HNRS 240: On the Nature of Things: Homework #2 Answers

B — A theory was scientific to Popper if and only if it was falsifiable.
B — "Not sufficient" means that if your condition holds, you still haven't proven what you set out to prove because it could still be false. In this case, you may have sensitivity to initial conditions, but your system can still be non-chaotic. Think x → 2^x. Note that answer C makes a true statement, but it has nothing to do with the sufficiency of the condition.
B — Just run this program.
```
x = 1.0
for i in range(1, 201):
  print i, x
  x = x * 2**0.03125
```
The orbit is certainly not chaotic, and because the power turns out to be a power of two, we are not subject to catastrophic roundoff error.

B — Just run this program, and note the convergence to an attractor of size two. No chaos.

x, y = 0, 0
for i in range(1, 501):
  print i, x, y
  x, y = x*x - y*y - 1.202370, 2*x*y-0.124405

D — Everything counts!
E and A are both lousy but better than the alternatives. A is answered with "their organization, du-uh!" and E is debatable, but the others are just wrong.
E — It's 4 copies of itself but the scale factor is sqrt(2)/4.
C — In the grammar, "swam" is an intransitive verb, and we don't allow those to be followed by prepositional phrases.
C
D — this says in the future it will not be possible for there to exists a sleeping green idea. Note that A is wrong because it says that in the future it says that it will not be possible for all green ideas to sleep.
D
E
B — but E might be acceptable, since the phrase "meaning nothing" is rather ambiguous.
B — A, C, and D are assuming consistency!
A
C
E — C and D are just 100% wrong; A and B are just made up.
B
D
E — You would know this if you saw the interview with Tyson that I included on the first page of the course notes.