Thomas T. Thomas writes:
From our perspective at the human scale, a tabletop is a flat plane
,but at the atomic level, the flat surface disappears into a lumpy swarm of molecules.
Aficionados of fractal imagery will understand this perfectly: any natural feature like the slope of a hill or shore of a coast can be broken down into smaller and smaller curves and angles, endlessly subject to refinement. In fractal geometry, which is driven by simple equations, the large curves mirror the small curves ad infinitum.
The emergent property is not an illusion… The flatness of the tabletop is just as real—and more useful for setting out silverware and plates—than the churning atoms that actually compose it. The hill and its slope are just as real—and more useful for climbing—than the myriad tiny angles and curves, the surfaces of the grains of sand and bits of rock, that underlie the slope.
Emergent property works on greater scales, too. From space the Earth presents as a nearly perfect sphere, a blue-white marble decorated with flashes of green and brown, but still quite smooth. That spherical shape only becomes apparent from a great distance. Viewed from the surface, it’s easy enough for the eye to see a flat plane bounded by the horizon and to focus on hills and valleys as objects of great stature which, from a distance of millions of miles, do not even register as wrinkles.
Emergent properties come into play only when the action of thousands, millions, or billions of separate and distinct elements are perceived and treated as a single entity. “Forest” is an emergent property of thousands of individual trees. The concept of emergent properties can be extremely useful to describe some of the situations and events that we wrestle with daily.
Conway’s game of life
BOIDS: Birds flocking
Classical physics is an emergent property of quantum mechanics
2016 Massachusetts Science and Technology/Engineering Curriculum Framework
Appendix VIII Value of Crosscutting Concepts and Nature of Science in Curricula
In grades 9–12, students can observe patterns in systems at different scales and cite patterns as empirical evidence for causality in supporting their explanations of phenomena. They recognize that classifications or explanations used at one scale may not be useful or need revision using a different scale, thus requiring improved investigations and experiments. They use mathematical representations to identify certain patterns and analyze patterns of performance in order to re-engineer and improve a designed system.
Next Gen Science Standards HS-PS2 Motion and Stability
Crosscutting Concepts: Different patterns may be observed at each of the scales at which a system is studied and can provide evidence for causality in explanations of phenomena. (HS-PS2-4)
A Framework for K-12 Science Education
Scale, proportion, and quantity. In considering phenomena, it is critical to recognize what is relevant at different measures of size, time, and energy and to recognize how changes in scale, proportion, or quantity affect a system’s structure or performance…. The understanding of relative magnitude is only a starting point. As noted in Benchmarks for Science Literacy, “The large idea is that the way in which things work may change with scale. Different aspects of nature change at different rates with changes in scale, and so the relationships among them change, too.” Appropriate understanding of scale relationships is critical as well to engineering—no structure could be conceived, much less constructed, without the engineer’s precise sense of scale.
Dimension 2, Crosscutting Concepts, A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)