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Advanced Combinations and Binary Compression

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  Advanced Combinations and Binary Compression Michael Harrington <michaelharrington4rep@gmail.com> - 2014-07-04 15:48 -0700
    Re: Advanced Combinations and Binary Compression Michael <michaelhh@gmail.com> - 2014-07-08 06:02 -0700
      Re: Advanced Combinations and Binary Compression Fibonacci Code <anglikai@gmail.com> - 2014-07-08 17:57 -0700
        Re: Advanced Combinations and Binary Compression Michael <michaelhh@gmail.com> - 2014-07-09 06:52 -0700
          Re: Advanced Combinations and Binary Compression Fibonacci Code <anglikai@gmail.com> - 2014-07-09 07:52 -0700
            Re: Advanced Combinations and Binary Compression Michael <michaelhh@gmail.com> - 2014-07-09 09:08 -0700
              Re: Advanced Combinations and Binary Compression Fibonacci Code <anglikai@gmail.com> - 2014-07-10 00:33 -0700
                Re: Advanced Combinations and Binary Compression Michael <michaelhh@gmail.com> - 2014-07-10 11:28 -0700
    Re: Advanced Combinations and Binary Compression Ernst <ernst_berg@sbcglobal.net> - 2014-07-10 13:05 -0700
      Re: Advanced Combinations and Binary Compression Michael <michaelhh@gmail.com> - 2014-07-10 14:29 -0700
        Re: Advanced Combinations and Binary Compression Michael Harrington <michaelharrington4rep@gmail.com> - 2014-07-11 17:37 -0700
          Re: Advanced Combinations and Binary Compression Michael Harrington <michaelharrington4rep@gmail.com> - 2014-07-11 20:39 -0700

#2428 — Advanced Combinations and Binary Compression

The idea of Advanced Combinations is simple, where I have a laymans description and the math definition. This is not an attempt to force a viewpoint like one of our *invest and then I will show you* guy, but an open question of "what is the actual answer?"

The laymans argument is one of cubes (though the pending patent allows for any method, this is the easier challenge). In a given dimension space a certain number of single cubes, or of larger shapes made up of cubes joined together, can fit, as well as represented empty spaces.

Another way to see this is a Rubik's cube, by itself it is 27 individual cubes if you add the center. By having two values, present and missing, we merely have 27 bits. But we if we merge two cubes we have (2^25)*54 [for the 18 locations per each of 3 different axis directions]. In larger formations this can very rapidly spiral out of control.

This creates a condition where it would seem possible, in a new manner, to encode more data via the act of creating Combinations, than the binary would normally allow. Note I said seem, were we have not yet advanced far enough to test if this is true.

I have two theories as to what is happening. The first is that similar to Earthquakes or Star Trek's Warp Drive reaching a 10.0 is impossible, but this almost feels imposible due to the rapid gains made by the advanced combinations. Under this theory the gains would have to slow down under the theory.

The second theory is that by incorporating a three dimensional structure it creates an artificial structure not limited by the existing rules.

In either event it would take 90 bits to encode the 36 in a 3x3x4 array, but for sure I have exceeded 78, and possibly 90 (no software to prove this). I also think that a 5x5x5 array would definitively lay to rest the entire question. The other possibility is I am over-estimating the probable outcomes from the number of shapes and combinations possible from the shapes.

I feel confident however that my estimation should be close, or even too low, to the real result. This is because my efforts to do preliminary math on 2x2x2 showed me the explosive capabilities of Advanced Combinations. Also my little effort in 3x3x3 was rather enlightening.

There is some existing software, in C and Python. All software is only written to find the maximum number of shapes, not the maximum number of combinations of shapes.

Now to the math.

 -----------------------------------------------------------------
 definition: legal object
 -----------------------------------------------------------------

 Let S be the set of solid unit cubes in R^3 with all vertices at lattice points.

 A legal object is a subset X of R^3 such that

 (1) X is a nonempty, finite union of elements of S.

 (2) The interior of X is connected.

