Benoit Mandelbrot: Fractals and the art of roughness
TED・13 minutes read
Roughness, often seen as chaotic, actually contains elements of order, explored through examples like cauliflower and quantifiable numbers. Mathematics aids in understanding complex systems, as seen in the study of Brownian motion and the speaker's career evolution.
Insights
- Roughness, often associated with chaos, actually contains elements of order that can be quantified and measured, challenging the perception of it being purely disordered.
- Mathematics plays a pivotal role in unraveling the complexity of natural and artificial rough surfaces, offering valuable insights into intricate systems like lungs and clouds, showcasing the interconnectedness of seemingly disparate fields of study.
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Recent questions
What term is preferred over "irregularity"?
Roughness
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Summary
00:00
Unraveling the Complexity of Roughness
- Roughness has been a long-standing aspect of human life, with ancient authors discussing its complexity and messiness.
- Despite roughness being perceived as uncontrollable chaos, traces of order have been discovered within it.
- The term "roughness" is preferred over "irregularity" due to the unique nature of rough shapes.
- A cauliflower is used as an example of a complex yet simple object, with each part resembling the whole but on a smaller scale.
- Roughness can be quantified by numbers like 2.3 or 1.2, aiding in measuring the complexity of surfaces.
- Artificial landscapes created on computers demonstrate varying levels of roughness, with the eye able to distinguish between rough and smooth surfaces.
- The length of coastlines and the surface area of lungs are examples of measurements that become more intricate as they are examined at smaller scales.
- Mathematics has played a crucial role in understanding the structure of complex systems like lungs and clouds, providing insights for medical and scientific advancements.
- The study of Brownian motion, with a roughness number of two, led to significant mathematical breakthroughs and the awarding of prestigious medals.
- The speaker's journey from studying stock market prices to exploring complex mathematical shapes like the Julia set highlights the evolution of his career and discoveries.
15:50
"Pilot finds Mandelbrot set in Cambridge"
- In 1990, while in Cambridge, U.K., a pilot discovered a shape resembling the Mandelbrot set, mistaken for an extraterrestrial creation, which actually emerged from a pure mathematical exercise.
