FRIENDLY OPEN LETTER TO M MAHONEY : in same spirit as Bohr - Einstein's

[LawCounsels]

Hi Matt :

Among the proven technical competent respected long time experts on comp.compression I have
established respected status for many
earlier 'breakthrough' 1st of its kind in world
works introduced to Forum... Among them I can
safely add the illustrious 'Thomas Richter'/
'James Dow Allen'/'David Scott's/'Sportman'

I can assure I was earlier had been similar
annoyed by many previous 'ill-conceived'
groundless completely wild claims circulated ( without any new 'proofs' supporting)

But as we all know time does nor stand still,
what was once 'bible' truth faces way to
mankind's new breakthrough discoveries :
At one time 'time-travel' has 0 probability, now
now after Einstein & the likes of recent Nobel
laureates New works

I am now 100% satisfied with New 'breakthrough'
Theory in place, that I can immediate now
confirm indeed it complete overturned centuries
old 'pigeonhole' beyond any doubt... & this is not
so difficult!

Perhaps we can agree to come to some private
confidential agreement, whereby this would
now be confidential peer reviewed by you...
Of course you may then announce publicly
whether you indeed find them true ( & we can proceed collaborate claim jointly various $1M Clay prizes) or 'same as many before groundless'

Let me know how to proceed : )

Warm Regards,
LawCounsels

[Piotr Tarsa]

Good luck, new Einstein!

[Matt Mahoney]

Science advances on open publication and independent replication of results. That doesn't mean you can't get rich from your discovery. That's what patents are for.

[LawCounsels]

THIS TO INTRODUCE THE 'BREAKTHROUGH' :

Stephen Wolfram's NEW KIND OF SCIENCE : simple basic rules CREATE COMPLEXITIESHe stumbled upon simple rules ( small # of bits of data ) creating generating RANDOM numbers (very large # of data bits ) : satisfied every single possible tests for RANDOMNESS

... This occupied him tremendous eventual wrote "ORIGIN OF RANDOMNESS" whereby he cryptically hypothesize various conclusions ...

he was held back because only able to generate RANDOM numbers from simple basic rules BUT could not start with the RANDOM numbers and reduce back to simple basic rules

WE HAVE SUCCEEDED START WITH RANDOM NUMBERS ITSELF VERY LARGE # OF DATA BITS & REDUCES BACK TO MUCH SMALLER # OF DATA BITS .... AND THIS WORKS FOR ANY POSSIBLE RANDOM NUMBERS SERIES !!!!

New future data inventor and implementor ... recruiting now : contact LawCo...@aol.com IMMEDIATE if fluent with C# or C++ or C & basic combinatorics index ranking/unranking & optional data compressions basics , ALSO if experienced CFO etc etc collaborators and research scientists welcome to contact with LawCo...@aol.com

URL : https://app.box.com/s/qisaye2da410jzbebdzk

[Bulat Ziganshin]

if you can squeeze any 2-bit data into single bit, it will be great math breakthrough

[Bloax]

Bulat: Are you implying that 0 and 1 can't be used to store either of 0, 1, 2 and 3 - and that 0, 1, 2 and 3 can't store either of 0, 1, 2, 3, 4, 5, 6 and 7? surely you ought to know better than that!1!1eleven

[LawCounsels]

if you can squeeze any 2-bit data into single bit, it will be great math breakthrough

I'm afraid this is impossible!

