I am running the Proof of concept run now. That is Encode and Decode the whole MDF while verifying the observation that only two choices are presented.

I will try and compress the “Choices” data. Maybe I might get lucky as that data is not directly derived from MDF

It will take a while. So I’ll update later.

Nice results to see mathematically solid results.

]]> I have come up with a new way to dissect binary numbers and wouldn’t ya-know, it will not let me get away with anything.

In fact it mocks me!

Just to be a little vague since this is new and an active work in progress. Imagine that to pattern match we generate a 16 bit data. We get an exact match with 16 bits but keeping the 16 bit data and using 14 bits to match with I get 4 , exactly 4 matches for all. Go to 15 bit all give exactly 2 matches.

The pisser is with the “4″ matches they end in 01, 10, 00 and 11 ALL of them! No duplicates! So in order to “match up I can pick those two bits on the end to match but that makes it 16 bits!!

So yes this effort is a valid maths but Physics is laughing at me.. Saying “Nice Try.”

OMG!

]]> The chances of pulling equal amounts of set and reset bits is a natural artifact of this MDF.

From all observations and efforts I have made and on every level and in every algorithm I have designed tell me I am in Random-Ville.

Mostly my efforts are Mathematical and deal with Value and Symbolism.

I enjoy this as a hobby because of Asperger Syndrome I do believe. I had an introduction to computer programming class with “C” in 1992 and discovered “cyclic” functions. That was it I was all in!

I love them. All I do is write these types of algorithms.

As for the prospects of ordering bits, I have to admit I can imagine writing algorithms. I know couple-three ways to do such things.

It would be a winner if we could separate 0s’ from 1s’ and be able to put them back in correct parity order.

Lets see that would be the size of the decoder and Two 32 bit integers? Naturally with MDF one 32-bit integer as a base value and two smaller integers as count offsets so actually less than 64 bits are needed.

Ah, I have gone back to the expand then compress efforts. I expanded to (2 * 415241) + 1 and last “compressed” count was down to 416,105 bytes.

I have no plan as I start to work this morning but I will review the file and see if I can find an exploit.

I was able to get the previous effort’s data stuffed back into 415241 bytes after a 4 stage process.

The thing is if I can get a consistent reduction without too much meta-data cost then I win. So far even on the bit level Physics always wins.

Alright, have a good one. I keep at this because it is fun for me. I already contributed to Science with Dynamic Unary, for all time so, I don’t face failure in life even if I never compress MDF

]]>Thank you for the info about Dynamic Unary. I’m afraid I don’t have any suggestions though. I have an idea about scrambling the file in a deterministic way for easier compression, but I’m not sure if it will help any yet. Good luck. ]]>

Both are 415241 bytes so heh.. MDF gets 5 bytes compression?

Oh well..

Back to looking for an exploit.. Found this one. Was able to get it down to 415241 from 467172

However gzip reports 412215 now after this last formatting.

So This is good! I actually have something to check up on that doesn’t look like magic compression and 3000 bytes is a doable size for a decoder if the text is compressed which i understand is allowed.

So cool..

Like always it isn’t done till it decodes.

]]> 1 > 519207

2 > 233685

3 > 58193

4 > 14642

5 > 3613

6 > 934

7 > 232

8 > 63

9 > 15

10 > 2

11 > 3

These are Unary codes. Any suggestions?

1 > 103740

2 > 103587

3 > 104111

4 > 25788

5 > 25958

6 > 25949

7 > 6485

8 > 6476

9 > 6566

10 > 1590

11 > 1661

12 > 1592

13 > 410

14 > 378

15 > 411

16 > 110

17 > 118

18 > 97

19 > 28

20 > 23

21 > 27

22 > 1

23 > 9

24 > 6

25 > 1

Close.

I’m looking hard for some exploit. Have to get the size down to start with.

I doubt any one ever got it down below 415241. Perhaps decode size should be waived.

