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Comment by theclaw | Hacker News Reader

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

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

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.

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.

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

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?

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.

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.

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"?

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.

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".

And finally the disc will never reach that, because it will not physically survive (or it's surroundings) to reach that time.

Not on Earth, not in space, when real considerations like impact resistance are in.

By that definition I can double the dimensionality of the storage by adding a second disk.

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.

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...

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.

Ya but that’s pretty much the same thing. Surely mathematically it’s the same thing.

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.

Aren't they synonyms?

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.

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