14 ms·

In case anyone is wondering what they mean by "5D": they mean it's a 3D array of marks, each of which has both size and orientation. The 3D array is three 2D la

by gjm11 5y ago

In case anyone is wondering what they mean by "5D": they mean it's a 3D array of marks, each of which has both size and orientation. The 3D array is three 2D layers. According to this definition, a DVD or Blu-Ray disc is "4D" because it can have multiple layers each of which stores 1-dimensional data (pit versus no pit). And a book is at least "7D" because it contains a 3D arrangement of marks, and marks can vary in (at least) what letter they are, how large, how bold, and how slanted. (It would be easy to add to that list.) I would describe this thing as 2.5D storage: it's basically 2-dimensional but with multiple layers. If it's genuinely 10000x denser than Blu-ray, great! If it's likely to last longer, also great! But there's no need for this "five-dimensional" bullshit. (It looks to me as if what they have at the moment is not anything like 10000x denser than Blu-ray. I'm not sure it's even 1x denser than Blu-ray at present.)

chmod775 5y ago
A better definition then would be: Assuming each dimension is infinite, how many dimensions do you need to uniquely address a bit. The infinite requirement is there so the answer can't be reduced to "1 dimension" every time (if you had a 10x10 matrix you could just turn it into an array of 100 elements).
- chriswarbo 5y ago
  Slight nit-pick, but any number of dimensions can be reduced to one, using a pairing function https://en.wikipedia.org/wiki/Pairing_function https://en.wikipedia.org/wiki/Pairing_function or a space-filling curve https://en.wikipedia.org/wiki/Space-filling_curve https://en.wikipedia.org/wiki/Space-filling_curve
  - chmod775 5y ago
    Right. I don't immediately see how either of those would work for uncountable infinite sets, but it may be possible. Clearly some other limitations are required to make "dimensions" a useful metric in this context.
    - chriswarbo 5y ago
      > I don't immediately see how either of those would work for uncountable infinite sets, but it may be possible. We can think of an N-dimensional space as a grid of (hyper)cube "cells": - Cantor's pairing function traces diagonal lines through the top-right quadrant of a (countable) 2D grid - We can extend Cantor pairing to the whole (countable) 2D plane by joining the diagonals of each quandrant (they meet at the axes). The resulting line spirals out from the origin, in a diamond shape. - We can extend the 2D plane to higher dimensions, again by joining diagonals when they meet at the axes. This results in a diamond-shaped "shell" spiralling out from the origin. The above gives us a 1D line which visits every cell one after another. Next we associate each unit-interval on our line with the cells we're traversing, i.e. the interval between 0 and 1 is associated with the 1st cell; the interval between 1 and 2 is associated with the 2nd cell; and so on. (We could also jump between positive and negative, like [0, 1), [-1, 0), [1, 2), [-2, -1), ... to include the negative half of our 1D line as well) Finally, we use a space-filling curve, like a Z-curve, to map each interval to the volume of its associated grid cell. This works for uncountable intervals and cell volumes. The result would be a line which starts at the origin, and gradually spirals outwards. From a distance, the line appears to form N-dimensional diamond-shaped 'shells'. If we look closer, we see each 'shell' has jagged edges, since it's formed of N-dimensional grid cells. If we look even closer, we see that the line traces a z-curve through each grid cell, filling its volume. The above works for any pairing function and space-filling curve, although I've written about cantor pairing at http://chriswarbo.net/projects/procedural/cantor.html http://chriswarbo.net/projects/procedural/cantor.html and z-curves at http://chriswarbo.net/projects/procedural/z.html http://chriswarbo.net/projects/procedural/z.html :)
    - ClumsyPilot 5y ago
      I think once you are talking about "uncountable infinite sets" and different kinds of infinities, the definition has become very niche.
- clairity 5y ago
