7 ms·

Just speculating, but if you can index in 5 dimensions to get your data, should it not be called 5D? data = read_bit(x, y, z, yaw, size) But i agree, i would

Just speculating, but if you can index in 5 dimensions to get your data, should it not be called 5D? data = read_bit(x, y, z, yaw, size) But i agree, i would appreciate more information if they are going to use buzz-words.

theclaw 7y ago
That seems more like five degrees of freedom than five dimensions.
- deskamess 7y ago
  Hmm... so the D could be for 'D'egrees of freedom? Who knows... like someone said, it is marketing, and hence a lot could be lost in translation just for easy/popular optics.
  - lvh 7y ago
    What is the difference between dimensionality and degrees of freedom? The standard definition of degrees of freedom is "number of variables that make up the state of the system" and the definition of the dimensionality of the state vector is...
    - jholloway7 7y ago
      There is no difference. I think people just get hung up on the word 'dimension' in the sense of degrees of freedom in a spatial state vector (to reuse your terms). Perhaps these are people who learned linear algebra only in the context of spatial dimensions / geometry and have never had to apply the concepts to any other problem domain.
- Scarblac 7y ago
  Aren't they synonyms?
  - deleted 7y ago
    [deleted]
  - close04 7y ago
    I'd rather call them parameters or indexes. Certainly not dimensions analogous to 1/2/3D. People have been storing things in 5D on wood substrate for years. Like clothes in the closet (the 2 extra Ds might be type and color). The terminology is clearly mean to impress the general audience that would normally not even bother to read a classic "engineering" title.
- djdidf 7y ago
  Ya but that’s pretty much the same thing. Surely mathematically it’s the same thing.
- ptero 7y ago
  To be the devil's advocate, it is often convenient to represent states of a system with N degrees of freedom as a subset of an N-dimensional space. For example, state space of two balls linked by a rigid rod in 3D would be seen as a 5-dimensional space. That said, the article is heavy on marketing (13.8 billion year claim is not scientific, at least in spirit) and looks like PR department product.
  - soVeryTired 7y ago
    By that definition I can double the dimensionality of the storage by adding a second disk.
  - lvh 7y ago
    The 13.8Gy claim is made by estimating, calculating and then confirming by experiment how quickly wear and tear works (the primary mechanism is nanograting, and the primary contributing physical quantity is temperature). It then specifically grabs 13.8Gy as an example data point because that's the age of the Universe, but they could've picked any other point on a time/temperature scale, like, say, "room temperature". In what sense is this "not scientific"?
    - modsiw 7y ago
      Because they first chose the result they wanted — age of universe and worked backwards to derive that result. Is it true? Sure, probably. The method flys in the face of the foundations of science and was done for sensationalism. What’s special about 462K? Is it a local min/max? Doesn’t seem so.
      - lvh 7y ago
        They computed, verified and measured wear and tear (lifespan in Gy) as a function of temperature. The paper, which I linked, includes the full plot. They had to pick _some number_ (temp or years) in order to communicate it as one data point. There's nothing special about 462K -- it's what happens when you pick the age of the Universe as how long you want it to last form now. Pick a billion years, or 10 billion, and you get a different temp. Given that they had a hypothesis, designed an experiment and validated the result, it seems a bit much to say it "flys[sic] in the face of the foundations of science".