There is some fundamental mathematical
requirement/ limitation that the compressed
bitstring be of certain minimum fundamental
size ( like Wolfram's basic rules requires certain
minimum storage, even 'blackhole' s compressed
information must be fundamentally minimum
proportional to its spherical area ( transforming
3 dimensions amount of volume of informations
dropped into it into 2 dimensions amount) )

[LawCounsels]

COINCIDENTAL : PHYSICISTS ALSO DISCUSS QUANTUM PIGEONHOLE PRINCIPLE , FROM THEIR
QUANTUM PERSPECTIVE

http://www.google.com/url?q=http%3A%...rAkTfvopgdE9sQ

[LawCounsels]

>>http://phys.org/news/2014-07-physici...principle.html

Those physicists will be mightily even more astounded to now find out realise traditional 'binary to binary direct mapping' pigeonhole was in fact had been a total complete illusion in 1st place ( Svengali like retarded advancements in world sciences)

... Needs not had proceed resort to seek a quantum solution : )

[Bloax]

Well how do you stuff four pigeons into two holes without there being two pigeons in either of the holes? Because if you can't do that then you can't stuff eight pigeons into four holes either, nor can you stuff 16 pigeons into 8 holes (continue ad nauseum).

[LawCounsels]

Well how do you stuff four pigeons into two holes without there being two pigeons in either of the holes? Because if you can't do that then you can't stuff eight pigeons into four holes either, nor can you stuff 16 pigeons into 8 holes (continue ad nauseum).

BUT so to speak Wolfram's basic rules ( or blackhole's
transform volume information into spherical area quantity) can SUPERCODE represent any sufficient large random inputs eg 1Mbytes into much smaller eg
200Kbytes equivalent compressed representations!

If you have 2^500,000 pairs of 2-bits of information
units, you can always group these together into
1Mbytes input random file, then proceed SUPERCODE
into smaller eg 200Kbytes compressed information
representations : )

NOTE : topmost mathematicians have always
known pigeonhole was never any kind of mathematical disprove of random compressibility ... it was always
from beginning like 'very good common sense housewife story/parable which stood the time acquired
mythical truth status ( because no one had
before succeed prove the other way )

[LawCounsels]

*If you have 8* 512K pairs of 2-bits of information units
........

[Kennon Conrad]

BUT so to speak Wolfram's basic rules ( or blackhole's
transform volume information into spherical area quantity) can SUPERCODE represent any sufficient large random inputs eg 1Mbytes into much smaller eg
200Kbytes equivalent compressed representations!

If you have 2^500,000 pairs of 2-bits of information
units, you can always group these together into
1Mbytes input random file, then proceed SUPERCODE
into smaller eg 200Kbytes compressed information
representations : )

NOTE : topmost mathematicians have always
known pigeonhole was never any kind of mathematical disprove of random compressibility ... it was always
from beginning like 'very good common sense housewife story/parable which stood the time acquired
mythical truth status ( because no one had
before succeed prove the other way )

*If you have 8* 512K pairs of 2-bits of information units
........

Ah, of course, SUPERCODE! What an amazing concept! If only we had thought of that sooner......

Has it occured to you that a compressor that consistently fits the 2^8,000,000 equally likely unique combinations of 4,000,000 pairs of random bits into only eg. 1,600,000 bits would defy basic laws of compression?

[LawCounsels]

In reply to Kenneth Conràd :

I will 1st digress post here another fast gaining reputation researcher's proof how he provable overcame illusory 'pigeonhole' myth :

[ this is his particular solution, there can be various
different solutions! Not only this here! RE : making
a rare enough bitsstring even RARER! ]

[ From comp.compression : Jacko ]

> >> if you can squeeze any 2-bit data into single bit, it will be great math breakthrough

it would

> I'm afraid this is impossible!

yes, but not for the exact reason you may suggest.

> There is some fundamental mathematical
>
> requirement/ limitation that the compressed bitstring be of certain minimum fundamental size ( like Wolfram's basic rules requires certain
>
> minimum storage, even 'blackhole' s compressed information must be fundamentally minimum proportional to its spherical area ( transforming
>
> 3 dimensions amount of volume of informations dropped into it into 2 dimensions amount) )

This is more like it. A possibility of a rare enough event which can be made rarer, so that over time this level of rarity can be detected does limit the minimum information size of a single stream.

http://phys.org/news/2014-07-physici...principle.html

Just for fun, discover the 3 things in two boxes with none being doubled up. I'm sure the experiment will be done. Non-commutative field algebra is not your standard binary to binary direct mapping.