  what you're dancing around is linear independence, which is the idea that two functions can't be described as a function of each other, which also means they can be used to specify every other function in the intervening function space. the least number of linearly independent coordinate functions (usually transformed down to unit vectors) is the dimensionality of the system. note that you can have linearly dependent functions/coordinate systems, which this '5d' moniker is akin to.
  - chmod775 5y ago
    > what you're dancing around is linear independence Thanks! That was a "ohhhhhh of course!" moment for me. At least that's more succinct and I don't see a way to cheat it.
MAGZine 5y ago
I think Dimension in the data sense of the word, not Dimension in the spatial sense of the word. Multi-dimension data is a thing, and it goes a lot higher than 4, 5, or 7.
- gruez 5y ago
  >I think Dimension in the data sense of the word Where else is that used? At least to me (and the common layperson), the only usage seems to be from people trying to hype up storage mediums. also, if we're using that definition, does that mean I have a 7D SSD? The NAND cells are arranged on both the planar axis, and stacked (3d NAND). That's 3 dimensions. Each NAND cell also encodes data using various charge levels, which currently tops out at 4 bits. In total that makes for 3 + 4 = 7 dimensions.
  - kortex 5y ago
    That is still O(N^3) in my opinion. If you scale up the media in all directions, your data scales like the cubic. The charge level makes it maybe 3.1 dimensions, but it isn't really scalable. Now if you could add arbitrary voltage levels without losing precision, that would be 4D.
  - emteycz 5y ago
    It's a math/information science term that was applied in physics (its most well known usage), not the other way around...
  - lelandbatey 5y ago
    It's mostly a mathematical term which also applies to pieces of data. See here: https://en.wikipedia.org/wiki/Dimension https://en.wikipedia.org/wiki/Dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
  - c5e3ebe93d2c 5y ago
    In my physics courses we would routinely talk about 6 dimensional spaces when discussing position-momentum space, also we would sometimes refer to two dimensional objects like a moebius strips as "1-dimensional". > also, if we're using that definition, does that mean I have a 7D SSD? Maybe. You can use whatever definitions you want if you feel it's helpful. However, based on your description, if you're using a single bit as a dimension, you should figure out how many bits the the dimensional information encodes. As it stands, it's not clear what you're counting as a 'dimension' in this context. Also, normally we think of degrees of freedom as being independent of each other (hence the claim to 5d in this example). The charge information would normally be thought of as a single degree of freedom, so you'd have a 4d nand disk. One reason it is helpful to think of "a dimension" as an independent degree of freedom, is that it becomes a parameter you can focus on improving. So if you say "Well what can we change, or make more precise?", the answer for the nand case is "Well, we can't easily add another spatial degree of freedom, but we can improve our stacking to improve how much we can pack into the vertical dimesion (but we're limited by Job's obsession with thinness). We can improve our measurements of spatial resolution, which will affect 3 of our dimensions, but not the charge. We can also improve our charge resolution. Let's figure out which one is cheapest to scale." Now granted, sometimes tweaking one parameter affects the other, so they aren't strictly independent. You can pack a lot of charge on a NAND, but as the other dimensions get smaller, you start having increased difficulty with leaking. Anyhow, I think there's more here than you're giving them credit for, even if they are guilty of tooting their own horn a bit (shocking). But yes, the article presented here would be greatly improved if it gave examples of how to classify existing technology using the researcher's dimensional classification scheme. It's a common scientific writing tactic that I'm surprised was not used here.
kmeisthax 5y ago
Counting size and orientation as extra dimensions would be justifiable if you could overlap dots of different sizes or orientations, even a little.
