transistordad
But the printer example is a great one. The value of printing the output is that then you can do things with it that help you think about it in ways that you couldn't do with the on screen interface. If you wanted to you could cut the paper up and rearrange it, draw diagrams etc.
There is a whole genre of interfaces, called Tangible User Interfaces or TUI, that is all about giving physical form to digital information and using physical objects / tokens to represent and modify information inside the computer. Here's a paper with an example task that's similar in many ways to the task in the paper in the original blog post.
https://www.cs.tufts.edu/~jacob/papers/chi02.pdf
So yeah, if an interface lets you organize things spatially in physical (or graphical) space, it can make you a lot more productive.
In situations where the cost of failure is low, and one wants to quickly explore a problem space in search of the best solution, you often want an interface that encourages "epistemic action". This is action taken using the interface to think about the problem rather than directly solve it. David Kirsh uses the example of Tetris: https://www.sciencedirect.com/science/article/abs/pii/036402... People often rotate pieces when they're falling to see which way they'll fit best, because that's faster than doing the rotation in your head.
So, the fact that users spend more time thinking before they engage with an interface may not be a good thing. It could be that the interface is just hard to use. Think about how you normally solve a jigsaw puzzle... There may be some amount of planning, but there's also a healthy amount of trial an error. The cost of making a mistake is low. Now imagine each piece of the puzzle weighed 50 pounds. In that case, one would make a detailed plan before moving many pieces around.