[LawCounsels]

In reply to Kennon Conrad :

More over the so-called
'Supercoded' compressed bitstring
DOES NOT need to be a fixed particular
Eg 1,600,000 bits... 'Supercoded' compressed
bitstring can be variable lengths from Eg 1,600,000 bits
to Eg close to 8Mbits ( slightly less) !

ITS EASY ENOUGH CLEAR SEE NOW THAT
'pigeonhole' weaved its illusions falsely
imposed its own unasked for biased-coin ( head I win - tail I win) restriction that
the compressed bitstring be ALWAYS an exact particular fixed size!!!!

[ ... there really are a lot more than
reasoned shown above : ) ]

[LawCounsels]

>>Ah, of course, SUPERCODE! What an amazing concept! If only we had thought of that sooner......

>>Has it occured to you that a compressor that consistently fits the 2^8,000,000 equally likely unique combinations of 4,000,000 pairs of random bits into only eg. 1,600,000 bits would defy basic laws of compression?
Last edited by Kennon Conrad; Today at 22:13.


BLACKHOLE ALREADY PROVEN BY BERKEINSTEIN/
LEONARD SUSSKIND ( holographic Universe fame) etal, to compresses 3 Dimensions volume of informations INTO
much smaller spherical area quantity of informations

... proving 'pigeonhole' fundamentally
illusory false

[Bulat Ziganshin]

If you have 2^500,000 pairs of 2-bits of information
units, you can always group these together into
1Mbytes input random file, then proceed SUPERCODE
into smaller eg 200Kbytes compressed information
representations : )

what is the minimum data size that can be squeezed with guarantee? i.e. is it enough to have 3,4,5... bits to reduce them by 1 bit with guarantee?

[LawCounsels]

what is the minimum data size that can be squeezed with guarantee? i.e. is it enough to have 3,4,5... bits to reduce them by 1 bit with guarantee?

( I'm sure you will certain appreciate professionals integrity/ courtesy here)

All I am allowed to say at this time, & as best I can :

If you have Eg 8,000,000 bits random input you
are already very highly certain you can 'squeeze'
8 bits savings ( actually paltry 1Millionth bits savings)

.. If you have Eg 10 Times as much
input random full-size THEN your are already closest
to 'GUARANTEED' ( which you sought)

This may look small 8 bits savings an literation ( you had thought just Eg few bits random input may guarantee 1 bit saving ?)

however resultant 8 bits smaller 10* 8,000,000 bits
can further be processed iterated upon, easily ends up
be some 2 * 8,000,000 bits 'Supercoded'
compressed information representation

[biject.bwts]

COINCIDENTAL : PHYSICISTS ALSO DISCUSS QUANTUM PIGEONHOLE PRINCIPLE , FROM THEIR
QUANTUM PERSPECTIVE

http://www.google.com/url?q=http%3A%...rAkTfvopgdE9sQ

I read the paper at http://arxiv.org/pdf/1407.3194v1.pdf I hope it was reviewed by sharper people than those that did the review of my stuff. And I hope it's not the same crowd that worships at the altar of Al Gore. But quantum bits are not the same as binary bits that are either exactly one or zero. I am under the impression so what quantum bits in my view carry more than one bit of information. They are not black and white but various dynamic shades of gray.

[Bulat Ziganshin]

however resultant 8 bits smaller 10* 8,000,000 bits
can further be processed iterated upon, easily ends up
be some 2 * 8,000,000 bits 'Supercoded'
compressed information representation

can it be further reduced to 2*8,000,000-1 bits? do you have problem with understanding meaning of the "minimum" word?

[LawCounsels]

>>can it be further reduced to 2*8,000,000-1 bits? do you have problem with understanding meaning of the "minimum" word?

