Repetition
in
Everyday Life
STOP+THINK
Why do we think this works?
Why does this work?
Why is this chemistry in the 21st century?
STOP+THINK
STOP+THINK
How
does nature
do this?
STOP+THINK
or this?
Iteration
Repetition
"Lather, rinse, repeat."
Turns Out Lots of Life's Problems
Can Be Solved with Repetition
"Iterate. Iterate. Iterate."
"Scrub until clean."
"Season to taste."
"Keep trying until you get it right."
Solve This Maze
F
Repetition II
Our iterative woodworker has a long term goal in mind - a beautiful finished product - but in each instant her experienced eye can compare the current state to a future state that is on the path toward beauty.
An Iteration Sneak Preview
From moment to moment she adjusts the position of her hands and tool and the pressure she applies.
If she can compute the derivative
How does she decide to adjust how she holds the tool as the seconds iterate on and on?
Maybe there is some calculus involved! Suppose her experience allows her to compute a function, f, that maps tool position to future state of the work from current state of the work. And a function g that assesses the beauty of that future state?
Recall our woodworker at the lathe. One element of iteration here is the rotation of the wood. But as it rotates, the woodworker is making a series of decisions about how to move the tool.
\frac{d(\text{beauty})}{dx,dy,dz}
= \frac{\partial b}{\partial x}
+ \frac{\partial b}{\partial y}
+ \frac{\partial b}{\partial z}
Then she might be able to constantly adjust her hand position to always be moving in the direction of a more beautiful result.
start lathe
put tool to work
repeat
adjust position → ↑beauty
until goal - beauty < epsilon
We are playing a little fast and loose with things here, but if we think back to how we used slow thinking to generate instructions for our robot sorting cards, maybe we can describe creating a beautiful object on the wood lathe as
Hook II
It's the end of the semester, exams and project deadlines loom.
You only have 20 hours of study time. How do you allocated it among your different courses?
You are currently running a C in sociology, a B in calculus and chemistry, an A in programing 101, and a C in swimming.
Two words that I can never remember which consonants are doubled in.
Fibonacci sequence
2 up is easy, but how about down?
3 fib(8)? f(7)+fib(6) etc.
4 tree and repetition. Look at how many steps for F(5)!
5 could save time with scratch pad
6 how to communicate this?
7 Heads down with our own ideas
8 Pitch our idea to a catcher (classmate)
9 Catcher gives iteration-forward feedback
10 Back to the drawing board, make use of feedback
Repetition Hooks
By Dan Ryan
