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).

It occurred to me that Kurzweil’s singularity might be better characterized as an event horizon. The difference is that a singularity is where something actually infinite happens, while an event horizon is a surface beyond which one can never know anything. An event horizon looks like a singularity from the perspective of a fixed external observer, but from the perspective an observer falling it in always appears to be further down.

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.

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.

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This is pretty sweet. It took me a bit to register that this was a real picture and not a photoshop trick. Nicely done, Mom. In the past we’ve always picked a tree the correct way, by searching through the woods and cutting one down (one year the tree was the top of a large tree removed from the edge of the yard). Mom claims we’ll fix it, but if we have to resort to buying one to do that the virtual tree might be a cooler alternative.