The Sigmoid Curve

The Road to Davy’s Bar

The Wicklow Mountains lie just outside Dublin in Ireland. It is an area of wild beauty, a place to which, as an Irishman born near there, I return as often as I may. It is still a bare and lonely place, with unmarked roads, and I still get lost.

Once, I stopped and asked the way. ‘Sure, it’s easy,’ the local replied. ‘Just keep going the way you are, straight ahead, and after a while you’ll cross a small bridge with Davy’s Bar on the far side, you can’t miss it!’ ‘Yes, I’ve got that,’ I said, ‘straight on to Davy’s Bar.’ ‘That’s right. Well, half a mile before you get there, turn to your right up the hill.’

It seemed so logical that I thanked him and drove off. By the time I realised that the logic made no sense he had disappeared. As I made my way down to Davy’s Bar wondering which of the roads to the right to take, I reflected that he had just given me a vivid example of paradox, perhaps even the paradox of our times: by the time you know where you ought to go, it’s too late to get there; or, more dramatically, if you keep on going the way you are, you will miss the road to the future.

Because, like my Irishman, it is easy to explain things looking backwards, we think we can then predict them forwards. It doesn’t work, as many economists know to their cost. The world keeps changing. It is one of the paradoxes of success that the things and the ways which got you where you are, are seldom the things to keep you there. If you think that they are, and that you know the way to the future because it is a continuation of where you’ve come from, you may well end up in Davy’s Bar, with nothing left but a change to drown your sorrows and reminisce about times past.

Although he knew it not, my Irish friend had also introduced me to the Sigmoid Curve, the curve which explains so many of our present discontents and confusions. It is this curve, and what follows from it, which is the first of the Pathways through Paradox, the first of the three devices for finding a balance between the contradictions.

The Sigmoid Curve

The Sigmoid Curve is the S-shaped curve which has intrigued people since time began.


The Sigmoid Curve sums up the story of life itself. We start slowly, experimentally and falteringly, we wax and then we wane. It is the story of the British Empire - and of the Russian Empire and of all empires always. It is the story of a product’s life-cycle and of many a corporation’s rise and fall. It even describes the course of love and of relationships. If that were all it would be a depressing image, with nothing to discuss except to decide where precisely on the curve one is now, and what units of time should go on the scale at the bottom. Those units of time are also getting depressingly small. They used to be decades, perhaps even generations. Now they are years, sometimes months. The accelerating pace of change shrinks every Sigmoid Curve.

Luckily, there is life beyond the curve. The secret of constant growth is to start a new Sigmoid Curve before the first one peters out. The right place to start that second curve is at point A, where there is the time, as well as the resources and the energy, to get the new curve through its initial explorations and flounderings before the first curve begins to dip downwards.


That would seem obvious; were it not for the fact that at point A all the messages coming through to the individual or the institution are that everything is going fine, that it would be folly to change when the current recipes are working so well. All that we know of change, be it personal change or change in organisations, tells us that the real energy for change only comes when you are looking disaster in the face, at point B on the first curve.

At this point, however, it is going to require a mighty effort to drag oneself up to where, by now, one should be on the second curve. To make it worse, the current leaders are now discredited because they are seen to have led the organisation down the hill, resources are depleted and energies are low. For an individual, an event like redundancy typically takes place at point B. It is hard, at that point, to mobilise the resources or to restore the credibility which one had at the peak. We should not be surprised, therefore, that people get depressed at this point or that institutions invariably start the change process, if they leave it until point B, by bringing in new people at the top, because only people who are new to the situation will have the credibility and the different vision to lift the place back on to the second curve.

Wise are they who start the second curve at point A, because that is the Pathway through Paradox, the way to build a new future while maintaining the present. Even then, however, the problems do not end. The second curve, be it a new product, a new way of operating, a new strategy or a new culture, is going to be noticeably different from the old. It has to be. The people also have to be different. Those who lead the second curve are not going to be the people who led the first curve. For one thing, the continuing responsibility of those original leaders is to keep that first curve going long enough to support the early stages of the second curve. For another, they will find it temperamentally difficult to abandon their first curve while it is doing so well, even if they recognise, intellectually, that a new curve is needed. For a time, therefore, new ideas and new people have to coexist with the old until the second curve is established and the first begins to wane.