The minimum unit of bits saved each time is 2 bits ( not 1 bit ) !

YES it can further reduced to 2*800,000 -2 bits , & continuously do so , BUT each time the chance of successful attaining the minimum 2-bits unit savings gets less & less ( UNTIL its no longer worthwhile continue , when chance of success goes below 50% chance )

ITS A CONTINUOUSLY LESSER CHANCE WITH SMALLER & SMALLER ITERATION'S INPUT BITSLENGTH, & CHANCE CONTINUOUS INCREASES WITH LARGER & LARGER ITERATION'S INPUT BITSLENGTH ( nearer & nearer to 'GUARANTEED' )

SO YOU CAN SEE THERE IS NO ABSOLUTE BITSLENGTH WHERE ITS 'ABSOLUTE GUARANTEED' , ONLY CONTINUOUS HIGHER & HIGHER CHANCE OF SUCCESS ( continuous approaching nearest to 'GUARANTEED' )

ON THE OTHER HAND , ITERATION'S INPUT BITSLENGTH MUST BE VERY MINIMUM OF say 1,000,000 bits ( I am withholding the real actual number ! for usual trade secret reason ) ... & yes it cannot work if iteration's input becomes 1,000,000 -1 bits

[ long before you even get to iteration's input bitslength 1,000,000 bits , it already long becomes not worthwhile continues at around eg 4,000,000 bitslength when success chance already goes below 50%

[LawCounsels]

>>can it be further reduced to 2*8,000,000-1 bits? do you have problem with understanding meaning of the "minimum" word?

The minimum unit of bits saved each time is 2 bits ( not 1 bit ) !

YES it can further reduced to 2*800,000 -2 bits , & continuously do so , BUT each time the chance of successful attaining the minimum 2-bits unit savings gets less & less ( UNTIL its no longer worthwhile continue , when chance of success goes below 50% chance )

ITS A CONTINUOUSLY LESSER CHANCE WITH SMALLER & SMALLER ITERATION'S INPUT BITSLENGTH, & CHANCE CONTINUOUS INCREASES WITH LARGER & LARGER ITERATION'S INPUT BITSLENGTH ( nearer & nearer to 'GUARANTEED' )

SO YOU CAN SEE THERE IS NO ABSOLUTE BITSLENGTH WHERE ITS 'ABSOLUTE GUARANTEED' , ONLY CONTINUOUS HIGHER & HIGHER CHANCE OF SUCCESS ( continuous approaching nearest to 'GUARANTEED' )

ON THE OTHER HAND , ITERATION'S INPUT BITSLENGTH MUST BE VERY MINIMUM OF say 1,000,000 bits ( I am withholding the real actual number ! for usual trade secret reason ) ... & yes it cannot work if iteration's input becomes 1,000,000 -1 bits

[ long before you even get to iteration's input bitslength 1,000,000 bits , it already long becomes not worthwhile continues at around eg 4,000,000 bitslength when success chance already goes below 50%

The more Astute readers in this Forum would undoubted now thinking :

That perhaps a sequence of random numbers, if
sufficiently long enough, invariable will ha've some kind of 'inherent' weakness so far no-one has realised' fundamental thing, renders it compressible reducible!
( yes, readers would also have been weaned of 'pigeonhole' parable)

In fact, Mark Nelson himself
has already said AMillionRandomDigit
likely able be compressed reduced smaller
by 1 byte!

[SoraK05]

http://encode.su/threads/2006-Hello-...e-an-algorithm
I've done some research in general on compression and determined there are general strategies to suit specific data arrangement, and prevalence in general is required (repetition).
This can look at specific patterns of 2 bit combinations for their prevalence in a row and locate specific sections of data to process individually for a more optimal compression where all sections have common/unique strings accounted for a more effective compression tree for distribution and this can also in general assist in detection of compressible/uncompressible areas, can get specific variable length strings for the least strings in a code tree and to have the smallest file from least relevant strings, repetition in a row, internal repeating and such, with a reasonable expectation from the potential 50% compression ability from prevalent data (generally close).


