Logistic and exponential growth 1

Logistic and exponential growth. 2. Logistic Growth (S-curves) The classic change model is the sigmoid function, or S-curve, given this name due to its shape. It is also called the Gompertz curve, after the mathematician who first discovered it in natural systems. Logistic growth may be the best-known example of S-curve behavior. Many growth processes, including population growth, the diffusion of innovations, human and machine learning, language change, and chemical reactions, exhibit varying speeds of exponential growth at first, then they hit an inflection point, where they start to mature, running into competition or resource scarcity, and the rate of growth decelerates. Next they enter a saturation phase, where growth greatly slows or even stops. The four phases of such growth (Initiation/Birth, Acceleration/Growth, Deceleration/Maturing, Saturation) can be seen in the logistic growth curve at right. GP (growth point), IP (inflection point) and SP (saturation point) are points on the curve after which careful observers can notice growth conditions have changed. Exponential growth usually runs only for as long as there are easily available resources. As a population’s interaction space expands to cover most of the relevant environment (a biome, a market, the easily available idea, knowledge, or variation space), its replication will start to slow, and it eventually saturates, reaching the “carrying capacity” of that particular environment, a point on the X-axis at or just above the saturation level. Forecaster Theodore Modis has done a lot of deep thinking about S-curves. His books Predictions (1992) and Predictions: Ten Years Later (2002), are great reads, and offer many insightful examples of these curves applied to processes of change. Nevertheless, he tends to see them everywhere, and to discount Exponential growth (E-curves) and ignore superexponential growth (J-curves), as in his article, The Singularity Myth, Technological Forecasting & Social Change (2006). We should always keep in mind that our favorite curves may not be the ones that are the most relevant to the particular system or period under study. S-Curve and Market Phases of Technology Diffusion (Adoption) Phases of technology adoption follow an S-curve, as Everett Rogers described in his classic, Diffusion of Innovations, 5th Ed . (2003). As adoption phases progress, from Innovators to Laggards, an initial exponential growth phase goes through an inflection, then saturates. Successive S-Curves of Mass-Market Technology Adoption (Excluding Software) The history of mass-market technology adoption shows these S-curves in historical data. Note that highly valuable technologies, like automobiles and radio, had nearly as steep initial adoption curves in the 1910’s and 1920’s as the initial curves for such modern must-haves as cellphones and the internet, in the 1990s. A range of factors, like technology cost, value, ease of use, and marketing, are important to driving these S-curves to their saturation points. Yet this big picture perspective also shows a general speedup in adoption of valuable new innovations the more connected we become. More recent innovations, like computers, cellphones, and the internet, have very steep exponential phases. Adoption of dematerialized products and services, like new software platforms or apps, is vastly faster still. If those had been included, this chart would be an even more valuable metric of accelerating adoption. Share your Feedback. Better Wording? References? Data? Images? Quotes? Mistakes? Thanks for helping us make the Guide the best intro to foresight on the web. Foresight University (4U) is a professional learning and development company, run by academically-trained foresight practitioners, entrepreneurs, technologists, and creatives. We offer high-quality training in personal, organizational, global, and universal (POGU) foresight and leadership, help leaders and entrepreneurs maximize their positive impact, and support the growing global foresight community. We're not around right now. But you can send us an email and we'll get back to you, asap. Chapter 1: Introduction. Our Emerging Foresight Field. Chapter 2: Personal Foresight. Becoming an Effective Self-Leader. Chapter 3: Career Options. Great Ways to Be a Foresight Leader. Chapter 4: Models. Foundations for Organizational Foresight. Chapter 5: The Do Loop: The Eight Skills of Adaptive Foresight. Chapter 6: Methods and Frameworks. Building Adaptive Foresight Skills. Chapter 7: Acceleration. Guiding Our Extraordinary Future (In Process) Innovation: Our Abundant Future Intelligence: Our Augmented Future Interdependence: Our Civil Future Immunity: Our Protected Future Sustainability: Our Rebalanced Future. Great Race to Inner Space: Our Surprising Future Entropy&Information: We’re Running Down & Up The Puzzle of Meaning: We