 Congruent objects are considered the same. 
_______________________

Now we were able to do a variety of lower level efforts, solving the exact count for a 2x2x2 container, and maximum shapes, a 3x3x3 container for maximum shapes, and a 3x3x4 container for maximum shapes. The exact results are below

A 2x2x2 container has 9472 total outcomes from 14 possible shapes.
A 3x3x3 container has 1,585,580 total shapes with an estimated quadrillion plus possible outcomes.
A 3x3x4 container has 1,828,003,418 possible shapes, and defies an estimation of possible outcomes (most certainly exceeds the quadrillion by a factor or two)



 2x2x2 = 9472 total combinations 
 For a 2x2x2 container, the number of distinct legal objects is 14. 

Exact Shapes count for a 3x3x3 array
Units     Shapes
   0:         0
   1:         1
   2:         1
   3:         2
   4:         7
   5:        25
   6:       111
   7:       485
   8:      1,844
   9:      6,134
  10:     17,322
  11:     41,998
  12:     86,803
  13:    152,959
  14:    226,410
  15:    277,767
  16:    277,390
  17:    223,802
  18:    145,803
  19:     77,251
  20:     33,413
  21:     11,772
  22:      3,356
  23:       769
  24:       138
  25:        22
  26:         4
  27:         1 


Exact Shapes Count for a 4x3x3 Array.
 #Bits     #Shapes
   1:         1
   2:         1
   3:         2
   4:        10
   5:        34
   6:       181
   7:       959
   8:      5,383
   9:     27,582
  10:    124,741
  11:    486,690
  12:   1,655,982
  13:   4,934,805
  14:  12,969,641
  15:  30,109,904
  16:  61,740,472
  17: 111,353,404
  18: 175,542,991
  19: 239,819,535
  20: 281,599,067
  21: 282,326,036
  22: 241,011,786
  23: 175,295,801
  24: 109,002,113
  25:  58,119,504
  26:  26,620,643
  27:  10,455,818
  28:   3,509,584
  29:    997,606
  30:    238,069
  31:     46,638
  32:      7,435
  33:       901
  34:        92
  35:         6 
  36:         1
 Total: 1,828,003,418 



So the question is, can anyone here make better software for this? Or perhaps someone here has access to a cluster and can run the computations faster than our systems?

Here is links to the existing software

http://pat7.com/js/3shapes/1cellcount.c
http://pat7.com/js/3shapes/4cuber.c
http://pat7.com/js/3shapes/4cuber-inc.c
http://pat7.com/js/3shapes/3cuber.py
http://pat7.com/js/3shapes/rotate24x8.py
*note some of the software functions in unique mannerisms


Please note, this is not a low level math effort, unless you know a trick I do not. In the 3x3x4 example, at 20 bit object size, if you utilized any combinations that allow a number of different other shapes it will spiral deeply out of control beyond the 16 bits/cubes possible, in a scary sort of way. Though the true worst will probably be under 10 in size mixed with other under 10 in size.

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#2429

Well amazingly I got the answer on my own.

Electronic representation of the physical form will always be the key.

Size is Physical <= Electronic Bits needed to count the physical size.

Ergo the maximum Size increase will be close, or under, Log(9)/Log(2), meaning I can probably get 3 times the information into my physical representation of data, but no more than that. 

The reason it does scale, is because at lower size levels it is enormously inefficient, so it scales very rapidly until it gets closer to the upper bound, then the gains drop off fast, and are very incremental. 

I am now thinking in new terms, as this can be a unique breakthrough... just how do I make a physical representation of binary have higher data yields than a 3 to 1 ratio. 

I need to achieve another 100 to 1 ratio to make it effective. Answer to first question found, I do not know, or at this point even think, an answer to the 2nd question is possible.

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#2430

But, at the end, the shape need to encode in binary (in order for computer to process), which is again bound to the limitation of representation in memory.
Unless you invent a memory chip which can process shape or internet line that transfer shape, or else the saving you have cannot be keep in HDD nor transfer via internet.

