Respect all of the structure and labels when you adopt this template.
- 1 Chaos
- 2 Chaos Metadata
- 3 To Do
This unit is about chaos. Chaos theory describes the behavior of certain dynamical systems, that is, systems whose states evolve with time, that may exhibit dynamics that are highly sensitive to initial conditions. As a result of this sensitivity, the behavior of chaotic systems appears to be random. This happens even though these systems are deterministic.
Chaotic behavior has been observed in the laboratory in a variety of systems including electrical circuits, lasers, oscillating chemical reactions, and fluid dynamics. Observations of chaotic behavior in nature include the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, the dynamics of the action potentials in neurons, and weather/climate.
An early pioneer of chaotic theory was Edward Lorenz. Lorenz was using a simple digital computer, a Royal McBee LGP-30, to run his weather simulation. To his surprise the weather that the machine began to predict was completely different from the weather calculated before even though he entered rounded 3 digit number like 0.506 which is close to original 6 digit number like 0.506127. Lorenz had discovered that small changes in initial conditions produced large changes in the long term outcome.
Background Reading for Teachers and TAs
- James Gleick "Chaos: Making a New Science"
- This book focuses as much on the scientists studying chaos as on the chaos itself.
- Chapter 1 include the story about Edward Lorenz.
- There is a copy in science library.
Reading Assignments for Students
- Chaos Theory: A Brief Introduction
- A brief introduction to chaos theory.
- This article starts from the story of Edward Lorenz.
- The Lorenz Attractor in 3D
- Some source codes for rendering Lorenz Attractor.
- This article will be the reference for the secondlife lab.
This is a very loose outline... give more detail! Agreed!
- Lecture 1:
- It is the lecture about Edward Lorenz.
- How did Lorenz find butterfly effect?
- It is the introduction to chaos theory.
- Lecture 2:
- It is Lorenz attractor lab.
- Students observe how the shape of Lorenz attractor change.
- Secondlife or GNUplot is used to render the graphics of attractor.
- Lecture 3:
- It is numerical weather prediction lab.
- Students receive data file from the weather station.
- Using spreadsheet, students predict statistically the weather on the day of next class.
- Students compare their prediction and the model analysis by NOAA.
- Lecture 4:
- Students check the weather today and how difference it is from their prediction.
- Students discuss how computer scientists predict climate 100 years later? For example, earth simulator.
- 3/29 - This was marked as done, but this isn't a step-by-step process of what to do. I think this may have been marked incorrectly.
So we've got 3 labs here and 2 weeks to use up; how will the split be made? What procedures are we looking at here?
This seems like a lot of stuff, particularly with the weather included. Which tool will be used for the weather simulation?
- Lab 1: Lorenz attractor lab
- What to do:
- To dive into Secondlife, and display Lorenz attractor in the metaverse.
- What to look for:
- To see how the shape of Lorenz attractor change depending on initial parameters.
- What to record:
- To sketch some patterns of Lorenz attractor and those parameters.
- What to do:
- Lab 2: Weather Data Mining lab
- What to do:
- Student receive the 5 years' weather data collected by HIP and predict statically the weather of near future.
- What to look for:
- To see how accurately weather forecast can be done by using past data.
- What to record:
- To record Students' expectation, NOAA's prediction, and the actual weather on that day. To compare how much gap those information have.
- What to do:
- Lorenz attractor in 3D
- Lorenz attractor C source code generates values in 3 dimensional coordinate.
- Students can generate infinite patterns of values by changing 3 parameters in 3 non-linear differential equations.
- The values can be plotted with GNUplot like this picture.
- There is the source code of Lorenz attractor for second life, but it includes numbers of bugs.
- Excel for statistical computation
- Yahoo! Answers: I'm looking for a good weather prediction software
- Weather Data @ Earlham College (January 2000 ~ March 2009)
- Cligen source code (stochastic weather generator)
- I need to know how to build it.
- NU-CAT (NUmerical weather foreCAsTer)
Bill of Materials
Make sure to answer your own questions
- The butterfly effect is summed up in the title "does the flap of a butterfly's wings in Brazil set off a tornado in Texas?" What does it refer to?
- a. Pandemonium principle
- b. The film from New Line Cinema
- c. Chaos theory
- d. Tip of insect collecting
- Answer: c
- Who found butterfly effect?
- a. Edward Lorenz
- b. Hendrik Lorentz
- c. Edward Teller
- d. Edward VIII
- Answer: a
- What is the chance of rain tomorrow?
