness? The very act of definition requires comparison. Whilst in Zambia some years ago a friend and I found ourselves in an open air restaurant by the side of the great Zambezi River. One of the meats cooking on the grill that night was crocodile. We ate and we tried to articulate what we were tasting. The best we could come up with was ‘fishy tasting chicken.’ Actually I had never tasted meat that was quite like crocodile but description without comparison was impossible.

With this in mind it may be helpful to begin an exploration of what individuality and uniqueness are not. Neither individuality nor uniqueness imply a lack of similarity. On the most basic level there are physical characteristics that define us as human. We can also categorise psychological characteristics. The building blocks that form our uniqueness and individuality are not themselves unique.  What defines our uniqueness is the combination of those building blocks.

Perhaps we need to go further. In the days of Charles Darwin the cell appeared to be a simple structure. With the understanding of his day it seemed reasonable to postulate the idea of the simple, single-celled organism. With today’s more powerful microscopes we know that the organisms that appeared so ‘simple’ are in fact complex. The similarities between people may also be an over simplification. The building blocks that create those similar characteristics may be dissimilar on closer examination. That is to say that completely different building blocks may lead to an impression of similarity.

Think back to when you were in your early biology lessons drawing diagrams of a cell. Animal cells were round and plant cells were square. At this level of study all animal cells were similar. Now recall what you know about the role of DNA within the nucleus of the cell. Can you still consider all animal cells to be similar? On closer examination cells have many different functions and, such is the complexity of our genetic programming, your skin cells are different to mine.

I am similar to you in so many ways and yet there is no one like me and no one like you. Our uniqueness is a combination of genetics and experience, of nature and nurture. We are unique and we haven’t even touched on the mystery of the human soul. Genetics and nurture fail to explain the unique response of every individual to both their genetic coding and the experiences of their lives.

One of the most profound journeys a man or a woman can make is the journey to the centre of self. A journey that travels in from life as it is lived to contemplate personal uniqueness. This is a profound journey indeed but it is only half of the journey. The journey is not complete until one journeys out from this newly understood centre back into a world that is fresh with new possibilities.

In the centre of the Fibonacci Framework is a quiet centre. It may not be a place that can be described. It is perhaps, in part, a place of mindfulness. It is a comfortable place in which I am me and I am happy to be me.

If this place can be described it may be best described by the almost abstract ways in which the brain processes our experiences. This is a world of metaphor. A collage of sound, sight and sensation. This place is explored in terms of the sub-modalities of our representational systems. It is not so much an experience to be communicated as one to be known.

I am me and I am the building block of my life. In my uniqueness I already have all the resources I need. These resources are not specific skills that may or may not have been acquired. They are the resourcefulness of my person to be everything I can be in every situation in which I find myself. In my uniqueness there is potential for an unimagined variety of possibilities.

July 25, 2011
by Ian
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There exists exactly one

In maths the designation ‘E!’ (the ‘E’ should be reversed but at present I can’t get the blog to accept the character) indicates uniqueness. It lies at the centre of the Fibonacci Framework. When one accepts that every individual human being is unique there is an inevitable conclusion: individual uniqueness is the centre and root of all human systems.

At the top left hand corner of the periodic table is Hydrogen with an atomic number of 1. Hydrogen is said to be the building block of everything. The hydrogen atom with its single electron and single neutron is the starting point for the construction of all chemical elements. When hydrogen gains a neutron it becomes deuterium or ‘heavy hydrogen.’ When two deuterium atoms fuse you get Helium and as more protons and neutrons are added so the elements are formed.

So what has this to do with you or with the organisation for which you work? Scientifically the answer is – nothing. Conceptually, the answer is more interesting. Imagine for a moment that the unique individual at the centre of our framework is a hydrogen atom. Where does that take your thoughts with regards to the possibilities that are inherent in every individual?

Some years ago a theoretical physicist, Geoffrey West, working out of the Santa Fe Institute measured the relationship between the levels of innovation and the size of a city. West discovered that innovation rises by a quarter power law in relationship to the size of the city. He discovered that a city that was 10 times larger than its neighbour was 17 times more innovative. The more individual atoms there are in proximity to one another the more possibilities exist.

Before we get carried away with the possibilities that exist further out on our framework it is important to pause and take in the vital contribution of the one in the centre of the framework. All potential lies in this unique one.

Thousands of years before scientists could describe the hydrogen atom another thinker pointed us to a similar thought. For Pythagoras all geometry began with a single point – the monad. In a fascinating quirk of history the monad, very like the hydrogen atom, was depicted as the point at the centre of a circle. Taking a point on the circumference of the circle the pythagoreans drew a second circle that intersected the monad. The two centre points were then joined with a line to form a ‘dyad’. A third point at the intersection of the two circles is used to form an equilateral triangle (the tryad). Further triangles can be formed to creates, squares, hexagons and the decad.

Once again the maths and geometry are merely a springboard for reflection. Pythagoras believed that the monad was the beginning of everything and that the dyad was the reflection of the monad and that out of this reflection came all the possibilities of geometry.

Once again we are brought to the one in the centre in which all possibilities exist. A unique entity from which all else grows and finds existence.

