From: CallmeaceOkay, very interesting reading your posts
I had kept thinking of how to respond and put across what I wanted, so here goes...
Many of you seem stuck on a problem of how to allow for 'all possible combinations' and of random numbers and so forth. These are presented as disapproving the concept I present, but in my concept,
These things are not an issue which will need to be dealt with. Let me explain I hope
I think this will answer Manaos post.
Data compression is a challenge. It's hard to compress data but it's not so hard to represent a long number by much less characters which can be put back into a formula, so we first represent the data which we want to compress as a number.
Do you recall in earlier posts here that I said about unique character string? And also that a number 'is only that number'?
Do you see that immediately we have a case in maths where (so long as you set the rules) equations will only give one result.
In stages, What the concept does is first present, via code-book and mapping, the data which you want to compress as a series of numbers, unique to that data for being derived from it. Note that the mapping and code-book use also allows essential 'reversing'. Then in following stages the number is broken down into equations which would use powers and algebra for example, until one is left with a character string.
When you want your original file back, the character string when fed back into the formula generates back up to your original data number, This is because it 'adds up' to the number mathematically, which at the end is reversely written (possible because of the code-book and mapping) back into your file.
Now, how could one get a number from some data? Hmm..... Well, here is one way just as a concept suggestion. On any computer.
Firstly, understand that functions can be performed on the hosting computer, so you want to get a number unique to any file? will you allow that the binary information of the file must exist with any PC? We could use that! It will be a unique number unique only to that file and derived from it.
So in stage one The formula maps this binary information of the input file as continuous code being a long number consisting only of the digits 1 and 0. Let me explain what I mean by that. We literally want to use this binary code as a long numbers without spaces, but there are naturally going to be limits hit on how big a number could be. imagine a string consisting of 0s and 1s in a text document being as an actual number (like 1001 is 'one thousand and one') but being much longer. So rather than having the binary data of the input file as a huge unmanageble number in the form of an incredibly long sequence of binary, this would be cut in sections which are mapped to blocks, as a number at the biggest size which can be handled.
So regarding the above, as the numbers only contain 1s and 0s, even better! How much easier to handle and compress
We know that they all must be multiples of ten plus with or without an added one!, and the numbers beginning with 0s must have their S.F. (significant figures count) accounted for too.
So, we have lots of mapped blocks each consisting of a big number whose digits are either 1s or 0s.
In case I have lost you, Remember that these blocks are just cut sections of the original huge continuous number which is the binary code of the input file. We want to break this number down through a series of formulas and various Mathematical and other compression techniques like mapping, to a string of characters. The string of characters when put back into the formula will then generate that number (which will then be put back to your original data)
For the sake of argument lets say that a thousand thousands are a million, a thousand millions are a billion, a thousand billions are a trillion, and a thousand trillions are a zillion. This is much much smaller than it would really be but lets say each number (block) doesn't exceed the zillions.
I will insert commas here just for clarity, Imagine then that the first block has the number
Block01: 10,010,001,010,011,100
the second has
Block02: 110,101,001,110,101,001
and so on
in this stage it would maybe be that every block is given a multiple or power of ten number and flagged as having plus one or not and a SF number - this is just a suggestion
Remember that all this work is taking place running through the process, to be under 64KB its only the formula and the character string total we are concerned about.
In the following stages I'll leave to your imagination the advanced calculations from years of mathematical thinking which could be employed. But you would end up with a character string.
In all this quite briefly stated above I think I have shown the concept better than before. Can you see that there is no need to worry about infinite combinations of numbers and the like, there is no concerns about hashes not being reversible or anything like that. Those issues would not be encountered. The maths itself is simple but the mathematical techniques and knowledge would assuredly be complex and advanced to generate the character string.
Dificult and a painstaking task requiring dedication, yes. But it's
not unrealistic, impossible or anything like that.
:edited add some clarity I hope
