The sigmoid curve - , I THE R O A D TO DAVY'S BAR I I I The...

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THE ROAD , I TO DAVY'S BAR I I I The Wicklow Mountains lie just outside Dublin, Ireland. It is an area of wild beauty, a place to which, as an Irish- man born near there, I return as ofteri as I can. It is still a bare and lonely spot, with unmarked roads, aqd I still get lost. Once I stopped and asked the way "Sure, it's easy," a local replied, "just keep going the way you are, straight ahead, adafter a while you'll cross a smaU 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 hill." His directions seemed so logical that I thanked him and drove off. By the time I realized 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 ex- ample of paradox, perhaps even the paradox of our times; by the time you know where ought to go, it's -
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too late to go 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 backward, we think that we can then pre- dict them forward. 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 those that keep you there. If you think 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 chance to drown your sorrows andreminisce about times past. Although he knew it not, the Irishman had also in- troduced me to the sigmoid curve, the curve that ex- plains so many of our present discontents and confu- sions. It is this curve, and what follows from it, that is the first of the pathways through paradox, the first of the three devices for finding a balance between the contradic- . . tions. ;; :I i ;I i CURVE 2 f 11 {I n ? I j I The sigmoid curve is the S-shaped curve that has in- 4 / trigued people since time began. The sigmoid curve ,(i ,' i sums up the story of life itself. We start slowly, experimen- J i 1 I ! tally, and falteringly; we wax and then we wane. It is the THE AGE OF PARADOX 50 1 story of the British Empire, and of the Soviet Empire, 1 and of all empires always. It is the story of a product's life '4 cycle and of many a corporation's rise and fd. It even de- i scribes the course of love and relationships. If that were i all, it would be a depressing image. There would be noth- 1 ing to discuss except to decide where precisely on the I I curve one is now, and what units of time should go on t i the scale at the bottom. Those units of time are also get- f I ting depressingly small. They used to be decades, per- haps even generations. Now they are years, sometimes months. The accelerating pace of change shrinks every sigmoid curve.
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The sigmoid curve - , I THE R O A D TO DAVY'S BAR I I I The...

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