Re: compression - insights into infinite

On Jun 2, 2:36 am, Thomas Richter <t...@xxxxxxxxxxxxxxxxx> wrote:
jules Gilbert schrieb:

Peter, if I thought you'd actually answer technical questions
intelligently, I'd ask -- and right now I have some questions!!  So
where are the folks with the doctorates in math?  

Their are all here, and they keep telling you that elementary logic is
enough to tell your two new schemes don't work if they compress
everything down to a byte. Well, the decompression at least won't work.
*Compressing* to zero bytes is actually the easy part. (-:

Because I was up
until 6AM or so Saturday morning trying to resolve a couple of topics
within my biz plan.

Before you setup a biz plan (unless it's the biz plan of a con-man) you
should get your decompressor working; and before that, you might want to
get your math straight. Just answer the following simple question:

How many different files of two bytes length are there?

That's your homework. Don't be shy if you cannot solve it, the math
cracks are all here.

So long,
        Thomas

I understand your logic Thomas, and would agree with your conclusion,
but for one small fact...

[Insert long and spirited defense here... Sigh. Just like you folks,
I am getting pretty tired of this.]

Briefly, one sentence, I can reduce randomness, even in a very small
amount of data, as I said, a buffer, measured before and after, shows
up as less random after the process -- and no additional information
must be conveyed to the receiver.

The 'measurement' is, as I have said, the "stats" routine in the C/
Math library, basic?, yes. Useful?, incredibly. Wrong?, not very
likely. I'd suggest that maybe I'm measuring something erroneously or
perhaps coming to the wrong conclusion from well constructed
measurements, but since I think I've done everything correctly my next
step is to work with someone who can help me to build a nice
compressor/decompressor package.

What might work is to publish some of this data, say in an FTP site
and let people examine it.

My early work with this method is best described this way:

a) An INPUT cell, let's stay with bytes for this example.

b) OUTPUT cell, residue, part A. The problem with this was that some
cells, say 5% (wrt a 1-byte organization,) were in excess of 8-bits.
Not very convenient for a compressor, of course. The other cells
were, typically, reduced by at least 1-bit.

Now, having done additional work, I have much smaller residue's and no
bytes in excess of 8-bits. In fact all output cells contain,
typically, less than four bits. Frequent output values are 4 and 5,
for example. Plus a sign bit, but the sign bits compress quite
handily. (They are best converted into sequences of primes.)

Another value, needed to reconstruct the original value, isn't sent.
It's inferred on the receiver side. Remember my two-bit compressor
that worked by inferring the sign bit? This reconstruction *may* be
imperfect, but I have a simple inductive proof that, worst case, the
information that must be sent is always less than 8-bits. (I don't
mean that the compressor may be lossy, I am concerned to produce a
space reduction all the time -- that's what I mean here.)

My proof depends on something I can do in a CAS but don't have the
math to work out by hand (ie., to understand.) Still, I can build a
symbolic system that I'm sure wouldn't work if the mathematics I am
depending on were deficient.

The savings (the information that need not be sent,) varies with the
organization, but I think I can demonstrate at least a single bit per
byte savings.

But before I commit to doing this, can I see a show of hands of people
who would look at the data, please.

--jg

.

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