More of my thoughts have been stolen: In my
previous job the customer wanted a progress bar displayed while information was copied off of proprietary hardware, during which the software didn't get any indication of progress until the copy
was finished. I joked (mostly) that we could display a progress bar that continuously slows down and never quite reaches the end until we know we're done getting info from the hardware. The amount
of progress would be a function of time where as time approaches infinity, progress approaches a value of at most 100 percent.
This is similar to Zeno's Paradox which says you can't cross a room because to do so first you must cross half the room, then you must cross half the remaining distance, then half the remaining again, and so on which means you must take an infinite number of steps. There's also an old joke inspired by Zeno's Paradox. The joke is the prototypical engineering vs sciences joke and is moderately humorous, but I think the fact that Wolfram has an interactive applet demonstrating the joke is funnier than the joke itself.
I recently found Lou Franco's blog post "Using Zeno's Paradox For Progress Bars" which covers the same concept as Zeno's Progress Bar but with real code. Apparently Lou wasn't making a joke and actually used this progress bar in an application. A progress bar that doesn't accurately represent progress seems dishonest. In cases like the Vista Defrag where the software can't make a reasonable guess about how long a process will take the software shouldn't display a progress bar.
Similarly a paper by Chris Harrison "Rethinking the Progress Bar" suggests that if a progress bar speeds up towards the end the user will perceive the operation as taking less time. The paper is interesting, but as in the previous case, I'd rather have progress accurately represented even if it means the user doesn't perceive the operation as being as fast.
Update: I should be clearer about Lou's post. He was actually making a practical and implementable suggestion as to how to handle the case of displaying progress when you have some idea of how long it will take but no indications of progress, whereas my suggestion is impractical and more of a joke concerning displaying progress with no indication of progress nor a general idea of how long it will take.
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