The hatched area beneath the peak is, therefore, a time of great confusion. Two groups of people, or more, and two sets of ideas are competing for the future. No matter how wise and benevolent they be, the leaders of the first curve must worry about their own futures when their curve begins to die. It requires great foresight, and even greater magnanimity, to foster others and plan one’s own departure or demise. Those who can do it, however, will ensure the renewal and the continued growth of their organisation.

I cannot pretend that is easy even with that foresight. I have sat and watched the chairman of a great company speak to his assembled barons. ‘I have two messages for you today,’ he said. ‘First, I want to remind you that we are very successful business, perhaps more successful today than we have ever been. Secondly, I must tell you that if we want to continue to be successful we shall have to change, fundamentally, the way we are working now.’ He went on to explain why the different futures he foresaw would require different responses, but no one was listening. The first message had drowned out the second. If they were so successful, they felt, it would be folly to change. He was right; he was standing at point A and looking over the hill, but he could not get his changes implemented. Three years later, by now at point B, the company knew it had to change but the first person they turned on, and removed, was the chairman. He was no longer credible, nor had his conviction that he was right endeared him to his colleagues.

What is true of organisations is as true of individuals and their relationships. A good life is probably a succession of second curves, started before the first curve fades. Lives and priorities change as one grows up and older. Every relationship will sometimes need its second curve. Too often, couples cling on to their old habits and contracts for too long. By the time they realise their need of that second curve they are already at point B. It is too late to do it together. They find other partners. On the other hand, I sometimes like to say, teasingly, that I am on my second marriage - but with the same partner, which makes it less expensive. Because we managed, in time, to find that very different second curve - together. I would not deny, however, that the hatched period beneath the peak was difficult, as we struggled to keep what was best in our past while we experimented with the new.

Capitalism, newly triumphant, probably has to reinvent itself. Things which we took for granted, like nation states and large organisations, seem to be impediments to progress not its helpers. When both monarchy and the judiciary, in Britain, are seen to be wanting, few institutions in that country can be sure that they are still on the upward curve. We ask our politicians for a lead, by which we mean a sight of the second curve, but we want them, all the same, to do nothing to disturb the first curve. In our own lives we sense that there is often another hill to climb now that life is longer and, in many ways, larger, but we have no sense of where to find it. We are, so many of us, living in that hatched area, worrying that the first curve will turn down before we find the second.

The second curve is the road up the hill to the right. We stand today at the crossroads, asking the way to our future. Words like hierarchy, loyalty and duty, no longer carry the weight they once did. Other words like freedom, choice and rights turn out to be more complicated than they seemed. What was once obvious, like the necessity of economic growth, is now hedged around with qualifications. We thought we knew how to run organisations, but the organisations of today bear no resemblance to the ones we knew, and so we have to think again, to find the second curve of management before it is too late. Meanwhile, we have to keep the first curve going. As long as we can do that, we will keep the balance between the present and the future; we can manage to live with paradox because we understand what is happening.

The Discipline of the Second Curve

The concept of the Sigmoid Curve has, I find, helped many people and many institutions to understand their current confusions. The question which they always ask, however, is ‘How do we know where we are on the first curve?’ One way of answering that is to ask them to make their own private and personal assessment of their position, or that of their organisation, to draw the first curve as they see it, and to mark an X on it to show where they are now. Almost invariably, when they reveal their perceptions of the curve, here is a consensus that they are farther along the curve that any of them would previously have admitted. They are nearer to point B than to point A.

Like the story of the road to Davy’s Bar, you will only know for sure where you are on the curve when you look back. It is easier, too, to see where others are on their curves than to see yourself. We must therefore proceed by guess and assumption. There is no science for this sort of thing.

The discipline of the second curve requires that you always assume that you are near the peak of the first curve, at point A, and should therefore be starting to prepare a second curve. Organisations should assume that their present strategies will need to be replaced within two or three years and that their product life-cycles are shorter than they were. Richard Foster of McKinsey studied 208 companies over 18 years in order to discover those who were consistently successful. There were only three who lasted the course for the whole 18 years. Fifty-three per cent could not maintain their record for more than two years. Individuals should also work on the assumption that life will not continue as it has for ever and that a new direction will be needed in two or three years.

