I’m very pleased to announce that after eight years of research and development, I can present the world’s most revolutionary filesystem: πfs!
What is πfs?
πfs is a revolutionary new file system that, instead of wasting space storing your data on your hard drive, stores your data in π! You’ll never run out of space again – π holds every file that could possibly exist, so why put your files anywhere else?! They said 100% compression was impossible? You’re looking at it!
What does π have to do with my data?
π (or pi) is one of the most important constants in mathematics and has a variety of interesting properties (which you can read about at wikipedia)
One of the properties that π is conjectured to have is that it is normal, which is to say that its digits are all distributed evenly, with the implication that it is a disjunctive sequence, meaning that all possible finite sequences of digits will be present somewhere in it. If we consider π in base 16 (hexadecimal) , it is trivial to see that if this conjecture is true, then all possible finite files must exist within π. The first record of this observation dates back to 2001.
From here, it is a small leap to see that if π contains all possible files, why are we wasting exabytes of space storing those files, when we could just look them up in π!
Every file that could possible exist?
That’s right! Every file you’ve ever created, or anyone else has created or will create! Copyright infringement? It’s just a few digits of π! They were always there!
But how do I look up my data in π?
As long as you know the index into π of your file and its length, its a simple task to extract the file using the Bailey–Borwein–Plouffe formula Similarly, you can use the formula to initially find the index of your file
Now, we all know that it can take a while to find a long sequence of digits in π, so for practical reasons, we should break the files up into smaller chunks that can be more readily found.
In this implementation, to maximise performance, we consider each individual byte of the file separately, and look it up in π.
So I’ve looked up my bytes in π, but how do I remember where they are?
Well, you’ve obviously got to write them down somewhere; you could use a piece of paper, but remember all that storage space we saved by moving our data into π? Why don’t we store our file locations there!?! Even better, the location of our files in π is metadata and as we all know metadata is becoming more and more important in everything we do. Doesn’t it feel great to have generated so much metadata? Why waste time with old fashioned data when you can just deal with metadata, and lots of it!
Yeah, but what happens if lose my file locations?
No problem, the locations are just metadata! Your files are still there, sitting in π – they’re never going away, are they?
Why is this thing so slow? It took me five minutes to store a 400 line text file!
Well, this is just an initial prototype, and don’t worry, there’s always Moore’s law!
Where do we go from here?
There’s lots of potential for the future!
- Variable run length search and lookup!
- Arithmetic Coding!
- Parallelizable lookup!
- Cloud based π lookup!
- πfs for Hadoop!