I looked at the notion of compressing data based on having a specific decimal number and treating it with an algorithm. While this may be a generally suitable approach, having an algorithm based on looking at multiples of 2 and some means to account for in a row and a repeated sequence, I also looked at the notion of hashing.

If you want to shrink data by a factor such as hashing where you have a length of data and you use less data to represent a specific chunk, this will need to be reflected in the executable which will host the data.
I.e. you are essentially taking a hash of a specific length of data, putting into the header, and having some extra data which in general will cumulatively equal the original length of data as there is no algorithm to compress/shrink from prevalence. This means you have a portion of a specific string of data embedded in the executable, and if you are dealing with large amounts of data, you can use this hashed header information repetitively for chunks of data.

It is appropriate to determine the exact strings which can be found in a file (as such in the heavy scan algorithm in the pdf) and perhaps a means to treat 'uncompressible' dispersed and balanced bit strings to fake decoding and then encode with a stronger algorithm (the concept does exist to take data which looks compressed and attempt to fake uncompress and recompress in a stronger fashion). This approach should result, including with the other aspects mentioned a generally specific and compact result than having a static hash of data in an executable and using it for chunks of data for example, requiring a fair amount of chunks to break even in a reasonable amount and where there are things like a lot of repetition and something like in a row the compression option is weak.



EDIT:
It is worth noting I also did research into the equation nCr which looks at prevalence of 0/1 bits, where on either side the more the number is away from 50/50 the less possible combinations/iterations of placing 0/1s there is.
I.e. you can have 256 bits, and 20 are 0 and 236 are 1, and with nCr there are 280437550101996454288136030400 possible iterations, and one can use this as a reference to ID the specific string. This is like 12 bytes (96 bits). When your number is more like 128 0s and 128 1s, the number is almost 256 bits, and the curve where compression like this is acceptable is of about 30% of total combinations outside of 0 being more and the opposite of 1.

However, where nCr is performed on very very very very large data there can be an exponential saving of very very little data considering, and it requires extreme computation.



It is suitable to treat the specific data for what it is and repetition it has to compress.

[LawCounsels]

[ From comp.compression ]

> >>Originally Posted by Bloax
>
>
>
> >>Well how do you stuff four pigeons into two holes without there being two pigeons in either of the holes? Because if you can't do that then you can't stuff eight pigeons into four holes either, nor can you stuff 16 pigeons into 8 holes (continue ad nauseum).
>

[ posting by Jacko ]

It's not stuffing a greater number of pigeons into a lesser number of holes that is important. It's stuffing a large number of pigeons into a virtual hole structure created in an abstract representation from a set of holes which constantly move into different organizations in an infinite reversible sequence.

[LawCounsels]

>[ From comp.compression posting by Jacko ]


> >>Originally Posted by Bloax
>
> >>Well how do you stuff four pigeons into two holes without there being two pigeons in either of the holes? Because if you can't do that then you can't stuff eight pigeons into four holes either, nor can you stuff 16 pigeons into 8 holes (continue ad nauseum).
>

It's not stuffing a greater number of pigeons into a lesser number of holes that is important. It's stuffing a large number of pigeons into a virtual hole structure created in an abstract representation from a set of holes which constantly move into different organizations in an infinite reversible sequence.

[Piotr Tarsa]

Many years ago I've thought that the size of entire universe of possible 3-minute MP3s is in the order of millions (ie under billion) so by iterating through some number generator it would be possible to generate every possible MP3 containing 3-minute song. Much later I've realized how dumb that was.

