I was thinking of it more like: if there's a certain place I can get to in (roughly) 102 hours going 98 mph, and I want to get there in 100 hours, I need to speed up to 100 mph. Similarly, if there's a another place that I can get to in roughly 102 hours going 980 mph, and I want to get to that place in 100 hours, I need to speed up to 1000 mph.

I kind of wanted to clarify that in the original post but I hadn't really thought of a good way to express it at the time.

Furthermore, I think that your interpretation of the example even makes it more clear that it makes sense to think of it in terms of a ratio. In the first case, you've sped up by 2 mph and gotten a gain of about 2 hours, straightforward enough. But in the second case, you've sped up by 20 mph, and only gotten a gain of about 0.2 hours. Here's where I think most people's intuition is probably screaming "whaaaaaaat!?"

But if we think of it in terms of the ratios, then everything fits together nicely again and the screaming intuition voice shuts up. Plus the math we have to do to get to the right answer is a lot easier.

Comment author:Kindly
15 June 2012 10:40:13PM
0 points
[-]

Oh, I see what you mean now.

(Incidentally, Eliezer's original objection can be resolved by taking logs. Suddenly although the ratios 102/100 and 100/102 are not symmetrical, log(102/100) and log(100/102) are.)

## Comments (66)

OldI was thinking of it more like: if there's a certain place I can get to in (roughly) 102 hours going 98 mph, and I want to get there in 100 hours, I need to speed up to 100 mph. Similarly, if there's a another place that I can get to in roughly 102 hours going 980 mph, and I want to get to that place in 100 hours, I need to speed up to 1000 mph.

I kind of wanted to clarify that in the original post but I hadn't really thought of a good way to express it at the time.

Furthermore, I think that your interpretation of the example even makes it more clear that it makes sense to think of it in terms of a ratio. In the first case, you've sped up by 2 mph and gotten a gain of about 2 hours, straightforward enough. But in the second case, you've sped up by 20 mph, and only gotten a gain of about 0.2 hours. Here's where I think most people's intuition is probably screaming "whaaaaaaat!?"

But if we think of it in terms of the ratios, then everything fits together nicely again and the screaming intuition voice shuts up. Plus the math we have to do to get to the right answer is a lot easier.

Oh, I see what you mean now.

(Incidentally, Eliezer's original objection can be resolved by taking logs. Suddenly although the ratios 102/100 and 100/102 are not symmetrical, log(102/100) and log(100/102) are.)