- Levis wants to be more sustainabile....
- Your final homework assignment is due Wednesday.
- Logo day is next time! Wednesday, 4/29. You will submit your logo
and logo paper to me at the time of class. You may not hand that in
late, so get cracking!
More about logo day:
Order will be randomly assigned at the time of class. You need to be here on time, and ready to present when called.
Your presentation should be about a minute long. Not much more. Please email me an image of your logo, so I can make a link and we can quickly move from student to student.
So far I have ONE logo from a student!
- A reminder, in advance of the final: you are allowed two kinds of
"cheat sheets":
- An 8.5x11 sheet of paper, cut into strip and turned into a mobius band; and
- The skeleton of an icosohedron, made up of 4x6 cards (or
smaller)
- Reading for today: Commuting (p. 23)
- Here's what one college in a university is proposing as a budget strategy:
- Departments within the college will be rewarded for passing students with more money.
- Departments within the college will be rewarded with more money for retaining more students.
The administration suggests that this will lead to more student success (in fact, I'm sure that they would tell you that it will lead to "more success all around!").
You tell me what you think will happen (that is, how will the system -- departments, college, students -- change through time -- this is a dynamical system, changing dynamically in time).
- Let's now turn to the situation that Strogatz describes, of his
"Romeo and Juliet" situation from college. I'll share another way to
think about that, in what I call "Ardor space".
- Let's look at a more realistic situation: what's called
predator-prey (rabbits and foxes).
We'll also look at the Lorenz system, which demonstrates chaos.
- What if we had a situation of two enemies. What would the situation look like?
- Nonetheless, let's start in the same place as Strogatz. He looks
at a hypothetical shopping experience, in which one is offered the
choice of taking a discount before paying tax, or of paying taxes
first, then taking the discount.
Strogatz shows that the order of these two operations doesn't matter. And he gives us an important lesson in shopping: rather than think of "20% off", think of "80% on". Rather than
Strogatz suggests
The commuting part comes about when we think about the tax -- which is similar:
Strogatz would suggest
Finally, tax first followed by discount is the same as discount first, followed by tax, because multiplication is commutative:
because
- An interesting example of non-commutativity is provided by
Strogatz and the example of Murray
Gell-Mann: that he was thinking about committing suicide when he
was consigned to MIT, but he resisted when he realized that suicide
followed by MIT was not the same as MIT followed by suicide -- and that
he preferred the latter, as it allowed for more options.
MIT then suicide is not the same as suicide then MIT A similar story is told by a Jewish storyteller, about Herschel and his underwear....
- Now let's move the discussion beyond the apparal aisle. into
household furnishing. I want to look back on "Group Think" (p. 211),
and the example of the mattress flipping and spinning.
By the way, it's spring, so you should be spinning your mattress.
We'll see that spinning, horizontal and vertical flipping are commutative operations.
We'll begin by thinking of each of these operations as directed graphs.
- Finally let's take a look at some knots under these same
operations. Some knots have two different configurations -- left-handed
and right-handed.
There are two different types of Mobius bands, left-handed and right-handed. There are also two distinctly different trefoil knots.