Ok. I studied Wolfram's ideas. And he implies, that there is a simple cellular automata, that can produce any structure in existence. The only problem left is locating that structure in the automata's output.
>>1 Its known as "magic formula" compression. My idea was considerably simpler, creating a large search space(x*y< gap >x*(y+1)) where a polynomial is constructed like x^8.4343+z^4.3434-k^232.34-...+... that converges into the <gap> of search space, that polynomial divided by y gives back x.zzz where fractional part is discarded and x-integer is converted back to file.
>>3
A simplified version that assumes a fixed base and only records the powers is described here:
http://void.wikidot.com/algorithms:polynom-encodings
Edit added the explanation of general method↵
http://void.wikidot.com/algorithms:polynomial-compression-explained
Naturally, heavy parallelism, chunking and maybe some sort of mutating fuzzy matching should be implemented to improve the time complexity.
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Anonymous2018-10-11 15:22
Note that polynomial compression is not the only compression idea i have, the other is Xor-wave bitflipping to reduce entropy of files, which is much faster in principle but doesn't seem to help compression despite entropy results. Its closer in principle to automata theory, basically the bits are mutated by the following: http://void.wikidot.com/algorithms:delta-encoding-with-bitflipping delta is the "xor wave over the same number shifted one position" 0010101 is recorded as 0011111 where 0 is no change, and 1 is a bitflip,1's in 0011111 signify change every cell. After N transitions the least-entropy form of number is discovered and compressed(by any suitable algorithm) along with number of transitions. The original is recovered by recovering bits from deltas . Example of 4 bit transform: 0110 delta-> 0101 delta-> 0111 delta-> least-entropy form 3 recovery-> 0111 reverse is bits from delta. 0101 (nochange,change,change,change) 0110 (nochange,change,nochange,change)
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Anonymous2018-10-11 19:53
>>5 This is evolving a CA to match your data...it has probability of being your data close to zero. Consider that a string of 256 bytes has 256^256=32317006071311007300714876688669951960444102669715484032130345427524655138867890893197201411522913463688717960921898019494119559150490921095088152386448283120630877367300996091750197750389652106796057638384067568276792218642619756161838094338476170470581645852036305042887575891541065808607552399123930385521914333389668342420684974786564569494856176035326322058077805659331026192708460314150258592864177116725943603718461857357598351152301645904403697613233287231227125684710820209725157101726931323469678542580656697935045997268352998638215525166389437335543602135433229604645318478604952148193555853611059596230656 possible combinations. That is assuming your CA even reaches all of them(most CA won't reach them). It will take (assuming you can check 10^9 of them per second, being generous) on average 16158503035655503650357438344334975980222051334857742016065172713762327569433945446598600705761456731844358980460949009747059779575245460547544076193224141560315438683650498045875098875194826053398028819192033784138396109321309878080919047169238085235290822926018152521443787945770532904303776199561965192760957166694834171210342487393282284747428088017663161029038902829665513096354230157075129296432088558362971801859230928678799175576150822952201848806616643615613562842355410104862578550863465661734839271290328348967522998634176499319107762583194718667771801067716614802322659239302476074096777926805529.798115328 seconds or 4488473065459862125099288428981937772283903148571595004462547976045090991509429290721833529378182425512321939016930280485294383215345961263206687831451150433420955189902916123854194131998562792610563560886676051149554474811474966133588624213677245898691895257227264589289941096047370251195493388767212553544710324081898380891761802053689523540952246671573100285844139674907086971209508376965313693453357932878603278294230813521888659882264117486722735779615734337670434122876502806906271819684296017148566464247313430268756388509493472033085489606442977407714389185476837445089627566472910020582438313001.53605503203555555556 hours or 187019711060827588545803684540914073845162631190483125185939499001878791312892887113409730390757601063013414125705428353553932633972748385966945326310464601392539799579288171827258088833273449692106815036944835464564769783811456922232859342236551912445495635717802691220414212335307093799812224531967189731029596836745765870490075085570396814206343611315545845243505819787795290467062849040221403893889913869941803262259617230078694161761004895280113990817322264069601421786520950287761325820179000714523602676971392927864849521228894668045228733601790725321432882728201560212067815269704584190934929708.39733562633481481481 days or 512382770029664626152886806961408421493596249836940069002573969868161072090117498940848576413034523460310723632069666722065568860199310646484781715919081099705588491998049785828104352967872464909881685032725576615245944613182073759542080389689183321768481193747404633480586883110430393972088286388951204742546840648618536631479657768686018669058475647439851630804125533665192576622089997370469599709287435260114529485642786931722449758249328480219490385800882915259181977497317672021263906356654796478146856649236692953054382249942177172726654064662440343346391459529319343046761137725218038879273780.02300639897625976662 years.(for reference the universe is only ~13799000000 years old) Just for a string of 256 bytes.
