From: LawCounsels on 12 Aug 2010 02:04 Warm Greetings : Am pleased now in position Press Release to experienced reputable Forum members ( Atomic bomb was thought a 'Newtoninan' impossibility , didnt stop many trying ... latest Iranian as yet unsucessful attempt, N Korea much luckier , India /Pakistan did it kept confidential .... C# knowledge prefers ) : kindly please reply email will do : " I shall keep all disclosure re new generation data compression methods in commercial confidentiality , only ever to do only with prior written consent " will forward the mathematics basis overview & mathematics proofs , to begin 'profit shares' confidential collaborations/ further developments etc. this forms the 'rigorous' mathematics basis , like so called Einstein's maths overturned all Newtonian this to begin 1st familiarise with an invented discovered mathematical object [ mathematics proven by Australia NSW senior Maths Professor, & Polish mathematician independently ] whereby any 'random (or not)' N bits (iteration's input string ) with 2^N possibilities can ALWAYS INVARIABLE be complete covered represented by ONLY a few smaller number of lesser length bits_string of length N1 or N2 or N3 ... NP [ P around log(base2)[N] ] .... you would then definite able decide => near infinite data representations follows mathematically [ naturally ] Australian Professor was even more sceptical but am now content with this 'new Maths foundations discovered like 50 years late than could have been invented discovered then with Kind Regards, Intellectual Properties Holding International LTD eFAX : +001 484 3464116 [ Q ] QUOTE (LawCounsels @ Aug 11 2010, 04:38 AM) whereby any 'random (or not)' N bits (iteration's input string ) with 2^N possibilities can ALWAYS INVARIABLE be complete covered represented by ONLY a few smaller number of lesser length bits_string of length N1 or N2 or N3 ... NP [ P around log(base2)[N] ] .... you would then definite able decide Then the logical implication of being able to compress any sequence of N bits to M<N bits is that by repeated application you end up with a single bit. You're claiming you have a perfect lossless compression algorithm for any input sequence, thus you're claiming you can encode any amount of data of any time into a single bit, which is obviously false. There's a mathematical theorem which formalises this. Lossless compression algorithms rely on the fact the algorithm will be applied to specific types of data. Human written text is easy to do, since it follows specific rules. Compressing random noise losslessly is impossible. Any compression algorithm which is lossless will be able to make a file for random noise but it will be bigger than the amount of data in the random noise (due to the algorithm file overheads). If you claim otherwise then you should be able to correctly decompress a single bit into anything. For instance, the three sequences 00000000, 01010101 and 11111111 could be compressed to the single bit, either 0 or 1. But if I give you 0 and 1 then you can only give me two of those three sets with confidence (and that's ignoring the infinitely many other sequences). Obviously your claim is impossible. [ A ] >>whereby any 'random (or not)' N bits (iteration's input string ) with 2^N possibilities can ALWAYS INVARIABLE be complete covered represented by ONLY a few smaller number of lesser length bits_string of length N1 or N2 or N3 ... NP [ P around log(base2)[N] ] .... you would then definite able decide the mathematics proof (independent proven by reputable University senoier maths professor, & Polish mathematicians) is as above stated .... mathematically it does not follow that any bits string can be compressed into 1 bit ... not difficult to deduce mathematically this is impossible (starting from above stated :) [ Q ] QUOTE (LawCounsels @ Aug 11 2010, 12:42 PM) >>whereby any 'random (or not)' N bits (iteration's input string ) with 2^N possibilities can ALWAYS INVARIABLE be complete covered represented by ONLY a few smaller number of lesser length bits_string of length N1 or N2 or N3 ... NP [ P around log(base2)[N] ] Those N bits don't sound too random, then. [ A ] >>Those N bits don't sound too random, then the maths proof (also further mundane practical verified TRUE by 'brute force'enumerations , like in Reimann's largest prime 'brute force' ) shows works whether N bits 'random' or even if not random N bits :) [ Q ] QUOTE (LawCounsels @ Aug 11 2010, 07:19 PM) >>Those N bits don't sound too random, then the maths proof (also further mundane practical verified TRUE by 'brute force'enumerations , like in Reimann's largest prime 'brute force' ) shows works whether N bits 'random' or even if not random N bits Yuk, yuk ... the definition of a "random bit string" is pretty much "not compressible". No, I'm not going to give a long treatise supporting that statement. Bye, bye. [ A ] >>Yuk, yuk ... the definition of a "random bit string" is pretty much "not compressible". No, I'm not going to give a long treatise supporting that statement. Newtonian defintion says pretty much the same thing .... thought there was this 'relativity' definition which profound changes things ( or just changed 'definitions' nothing more (?) ) [ Q ] QUOTE (AlphaNumeric @ Aug 11 2010, 12:30 PM) Lossless compression algorithms rely on the fact the algorithm will be applied to specific types of data. Human written text is easy to do, since it follows specific rules. Compressing random noise losslessly is impossible. Any compression algorithm which is lossless will be able to make a file for random noise but it will be bigger than the amount of data in the random noise (due to the algorithm file overheads). This is untrue. Simple runlength encoding can losslessly compress random noise and obtain a smaller byte count than the original. it's not LIKELY to happen given true random data, but it is possible. I can demonstrate this with a simple example if you would like. [ A ] >>This is untrue. >>Simple runlength encoding can losslessly compress random noise and obtain a smaller byte count than the original. it's not LIKELY to happen given true random data, but it is possible. yes like all Newtonian Mechanics will say Relativity simply untrue given all known Newtonian many real observations examples mathematics proof of Einstein was then understood by few , but these few are the ones whom really matters because all mankind's earthconfined Newtonian observations of light in a straightline , it took physicists some Solar Eclipse years to affirm new bendlight observations earlier was it Corpenicus (?) says earth is round not flat , & for decades no one has observed this even after suggested
From: LawCounsels on 12 Aug 2010 06:21 here is link to download a 'mathematics structure' encoding of a complete random 4,074 bits long file (a random chosen part of Mark Nelson's AMillionRandomDigits.bin challenge) www dot box dot net/shared/eyy2v28dbf download link's new discovered 'mathematics structure' endoded file's details .. in a file with N bits (sufficient large like 8Kbits onwards to 1Mbits) , assume the distributions of unique prefix '0's or '10' or '110' or '1110' ... or '111...10' (always ends with a '0') is standard binomial power (ie random) , BUT with added constraints/ restriction that the maximum length of '111....10' at any time could only be at most log(base2)[R] where R is the total # of bits from present bit position to the end Least Significant Bit position [ eg if bits_string is 0 111110 11110 10 0 10 110 10 0 10 0 10 0 0 ' then here 110 is the 13th bits , there can be no unique prefix of total# of bits length > log(base2)[R] at any time, where R is the bit position # of the unique prefix counting from end Least Significant position bit ....] .....so this is not simple regular usual normal binomial power series/ random distributions [ usual normal binomial power series/ random distributions is 'god gifted' not to be compressible] , but here there is added constraint/ restriction that eg '1110' ( of length 4 bits long) could not occur at position R = 15 or smaller (since log(base2) [R=15 or smaller value of R] will not allow unique prefix of total# of bits >= 4 to occur at position R < 16 ...... THIS IS IMMEDIATE APPARENT READY COMPRESSIBLE 4,073 bits 'constraint' 'mathematics structures' encoded (1 bit smaller) file , from input random 4,074 bits 'random' file

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