It may well be that the assumption turns out to be wrong, that the present trends can be prolonged much longer, and that the first curve was really only in its infancy. Nothing has been lost. Only the exploratory phase of the second curve has been done. No major commitments will have been undertaken until the second curve overtakes the first, which will never happen as long as the first curve is still on the rise. Keeping the two curves going will become a habit.

The discipline of devising that second curve will, however, have had its effect. It will have forced one to challenge the assumptions underlying the first curve and to devise some possible alternatives. It is tempting to think that the world has always been arranged the way it is and to delude ourselves that nothing will ever change. The discipline of the second curve keeps one skeptical, curious and inventive - attitudes essential in a time of change, and the best way of coping with the contradictions which accompany such a time.

The discipline of the second curve follows the traditional four-stage cycle of discovery. Questions start it off. The questions spark off ideas, possibilities, hypotheses. The best of these must then be tested out, tentatively and experimentally. Finally, the results of the experiments are reviewed. The first two stages cost nothing except the time for imagination. They can be very stimulating, particularly if they start from the greenfield hypothesis - ‘If we did not exist would we reinvent ourselves and, if so, what would we look like?’ Or, in a more personal example of second curve thinking, ‘If we did not live here, or do what we are doing, what would we be doing, where and how would we be living if we had the chance to start again?’ The discipline of the second curve requires that you do not reinvent the same life, because that would merely perpetuate the first curve. The second curve is always different, although it builds on the first and grows out of it.

In The Paradox of Success, his book on the personal renewal of leaders, John O’Neil uses the model of the second curve to describe how leaders do, or do not, move on in life. He points out that one essential is to let go of your past. If one is too emotionally attached to what has gone before, it is difficult to be different in any way. One can then cling on until it is too late. He quotes Odysseus as an example of a young warrior chief who was so committed to roaming and raiding, at which he once excelled, that he spent 20 years coming back from the war in Troy to his kingdom of Ithaca, reluctant to assume the responsibilities of government. By the time he did get home he was a failed commander, in rags, with his kingdom in a mess. It is the story of the man who did not want to grow up.

If success comes early, it can be particularly hard to turn one’s back on it when one’s star begins to wane. It was sad to watch Bjorn Borg return to the tennis courts in an attempt to recapture past glories, long after his talents had faded. It is often easier to move on from disasters than from successes. I have always, therefore, been impressed by people like Leonard Cheshire, the distinguished and heroic British fighter pilot who, after the war was over, left all that behind and set out to create a network of homes for the elderly and disabled. I am impressed by the family business in France which, at just the right time, turned its back on the textile industry in which it had made its name, and launched a chain of supermarkets. ‘Where did you find the courage to do something so completely different?’ I asked. ‘It would have required more courage to do nothing,’ the head of the family replied. ‘We had the responsibility to provide a future for the family, and the past, distinguished though it was, could not have been that future.’

Curvilinear Logic

Moving on requires a belief in what Schumacher used to call curvilinear logic, the conviction that the world and everything in it really is a Sigmoid Curve, that everything has its ups and then its downs, and that nothing lasts for ever or was there for ever. Just-In-Time Manufacturing was developed in Japan, and later copied everywhere. The idea of a constant stream of deliveries to your factory door, as and when you needed them, was blindingly obvious when you thought about it. Cut out the warehouse and all those storage costs. Let the suppliers carry the inventory costs instead, or rather, eliminate them completely, provided always that you can guarantee that the lorries with the bits will arrive ‘just-in-time’. Unfortunately, the idea became too popular. They tell me that the delivery vehicles now jam all the freeways around Tokyo, meaning that just-in time often gives way to just-too-late. The costs of the traffic jams are beginning to outweigh the costs of the original warehouses, to say nothing of all the environmental damage caused by those idling exhausts. You can have too much of a good thing, or, curvilinear logic strikes again.

Curvilinear logic is not intuitively obvious if you are still ascending the first curve. Business history is littered with the stories of founding fathers who thought that their way was the only way. The French textile business mentioned above is a notable rarity among family businesses. The paradox of success, that what got you where you are won’t keep you where you are, is a hard lesson to learn. Curvilinear logic means starting life over again, something which gets harder as one gets older. It is better, therefore, in organisations, to entrust the curvilinear thinking to the next generation. They can see more clearly where the first curve is heading and what the next curve might look like. It is the job of their elders to give them permission to be different, and then, when the next curve is established, to get out of the way. For that to happen, there has to be a new curve for them, outside.