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Anonymous2018-10-11 20:11
There is a way to compress with Conway's Game of life. 1.Load the file as final state of Conway's game of Life X/Y grid. 2.Run the algorithm in reverse to find a state which minimizes the amount of live cells. This is the step which is problematic: Will the number of live cells decreases or increase? Maybe some ruleset guarantees growth in one direction, that would be suitable for this task(original 23/3 ruleset is too chaotic imho). 3.Compress it with zip/gzip. Write the file+ number of backward generations. 4.Decompress the file. 5.Run Conways game of life normally for number of generations specified. 6.Record the original file.
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Anonymous2018-10-11 20:35
>> 7 I wouldn't shoot the moon and go for the whole file. Perhaps chunking it into n parts and working on those in parallel would be sensible. Part size would probably depend on what you could push through the architecture & algo as quickly as possible.
Also would it not make more sense to search for parts that only needed to be a near match? Then you could store the position in the rule30 chain with a mutation factor (bit flipping look up table) as the representation of the compressed data.
You could of course run it back through, making compression a factor of time. Alas this is all just theoretical and I'll admit might need a few qubits for a working PoC.
How else are we supposed to send a hologram through a wormhole?
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Anonymous2018-10-11 20:36
>>8 that's basically a "seed" idea see: minecraft the seed is very short but generates an entire world
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Anonymous2018-10-11 20:44
>>10 The idea is to compress the world down to the "seed" the backwards state from which CA rules evolve back the seed to the full world. I think the problem is getting to these backward steps, as some states probably lack a "parent step" and thus incompressible Its called "Garden of Eden pattern". https://en.wikipedia.org/wiki/Garden_of_Eden_(cellular_automaton)
>>10 pseudo random number generators are cell 0d cell automatas?
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Anonymous2018-10-11 23:00
Yes, brute force can do absolutely anything, we already know that (we've known it for a long time), and this is just another instance of it if you look at it well, the problem is the time it actually takes when we run it for real.
>where sender and receiver know what kind of data recipes can be transferred, without the data itself actually being sent."[4] Wait, did Romke Jan Bernhard Sloot innovate a general quantum encoding? It was theorized for a long time: https://en.wikipedia.org/wiki/Quantum_computing#Timeline
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Anonymous2018-10-12 13:22
This sort of thing would pop up on alt.compression every so often, surprisingly handled more kindly here. Maybe the game of Go being beaten 10 or so years ahead of expert predictions has made us a little more open minded.
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Anonymous2018-10-12 13:27
>>21 Are they still obsessed with useless "random data" being incompressible? All useful subsets of data have structure and lower-entropy parts.
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Anonymous2018-10-12 13:56
>>21 Open minded to mathematically impossible bullshit
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Anonymous2018-10-12 14:21
>>23 I wonder how the universe was able to reduce the search space required evolve a single cell through plasma ball power stations into your kind self.
Kolmogorov complexity tells me it's not possible, you must not exist.
most things we observe about mathematics, physics, etc. are just emergent properties
what we really need to find is the unifying theory that explains everything
what modern STEM is is basically like studying complex patterns in conway's game of life without knowing or thinking about the basic rules that result in said complex patterns
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Anonymous2018-10-12 16:50
we are studying emergent properties of cellular automata instead of the cellular automata itself
>>3 The key problem is optimizing the polynomial into a shorter form: essentially on one side you have sum of (x^y+z^k+m^N) subtracted by another sum (l^z+a^b+u^d) which have to balance out to a number inside the search range.