[SoraK05]

http://www.masmforum.com/board/index.php?topic=13454.0
I posted on this forum before learning of this one and was referred to this thread about super compression

Like I mentioned, you require the data to refer at some point, and will ultimately be 'hashed' in a sense in the header/exe (exaggerated by the compression BARF).
Tools that have schemes for data types are perhaps automating a structure for detecting specific expected patterns, but beyond this you are putting data into the header/exe.

Converting a string of bits to something that makes it more compressible requires data stored for that reference, and this is going along lines of being a hash.
Having data to convert 1MB to 200KB means 256^(1024x1024) possibilities being represented in 256^(1024*200) possibilities. This is almost the same as representing 100% of data in 20% of its space. Without having some data externally stored like in a header, this is generally impossible. In general the expectation for a max compressing is accommodating a 50/50 targeting prevalence, where you have data and its compressed/represented version of a range of data (<reasonable> length), with the benefit being where in common use there is a lot of repetition it can reduce the total size.


EDIT:
To demonstrate what I mean, if you have a file with a decimal number when looking at its data as decimal and accounting for any 0s in the beginning before the first 1 bit, to use this number you will need all the bits the file consumes. If you decide to have 256^1024 for a 1KB file and that is the length, and then you use a number to represent the rest you pretty much end with a file of the exact same length except rewritten if accounting for general expectations/options, and otherwise depending on the number/content you can gain compression (ideally 1s being as close to the far right/end).
You can rewrite a file in ways, and uses in general the same amount of data, and where you do this to make data more compressible you can gain compression depending, and is considered shuffling/moving data and retaining this movement calculating. This allows for breaking even with repetition/prevalence when rewriting that specific repetitive/prevalent data.

Where you have many many 0 bits, you can use nCr for example which guarantees less total data. If a majority of the data is constituted of something like 8 byte patterns and then with a couple more, the fact that out of 256 options only 10 are used cuts down space, and then you have prevalence of 8 patterns meaning you can write these 8 once and give it a representation of very little data like 2-5 bits each instead of a static 4 bits, breaking even by rewriting the repetitive data in less bits and its data storage info.

Prevalence in general is required to be used to rewrite the repetitive data in less bits as well as its database entry, and break even providing that this process will result in a smaller file with any other data around it.


1MB as 200KB means storing something like 80% of data in the header and then using 20% data, and otherwise you have something like each increment of data will result in iterations of the equivalent of adding 10 instead of 1, and this is not specific to cater for the entire range. This can work if your expected values of data are always a multiple of 10, and in a way is doing something similar to shrinking the 10 byte patterns above from 256 to even a static 4 bits instead of 8 each.

[LawCounsels]

Yes far more profitable useful do the other way,
take the 3 mins MP3 music THEN try make a
particular Number Generator unique to it which is
smaller in size

This may initially also at 1st sight seems like hard
P=NP intractable time, which Wolfram was not
able solve earlier ( world's P=NP experts are
at this time divided out whether P=NP? )

solved now!

[biject.bwts]

The more Astute readers in this Forum would undoubted now thinking :

That perhaps a sequence of random numbers, if
sufficiently long enough, invariable will ha've some kind of 'inherent' weakness so far no-one has realised' fundamental thing, renders it compressible reducible!
( yes, readers would also have been weaned of 'pigeonhole' parable)

In fact, Mark Nelson himself
has already said AMillionRandomDigit
likely able be compressed reduced smaller
by 1 byte!

Yes I am sure the so called one million random digit file can be compressed a byte or more. I have a gut feeling that if you do a enough bijective transforms for example BWTS enough times then do something like my bijective LZW it will compress to a smaller size. However that's not fair since you have to take into account the number of times the BWTS was done. The number of BWTS would likely be so great that most computers could never do the number of BWTS needed before they break down since BWTS just creates a new permutation of the data each time until the starting one is recreated again after many many iterations.

[Kennon Conrad]

Yes I am sure the so called one million random digit file can be compressed a byte or more.

We could get it down to 1 bit if allowed to customize the compressor and decompressor