- rbanffy 5y ago
  You still need 5 values to retrieve a single bit of data, even if only two of those numbers have more than 3 bits.
AtlasBarfed 5y ago
They mentioned 500TB for a single glass disk, isn't that 100,000x more than a 5GB blu-ray, or are they comparing it with the 10-layer blu-rays that never really hit the market? Is this the same UK group that did all the holographic disc research that is basically vaporware in the mass market (I don't want to call their research vaporware, just that it never hit the consumer market)? Edit: Whoops. 4.7 geebees is for a regular DVD, not a Blu-ray. Dual layer blu-ray is 50GB
- gjm11 5y ago
  They did indeed mention 500TB. That doesn't mean they have actually stored 500TB anywhere, or that they have a system that's currently capable of storing 500TB anywhere, or even that they genuinely have good reason to think that their system can practically be made to store 500TB in something the size of a Blu-Ray disc. Maybe it can! But so far as I can tell the 10000x figure is much more what they hope might be achievable than what they are in any position to do. I don't have access to their actual paper. But the reports in the popular press seem to indicate that the individual voxels are on the order of 500x50nm in size, compared with Blu-Ray pits which are about 500x500nm. So that's a density increase of 10x within each layer. Each voxel apparently stores 4 bits, compared with one bit for a Blu-Ray pit, so that's a density increase of 40x. So if they're claiming 10000x, I think most of that increase has to be from having many many layers. They'd need 250 layers. So far they have done 3. It seems to me that the technical challenges in increasing the number of layers so greatly without reducing the density of voxels might be very great, because to read or write a voxel you need to point a laser at it, and as the number of layers increases they start getting in one another's way. Maybe they already have some ingenious solution to that problem -- again, I don't have access to their actual article. But I tend to think that if they'd solved that problem then (1) they would be making sure that the articles in the popular press tell the world of that achievement and (2) they would have demonstrated it with more than 3 layers. [EDITED to add:] Oh, wait, at least one of their publications is available to read: https://www.osapublishing.org/optica/fulltext.cfm?uri=optica-8-11-1365&id=462661 https://www.osapublishing.org/optica/fulltext.cfm?uri=optica... This one talks about "50 layers", though I'm not 100% sure whether they mean 50 full two-dimensional layers stacked on top of one another (their diagrams seem to suggest not), and says that with the parameters they used the amount they could fit on one disc would be ... 1.64TB. That's a ~30x increase over a dual-layer Blu-ray disc. Not to be sneezed at, for sure, but it's a lot less than 10000x. That paper is entitled "High speed ultrafast laser anisotropic nanostructuring by energy deposition control via near-field enhancement". It seems there's another one called "5D optical data storage with 100% readout accuracy in silica glass". Same authors, approximately same publication date, so it seems a bit unlikely that one of them is claiming 300x denser data storage than the other, but who knows?
guerrilla 5y ago
> But there's no need for this "five-dimensional" bullshit. Sure there is. It's going to sell great with idiots. I still remember morons super hyped about Opteron trying to claim it was an optical CPU.
- 1_player 5y ago
  I don't know, in my book the idiots are the big brains that thought that calling it 5D would be a smashing idea. Can't wait for the next version being sold as 6D+ It's probably the same type of people that decide the USB technology names (SuperSpeed, UltraSpeed, HumoungousSpeed) that are hard to follow and understand even for hardcore nerds like us. Marketing would be more appreciated if it didn't take laymen for morons, as you call them.
  - guerrilla 5y ago
    Yes, the same ones that keep bumping version numbers absurdly. They do it because it works. It doesn't assume all laymen are morons; the people that know it's value will buy it anyway.

