Four Letters
The oldest stored information there is, and the one file everybody carries.
This is a small piece of a human being. It is the DNA of the mitochondria, which is handed down from the mother, and it is 16,569 letters long.
It was first read in full in Cambridge in 1981. There are only four different letters in it.
A text file spends eight bits on every letter. Four letters need only two.
That divides the file by four before anybody has had an idea.
Now try the methods from the first room on something larger, the 4,641,652 letters of a bacterium that lives in the gut. The line marks two bits a letter.
gzip does worse than the plain two bits. The best of them only just gets under the line.
A model built to guess each letter from the ones before it reaches 1.94 bits.
Read along its length, DNA is close to the random file from the first room. There is very little pattern to find.
The saving lies somewhere else. Lay one person's DNA beside another's and they agree almost everywhere.
These two people differ at 42 places out of 16,569. Step through them.
Here is a Neanderthal who died in what is now Croatia about 38,000 years ago, beside the same modern reference.
There are 212 differences.
So do not store the genome. Keep one reference for everybody, and for each individual keep only the list of differences.
The Neanderthal's list takes 465 B. The sequence itself takes 4.15 kB even at two bits a letter, which is 8.9 times as much.
Your whole genome is about three billion letters, some 775 MB at two bits each. Any two people agree at about 999 letters in every thousand.
In 2008 a team in California stored the genome of James Watson, who helped to work out the structure of DNA, as its differences from a reference. It came to 4 MB, small enough to send as an email attachment.
You have seen this move before. A frame of film is an earlier frame with corrections. A point on a rabbit is a guess with a small miss.
A genome is somebody else's genome with a list attached.