By James Gleick Presentation By Chantal Ivenso University of Cincinnati 5 Main Points Exploring and Embracing Chaos Linear vs Nonlinear mathematics Fractal Attractors Mathematics amp Biology ID: 463634
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Slide1
Chaos : Making a New Science
By: James Gleick
Presentation By: Chantal Ivenso
University of CincinnatiSlide2
5 Main Points
Exploring and Embracing ChaosLinear vs. Non-linear mathematics
FractalAttractorsMathematics & BiologySlide3
Exploring and Embracing Chaos
Gleick introduces chaos through a number of scientist and mathematicians. However, the science of chaos began in a weather simulator with meteorologist, Edward Lorenz.
Lorenz brought to light the Butterfly Effect. By changing the significance of a number that he entered in for a run, the weather pattern that wanted to duplicate came out completely different.Before Lorenz, we encounter
Smale
who paired chaos with instability. Later,
Smale
was proved wrong. An example of a stable chaotic system was created by Lorenz- The WaterwheelSlide4
Linear vs. Non-linear mathematics
Lorenz findings led him into the study of convection. To do this, he used non-linear simplified equations.
Non-linear equations “express relationships that [are] not strictly proportional. Linear relationships can be captured with a straight line on a graph”. Linear equations are basically solvable and non-linear equations are not.Slide5
Fractal
Benoit Mandelbrot was able to magnify with his mind what would take place between the periods with and without errors. With scaling and understanding of dimensions, Mandelbrot introduced fractal as a fragmented geometric shape that has self similarity.
Self similarity is the “symmetry across a scale.” “...recursion pattern inside of pattern.”He used this idea in trying to find the length of a coast.Slide6
Attractors
Gleick mentions attractors studied in dynamic systems, such as turbulence and phase space.The Chaos theory help explain some of these attractors. A. N. Kolmogorov
used math to understand eddies. While a pendulum is used to understand the state of a of dynamic system at any given instant.Slide7
Mathematics & Biology
Chaotic mathematics takes a role in biology in two major areas, as suggested by Gleick
.Ecology embraces the chaos theory and its tools to follow the populations of species in different habitats.Chaos continues pass the external level to the internal more invasive level of organism. It is used to explain psychiatric disorders such as schizophrenia; or mysteries of the cardiovascular system. Slide8
Chaotic Conclusion
James Gleick competently portrays the connection and roles chaos plays in all scholarly fields and daily lives. Whether it be in biology or math, there is a disorder that is keeps the norm and trend in our world.
Gleick, James. Chaos: Making a New Science. Viking Penguin Inc, New York: 1988.