by gjm11 5y ago

chmod775 5y ago

A better definition then would be: Assuming each dimension is infinite, how many dimensions do you need to uniquely address a bit. The infinite requirement is there so the answer can't be reduced to "1 dimension" every time (if you had a 10x10 matrix you could just turn it into an array of 100 elements).

chriswarbo 5y ago
Slight nit-pick, but any number of dimensions can be reduced to one, using a pairing function https://en.wikipedia.org/wiki/Pairing_function https://en.wikipedia.org/wiki/Pairing_function or a space-filling curve https://en.wikipedia.org/wiki/Space-filling_curve https://en.wikipedia.org/wiki/Space-filling_curve
- chmod775 5y ago
  Right. I don't immediately see how either of those would work for uncountable infinite sets, but it may be possible. Clearly some other limitations are required to make "dimensions" a useful metric in this context.
  - chriswarbo 5y ago
    > I don't immediately see how either of those would work for uncountable infinite sets, but it may be possible. We can think of an N-dimensional space as a grid of (hyper)cube "cells": - Cantor's pairing function traces diagonal lines through the top-right quadrant of a (countable) 2D grid - We can extend Cantor pairing to the whole (countable) 2D plane by joining the diagonals of each quandrant (they meet at the axes). The resulting line spirals out from the origin, in a diamond shape. - We can extend the 2D plane to higher dimensions, again by joining diagonals when they meet at the axes. This results in a diamond-shaped "shell" spiralling out from the origin. The above gives us a 1D line which visits every cell one after another. Next we associate each unit-interval on our line with the cells we're traversing, i.e. the interval between 0 and 1 is associated with the 1st cell; the interval between 1 and 2 is associated with the 2nd cell; and so on. (We could also jump between positive and negative, like [0, 1), [-1, 0), [1, 2), [-2, -1), ... to include the negative half of our 1D line as well) Finally, we use a space-filling curve, like a Z-curve, to map each interval to the volume of its associated grid cell. This works for uncountable intervals and cell volumes. The result would be a line which starts at the origin, and gradually spirals outwards. From a distance, the line appears to form N-dimensional diamond-shaped 'shells'. If we look closer, we see each 'shell' has jagged edges, since it's formed of N-dimensional grid cells. If we look even closer, we see that the line traces a z-curve through each grid cell, filling its volume. The above works for any pairing function and space-filling curve, although I've written about cantor pairing at http://chriswarbo.net/projects/procedural/cantor.html http://chriswarbo.net/projects/procedural/cantor.html and z-curves at http://chriswarbo.net/projects/procedural/z.html http://chriswarbo.net/projects/procedural/z.html :)
  - ClumsyPilot 5y ago
    I think once you are talking about "uncountable infinite sets" and different kinds of infinities, the definition has become very niche.
clairity 5y ago
what you're dancing around is linear independence, which is the idea that two functions can't be described as a function of each other, which also means they can be used to specify every other function in the intervening function space. the least number of linearly independent coordinate functions (usually transformed down to unit vectors) is the dimensionality of the system. note that you can have linearly dependent functions/coordinate systems, which this '5d' moniker is akin to.
- chmod775 5y ago
  > what you're dancing around is linear independence Thanks! That was a "ohhhhhh of course!" moment for me. At least that's more succinct and I don't see a way to cheat it.

MAGZine 5y ago

I think Dimension in the data sense of the word, not Dimension in the spatial sense of the word. Multi-dimension data is a thing, and it goes a lot higher than 4, 5, or 7.

gruez 5y ago
>I think Dimension in the data sense of the word Where else is that used? At least to me (and the common layperson), the only usage seems to be from people trying to hype up storage mediums. also, if we're using that definition, does that mean I have a 7D SSD? The NAND cells are arranged on both the planar axis, and stacked (3d NAND). That's 3 dimensions. Each NAND cell also encodes data using various charge levels, which currently tops out at 4 bits. In total that makes for 3 + 4 = 7 dimensions.
- kortex 5y ago
  That is still O(N^3) in my opinion. If you scale up the media in all directions, your data scales like the cubic. The charge level makes it maybe 3.1 dimensions, but it isn't really scalable. Now if you could add arbitrary voltage levels without losing precision, that would be 4D.
- emteycz 5y ago
  It's a math/information science term that was applied in physics (its most well known usage), not the other way around...
- lelandbatey 5y ago
  It's mostly a mathematical term which also applies to pieces of data. See here: https://en.wikipedia.org/wiki/Dimension https://en.wikipedia.org/wiki/Dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
- c5e3ebe93d2c 5y ago
  In my physics courses we would routinely talk about 6 dimensional spaces when discussing position-momentum space, also we would sometimes refer to two dimensional objects like a moebius strips as "1-dimensional". > also, if we're using that definition, does that mean I have a 7D SSD? Maybe. You can use whatever definitions you want if you feel it's helpful. However, based on your description, if you're using a single bit as a dimension, you should figure out how many bits the the dimensional information encodes. As it stands, it's not clear what you're counting as a 'dimension' in this context. Also, normally we think of degrees of freedom as being independent of each other (hence the claim to 5d in this example). The charge information would normally be thought of as a single degree of freedom, so you'd have a 4d nand disk. One reason it is helpful to think of "a dimension" as an independent degree of freedom, is that it becomes a parameter you can focus on improving. So if you say "Well what can we change, or make more precise?", the answer for the nand case is "Well, we can't easily add another spatial degree of freedom, but we can improve our stacking to improve how much we can pack into the vertical dimesion (but we're limited by Job's obsession with thinness). We can improve our measurements of spatial resolution, which will affect 3 of our dimensions, but not the charge. We can also improve our charge resolution. Let's figure out which one is cheapest to scale." Now granted, sometimes tweaking one parameter affects the other, so they aren't strictly independent. You can pack a lot of charge on a NAND, but as the other dimensions get smaller, you start having increased difficulty with leaking. Anyhow, I think there's more here than you're giving them credit for, even if they are guilty of tooting their own horn a bit (shocking). But yes, the article presented here would be greatly improved if it gave examples of how to classify existing technology using the researcher's dimensional classification scheme. It's a common scientific writing tactic that I'm surprised was not used here.

