Quantum theory + NURBS curves + P2P.

I was hallucinating while sitting there on the bed and a few thoughts crossed my mind in a flash. And luckily, I was able to remember them quite vivdly too. Actually, these were the questions I was toying with for quite some time.

So on with the questions:
1. We know that the data from a wave file can be represented in the form of waves, which in turn can be represented mathematically. The mathematical expression can be quite smaller than the sampled version in the wave file.
In 3D softwares, there's an equivalent version of mathematically efficient method of representing a 3D model, NURBS. Non-Uniform Rational B-Splines, are mathematical representations of 3-D geometry that can accurately describe any shape from a simple 2-D line, circle, arc, or curve to the most complex 3-D organic free-form surface or solid.
So the question is,
"So why not a mathematically efficient form for defining an arbitrary data file?"
Ofcourse, I understand that wave files and 3D models have certain parameters and a basic structure to it which is lacking in our arbitrary data file. But I want to try and see for myself why and how it WON'T work.

2. If you thought the first thought was crazy, wait till you hear this. I was thinking of the parallel universe as explained by quantum theory. The theory in its basic form tells us that, if the is a probablity of one event happenning is 1 in 100 then, there will be 100 parallel universes where each unique outcome exist in each universe. Mind bogling it may seem, the whole concept of quantum cryptography relies on parallel universes' existence, and it seems to work too. So no questions there.
So, following this theory, if we look into our past, it looks like we have had a pre-determined path down the time line. So I thought,
'Is this what people mean by fate/detiny? And can we predict in which branch we will be in the future? And if so, it is as if there was no probablity in the first place.'
Whatever.
But my real musings were to trace the tree back to its root and find out what the odds of our current universe being created looked like. This looks like the famous 'Sum over Histories' theory by the inimitable doctor Richard C Feynman, though I don't know much of it to conclude if it is the same.

3. Now the third question combines both the quantum theory and mathematical curves with Peer-to-Peer communication. No, it's not encrypting a wave file with quantum cryptography and P2P ing it.
I was involved, along with my friend Balakrishnan, in a project that aimed to create a P2P architecture that eliminated discovery servers in the form of central, napster-like one or a distributed, gnutella-like one. We chose to experiment with pinging the IP addresses of clients returned by a deterministic formula sequentially throughout the ISP's IP space and hope that there is a client running a P2P protocol in the IP pinged. As expected, this is very inefficient and unreliable, since the client is assigned a dynamic IP from a pool of IP addresses by the ISP. There is no pattern for predicting where in the IP address space of the ISP an online client exists.
Quantum theory suggests that electrons in an atom are not exactly locatable due to Heisenberg's uncertainity principle. So they are represented as Electron clouds rather than individual particles. If we consider the ISP as an atom, its IP address space as the volume of the electron cloud and each position in that volume as an unique IP address, then each electron is a client. And at any instance, the position(IP address) of the electron (client) cannot be found out, ever. I know that I am omitting the 'momentum' factor here, but I can't find a relevant equivalent anywhere in this picture. So, I wanted to know,
'Can quantum theory be applied in P2P models (if not ours)?'
Wait...where's the mathematical curve idea in the third question? It's just that, I wanted to use the mathematically compressed files in P2P to reduce traffic, that's all.

So there ya go. The awesome ponderings of the idle mind.
(Warning: The above were from my own mind. Some of the information maybe correct and if so, I hold the IP right ;) )