- Shorel 7y ago
  From a linear algebra point of view, there's no difference. Neural networks used for AI are represented by N-dimensional spaces of, for example, 1024 dimensions.
- dTal 7y ago
  What's the distinction? Wikipedia seems to think there isn't one: "In mathematics, the dimension of an object is, roughly speaking, the number of degrees of freedom of a point that moves on this object." https://en.wikipedia.org/wiki/Dimension https://en.wikipedia.org/wiki/Dimension
  - bscphil 7y ago
    The difference is that people don't read the titles of press releases with pre-conceived notions of what a degree of freedom is, so it's not as useful for making clickbait.
    - lvh 7y ago
      5D has been a term of art for years, and was not made up by this article. https://en.wikipedia.org/wiki/5D_optical_data_storage https://en.wikipedia.org/wiki/5D_optical_data_storage
      - nirvdrum 7y ago
        I don't know the optical storage space one way or another, so I was curious to learn more. As far as I can tell, that Wikipedia page you've linked to is solely about the same work by the same researchers as the article. Am I overlooking something? Has there been work by others using the same term? Or is the idea that the process of becoming a Wikipedia title is what makes it a term of art?
        lvh 7y ago
        Even the Wikipedia page contains information about the original Tokio research team that only has one shared author. Furthermore, 5D is the natural extension of 3D, which was already used to distinguish it from traditional 2D (like, say, CDs). "Term of art" might be a subjective concept, but the article making it up or not is objective.
  - logfromblammo 7y ago
    N dimensions can give you 2^N degrees of freedom. If you have 3 spatial dimensions x, y, z, then you can have 3 degrees of freedom by translation and scaling along those dimensions. You can also have another 3 degrees of freedom by rotation around planes x^y, x^z, and y^z. I'm not sure what degrees of freedom are represented by the dimensionless scalar and pseudoscalar x^y^z, but probably one of them is mana points, and the other is hit points. Two spatial dimensions give you two translation/scaling axes (x, y), one rotation (x^y), and one stamina points (scalar). A 4x4 transformation matrix has 16 values, suggesting 4 dimensions, but it doesn't have 16 degrees of freedom, because several values are constrained. Nine values have three degrees of freedom, three other values have three more, and four are fixed, with zero degrees of freedom. Those six degrees of freedom suggest three dimensions, where two of the potential degrees of freedom are ignored. So a higher-dimensional mathematical space can embed a lower-dimensional model, if the constraints are clever enough, and map the degrees of freedom onto the right dimensions or combination of dimensions. This might be useful for generating smoother animations using linear interpolation, or avoiding gimbal lock, or attempting to unify gravitation with electronuclear forces, or something else.
im3w1l 7y ago
With 1d data storage I can double the length to double the capacity. With 2d I can double the length or width to double the capacity. With 3d I can double the length width or height to double capacity. That's why 3d storage is interesting.

