This week in TOK…

we have been watching the film “Pi” and exploring the insane world of Max Cohen.  The following concepts have been discussed and are worthy of additional research:

  • Pi
  • Theta
  • The golden ratio
  • The golden rectangle
  • DaVinci
  • Fractals
  • Tai Chi
  • Numerology
  • Number Theory
  • Icarus
  • Go
  • Chaos Theory

On Friday, we will be writing an in-class writing piece related to reflections on the film.  Students will submit both their essay and their journals before leaving for break.  Both are due no later than Friday after class.

February 9th

In TOK today…

Diploma Candidates should work on their essays.  The minimum expectation for tomorrow is that they have a complete draft that covers the scope of what they hope to say.

The prompts can be found here.

Junior diploma candidates can work on their essays [which will be submitted next year] on prompts for May 2013.  [I can’t find the prompts online just yet… Ms. Lund should know them, however…]

Normal people should…

View the TED talk: Benoit Mandelbrot: Fractals and the art of roughness [if you need a password, have the sub show it on my computer…]

“I found myself… constructing a geometry of things that had no geometry” – Benoit Mandlebrot

After listening to Mandlebrot’s speech, consider the role of Fractals in the world.  Include personal reflection and examples [both visual and textual] in your response.

You are invited to do additional research online, but be sure to leave at least 20 minutes in order to do some reflective writing about what you have found.  Your written reflection will go into your journal.  Be sure to print it and include it before Friday.

If you need to do more to learn the following, do so:

iteration

self-similar

recursive

Additional fractals resources:

http://www.physicsforums.com/showthread.php?t=512147

 http://homepages.rpi.edu/~eglash/eglash.dir/afractal/afractal.htm

Tonight’s homework has been altered…

Sorry to disappoint, but, given my absence tomorrow, I’ve chosen to give you a reflection question to write about tomorrow in class… instead of writing it tonight.

So, if you’re not an IB Diploma candidate, enjoy the evening. 🙂

If you’re a diploma candidate, you only need to make certain that you can be productive working on your essay tomorrow in class.

That requires that you’ve chosen a prompt and that you plan to bring a draft (in digital form) of what you’ve begun to class.

I will have the Sub bring the laptops – if there’s some malfunction, students can assist… the Cart I’ve signed up for is #13 in the 1400 offices.

Diploma candidates should expect to know what prompt they will write on before they come to school.. and then they should enjoy the rest of the evening. 🙂

Systems of thought

Today, we considered ‘systems of thought’ and how Euclidean Geometry was both –

a) a system of thought by iteself

b) an influence on other systems of thought.

In period 4 we stumbled into the world of ethics and wondered if an ethical system of thought could be created based on ethical ‘postulates’ that would apply universally… and the answer is ‘yes’.  Immanuel Kant’s categorical imperative is an example of such a system.  Read more about Kant’s categorical imperative ahead of time if you wish (we will explore the categorical imperative in our ethics unit).

Act only according to that maxim whereby you can at the same time will that it should become a universal law. (Kant 1993: 30)

In period 5, we discussed language,  non-euclidean geometry, and ethical systems of thought (much like the categorical imperative).

We ended both classes with the assignment to create a mathematical system different from our current system.

Effective systems can:

  1. effectively convey the ideas of quantity
  2. clearly communicate the operations of addition, subtraction, multiplication, and division

Students should arrive in class prepared to explain the system.

 

Mathematical Assumptions

We started the day reading excerpts from the essay “What Euclid Did” by Douglas Muder.  http://www.gurus.org/dougdeb/Essays/Geometry/geometry.html .

We started here: http://www.gurus.org/dougdeb/Essays/Geometry/Euclid.html 

During class, we analyzed the document and prepared to discuss the validity of his assertions.

We answered, in partners, the following questions:

  1. What is his thesis?  Where does he state it?
  2. Where in the essay does he best support his argument?
  3. Is he right?  If so, what are some examples (not in the article) that would support his assertions?  If not, what does he fail to consider? 
  4. How does this text help us explore our own assumptions about what we know?

The text mentions the following philosophers, each of whom would be a great starting place for additional reseach for one’s journal:

Pythagoras, the Gospel of John, Mr. Spock, Hume, Plato, Descartes, Spinoza, Leibniz, Kant, Aquinas, and Newton.