Call me a pedant, but 1024x768 to 2048x1536 isn't doubling the resolution, nor was the step up from iPhone 3GS (480x320 to 960x640).
Both of those are increasing the resolution by 4x not 2x.
1024x768 = 786,432 pixels
2048x1536 = 3,145,728 pixels
3,145,728 / 786,432 = 4.
It is doubling the resolution. 2048x1536 is doubling the vertical and horizontal dimensions.
Total number of pixels are quadrupling but no one really talks about pixel count.
AxB is resolution, pixels are pixels obviously.