I had a manager once tell me during a casual conversation with complete sincerity that one day with advancements in compression algorithms we could get any file down to a single bit. I really didn’t know what to say to that level of absurdity. I just nodded.
It’s an interesting question, though. How far CAN you compress? At some point you’ve extracted every information contained and increased the density to a maximum amount - but what is that density?
I believe the general answer is, until the compressed file is indistinguishable from randomness. At that point there is no more redundant information left to compress. Like you said, the ‘information content’ of a message can be measured.
(Note that there are ways to get a file to look like randomness that don’t compress it)
I think by the time we reach some future extreme of data density, it will be in a method of storage beyond our current understanding. It will be measured in coordinates or atoms or fractions of a dimension that we nullify.
I had a manager once tell me during a casual conversation with complete sincerity that one day with advancements in compression algorithms we could get any file down to a single bit. I really didn’t know what to say to that level of absurdity. I just nodded.
Well he’s not wrong. The decompression would be a problem though.
You can give me any file, and I can create a compression algorithm that reduces it to 1 bit. (*)
spoiler
(*) No guarantees about the size of the decompression algorithm or its efficacy on other files
u can have everthing in a single bit, if the decompressor includes the whole universe
It’s an interesting question, though. How far CAN you compress? At some point you’ve extracted every information contained and increased the density to a maximum amount - but what is that density?
This is a really good question!
I believe the general answer is, until the compressed file is indistinguishable from randomness. At that point there is no more redundant information left to compress. Like you said, the ‘information content’ of a message can be measured.
(Note that there are ways to get a file to look like randomness that don’t compress it)
I think by the time we reach some future extreme of data density, it will be in a method of storage beyond our current understanding. It will be measured in coordinates or atoms or fractions of a dimension that we nullify.
Send him your work: 1 (or 0 ofc)
https://xkcd.com/1381/
Just make a file system that maps each file name to 2 files. The 0 file and the 1 file.
Now with just a filename and 1 bit, you can have any file! The file is just 1 bit. It’s the filesystems that needs more than that.
That’s precisely when you bet on it.