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#2432

On Tuesday, July 8, 2014 5:57:59 PM UTC-7, Fibonacci Code wrote:
> But, at the end, the shape need to encode in binary (in order for computer to process), which is again bound to the limitation of representation in memory.
> 
> Unless you invent a memory chip which can process shape or internet line that transfer shape, or else the saving you have cannot be keep in HDD nor transfer via internet.

Yes in internet it would be impossible.

My goal was a "very long term memory storage" system made of plastics in near full color. 3D printed, it would be a single write, but infinite reads. 

The sad thing is I get 10mb, that is all now...

unless some of my other tricks can increase it, but I am a bit bummed out that this one fell down so quickly :(

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#2433

On Wednesday, 9 July 2014 21:52:58 UTC+8, Michael  wrote:
> On Tuesday, July 8, 2014 5:57:59 PM UTC-7, Fibonacci Code wrote:
> 
> > But, at the end, the shape need to encode in binary (in order for computer to process), which is again bound to the limitation of representation in memory.
> 
> > 
> 
> > Unless you invent a memory chip which can process shape or internet line that transfer shape, or else the saving you have cannot be keep in HDD nor transfer via internet.
> 
> 
> 
> Yes in internet it would be impossible.
> 
> 
> 
> My goal was a "very long term memory storage" system made of plastics in near full color. 3D printed, it would be a single write, but infinite reads. 
> 
> 
> 
> The sad thing is I get 10mb, that is all now...
> 
> 
> 
> unless some of my other tricks can increase it, but I am a bit bummed out that this one fell down so quickly :(

Well just, make the solid shape storage small with different index glass cube, and stack it by 100 x 100. You'll have just created a new medium, which it can be read with laser. Just like the past CD ROM but in a perfect cube.

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#2434

On Wednesday, July 9, 2014 7:52:19 AM UTC-7, Fibonacci Code wrote:
> On Wednesday, 9 July 2014 21:52:58 UTC+8, Michael  wrote:
> 
> > On Tuesday, July 8, 2014 5:57:59 PM UTC-7, Fibonacci Code wrote:
> 
> > 
> 
> > > But, at the end, the shape need to encode in binary (in order for computer to process), which is again bound to the limitation of representation in memory.
> 
> > 
> 
> > > 
> 
> > 
> 
> > > Unless you invent a memory chip which can process shape or internet line that transfer shape, or else the saving you have cannot be keep in HDD nor transfer via internet.
> 
> > 
> 
> > 
> 
> > 
> 
> > Yes in internet it would be impossible.
> 
> > 
> 
> > 
> 
> > 
> 
> > My goal was a "very long term memory storage" system made of plastics in near full color. 3D printed, it would be a single write, but infinite reads. 
> 
> > 
> 
> > 
> 
> > 
> 
> > The sad thing is I get 10mb, that is all now...
> 
> > 
> 
> > 
> 
> > 
> 
> > unless some of my other tricks can increase it, but I am a bit bummed out that this one fell down so quickly :(
> 
> 
> 
> Well just, make the solid shape storage small with different index glass cube, and stack it by 100 x 100. You'll have just created a new medium, which it can be read with laser. Just like the past CD ROM but in a perfect cube.

Well it would be able to hold 3 times the data via my Advanced Combinations method, but how much data density can we get in glass?

Can it go under 150um per spot?

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#2435

If suppose the material of glass is 75% silicon oxide, and a computer processor chip is also made with silicon, I believe it would have no problem for creating 14nm per spot in the year 2014.

http://en.wikipedia.org/wiki/14_nanometer

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#2436

Hmmmmm

Width 4 in
Depth 5.8 in
Height 1 in

1 inch = 25,400 micrometers

101,600 x 147,320 x 25,400

3,879,386,579,591 bits
3,788,463,456kbits
3,699,671mbits
3,612gbits
3.528tbits
451.62gb

All of this prior to any of my drive size increasors. Of course it cannot all be 14um, it would probably be more like 28um or larger initially.

