https://community.wolfram.com RSS Feed for Wolfram Community showing ideas tagged with Business Analytics sorted by active. https://community.wolfram.com/groups/-/m/t/3560688 ![enter image description here][1] This year’s Nobel Prize in Economic Sciences was awarded to Joel Mokyr, Philippe Aghion, and Peter Howitt > “for having explained innovation-driven economic growth.” Mokyr received half “for identifying the prerequisites for sustained growth through technological progress,” while Aghion and Howitt shared the other half “for their theory of sustained growth through creative destruction.” Together, they explain why modern economies continue to improve. In this post, I’ll zoom in on Mokyr’s contribution—the part about how the knowledge engine became self-sustaining—because it maps directly to how engineers, scientists, and managers design systems that improve over time. ---------- Why Economic Growth Suddenly Took Off ------------------------------------- If you look at GDP per capita for England or Sweden from 1300 to 1700, the line is almost flat. Despite inventions like the windmill, plough, and printing press, the economy hardly grew. Then, from the Industrial Revolution onward, growth averaged 1-2% per year—a steady climb that continues even today. **What changed?** ![enter image description here][2] Mokyr’s answer: knowledge began to feed on itself. Science started explaining why things worked, not just how to make them work. That feedback turned innovation from random sparks into a self-sustaining flame. ---------- Two Types of Knowledge ---------------------- Mokyr distinguishes between two kinds of knowledge: *Prescriptive knowledge* – what works, based on experience and observation. *Propositional knowledge* – why it works, based on scientific understanding. Before the 18th century, progress relied mainly on prescriptive knowledge—trial, error, and habit. After the Industrial Revolution, propositional knowledge started reinforcing it, forming a feedback loop that powered continuous innovation. ---------- Sports Analogy: From Routine to Science --------------------------------------- Think of an athlete a few decades ago who swore by a fixed pre-match meal because it seems to help. That’s prescriptive knowledge Modern sports science, however, studies energy metabolism, glycogen storage, and recovery cycles. We now know why certain meals improve endurance and when to take them. That’s propositional knowledge feeding back into training and nutrition plans—creating a loop of sustained improvement. ---------- Modeling the Knowledge Loop =========================== To make this more tangible, I built a simple system-dynamics model showing how knowledge evolves. Imagine a “tank” that stores our useful knowledge — the mix of scientific (propositional) and practical (prescriptive) understanding that drives innovation. Model 1 – Before the Industrial Revolution ------------------------------------------ In the pre-1700 world, innovation was mostly trial and error. New ideas appeared sporadically—say, one invention every few years. But there was no strong feedback between science and practice. If you simulate this, the “knowledge stock” rises slightly, then levels off — a flat line similar to the GDP curves of England or Sweden before 1750. Innovation happens, but it doesn’t compound. ![enter image description here][3] ![enter image description here][4] Knowledge growth before the feedback era, flat curve due to weak reinforcement. Model 2 – The Feedback Era (Industrial Revolution Onward) --------------------------------------------------------- What changed after 1750 wasn’t just the pace of invention—it was the wiring of the system itself. For the first time, knowledge began to loop back on itself. - Research → Scientific Discovery → Useful Knowledge (why it works + what works) ![enter image description here][5] - Useful Knowledge → Applications → New Questions → More Research ![enter image description here][6] In system-dynamics terms, an open-loop world became a closed-loop one. Research led to discovery, discovery built useful knowledge, and every successful application raised new questions that fed back into research—a continuous cycle of learning and doing. ![enter image description here][7] ![enter image description here][8] As this feedback strengthened, innovation became self-propelling. The model shows the knowledge curve bending upward—the hallmark of positive feedback. These two plots visualize exactly what Mokyr described: - Before the loop, innovation behaves