theclaw 7y ago

That seems more like five degrees of freedom than five dimensions.

deskamess 7y ago
Hmm... so the D could be for 'D'egrees of freedom? Who knows... like someone said, it is marketing, and hence a lot could be lost in translation just for easy/popular optics.
- lvh 7y ago
  What is the difference between dimensionality and degrees of freedom? The standard definition of degrees of freedom is "number of variables that make up the state of the system" and the definition of the dimensionality of the state vector is...
  - jholloway7 7y ago
    There is no difference. I think people just get hung up on the word 'dimension' in the sense of degrees of freedom in a spatial state vector (to reuse your terms). Perhaps these are people who learned linear algebra only in the context of spatial dimensions / geometry and have never had to apply the concepts to any other problem domain.
Scarblac 7y ago
Aren't they synonyms?
- deleted 7y ago
  [deleted]
- close04 7y ago
  I'd rather call them parameters or indexes. Certainly not dimensions analogous to 1/2/3D. People have been storing things in 5D on wood substrate for years. Like clothes in the closet (the 2 extra Ds might be type and color). The terminology is clearly mean to impress the general audience that would normally not even bother to read a classic "engineering" title.
djdidf 7y ago
Ya but that’s pretty much the same thing. Surely mathematically it’s the same thing.
ptero 7y ago
To be the devil's advocate, it is often convenient to represent states of a system with N degrees of freedom as a subset of an N-dimensional space. For example, state space of two balls linked by a rigid rod in 3D would be seen as a 5-dimensional space. That said, the article is heavy on marketing (13.8 billion year claim is not scientific, at least in spirit) and looks like PR department product.
- soVeryTired 7y ago
  By that definition I can double the dimensionality of the storage by adding a second disk.
- lvh 7y ago
  The 13.8Gy claim is made by estimating, calculating and then confirming by experiment how quickly wear and tear works (the primary mechanism is nanograting, and the primary contributing physical quantity is temperature). It then specifically grabs 13.8Gy as an example data point because that's the age of the Universe, but they could've picked any other point on a time/temperature scale, like, say, "room temperature". In what sense is this "not scientific"?
  - modsiw 7y ago
    Because they first chose the result they wanted — age of universe and worked backwards to derive that result. Is it true? Sure, probably. The method flys in the face of the foundations of science and was done for sensationalism. What’s special about 462K? Is it a local min/max? Doesn’t seem so.
    - lvh 7y ago
      They computed, verified and measured wear and tear (lifespan in Gy) as a function of temperature. The paper, which I linked, includes the full plot. They had to pick _some number_ (temp or years) in order to communicate it as one data point. There's nothing special about 462K -- it's what happens when you pick the age of the Universe as how long you want it to last form now. Pick a billion years, or 10 billion, and you get a different temp. Given that they had a hypothesis, designed an experiment and validated the result, it seems a bit much to say it "flys[sic] in the face of the foundations of science".
Shorel 7y ago
From a linear algebra point of view, there's no difference. Neural networks used for AI are represented by N-dimensional spaces of, for example, 1024 dimensions.
dTal 7y ago
What's the distinction? Wikipedia seems to think there isn't one: "In mathematics, the dimension of an object is, roughly speaking, the number of degrees of freedom of a point that moves on this object." https://en.wikipedia.org/wiki/Dimension https://en.wikipedia.org/wiki/Dimension
- bscphil 7y ago
  The difference is that people don't read the titles of press releases with pre-conceived notions of what a degree of freedom is, so it's not as useful for making clickbait.
  - lvh 7y ago
    5D has been a term of art for years, and was not made up by this article. https://en.wikipedia.org/wiki/5D_optical_data_storage https://en.wikipedia.org/wiki/5D_optical_data_storage
    - nirvdrum 7y ago
      I don't know the optical storage space one way or another, so I was curious to learn more. As far as I can tell, that Wikipedia page you've linked to is solely about the same work by the same researchers as the article. Am I overlooking something? Has there been work by others using the same term? Or is the idea that the process of becoming a Wikipedia title is what makes it a term of art?
      - lvh 7y ago
        Even the Wikipedia page contains information about the original Tokio research team that only has one shared author. Furthermore, 5D is the natural extension of 3D, which was already used to distinguish it from traditional 2D (like, say, CDs). "Term of art" might be a subjective concept, but the article making it up or not is objective.
- logfromblammo 7y ago
  N dimensions can give you 2^N degrees of freedom. If you have 3 spatial dimensions x, y, z, then you can have 3 degrees of freedom by translation and scaling along those dimensions. You can also have another 3 degrees of freedom by rotation around planes x^y, x^z, and y^z. I'm not sure what degrees of freedom are represented by the dimensionless scalar and pseudoscalar x^y^z, but probably one of them is mana points, and the other is hit points. Two spatial dimensions give you two translation/scaling axes (x, y), one rotation (x^y), and one stamina points (scalar). A 4x4 transformation matrix has 16 values, suggesting 4 dimensions, but it doesn't have 16 degrees of freedom, because several values are constrained. Nine values have three degrees of freedom, three other values have three more, and four are fixed, with zero degrees of freedom. Those six degrees of freedom suggest three dimensions, where two of the potential degrees of freedom are ignored. So a higher-dimensional mathematical space can embed a lower-dimensional model, if the constraints are clever enough, and map the degrees of freedom onto the right dimensions or combination of dimensions. This might be useful for generating smoother animations using linear interpolation, or avoiding gimbal lock, or attempting to unify gravitation with electronuclear forces, or something else.

im3w1l 7y ago

With 1d data storage I can double the length to double the capacity. With 2d I can double the length or width to double the capacity. With 3d I can double the length width or height to double capacity. That's why 3d storage is interesting.