kmeisthax 5y ago

Counting size and orientation as extra dimensions would be justifiable if you could overlap dots of different sizes or orientations, even a little.

rbanffy 5y ago
You still need 5 values to retrieve a single bit of data, even if only two of those numbers have more than 3 bits.

AtlasBarfed 5y ago

They mentioned 500TB for a single glass disk, isn't that 100,000x more than a 5GB blu-ray, or are they comparing it with the 10-layer blu-rays that never really hit the market? Is this the same UK group that did all the holographic disc research that is basically vaporware in the mass market (I don't want to call their research vaporware, just that it never hit the consumer market)? Edit: Whoops. 4.7 geebees is for a regular DVD, not a Blu-ray. Dual layer blu-ray is 50GB

gjm11 5y ago
They did indeed mention 500TB. That doesn't mean they have actually stored 500TB anywhere, or that they have a system that's currently capable of storing 500TB anywhere, or even that they genuinely have good reason to think that their system can practically be made to store 500TB in something the size of a Blu-Ray disc. Maybe it can! But so far as I can tell the 10000x figure is much more what they hope might be achievable than what they are in any position to do. I don't have access to their actual paper. But the reports in the popular press seem to indicate that the individual voxels are on the order of 500x50nm in size, compared with Blu-Ray pits which are about 500x500nm. So that's a density increase of 10x within each layer. Each voxel apparently stores 4 bits, compared with one bit for a Blu-Ray pit, so that's a density increase of 40x. So if they're claiming 10000x, I think most of that increase has to be from having many many layers. They'd need 250 layers. So far they have done 3. It seems to me that the technical challenges in increasing the number of layers so greatly without reducing the density of voxels might be very great, because to read or write a voxel you need to point a laser at it, and as the number of layers increases they start getting in one another's way. Maybe they already have some ingenious solution to that problem -- again, I don't have access to their actual article. But I tend to think that if they'd solved that problem then (1) they would be making sure that the articles in the popular press tell the world of that achievement and (2) they would have demonstrated it with more than 3 layers. [EDITED to add:] Oh, wait, at least one of their publications is available to read: https://www.osapublishing.org/optica/fulltext.cfm?uri=optica-8-11-1365&id=462661 https://www.osapublishing.org/optica/fulltext.cfm?uri=optica... This one talks about "50 layers", though I'm not 100% sure whether they mean 50 full two-dimensional layers stacked on top of one another (their diagrams seem to suggest not), and says that with the parameters they used the amount they could fit on one disc would be ... 1.64TB. That's a ~30x increase over a dual-layer Blu-ray disc. Not to be sneezed at, for sure, but it's a lot less than 10000x. That paper is entitled "High speed ultrafast laser anisotropic nanostructuring by energy deposition control via near-field enhancement". It seems there's another one called "5D optical data storage with 100% readout accuracy in silica glass". Same authors, approximately same publication date, so it seems a bit unlikely that one of them is claiming 300x denser data storage than the other, but who knows?

guerrilla 5y ago

> But there's no need for this "five-dimensional" bullshit. Sure there is. It's going to sell great with idiots. I still remember morons super hyped about Opteron trying to claim it was an optical CPU.

1_player 5y ago
I don't know, in my book the idiots are the big brains that thought that calling it 5D would be a smashing idea. Can't wait for the next version being sold as 6D+ It's probably the same type of people that decide the USB technology names (SuperSpeed, UltraSpeed, HumoungousSpeed) that are hard to follow and understand even for hardcore nerds like us. Marketing would be more appreciated if it didn't take laymen for morons, as you call them.
- guerrilla 5y ago
  Yes, the same ones that keep bumping version numbers absurdly. They do it because it works. It doesn't assume all laymen are morons; the people that know it's value will buy it anyway.