- a. 30%
- b. 40%
- c. 50%
- d. some percentage
- Answer: c (on March 25th)
- Describe how we can develop deterministic climate model.
- The answer is, for example, because climate models are systems of differential equations based on the basic laws of physics, fluid motion, and chemistry, they need to be implemented those function. To “run” a model, you divide the planet into a 3-dimensional grid, apply the basic equations, and evaluate the results. Atmospheric models calculate winds, heat transfer, radiation, relative humidity, and surface hydrology within each grid and evaluate interactions with neighboring points.
- Explain why numerical weather forecasts miss their guess.
- The answer will be like, because weather forecaster have to count too many parameters of infinite precision and there is no such computer which can compute all of those.
- To learn that it's next to impossible to predict the future since it's too much complicated.
- To abstract chaos behavior and understand the mechanism.
Late in semester.
Concepts and Techniques
- Selecting from infinite numbers of parameters for climate model.
- Realizing simple-looks situation causes chaos behavior.
- Transforming data to knowledge by visualizing.
General Education Alignment
Analytical Reasoning Requirement
From the [Catalog Description] Courses qualifying for credit in Abstract Reasoning typically share these characteristics:
- They focus substantially on properties of classes of abstract models and operations that apply to them.
- Complete. They are handling abstract model of chaos and applying it in metaverse.
- They provide experience in generalizing from specific instances to appropriate classes of abstract models.
- Partial. From specific instances of weather data, they generalize chaos model.
- They provide experience in solving concrete problems by a process of abstraction and manipulation at the abstract level. Typically this experience is provided by word problems which require students to formalize real-world problems in abstract terms, to solve them with techniques that apply at that abstract level, and to convert the solutions back into concrete results.
- Complete. They provide experience in solving weather forecasting problem. The process is abstraction of weather data, manipulation, and Analysis. They formalize real-world short-term/long-term climate model problem in words.
From the [Catalog Description] General Education courses in Quantitative Reasoning foster students' abilities to generate, interpret and evaluate quantitative information. In particular, Quantitative Reasoning courses help students develop abilities in such areas as:
- Using and interpreting formulas, graphs and tables.
- Complete. They have formulas of attractor, generate graph of climate change, and analyze big table of climate data.
- Representing mathematical ideas symbolically, graphically, numerically and verbally.
- Complete. Lorentz attractor is representing chaos mathematically, symbolically, graphically, numerically, and verbally.
- Using mathematical and statistical ideas to solve problems in a variety of contexts.
- Complete. They require mathematical and statistical ideas to solve data mining problem of climate data.
- Using simple models such as linear dependence, exponential growth or decay, or normal distribution.
- Partial. Chaos model will never be simple. But Lorenz attractor abstract chaos theory a lot.
- Understanding basic statistical ideas such as averages, variability and probability.
- Complete. Students will develop those skills through analyzing weather data.
- Making estimates and checking the reasonableness of answers.
- Partial. Students just can review their estimate because of actual weather and professional's weather prediction.
- Recognizing the limitations of mathematical and statistical methods.
- None. This unit require unlimited amount of calculation for accurate forecast.
Scientific Inquiry Requirement
From the [Catalog Description] Scientific inquiry:
- Develops students' understanding of the natural world.
- Complete. This unit develops students' understanding of chaotic flow of climate change.
- Strengthens students' knowledge of the scientific way of knowing — the use of systematic observation and experimentation to develop theories and test hypotheses.
- Complete. This unit strengthens students' knowledge of the scientific way of reading weather data and developing weather forecasting theory.
- Emphasizes and provides first-hand experience with both theoretical analysis and the collection of empirical data.
- Partial. Theoretical analysis of chaos model will derive infinite variation. Students have to guess the result from the collection of empirical data of weather.
The source code of Lorenz Attractor for second life has bugs. If students fix the bugs and modify by themselves, it would be a practice of coding and understanding chaos behavior.
Inquiry Based Learning
Guessing climate in near future by considering our weather station database will relate to discovering a new point of view about nature.
- Fitz is going to try to see if he can get the Lorenz equations to work in Second Life
- Mikio is going to try to finish the rest of it, assuming that Second Life simulation will work at this point
- Mikio is going to contact to Madonna and Skyler about climate model.
- Mikio is going to dig Cligen out.
- Mikio is going to build Cligen from its source code.