Have No Einstein Yet Trees, Funnels & Landscapes: Intro to Evo Devo Big Picture Change: Five Scales of Accelerating ED Transcension Hypothesis: Where Acceleratn Ends? IDABDAK: Social Response to Accel & Developmnt We’re On a Runaway Train: Being Accelaware. IV. Evo Devo and Exponential Foresight. Seeing It All: Accel., Diverg, Adapt, Convrg, Decel. Natural (I4S) Innovation: The Evolutionary Drive Natural (I4S) Intelligence: The Human-AI Partnership Natural (I4S) Morality: Why Empathy and Ethics Rule Natural (I4S) Security: Strength from Disruption Natural (I4S) Sustainability: The Developmental Drive S-Curves: Managing the Four Constituencies Pain to Gain: Traversing the Three Kuznets Phases Hype to Reality: Beyond Hype Cycles to Reality Checks Exponentials Database: Measuring Accelerations TINA Trends: Societal Evolutionary Development Managing Change: STEEPCOP Events, Probs, Ideas A Great Shift: A Survival to a Sentient Economy. V. Evo Devo and Exponential Activism. Building Protopias: Five Goals of Social Progress Normative Foresight: Ten Values of Society Top & STEEPCOP Acceleratns: Positive & Negative Dystopias, Risks, and Failure States Three Levels of Activism: People, Tech & Universe A Great Opportunity: Exponential Empowerment. Chapter 8: Your Digital Self. The Human Face of the Coming Singularity (In Process) I. Your Personal AI (PAI): Your Digital Self. Digital Society: Data, Mediation, and Agents Personal AIs: Advancing the Five Goals PAI Innovation: Abundance and Diversity PAI Intelligence: Bio-Inspired AI PAI Morality: Selection and Groupnets PAI Security: Safe Learning Agents PAI Sustainability: Science and Balance The Human Face of the Coming Singularity. II. PAI Protopias & Dystopias in 8 Domains. 1. Personal Agents : News, Ent., Education 2. Social Agents : Relat. and Social Justice 3. Political Agents : Activism & Represent. 4. Economic Agents : Retail, Finance, Entrep 5. Builder Agents : Work, Innov. & Science 6. Environ. Agents : Pop. and Sustainability 7. Health Agents : Health, Wellness, Death 8. Security Agents : Def., Crime, Corrections. III. PAI Activism & Exponential Empowerment. Next Government: PAIs, Groupnets, Democ. Next Economy: Creat. Destr. & Basic Income Next Society: PAI Ent., Mortality & Uploading What Will Your PAI Contribution Be? Chapter 9: Trends and Progress. Leading Positive Change. Chapter 10: Startup Ideas. Great Product and Service Challenges for Entrepreneurs (In Process) Air Deliveries and Air Taxis: Finally Solving Urban Gridlock Ballistic Shields and Gun Control: Protecting Us All from Lone Shooters Bioinspiration Wiki: Biomimetics and Bio-Inspired Design Brain Preservation Services: Memory and Mortality Redefined Carcams: Document Thieves, Bad Driving, and Bad Behavior Competition in Govt Services: Less Corruption, More Innovation Computer Adaptive Education (CAE): Better Learning and Training Conversational Deep Learning Devsuites: Millions of AI Coders Digital Tables: Telepresence, Games, Entertainment & Education Dynaships: Sustainable Low-Speed Cargo Shipping Electromagnetic Suspension: Nausea-Free Working & Reading in Cars Epigenetic Health Tests: Cellular Aging, Bad Diet, Body Abuse Feedback Fireline Explosives and Ember Drones: Next-Gen Fire Control Global English: Empowering the Next Generation of Global Youth Greenbots: Drone Seeders and Robotic Waterers for Mass Regreening High-Density Housing and Zoning: Making Our Cities Affordable Again Highway Enclosures and Trail Networks: Green and Quiet Urban Space Inflatable Packaging: Faster and Greener Shipping and Returns Internet of Families: Connecting People Over Things Kidcams: Next-Gen Security for Child Safety and Empowerment Kidpods: Indoor & Outdoor Parent-Assistive Toyboxes Microdesalination: Democratizing Sustainable Fresh Water Production Noise Monitors: Documenting and Reducing Noise Pollution Oceanside Baths: Sustainable Year Round Beach Enjoyment Open Blood Scanners: DIY Citizen Health Care Sensor Tech Open Streaming Radio: User-Centered Audio Creation and Rating Open Streaming Video: User-Centered Video Creation and Rating Open Values Filters: Social Rankers, Arg. Mappers, and Consensus Finders Personal AIs: Your Private Advisor, Activist, and Interface to the World Pet Empowerment: Next-Gen Rights and Abilities for Our Domestic Animals Safe Closets: Fire-, Earthquake-, and Intruder-Proof Retreat Spaces Safe Cars: Reducing Our Insane 1.3M Annual Auto Deaths Today Safe Motorcycles: Lane Splitting in Gridlock Without Risk of Death Shared Value Insurance: User-Centered Risk Reduction Services Sleeperbuses and Microhotels: Demonetized Intercity Travel Space-Based Solar Power: Stratellite Powering and Weather Management Stratellites: Next-Gen Urban Broadband, Transparency, and Security Touch DNA: Next-Gen Home Security and Crime Deterrence View Towers: Improving Urban Walkability, Inspiration, and Community.