That would be rather impressive printed in silicon, and it is within the patents total allowances. I have seen no other existing patents which cover a "permanent one time write memory"

Of course that assumes cards which take the same space, of 40um in thickness, which might not be plausible (that is way thin). Of course making the depth deeper allows for us to play games with the depth, with deeper trenches...

However even if I allowed a depth of 150um per card (costing me about 3/4 of the space per drive?).. Damn... this would most certainly work, and work extremely well for long-term data storage, provided of course there was no issue with quality control at that level, and in reading it accurately. As a "Permanent backup" this does not need to be efficient, just needs to be 100% accurate. 

Even if it was only 50 gigabytes per a PHD... then this would be rather cheap I suspect.


hmmmm, except silicon prices are so very high. Still this bears thinking on. And pricing research, research in materials that can be eteched at 30um or smaller, and material strengths.

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#2437

On Friday, July 4, 2014 3:48:53 PM UTC-7, Michael Harrington wrote:
> The idea of Advanced Combinations is simple, where I have a laymans description and the math definition. This is not an attempt to force a viewpoint like one of our *invest and then I will show you* guy, but an open question of "what is the actual answer?"
> 
> 
> 
> The laymans argument is one of cubes (though the pending patent allows for any method, this is the easier challenge). In a given dimension space a certain number of single cubes, or of larger shapes made up of cubes joined together, can fit, as well as represented empty spaces.
> 
> 
> 
> Another way to see this is a Rubik's cube, by itself it is 27 individual cubes if you add the center. By having two values, present and missing, we merely have 27 bits. But we if we merge two cubes we have (2^25)*54 [for the 18 locations per each of 3 different axis directions]. In larger formations this can very rapidly spiral out of control.
> 
> 
> 
> This creates a condition where it would seem possible, in a new manner, to encode more data via the act of creating Combinations, than the binary would normally allow. Note I said seem, were we have not yet advanced far enough to test if this is true.
> 
> 
> 
> I have two theories as to what is happening. The first is that similar to Earthquakes or Star Trek's Warp Drive reaching a 10.0 is impossible, but this almost feels imposible due to the rapid gains made by the advanced combinations. Under this theory the gains would have to slow down under the theory.
> 
> 
> 
> The second theory is that by incorporating a three dimensional structure it creates an artificial structure not limited by the existing rules.
> 
> 
> 
> In either event it would take 90 bits to encode the 36 in a 3x3x4 array, but for sure I have exceeded 78, and possibly 90 (no software to prove this). I also think that a 5x5x5 array would definitively lay to rest the entire question. The other possibility is I am over-estimating the probable outcomes from the number of shapes and combinations possible from the shapes.
> 
> 
> 
> I feel confident however that my estimation should be close, or even too low, to the real result. This is because my efforts to do preliminary math on 2x2x2 showed me the explosive capabilities of Advanced Combinations. Also my little effort in 3x3x3 was rather enlightening.
> 
> 
> 
> There is some existing software, in C and Python. All software is only written to find the maximum number of shapes, not the maximum number of combinations of shapes.
> 
> 
> 
> Now to the math.
> 
> 
> 
>  -----------------------------------------------------------------
> 
>  definition: legal object
> 
>  -----------------------------------------------------------------
> 
> 
> 
>  Let S be the set of solid unit cubes in R^3 with all vertices at lattice points.
> 
> 
> 
>  A legal object is a subset X of R^3 such that
> 
> 
> 
>  (1) X is a nonempty, finite union of elements of S.
