The string that you emailed me: Remember my string
(15P) What are the three most important and recurring ideas in GEB (according to me)?(Hint: Recall that Gödel's Incompleteness Theorems and Zen are pertinent to all of them. If you weren't there, see the slides and make an educated guess.)
Achilles and TortoiseBrain in a VatFugues and counterpointInherent imperfectionPrincipia MathematicaRace carsReality and fantasyStrange loopsTrigonometryZen and afterlife
The next two questions refer to the dialogue Three-Part Invention (pp. 29).
(10P) Before Achilles and Tortoise met Zeno, Achilles mistook Zeno for someone named . (Hint: his name appeared in not the dialogue but the slides.)
(10P) Point out a wordplay in the dialogue.
The next two questions are about our grade policy. Something I forgot to emphasize was that the exchange rate of a conversion depends only on the number of Ps before that conversion.
(20NP) The smartest move. Throughout a semester of GEB Stuco, Achilles got the entirety of 600P and xNP from the homework. He, the biggest of brain of all mortals, (by doing the smartest conversions all along,) eventually got an insane grade combination of yP and 0NP. What is y, in terms of x?
(40NP) The stupidest move. Throughout the semester, the Tortoise also received the entire 600P and xNP. He, the slowest of all half-wits (it requires quite some wisdom to be as stupid as he!), eventually got an insane grade combination of zP and 0NP. What is z, in terms of x?
(1NP) Consider a programming language which represents the memory as an integer list (denoted as A, A, ...), and has three kinds of instructions (all of which takes up a whole line):
+ i j : increment A[i] by 1, and go to line j- i j k : if A[i] is positive, decrement A[i] by 1 and go to line j; otherwise, go to line kH : halt
+ i j
- i j k
When a program is executed, the memory is set to all zeros; then the instruction at line 1 is executed. A program is said to output x if it terminates with A = x, A = A = ... = 0.
Here are two sample programs:+ 1 2+ 1 3- 2 5 4+ 2 1H // outputs 4 (order: L1->L2->L3->L4->L1->L2->L3->L5)
+ 1 2+ 1 3- 2 5 4+ 2 1H // outputs 4 (order: L1->L2->L3->L4->L1->L2->L3->L5)
+ 2 2+ 2 3+ 1 4- 2 5 10- 1 6 8+ 3 7+ 3 5- 3 9 4+ 1 8H // outputs 4
Within 15 lines, write a program whose output is greater than . (I can't let you just copy the examples...) Output (in decimal):
(10NP) (Meta-problem. Partial credits given.) Predict two problems that will appear on next week's homework (remember to predict their values).