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Anonymous2018-10-13 11:37
On July 11, 1999 Sloot was found dead, in his garden[2] at his home in Nieuwegein of an apparent heart attack.[1] He died one day before an attractive deal was signed with Roel Pieper, former CTO and board member of Philips.
data encoding technique that could store an entire feature film in only 8 kilobytes.
Lets take minimum: super jerky 8 frames per second, and 30 minutes film. That will require: 8*60*30 = 14400 (14kb), or ~0.6 bytes per frame.
I doubt you can compress even the soundtrack to that number of bytes. Even if you convert it into text, compress and do text to speech for restoration.
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Anonymous2018-10-14 20:05
>>32 I don't know much about this dumb sloot, but it sounds like they're confusing compression with checksums
md5 is not compression, unless you don't mind going through every single combination to try and brute force it, if you would consider that to be decompression
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Anonymous2018-10-14 20:06
>>32 The only way to restore the story of such film is to do a simulating under a set of constraints (i.e. from synopsis). But that is impossible even with modern technology.
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Anonymous2018-10-14 20:06
OR maybe they were talking about vector graphics or something, like flash instead of raster graphics
also I read a little bit about h264 and i frames vs. p frames and how you can convey motion instead of individual pixels
also fax machines say pixels are white or black follower by how many are the same color contiguously
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Anonymous2018-10-14 20:08
>>34 Because even film's script would be too big to produce a film from.
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Anonymous2018-10-14 20:13
>>35 Consider compressing Star Wars plot into 8000kb of plain text. Of course picture is worth a thousand of words, but still...
>>32,35 I thought >>19 already implied it is instruction code, the difference is that it's based on a goal and result mathematical functions. f(x) -> x(f). In Postscript, when you "draw", you're preparing statements about how a needle is supposed to plot the canvas. The printer needs transcode the plot instructions into the firmware protocol that handles the actual needle. In the case of SDCS, I assume Stool made something similar, since at result, the monitor needs to flicker on/off the RGB dots in respect to time in its grid. He would have had to designed a basic programming language that would get transcoded into monitor instructions. Extended Vector Animation format was extremely similar Stool's description, but I assume he was granular to his bytecode compiler.
In the case of finite compression, you would need to design a filesystem similar to the above, plotting disc or solid state data blocks. With a libre firmware for a NAND or NOR gate, it should be easier than a HDD platter. I don't believe in infinity, but omega: the last number. Plus, in terms of storage, we have finite physical limitations like their sizes.
If you know the entire length of the movie, you don't even need to consider "frames": only calculate the function of the R,G,B X-Y axises plots across the entire time of the movie.. 4kb for the desired goal functions, and 4kb for the "results" functions. I think the entire bytecode can be summarized with just a few bytes describing the entire formula compositions, like in chmod' rwx permissions are just primes 1,2&3. I mean, what other math do you need than what most CISCs already have?
>>42 ActionScript is based of Frames: you can have infinite amount of frames per X time. E.g. in one second you could have 1 frame, or a trillion frames. It also has some objects like circles, rectangles, lines, bezier curves, etc. It's too wordy, and not based on the goal: the monitors' RGB functions.
I could autistically expand it, but it's just understanding how to write formulas: passing math theory required here: you're effectively designing your general compression formula. None have beat LZMA yet.
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Anonymous2018-10-15 0:41
>>41,43 so basically, you want to vectorize all the frames of the movie and come up with a function that interpolates between all the frames.
that's going to be much larger than the frames themselves, unless the movie is just 2 hours of a triangle rotating.
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Anonymous2018-10-15 0:49
SVGs and flash already exist, how is this so revolutionary?