‘My father brought me back from America to run the business here in Treviso,’ his daughter said. ‘But he still comes into the office every day, even Sundays. He wants me to run the business as if I was him, and I’m not. And the business has to change, if he would only let it. It’s very frustrating.’ Her story was not unusual. The father had nothing else he wanted to do. The business had been his life, and now he had no other. ‘Wet leaves, we call them in Japan,’ said the Japanese lady, describing the reaction of Japan’s women to their retired executive husbands. ‘You know how it is with wet leaves, they just stick around!’ For curvilinear logic to work in the organisation there has to be a life beyond the organisation for the heroes of the first curve.

The Coca-Cola Company is, on the face of it, the great exception to the concept of the second curve. For 104 years they have sold the same product in the same packaging with much the same advertising. The only time they changed the formula they were forced by their customers to reverse the decision. Their secret may lie, however, in the motto which is inscribed in their central offices and in the minds of all its officers - ‘The world belongs to the discontented’. It was the favourite saying of their early and long-time chairman, Robert Woodruff. He was warning against complacency and advocating a perpetual curiosity - the itch of the second curve. Coca-Cola’s Japanese company, I was told, test-markets a new soft-drink variety or other product every month. Even if most of them fail most of the time, it keeps the questing spirit alive. When and if Coca-Cola’s 104-year curve turns down, they hope that they will be prepared.

The Japanese, of course, have their own word for it - kaizen, or continuous improvement. The assumption behind kaizen is the assumption behind this book - that there is no perfect answer in a changing world. We must therefore be forever searching. Anita Roddick, of the Body Shop, puts it more succinctly: ‘What is so wonderful about the Body Shop is that we still don’t know the rules.’ As long as they think that way, so long will they thrive. Complacency is the enemy of curiosity.

The Royal Dutch Shell Group has yet another approach. They call it scenario planning. It has been well explained by Peter Schwartz, one of the early members of the planning group, in his book about it, The Art of the Long View. A group of executives, aided by some outsiders, spends a year or more drawing up alternative scenarios for the oil business and the countries and cultures in which it operates. These are not plans but possibilities, deliberately set at the opposite ends of a spectrum. The planning group then uses these scenarios educationally, exposing their managers around the world to the alternatives and asking them to consider how they would respond if either happened. Shell want no surprises, and were not surprised by the oil crisis of the early 1970s nor by the collapse of the Russian Empire. Their second-curve thinking was ready. It was not so, says Schwartz, in the case of the American military. They made every sort of contingency plan for the Cold War but they never asked the scenario question ‘What if we won?’ When they did win, they knew not what to do.

Peter Senge, in his classic book on the learning organisation, reminds us that our mental models, or private scenarios, are crucial to the learning process. We all carry mental maps around with us - that hierarchy is natural, for instance, that women can’t manage or that men don’t care; that careers last until 65 or that every next job has to be a promotion. We need to check that these assumptions are still valid because they lock us into our existing curve. They inhibit second-curve thinking. My first book on organisations was written 20 years ago. Quite unconsciously, I used the male pronoun exclusively throughout the book. It became a standard textbook, used by those training to work in schools, hospitals and social services as well as business. My book caused a great deal of offence to the many women who had to study it because it appeared to imply that I, the supposed authority, thought that there was no place for them in management. My unconscious mental map of 20 years ago only mirrored what many men felt then, and some still do. That map locked them into their first curve; it made it difficult for them to envisage another kind of world and another way of doing things. My book was not only offensive, it was harmful.

Many of the ideas in this book stem from second-curve thinking - the discipline which says that the past might not be the best guide to the future, that there can be another way, and that some ‘myths of the future’, as Schwartz calls them, will help. We must, however, beware that we do not abandon the first curve too early. The second curve needs the resources and the time which only the first curve can provide. It has to grow out of the first. ‘Dreams give wings to fools,’ my young daughter used to tell me when she heard me fantasising about other lives which we might live. She was expressing her instinct that the future needs to be rooted in the past if it is to be real. The secret of balance in a time of paradox is to allow the past and the future to coexist in the present.