July 23, 2011
by Ian
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The individual at the centre

There are times when it is useful to distinguish between being and doing, what you are and what you do. There is a tinge of sadness in hearing someone identify themselves with the occupation for which they are paid. The words: “I am a ….” Can be anything from an unfortunate turn of phrase to a defining  statement. The inadequacy of the words “I am a…” are exposed by simply pausing and realising the number of such statements we can make about ourselves at any one time.

Take some time to write out the various ways you could complete the sentence “I am…” You will probably find that each one is specific to a context or relationship. Remove some of them from that context and you might find yourself in deep water.

Having recognised the potential poverty of these statements we need to recognise that what I do is an expression of who/ what I am. More precisely, the way I do what I do is an expression of who I am. When people persuade themselves to act in a way that conflicts with who/ what they are there will always be problems. We simply cannot sustain a life that denies our intrinsic identity.

There is an assumption that runs through this book. That assumption is that you exist. That is to say, that there is a core ‘you’, a real and authentic ‘you’. What is more, we will assume that ‘you’ are unique. There is no one like you. If you are a printer the statement ‘I am a printer’ cannot distinguish you from other printers. Likewise when I say ‘I am a father’, so are many other men.

In the 1950s Ludwig Wittgenstein argued that a word only gained meaning in its context. To illustrate this Wittgenstein challenged people to define the word ‘game.’ Without a context the word is meaningless and yet we are able to understand it and even correct its definition when it is used in context. As individuals we can come to a similar view of ourselves. We come to define ourselves according to our context. This approach will always lead to conformity, to blandness and to monotone groupings. At worst we will lose ourselves and at best we will lack any real sense of fulfilment. When organisations value conformity too highly then they too will become bland and colourless. Levels of engagement will be low and quality people will rarely stay.

A nodding agreement to this kind of thinking is easy. What is far more challenging is when you will stop and consider who you are separate from your context. Try to describe yourself without reference to context or relationships. To what extent is your personal definition reliant on reference to others?

In the town in which I spent my teenage years there was an undercover shopping centre in which there was a fountain and pool surrounded by benches. Every Saturday this space was occupied by ‘the punks’. On one level each of the gang was different. Their brightly coloured Mohican haircuts, body piercing and tartan bondage trousers made them stand out. They were the embodiment of the rejection of conformity and yet they were also the embodiment of conformity to their own social group. It would have been pointless, not to say dangerous, to arrive in a green parka with an RAF roundel on the back and claim to be a punk. If as apunk you rejected conformity you would never dress like a ‘mod’.

Group think is both essential and stifling. Without some level of conformity society could not exist. Every relationship shapes us. The ability to adapt is essential to good communication and functional society. This is not ‘bad’ but it is challenging to our uniqueness.

The question is: how do we create a society of the unique? How do I fit in without denying who I am? What will organisations gain when they encourage and exploit individual uniqueness? How will such organisations maintain their values? What would it mean to be who you are and to let yourself fill the space you currently occupy?

July 23, 2011
by Ian
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Introducing Fibonacci

What can the world learn from a man whose name translates into English as ‘Blockhead’? The question seems to be both necessary and judgemental. Perhaps most disturbing is the thought that we are constantly making these kind of judgments about others and about ourselves. All too often we can ignore the unique potential of a person on the basis of their name or their appearance. All too often we fail to realise our own potential because we are forced to fit into a mould or we feel obliged to live the lives others expect us to live. The result is that we are often robbed of possibilities and the economy is robbed of our unique contribution.

In 1202 Leonardo Pisano, more commonly known as Fibonacci (Blockhead/ son of a simpleton) released his Liber Abaci (Book of the Abacus). This work became the foundation of western mathematics. Perhaps best known from this book is the series of numbers now known as the Fibonacci series. The author had set about to resolve the problem of the multiplication of breeding rabbits. The result was a series of numbers that is arrived at by each number being the sum of the two previous numbers – 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377….

Perhaps more significant is the discovery that if you divide any of these numbers by the next higher number then, from 3 to 89 the answer is always 0.625. After 89 the answer is always 0.618. Similarly if you divide any of the numbers in the series by the preceding number then, after 2 the answer is 1.6 and after 144 the answer is always 1.618.

The Greeks called this pattern ‘The Golden Mean’ and it appears everywhere both in nature and in man-made structures. The ratios contained within the Fibonacci series create a mathematical definition of what constitutes beauty. Each number is unique and each number makes a vital contribution to the proportionality of the whole. These ratios appear in flowers, in leaves, in the human finger and the human face. We may not grasp the maths but our brains appreciate the beauty of the proportionality.

One manifestation of the Fibonnaci series is the Fibonacci Spiral. A grid is created beginning with a 1 unit square to which a second identical square is attached. To these a 2 unit square is attached where it fits. This same process is followed as squares are attached of 3, 5, 8, 13, 21, 34…. units

Starting with the smallest squares, quarter circle arcs are used to connect the opposite corners of the squares.

It turns out that this spiral is also found in nature from sea shells to flower heads. The Fibonacci Series turns out to be a profound insight into mathematical proportionality in nature and in  that which is perceived as beautiful to the human eye. Not bad for the contribution of a ‘Blockhead’.