Imagine a computer stored in a box with a single small hole connecting it to the outside world. We are able to run programs inside the box and receive the results through the hole. In fact, in a sense results are all we can see; if the program makes efficient use of the hardware inside, the size of the hole will prevent us from knowing exactly what went on inside the box (unless we simulate the workings of the box somewhere else, but then the box is useless).

I’m in the middle of listening to this, and had to take a break to rant for a minute. They’re currently interviewing Alister McGrath, who has written two books complaining about Dawkins. Here’s a quote (emphasis mine):

Well I think one very important point here is simply that it’s fairly clear that science is limited in terms of what it can tell us. It is marvelous in clarifying the relationship between entities and forces in the material world, but when it comes to questions of value or meaning it isn’t really quite so good. In fact Dawkins and I disagree on many things but on that point I think we are agreed: science cannot tell us what is ethical, but for me and I sure everyone who is listening I’m sure what is ethical is actually enormously important.

Imagine that you throw a ball in the air, and lands on the ground and stops (i.e., the collision is inelastic). What happened to the energy and momentum? The answer for energy is completely different from that for momentum, which is a trivial but interesting illustration of the differences between them. Also we get fun with infinities.

Assume a ball of mass $m$ and velocity $v$ hits the ground and stops. Before it hits, it has energy $\frac{1}{2}m v^2$ and momentum $m v$. After it hits, the energy and momentum of the ball are both zero, so by conservation they must have gone elsewhere.

whl g w wr dscssng th vrs trnsfrmtns y cn pply t txt wtht mkng t nrdbl.  Fr xmpl,  sm t rcll xmpls shwng tht txt wth ll bt th frst nd lst lttr f ch wrd rrrngd s stll rdbl.  Smn ls rclld sng rdbl xmpl wth ll vwls rmvd, bt thght t mght hv bn spclly cnstrctd fr tht prps.  Thrfr,  md  nt t try strppng th vwls t f  lrg blck f txt.  Ths s tht txt.