We kicked things off today with a video on Musical Fractals in jazz music that I came across this weekend. It is pretty awesome, and if you can get through the somewhat tricky bit in the middle, the pay off at the end is really cool (there’s another interesting video that Vox just released about the song central to this video – Coltrane’s Giant Steps – that I recommend checking out as well for an interesting lesson in music theory and the circle of fifths).
After this, we shared some of our planetary designs, and then finished off the Nova Documentary from last week.
Tomorrow, we start our work on understanding the mathematics of chaos. Don’t miss it!
Your Unit 2 Test is tomorrow. Here are some ideas on how to prepare:
- Review the Study Guide we made in class. I’ve made a video showing the solutions to the six questions here.
- Complete Test Review 2 (answers here)
- Note: I’ll be collecting both review 1 and 2 in class tomorrow for homework checks!
- Read over your notes and make a list of steps for each process we’ve discussed
- Rewatch some of the videos I’ve posted
- Work on some IXL practice modules, linked below.
Finish reading Chapter 11, pages 291-299, then from pages 301-302, do exercises 9, 13, 17, 19
We discussed the reading from Fractals: The Patterns of Chaos and looked at some references to the “Butterfly Effect” in popular culture. We spent most of the rest of the period playing with the Solar System simulator online.
For Monday, please read pages 49-54 from your book, the section on “The Fractals and Chaos of Outer Space.”
Your Unit 2 test will be on Wednesday, November 14. We played a game of survivor to review much of the unit so far, and your homework tonight is the first of two test review sheets.
Over the weekend, continue reading chapter 11: pages 285-291, up to “The Valid Survey,” then do exercises 4, 7, 8, 12 from pages 300-301.
We discussed some key terms that we observed in the first part of the Nova documentary (specifically: fixed point, attractor vs repeller, and strange attractor) and we modeled some of these terms in action with some magnet pendulums. At the close of the period, we also looked briefly at a Solar System simulator found here.
For tomorrow, please read the three sections mentioned on yesterday’s post from Fractals: The Patterns of Chaos
We did some more review with solving rational equations today, focusing especially on dealing with equations that require us to factor denominators to find a common denominator.
Finish the Chapter 10 Investigative Task assignment that you started in class. This will be due at the start of class tomorrow, and as usual, your response should be completed in a Google Document and submitted to me (email@example.com). Please name your file appropriately. The file name should have the format “LastName.FirstName.Ch10InvTask”. For example, mine would be “Kirk.Benjamin.Ch10InvTask”.
Please also read the first part of Chapter 11, pages 280-285 (up to the section on “Simple Random Samples”). There will be a reading quiz tomorrow using the “Just Checking” questions in that section.
We started watching a Nova documentary on The Strange New Science of Chaos. It’s from 1989, but it has held up well and serves as an excellent introduction to this strange new world of constrained randomness and sensitivity to initial conditions.
For Friday, there are three sections from Fractals: The Patterns of Chaos that I would like you to read:
- Pages 55-60 – Our Weather Today is Chaos
- Pages 93-97 – Chaos and Symmetry Hybrids
- Pages 99-106 – Chaos Sculpts Fractal Landscapes
We spent some time reviewing and going over our past quizzes today. Take tonight to work on quiz corrections (the end of the marking period is on Friday, after all!)
- HW – “Did You Hear About…” – This is an optional homework assignment. Completing it will replace a past missed homework credit.
- Video archive (some of these links include links to additional examples)
From page 279, do exercises 37 and 38
If you’re looking for my fully worked out solutions to yesterday’s simulation sheets, you can find them here (4-H eggs) and here (Duck Hunt)
In class with Mr. Drix today you had your debrief of the Chaos Hits Wall Street article, pointing out some key phrases like state space, which is a broad term that describes the current status (state) of a dynamic, changing system (space). You drew some sketches of state space diagrams for a perfect frictionless pendulum, then a more realistic damped pendulum, closing out the lesson with a look at the random, chaotic behavior of a double pendulum. Through this you learned a new property of chaos (in addition to the constrained randomness from yesterday): sensitivity to initial conditions. Changing the starting state of the double pendulum even slightly resulted in a wildly different oscillation pattern
For a more modern take on Chaos Theory in the financial investment industry, check out this 2010 blog post from MoneyMorning.com: What We Can Learn from the Stock Market Genius That Wall Street Loves to Ignore.
Keep in mind, however, that this “technical analysis” approach of stock market forecasting (as opposed to the “fundamental analysis” approach of looking at the strength of a company) is not without its detractors. For a counterpoint, see this bluntly-titled post from The Motley Fool, also from 2010: Technical Analysis is Stupid
For the last major lesson of the unit, we are looking at solving rational equations. I made a notes sheet for today’s lesson and a custom video for reviewing it here.
From pages 278-279, do exercises 28, 29, 33, 36
You will be given an Investigative Task in class tomorrow to review and start, then finish for tomorrow night’s homework.
We put up the random zig-zags that you created over the weekend and noticed that while the pattern tendered to wander away from the central line, it would eventually trend back as well. The pattern of central line crosses came in “bursts,” and the frequency of these bursts demonstrated fractal-like, self-similar qualities.
We returned to the classroom to examine another version of this, a Chaos Game app designed by Fractals & Chaos alum Istvan Burbank. We saw the impact that different constraints on random movement had on the pattern that movement created, including one very surprising result. We closed out the period investigating and playing with this app some more.
Remember: for tomorrow please read Chaos Hits Wall Street. This is required reading, and I will expect everybody to contribute to tomorrow’s discussion.
After today’s quiz, you got three extra credit challenge problems. Work on those tonight and turn them in tomorrow for bonus points on your quiz from today.
Record your results for simulations in class here.
For tonight, from pages 277-278, do exercises 7, 12, 14, 20
In class with Ms. Csaki today, you made your very own 3D models of 4-dimensional hypercubes! Take good care of it!
After you finished your model, Ms. Csaki should have given you a copy of the Discover Magazine article Chaos Hits Wall Street to read by Tuesday. While this is an old article (1993!) it addresses a lot of the topics we’ll be discussing in the second part of the course. We’ll see some updated takes on the theories presented in the next articles.
Finally, you should have also been given a piece of graph paper in class and told to come here to find out what to do with it. Here’s what you do:
- Fold it in half lengthwise (“hot dog” style).
- Unfold and put a dot on the left edge of your crease.
- Flip a coin (or use some other random procedure). If the coin lands heads, draw a diagonal that goes over and up one square. If the coin lands tails, draw a diagonal that goes over and down one square.
- Continue with this pattern, creating a zig-zag across your paper, until you reach the other side. Bring that in on Monday as well.
Your second quiz from Unit 2 is on Monday, November 5th. This weekend, you should study.
- Work on HW 2.14 – Quiz 2 Review 2 (this will be collected on Monday!)
- Look over the answers to Review 1 here, and to Review 2 here.
- Rewatch some of the videos connected to previous lessons:
- Work on some IXL modules:
- Reread your notes, and especially the study guides we have created.
You have options. Take advantage of them!