like a first-order linear system—progress stalls. - After the loop, it becomes a self-propelling system—progress compounds. ---------- My Learnings from this ---------------------- - Don’t stop at what works—ask why it works. The leap from “trial and error” to “understanding and prediction” turns local optimizations into global breakthroughs. - Design reinforcing loops. Whether in R&D, AI, or manufacturing, connect research, data, and practice so that each improvement fuels the next. - Encourage creative destruction. New ideas often disrupt existing systems—but that’s exactly how sustained growth happens. ---------- From Industrial to Innovation Revolution ---------------------------------------- Mokyr’s framework shows that sustained progress doesn’t depend solely on capital or labor—it depends on how fast knowledge can reinforce itself. In engineering terms, the system became closed-loop. Today, AI, renewable energy, and biotechnology are continuing that same trajectory—the S-curve that started in the 18th century. [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=ModelingQuantumPhenomenawithClassicalTools%282%29.png&userId=1522613 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=gdp-per-capita-maddison-project-database%282%29.png&userId=1522613 [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1760514716884.png&userId=1522613 [4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1760514776874.png&userId=1522613 [5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1760529221154.png&userId=1522613 [6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1760529357289.png&userId=1522613 [7]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1760514893414.png&userId=1522613 [8]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1760514911866.png&userId=1522613 Ankit Naik 2025-10-15T12:49:00Z https://community.wolfram.com/groups/-/m/t/3551033 ![An application for portfolio optimization, risk sensitivity and efficient frontier visualization in Mathematica][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Anapplicationforportfoliooptimization,risksensitivity.png&userId=20103 [2]: https://www.wolframcloud.com/obj/7963e970-e9ea-4c03-860d-cdf93ae98de7 Charalampos-Marios Pelekoudas 2025-09-25T18:03:12Z https://community.wolfram.com/groups/-/m/t/3168773 ![Optimal market size as a function of pool size and product differentiation][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=8318main.png&userId=20103 [2]: https://www.wolframcloud.com/obj/2961d69f-c783-46ed-8c33-9aa74a8d9aa2 Colin von Negenborn 2024-05-02T16:28:00Z https://community.wolfram.com/groups/-/m/t/3128728 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/2b49b169-fd6a-474b-b2b3-2711aaab5e51 Casey Mulligan 2024-02-22T20:02:37Z https://community.wolfram.com/groups/-/m/t/3125647 This is the dedicated discussion of Wolfram U's course: Introduction to Stochastic Processes for Finance Research and Trading. > **Take the course here:** https://www.wolfram.com/wolfram-u/courses/finance/stochastic-processes-finance-research-trading/ Please feel free to use this thread to collaborate and share ideas, materials and links to other resources with fellow learners as you work through the Introduction to Stochastic Processes for Finance Research and Trading course! Join Jonathan Kinlay and fellow learners to learn about modeling financial data with stochastic processes for quantitative research and trading. Course topics include properties and applications for various stochastic processes such as a random walk, the Wiener process and geometric Brownian motion. Analysts and portfolio managers in the financial sector often rely on computational models for managing assets and optimizing investment portfolios, and modeling stochastic processes helps you make sense of and predict outcomes in random data, like stock prices. If you want more, try out Modeling Market Prices Using Stochastic Processes, Random Processes in Finance and Optimization of Portfolios and Investments on Wolfram U! ![enter image description here][1] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=WolframUBanner.png&userId=773999 Jonathan Kinlay 2024-02-21T09:32:02Z https://community.wolfram.com/groups/-/m/t/3113079 ![enter image description here][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Mainimage.png&userId=20103 [2]: https://www.wolframcloud.com/obj/e764d15f-d1e0-405c-91f6-b16f750097d1 Karl Akbari 2024-01-30T21:18:48Z https://community.wolfram.com/groups/-/m/t/3074816 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/53a19ad7-5777-4453-999e-88da6df308e3 