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Anonymous2018-10-15 1:11
>>44 Vectorize the entire plot functions for plots R, G, and B across the X-Y which can simply be primes, across the entire length of the movie. Similar like how in chess you have pawn, rook, knight, bishop, queen, and king, it's a 8x8 board, positions of legal moves can be described in functions of pieces and their effects to other pieces, and how they are affected by the opponent. The function/plot of let's say pawn white A2 to become queen, ignorant of black's moves, would look something like p(a2,a3,a4,a5,a6,[a7,b7],[b8,[a8,c8]]), which can be reduced to numbers pa2(1,2,3,5) since that pawn only has 4 possible choices in its entire goal to be queen, two of which are absolute if black never moved their pawns, rook, knight and bishop. Why you'll need two formulas, since you'll have two functions contradicting each other, plotting the entire movie's on/off state of the RGB plot. You are essentially drafting a "wack'a'mole" state formula: runtime of play is fixed, the "random"state of positions are plotted by sums of 1,2&3:RGB.
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Anonymous2018-10-15 1:14
>>32 8kb is pretty tiny, but we don't count pre-shared data dictionaries/etc in compression. ie compressing the mnist dataset with a pre-trained neural net and not counting the net if it doesn't need to be transferred is acceptable.
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Anonymous2018-10-15 1:23
So 8kb could probably do 1024 frames with 2^64 possible frame encodings?
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Anonymous2018-10-15 1:41
Gives about a 30 sec clip at 30 fps, with room for ~18,000,000,000,000,000 different clips without sharing a frame
>>47 Something like a black and white movie would have RGB on definite values for their plots. Heck, I think the Z-axis would be 0/1 for on/off. Or a simple boolean stating the functions can be ignored in favor of reduced plot graphs. >>48,49 You are still thinking in frames/time, think functions to state, why >>20 assumed Stool developed a generic quantum encoder. I assume Stool had a fixed resolution, time was the variable, and RGB were 3seperate functions across the on/off state.
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Anonymous2018-10-15 1:57
~1Mb per hour of video, but it might need a 1GB decoding model
Vectorize the entire plot functions for plots R, G, and B across the X-Y which can simply be primes, across the entire length of the movie.
I don't think you can come up with generalizable functions that compress any movie frame the same way a chess move can be compressed. The chess board comes with a strong prior--all the rules of chess. An image from a movie, by contrast, is completely arbitrary. There aren't any built in patterns you can exploit with the movie image.
What would be interesting is a superintelligence that could come up with a mathematical function that outputs an entire movie. For example, a video of a circle moving from the left to the right of the screen can be easily specified by the function for a circle with a varying horizontal coordinate. Imagine a superintelligence figuring out enough patterns on a larger scale over all the pixels in a movie such that it could reconstruct any frame by its index. I think that would be the closest you could get to infinite compression.
So you'd get a supercomputer to compress every known video frame into a 1Gb (hopefully) model, and then you could store thousands of movies for 1Mb a pop.. But you'd still need to update the model yearly or whatever to get the latest movies
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Anonymous2018-10-15 6:02
Sounds like using a URL minifier would be an infinite compression.
>>52 You can model all objects by ellipses, but that would still require a lot of motion data.
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Anonymous2018-10-15 10:04
>>53 You will still need to define each possible frame somehow. And here we have that problem: frame index could be as large as the frame itself, if the set of all possible frames is too large. But yeah, in practice we have just 45000 hollywood movies, so it is possible to compress them all to just an index picking the movie.
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Anonymous2018-10-15 10:37
If you stack frames of a movies, as layers of voxels, you can apply octree compression, because movies always have large areas of slowly changing gradients. In fact, modern video compression schemes, like AV1, indeed use octree compression: https://hackernoon.com/av1-bitstream-analyzer-d25f1c27072b
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Anonymous2018-10-15 12:42
The problem most of you are failing to overcome is that algorithms don't have to be perfect.
You probably use one every day that is sort of 'good enough', it's called Page Rank. The fact that one of the largest companies in the world's success is based on an algorithm that is 'good enough' still surprises me.
Maybe this is what Wolfram means, his new kind of science is something else, that we have yet to describe. A fabric we know is there, the empirical biological evidence is all around us; guess what; it's not perfect yet surprisingly effective.
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Anonymous2018-10-15 17:02
>>59 Wolfram meant using computers to explore otherwise inaccessible math regions. But some math structures, like monster group, are hard to explore even using computers, because it is the size of our galaxy in atoms. Yet, at the same time, this monster group is intrinsically related with physics: https://en.wikipedia.org/wiki/Monstrous_moonshine