Fertilising the Second Curve

Second-curve thinking will come most naturally from the second generation, those who will inherit the future of the institution or the society. They will, however, need both permission and encouragement. They must realise that what they might privately think of as revolution, or even sedition, is possibly the way ahead in due course. New ideas can coexist with old.

One organisation openly entrusted its second-curve thinking to a group of executives in their early thirties. It happened, however, almost by accident. They wanted to celebrate the twenty-fifth anniversary of their organisation. Their first thought was to commission a history of those first 25 years. That seemed, on reflection, to be too self- indulgent and uninteresting. They therefore decided to commission an outside look at the next 25 years for their industry. They were persuaded that the most fruitful way to do that would be to entrust that forward look to the brightest and best of their own people, people who might be leading their organisation when those years arrived. The look at the future should, therefore, include some thoughts and recommendations on how the organisation should adapt to the changes they might foresee for their industry and the world around them. They were giving these young people the responsibility for their inheritance.

I was asked to act as mentor to the study. I agreed, provided that the board of the organisation agreed to publish the non-confidential part of the exercise as a booklet, without censoring it in any way. The board agreed, but went further. They offered to invite all their customers to a reception to celebrate the anniversary, to listen to a presentation of the findings of the group, whatever they might be, and to receive a free copy of the uncensored booklet. The effect of this advance commitment was impressive. The group saw that this was not some ingenious educational exercise but a genuine attempt to build some new thinking into the existing fabric of the organisation. They were begin publicly trusted by their seniors to develop some new thinking. Their seniors were not only impressed by the results of the study, they took them to heart. Their advance commitment had ensured that they would not feel it necessary to defend the status quo, the first curve, and squash the beginnings of the second.

It is important that the seniors give permission and encouragement. It is also important that the next generation accepts their responsibility for second-curve thinking. Preoccupied with the immediacy of their own careers, it is tempting to think that second-curve thinking can be left until later, that the present is their proper priority, the Future the priority of those in charge. In actual fact, it should be the other way round.

I helped, once, to organise what came to be called the Windsor Meetings. They took place at St George’s House, a small study centre in the middle of Windsor Castle, often leased for weekend gatherings of influential individuals to discuss, privately and informally, social and ethical issues. They were, inevitably, discussions about the present, because the people who came were in charge of the present. We decided, with the help and support of some businesses, to bring together representatives of the next generation of influential people, individuals from all sectors of society who were identified for us as likely future leaders in their spheres.

Thus it was that a young colonel, tipped as a future general, found himself beside a rising trades-union official, a talented young headmistress, a banker, some civil servants, three of the younger and more thoughtful politicians from the different parties, a campaigner for human rights, the new editor of one of the quality newspapers, a television newscaster, a doctor and a lawyer, five business executives - all people successful in their thirties, but pre-occupied with their own careers, too busy, at this stage, to look outside or to know anyone not involved in their line of work. They were all at the lower end of their personal curves, and rising fast. Invited to Windsor Castle, as guests, for a week, they were asked to debate and discuss the shape of the society which they would inherit, as people likely to reach the higher level of their spheres of influence.

Few of them had thought about such broad issues. None of them had met such a wide range of other interests. Their discussions were always stimulating and their reports insightful, but the ultimate benefit was the realisation that they had a responsibility to help shape the society which they were likely to inherit. It was a consciously elitist exercise, because if those soon to be in power are not conscious of their responsibility to shape a second curve, who is? Many of those groups still meet, because, in spite of their very different preoccupations, they found that they also shared a concern for the future of their society, that it should be civilised as well as rich, humane as well as adventurous. There is strength in companionship when it comes to shaping the second curve. We have to hope that, when and if they reach positions of eminence, they will not forget their commitment to that second curve.

Both of these examples used insiders. Some organisations prefer outsiders, feeling that they may have a more objective view and a clearer perspective. Consultants thrive on contacts for what are, effectively, second-curve thinking. The thinking, however, is only part of it. There needs to be the commitment to carry it through, to endure the early dip before the curve climbs upwards, to live with the first curve while the second one develops. These things cannot be done by outsiders. To manage paradox, you need to live with it as well as analyse it.

Reproduced from 'The Empty Raincoat' by Charles Handy, published by Random House Business; New edition (17 Aug 1995)