> 
> 
> 
>  (2) The interior of X is connected.
> 
> 
> 
>  Congruent objects are considered the same. 
> 
> _______________________
> 
> 
> 
> Now we were able to do a variety of lower level efforts, solving the exact count for a 2x2x2 container, and maximum shapes, a 3x3x3 container for maximum shapes, and a 3x3x4 container for maximum shapes. The exact results are below
> 
> 
> 
> A 2x2x2 container has 9472 total outcomes from 14 possible shapes.
> 
> A 3x3x3 container has 1,585,580 total shapes with an estimated quadrillion plus possible outcomes.
> 
> A 3x3x4 container has 1,828,003,418 possible shapes, and defies an estimation of possible outcomes (most certainly exceeds the quadrillion by a factor or two)
> 
> 
> 
> 
> 
> 
> 
>  2x2x2 = 9472 total combinations 
> 
>  For a 2x2x2 container, the number of distinct legal objects is 14. 
> 
> 
> 
> Exact Shapes count for a 3x3x3 array
> 
> Units     Shapes
> 
>    0:         0
> 
>    1:         1
> 
>    2:         1
> 
>    3:         2
> 
>    4:         7
> 
>    5:        25
> 
>    6:       111
> 
>    7:       485
> 
>    8:      1,844
> 
>    9:      6,134
> 
>   10:     17,322
> 
>   11:     41,998
> 
>   12:     86,803
> 
>   13:    152,959
> 
>   14:    226,410
> 
>   15:    277,767
> 
>   16:    277,390
> 
>   17:    223,802
> 
>   18:    145,803
> 
>   19:     77,251
> 
>   20:     33,413
> 
>   21:     11,772
> 
>   22:      3,356
> 
>   23:       769
> 
>   24:       138
> 
>   25:        22
> 
>   26:         4
> 
>   27:         1 
> 
> 
> 
> 
> 
> Exact Shapes Count for a 4x3x3 Array.
> 
>  #Bits     #Shapes
> 
>    1:         1
> 
>    2:         1
> 
>    3:         2
> 
>    4:        10
> 
>    5:        34
> 
>    6:       181
> 
>    7:       959
> 
>    8:      5,383
> 
>    9:     27,582
> 
>   10:    124,741
> 
>   11:    486,690
> 
>   12:   1,655,982
> 
>   13:   4,934,805
> 
>   14:  12,969,641
> 
>   15:  30,109,904
> 
>   16:  61,740,472
> 
>   17: 111,353,404
> 
>   18: 175,542,991
> 
>   19: 239,819,535
> 
>   20: 281,599,067
> 
>   21: 282,326,036
> 
>   22: 241,011,786
> 
>   23: 175,295,801
> 
>   24: 109,002,113
> 
>   25:  58,119,504
> 
>   26:  26,620,643
> 
>   27:  10,455,818
> 
>   28:   3,509,584
> 
>   29:    997,606
> 
>   30:    238,069
> 
>   31:     46,638
> 
>   32:      7,435
> 
>   33:       901
> 
>   34:        92
> 
>   35:         6 
> 
>   36:         1
> 
>  Total: 1,828,003,418 
> 
> 
> 
> 
> 
> 
> 
> So the question is, can anyone here make better software for this? Or perhaps someone here has access to a cluster and can run the computations faster than our systems?
> 
> 
> 
> Here is links to the existing software
> 
> 
> 
> http://pat7.com/js/3shapes/1cellcount.c
> 
> http://pat7.com/js/3shapes/4cuber.c
> 
> http://pat7.com/js/3shapes/4cuber-inc.c
> 
> http://pat7.com/js/3shapes/3cuber.py
> 
> http://pat7.com/js/3shapes/rotate24x8.py
> 
> *note some of the software functions in unique mannerisms
> 
> 
> 
> 
> 
> Please note, this is not a low level math effort, unless you know a trick I do not. In the 3x3x4 example, at 20 bit object size, if you utilized any combinations that allow a number of different other shapes it will spiral deeply out of control beyond the 16 bits/cubes possible, in a scary sort of way. Though the true worst will probably be under 10 in size mixed with other under 10 in size.


I enjoyed this thread. I especially liked the distribution frequencies tha's bomb!

 I will look at that again.  Not so sure what this is all about yet so I will look again.

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#2439

Ernst this is the distribution of possible shapes in a given sized array consisting of solo, or joined cubes. 

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#2441

Surprisingly relevant to my technology idea...

http://www.technologyreview.com/news/528921/self-assembly-shows-promise-for-extending-moores-law/

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#2442

And my last numbers post went to Microns, not nm. Interesting :o

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