Entropy based progress bar [closed]

Would it be possible to build a progress bar that estimates progress using entropy?

Consider a web browser that is downloading a large file (for instance), which displays a progress bar indicating the amount of progress in the download. Let $X$ denote the value of the complete file; it is not known until the download completes. At time $t$, we have downloaded part of the time, so let $Y_t$ denote the information/data received by time $t$. Initially, at $t=0$, we do not know $X$ (there is some prior distribution on $X$). The observed data narrows down the set of possible values of $X$. The more we observe, the less uncertainty there is about $X$; once we've finished downloading the entire thing, the value of $X$ is known and there is no more uncertainty.

Could we use the entropy $H(X | Y_t)$, or something like that, to estimate progress so far and build the progress bar? Would this work theoretically? Would it work in practice? Would it be useful?

Would something similar work for software installation or other uses of progress bars?

• $X^n$ represents the content of those memory cells, which clearly is random to us. $X_i^n$ is the $i:th$ memory cell of the memory block we are reserving. If we have no uncertainty in what we want to write to our reserved block, then we can break transmission and thus progress is complete. May 15, 2015 at 7:10
• I thought it was a rather well-posed model, feel free to point out what makes it faulty/confusing. May 15, 2015 at 7:13
• Actually, I suspect this definition would be 100% equivalent to the 'normal' definition of progress... May 15, 2015 at 7:20
• If you KNEW what the web page wanted to transmit before hand, obviously it wouldn't have any uncertainty, but in that case, then why are you transmitting it at all? May 15, 2015 at 7:22
• OK, I've tried editing the question based upon my understanding of what you are saying, going by your comments and your example of downloading a web page. I've tried to turn this into a more well-defined, answerable question. Does this edit accurately reflect your intent?
– D.W.
May 15, 2015 at 7:30

For a file download, there is a much simpler method: let $n$ be the total number of bytes of the file to be downloaded, and $k$ the number of bytes we have downloaded so far; then $k/n$ is a good estimate of our progress (the fraction of the file we've downloaded so far).