Kresimir Zigic 2023-11-30T18:52:40Z https://community.wolfram.com/groups/-/m/t/3036618 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/8dba7493-e33d-476e-8211-02a16ae7bc3e Robert Rimmer 2023-10-15T19:15:18Z https://community.wolfram.com/groups/-/m/t/2992791 ![enter image description here][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=RevisitingRicardo%E2%80%99sandMarx%E2%80%99sbusinesscyclemodel.png&userId=20103 [2]: https://www.wolframcloud.com/obj/f198c64a-89d5-4ad7-b3c2-92663ae1b649 Hee-Young Shin 2023-08-17T18:42:56Z https://community.wolfram.com/groups/-/m/t/2854449 A Wolfram U Daily Study Group on "**Introduction to Statistics**" begins on April 3, 2023. Join a cohort of fellow statistics enthusiasts to learn about collecting, describing, analyzing and interpreting data and trends in science, industry and society. Learn about techniques for data visualization and descriptive statistics, methods for calculating confidence intervals and tools for hypothesis testing from video lessons created by veteran instructor and developer [David Withoff][1]. Participate in live Q&A and review your understanding through interactive in-session polls. Complete quizzes at the end of the study group to get your certificate of program completion. April 3-14, 2023, 11am-12pm CT (4-5pm GMT) >[**REGISTER HERE**][2] ![enter image description here][3] Please feel free to use this thread to collaborate and share ideas, additional resources and questions with the instructors as well as with other members of the study group. [1]: https://www.wolfram.com/wolfram-u/instructors/withoff.html [2]: https://www.bigmarker.com/series/daily-study-group-statistics-wsg37/series_details [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=wolframu-banner.png&userId=130003 Abrita Chakravarty 2023-03-17T21:21:45Z https://community.wolfram.com/groups/-/m/t/2959055 ![Stock Prices Over Time][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Stock.gif&userId=2955119 [2]: https://www.wolframcloud.com/obj/85891b5d-fa9f-4426-af63-b231e5b40b9c Vatsal Piyush Shah 2023-07-12T21:50:54Z https://community.wolfram.com/groups/-/m/t/2957901 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/6601ee70-8105-4127-b16c-5717b9e86063 David DeBrota 2023-07-12T12:51:45Z https://community.wolfram.com/groups/-/m/t/2953857 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/a649c646-3252-478b-ae40-3100e37f2b79 Robert Rimmer 2023-07-07T20:18:59Z https://community.wolfram.com/groups/-/m/t/2941335 [![enter image description here][1]][2] [![enter image description here][3]][4] [![enter image description here][5]][6] &[Wolfram Notebook][7] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=6550dfg54wfbsgw.jpg&userId=11733 [2]: https://equityanalytics.store/ [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2023-06-21at4.42.28PM.jpg&userId=11733 [4]: https://equityanalytics.store/ [5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=456yethdfgsd.jpg&userId=11733 [6]: https://equityanalytics.store/ [7]: https://www.wolframcloud.com/obj/da973799-063b-40c4-bbb6-314562ab5371 Jonathan Kinlay 2023-06-21T21:22:49Z https://community.wolfram.com/groups/-/m/t/2792518 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/0c4bd03c-b0ce-4fb9-ba31-c3bcef8d8b48 Jürgen Kanz 2023-01-18T14:12:31Z https://community.wolfram.com/groups/-/m/t/2916450 ![enter image description here][1] Join the [two-week online boot camp][2], to connect remotely with Wolfram instructors for a guided online introduction to applied multiparadigm data science. 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Join a cohort of fellow learners and expand your understanding of how the Wolfram Notebook interface can be used to express your ideas and develop technical workflows for data science, modeling, research, education and more. No previous experience with Mathematica or the Wolfram Language is required. August 15–20, 11am–12pm US CT (4–5pm GMT) **[REGISTER HERE][1]** ![enter image description here][2] [1]: https://www.bigmarker.com/series/dsg-building-and-sharing-technical-workflows/series_details?utm_bmcr_source=community [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=WolframUBanner.jpeg&userId=130003 Abrita Chakravarty 2022-08-03T22:02:14Z https://community.wolfram.com/groups/-/m/t/2818081 ![stock prices graph][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=stocks.jpeg&userId=911151 [2]: https://www.wolframcloud.com/obj/8992a377-2cce-464c-a8a6-9408a539f2c6 Wolfram Education Programs 2023-01-27T17:00:32Z