Illustration on PG's hill climbing algo and CSAllen's take on it

Thanks for drawing it!

I've actually thought about a visual a few times, and I've never been able figure out a perfect way to capture all the metaphors that come to mind when I think about doing this kind of hill climbing.

For example, I didn't mention this on the podcast, but I think of every hill as a bit of an S-curve. Progress is slow when you're just getting started, because you're a total beginner. After you figure out the ropes, you start to progress quite rapidly in the middle of your climb. But as you closer to the top, the curve flattens out a bit, and you're making very slow progress while not even gaining that much height. So you want to parachute off right as you get into those diminishing returns.

The problem is this doesn't work well visually, as we interpret difficulty in the exact opposite way. On an S-curve, the flat parts are bad because it means you're making little progress over time, and the steep parts are good for the opposite reason. But looking at an actual, mountain we perceive the flat parts as being easy and the steep parts as being hard. So the visual metaphor falls apart.

There are other things to consider, too, that I think would be hard to illustrate:

• There are numerous hills in the vicinity to choose from.
• Some hills are so difficult to climb at their base that your only option is to parachute to the middle of them once you're high enough on some other hill.
• It's not always obvious how tall a hill is, even if it's the hill you're presently climbing.
• etc.

Anyway, I think this is all needless complication. The way you've done it here is quite simple and accurately describes how I talked about it on the show. Thanks for drawing@

I love this! As a CS major, so much is taught using equations and math. If only more professors taught with illustrations like you :)

If you'd like to see more such illustrations, do follow me on twitter :)