]]>Simmons saw the “Half Cycle” of dynamic unary for parity reference b(n-1)where n-bit is the n and b0 is the first bit. He uses xor cleverly so if we start with a string with infinite zeros to the left and we progress xor bitwise such as …00000001010 Starting left 0 xor 0 = 0 and is so until we get to the first set bit so 0 xor 1 is 1. Set that bit in an out string and the result is 1 so xor that with the next which is 0 and the result is 1 so out that.then next bit to the right is 1 so 1 xor 1 is 0 so out that parity, then last is a 0 bit and xor 0 is 0 so for this clever observation : 01010 ( 4 significant bits ) length 4 in Dynamic unary the cycle is 1010 > 1100 :

You may apply that to this new value and get “1000″ then “1111″ and 1010. So in cycle notation ( 1010 1100 1000 1111 ) and back to 1010

Okay so I did find his work, his last paper published that I know of, as I was writing my attempt at presenting Dynamic Unary.

In dynamic unary we count same parity segments and record them with unary code whose terminus is the parity of the bit at a specific bit position.

For “1010″ the b0 is 0 and the b3 is 1 we will choose parity reference b3 and so our terminus is a set bit this time. So Pref b3

1010 from b(0) to b(n) count 1 bit of 0 parity write unary code 1 because 1 = 1 and “10″ is two. so b(0 in new is 1, then 1 bit of 1 parity write 1 again next 1 bit of 0 parity again write a 1 and last one bit b(3) is a 1 parity also write a 1. so 1010 > 1111

Now 1111 and again PRef is b3 so Terminus is a set bit but we have 4 set bits so code is “1000″ now ( 1010 111 1000 ? ) 1000 Pref again 1 three “000″ and one “1″ so “1100″ now ( 1010 111 1000 1100)

So 1100 Pref still b3 and we have “” and “11″ so “1010″ complete cycle.

Simmons hypothesized about the full cycle but even with help they did not discover dynamic unary and in his paper “Parity Encoding of Binary Sequences” we see the master work of one who truly can write a paper!

So I feel good to have found supporting work for Introduction to Dynamic Unary encoding”. I felt even better to find they had searched and failed to find the bigger picture naturally. What a disappointment it would have been if I had found complete prior art huh!

I followed the example Simmons set down. Simmons does not spell out the algorithm directly. He expects the reader to “reason” and realize what he is saying. A True “Ah HA!” moment and I really liked that.

However, too much of that is what I did with Introduction to Dynamic Unary Encoding.” I expect the reader to delve into deep “Ah Ha(s)’!

Basically just pick a reference point. whatever parity is there that is your termius parity. So 100 is equal to 011 and both are three in Western Positional Notation.

Hence 10010101 with a parity reference of b0 (PRef b0) becomes 11011111 -8-bit n-bit there PRef b0 encode direction

It is true I have done it so much I can simple read it straight away encode and decode directions with ease.

——————-

Now once we realize that with any n-bit the whole 2^n number of integers partition into disjoint cycles. and with PRef b0 and PRef b1 add all the integers up in each separate cycle and each cycle ” sums to the same value as all cycles do.. How cool is that.

Anyway pick three n-bits and cycle them and pick a source such as MDF. Now A, B, C are cycling and we MDF xor A xor B xor C and cycle A,B and C then repeat with the result of the first. In time MDF will show back up but like 5 million 415241 files later.

So yeah if we have the right A,B and C and pick maybe PRef b1 as PRf b0 generates a set of parity inverted as part of the cycle then in one of those 5 million there will be some file that will compress.

Hell in one of those 5 million files might be the formula for the Theory of everything.

Mark talks about infinite files but with dynamic unary it is always finite.

Personally, I should reinvest my time this next over-winter and try to do just that.

I should search for a compressible file in a constructed cycle.

I also should write a much more simpler work on dynamic unary. It is a real maths.

As Simmons was looking for it is the Universe of logical operations. The “Complete cycling of XOR.”

———————-

Now on to some fun I did last night.

I took and looked bit by bit at MDF. From the Byte0 and from Byte 415240: I skipped the byte in the middle.

If the two bits matched 1 == 1 0 == 0 I set a bit in position in an outfile. If they were different say low end bit was 1 and high end bit was 0 that too got a set bit in its file.

So three files. One for if 1 && 1 one for 0 && 0 and one for 1 && 0

The positions of 0 && 1 are relative to what was left. No need for a file of it’s own.

So I have been playing around with that. Had as low as 454,000 ish bytes at one point. Last try with a new format was 501,000 bytes.

Any ideas on processing? It was a silly whim but turned out interesting.