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256GB Geometrically Encoded Paper Storage Device
jrieth50 noted that a method of using geometric shapes combined with color to store up to 256GB of data on a sheet of paper or plastic. The article says "Files such as text, images, sounds and video clips are encoded in 'rainbow format' as colored circles, triangles, squares and so on, and printed as dense graphics on paper at a density of 2.7GB per square inch. The paper can then be read through a specially developed scanner and the contents decoded into their original digital format and viewed or played."
according to this Indian blogger.
http://itsoup.blogspot.com/2006/11/scam-of-indian- student-developing.htmle nt_developing_technology_to_store_450_GB_on_paper
http://www.digg.com/tech_news/Scam_of_Indian_stud
I expect to see a story like this on Digg, but I thought Slashdot was better than this.
It's a scam.
I dunno who it is
but it prolly is fhqwhgads.
2.7GB per square inch would would require a linear data density of 152292 dpi. Neither my scanner nor my printer come within a hundredth of this. The main problem with the printer at such resolutions is bleeding of the inks into the paper. To form the different shapes several dots would be necessary, which would further decrease the effective resolution by an order of magnitude. For example, suppose a 3x3 grid was used to form each character, the article states that there are four different shapes used, yet that 3x3 grid could encode 512 different patterns. Realistically, at 600dpi (giving 360000 dots per square inch), with 3 ink colours (yielding 8 different colours) you would get 360000 bytes per square inch, or 33MB per A4 page - somewhat short of the 256GB promised. You'd also need to dedicate around 25% of the capacity for error correction. This is complete and utter bollocks.
Like tinyurl, but one letter less! http://qurl.co.uk/
You are an idiot because: You ignored the one and only thing he /did/ say, which was that he was doing something differently.
Bzzt.
Encoding data using dots is the most efficient method possible. He has to print the image somehow, and scan it back in again. No combination of triangles and circles can circumvent the resolution limit, which is what is being calculated here.
By showing that the claim exceeds all practical limits of optical resolution (and probably the absolute physical limits), we show that what we have is just another magical compression scam.
He says that he's "doing something differently"; we've proved that what he claims to be doing is impossible. End of story.
Okay, let's look at some math. First, calculate the number of bits that must be stored to reliably archive 256GB:
.426 micro meters = 426 nm
256*1024*1024*1024*8*(10/8) = 2.749 * 10^12 [allowing for 25% extra - error detection/correction]
Now, the area of a sheet of paper in mm^2:
210 mm * 297 mm = 6.237 * 10^4
Let's make an assumption: it would be tough for a scanner to correctly identify more than 256 colors (blues especially are problematic). So, going by a pixel based method, we can store 8 bits per pixel, so the number of pixels needed is:
2.749 * 10^12 / 8 = 3.436 * 10^11
Pixels per mm^2 will therefore be:
3.436 * 10^11 / 6.237 * 10^4 = 5.509 * 10^6
Taking the square root of this figure and inverting will give us the size of one side of a pixel in mm, so:
1 / (5.509 * 10^6)^.5 = 4.260 * 10^-4 mm =
This is smaller than the wavelengths of some frequencies of visible light, therefore a large portion of the spectrum is gone in terms of colors that can be used. Eliminate these colors and you increase density yet again, requiring you eliminate more colours. By the time you get to monochromatic (black white), which you will, the size is smaller than the wavelength of ANY visible light.
So, for this storage density, either you are scanning in ultraviolet light (and printing using an appropriate ink) to get a small enough wavelength, or you have thrown out light all together and you are using an electron microscope as your scanner. (Note - ever see electron microscope images in color? Can't exist unless colorized).
Fairly clever hoax though - if they had stuck with, say, 16GB then it would not have edged into the impossible.
You are an idiot because: You ignored the one and only thing he /did/ say, which was that he was doing something differently.
Bzzt.
Encoding data using dots is the most efficient method possible. He has to print the image somehow, and scan it back in again. No combination of triangles and circles can circumvent the resolution limit, which is what is being calculated here.
By showing that the claim exceeds all practical limits of optical resolution (and probably the absolute physical limits), we show that what we have is just another magical compression scam.
He says that he's "doing something differently"; we've proved that what he claims to be doing is impossible. End of story.Indeed. For those not inclined to simple mathematics, here it is in a nutshell-
Assumptions (none of them unreasonable, all of them quite generous even):
1440dpi
8 bit color
8" x 10.5" printing area
Even assuming perfect readability, this resolution yields only 1.4GB per page. Talk of "shapes" is smoke and mirrors to obfuscate one of the cold hard facts of information theory: you cannot accurately represent all permutations of 8 bits of information if you've budgeted less than 8 bits. Compression schemes allow you to compress repetitive patterns is you know they're going to be there beforehand (e.g. an almost arbitrarily large number of only 1's or only 0's can be represented with run length encoding), but X bits of random data requires X bits of allocated space.
If a job's not worth doing, it's not worth doing right.
Here's an upper bound as a check on your numbers (not restricting ourselves to a small dictionary of shapes). I'll give away the punchline: My numbers agree with yours, but 256 GB is not possible using printers and paper.
Assumptions: I use your printer linear resolution of 1200 dpi, and assume that adjacent pixels can be resolved at this resolution. I also assume that 256 different colors can be distinguished, as you do, and that the paper we are using has an area of 96.6763 inches^2, also as you do.
Calculation: With a linear resolution of 1200 dpi, one can fit 1440000 dots per square inch (Check!), and so 139213872 dots on a sheet of A4. With 256 colors we can store a number as large as (number_of_colors)^(number_of_dots). So:
256^139213872 = 2^N (where N is the equivalent number of bits)
(2^8)^(139213872) = 2^N (recognizing that 256 = 2^8)
2^(8*139213872) = 2^N
N = 8*139213872 (bits)
(and if we just divide by 8 again to get bytes...) => 139213872 bytes = 139 MB
Discussion: This theoretical upper bound is three orders of magnitude smaller than what is being claimed by the article: It is not possible to store 256 GB on a sheet of A4. My result does however agree with your result in that the inequality (my_result)>(your_result) holds, as it should. Ad it's really not too shabby: Accounting for 8-to-14 conversion for some error correction, we can store slightly under 80 MB in this way.
Different assumptions: If I instead use your 2000 dpi laser printer figure, then I can fit 4000000 dots per square inch, and so 386705200 dots on a sheet of A4 and so almost 386 MB. (Including error correction, one might store 220 MB.) Pretty impressive!
The Absurd: Right now, many modern semiconductor fabs have working 90 nm photolithographic processes. That means that the smallest feature size is 3.54330709×10^(-6) in, and the linear resolution is about 282222 dpi. If all we print is the first metal layer, then a dot can either be "with metal" or "without metal" -- that is, one bit. And on a silicon wafer with an area the same as that of a sheet of A4 paper, we can then fit 7700207603555 dots, or 962 GB. Hard drives are about halfway there!