## Can 4D beings read our books?

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

### Can 4D beings read our books?

So a 4D being can look down on our "flat" 3D space and see everything at once, at least everything close to him. Let's say he can also drop down into our space, Flatland-style. I argue that even though he can see everything as if it were flat, he would have difficulty reading our paper books, even if he knew our languages.

Here's why:
Let's bring the analogy down one dimension. You're looking down on a 2D space, trying to read their "books." What do their books look like? I imagine they might be one long string of a scroll, or maybe a bunch of lines bound together by a spine, like the teeth on a comb. The written language might look something like Morse Code. The words are printed on both sides of the thin strands, and the ink, much like ours, penetrates the thin strand of paper to a depth of just a few micrometers. That's much too small to see from "above." And if the book is closed, all of these micrometer-thin words will be smashed up against each other, so it would look like a jumble of black and white static.

Even if you could put your eyeball exactly on the 2D plane, looking at a book like a flatlander would, you'd only see the 1D "side" of the page. I can't imagine that our eyes would see anything at all. And if they did, it'd be an infinitely-thin strand of light from which you'd need to discern the Morse Code words on the page.

Returning to thicker problems, I think the 4D being would have the same problems trying to read one of our 3D books. The ink on the pages is just too thin, and their 4D eyes aren't equipped to view 3D shapes on the 3D hyperplane like ours are.

But if you disagree, I'd love to hear why. This is a thought I've had for a while, but I haven't heard of anyone else proposing the problem. I'd like to know if my answer is totally off-base, or if my reasoning is sound.

neverhood311
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### Re: Can 4D beings read our books?

A 4D being can actually see every portion of the 3D world, including the interiors of opaque objects. 4D beings can actually reason out 3D shapes, since they are much simpler than 4D shapes.

The most common shape of a book in 3D is that of a cuboid. The cuboid is special in that one side contains a layer of paper supported by a hard cover that covers all sides except that one. The opposite side from it holds the pages, so the cuboid can be opened at a designated page through holding one of the many papers. Then the cuboid approximately becomes a wider cuboid that shows two papers, filled with text.

The average 3D reader, of which the book is also native to, finds the book readable since the papers are opaque, allowing for text to be distinguished between neighboring pages. For a 4D reader, let's say that the 3D world is part of a facet of a huge cubic wall inside a tesseract. It is well-known that a tesseract has mutually perpendicular cubic cells. Therefore, for a 4D being whose line of sight is parallel to the cubic floor, he/she can actually see the fullness of the 3D world, though parts farther from it tend to slant because of perspective projection.

If your 4D being tries to look at a 3D book that is closed, there will be a scattering of black spots that form a 3D irregular structure (in actuality, these are all of the text that can be seen by a 4D being) making it hard (presumably) for them to understand. They wouldn't even recognize the method because their way of reading would be vastly different to accommodate for the extra dimension. If we assume perfect 3D space, the book would literally be weightless because it has 0 w-length (4D length, look at the zero product rule). He/she can only see it, not manipulate it.

For your 2D analogy, yes, it can. By extrapolating the analogy, you can fully observe the 2D world since you have a much greater line of sight than 2D beings. But the main problem is confusion, recognition, and the thickness of a lower-dimensional world compared to a higher-dimensional one. The book would not even look like an ordinary 3D book due to sight restrictions in dimensions.
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All human beings are born free and equal in dignity and rights. They are endowed with reason and conscience and should act towards one another in a spirit of brotherhood.
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### Re: Can 4D beings read our books?

I guess my argument boils down to this:
Some object of some dimension that is considered flat by a being of the same number of dimensions is too thin for a being of a higher dimension to see properly since it occupies nearly zero hypervolume in their field of view.

I argue that this is true for 3D->2D, but does this idea extrapolate to higher dimensions?
neverhood311
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### Re: Can 4D beings read our books?

I realized that I'm making a pretty big assumption about how 4D vision systems and brains work. It would be hard for us (me, at least) to extract a 1D slice of my field of view, mentally stretch it to 2D, and "read" it in 2D. But, as Cliff Pickover suggests in Surfing Through Hyperspace, a 4D brain has so much more room for neural connections than our flat 3D ones that they could have exponentially more brainpower. Who knows what their brains are capable of?
neverhood311
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### Re: Can 4D beings read our books?

It would be hard. They might be able to. Carved messages are different.

In essence, if you have a look at a book, it's about varying amounts of ink on thin layers of dead tree. The 4d person would be able to see these layers of paper like tree-rings, and follow the extent, but the writing is pigmentation on the surface, that is, towards the edge. We grasp it, only by opening the book and seeing this pigmentation cover the width of our view. But they would be looking at variations in the stitching down the edge of the book for their words.

The closest we get to it is when you see the coloured sections going down the edge of the page, which helps you open the book.
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wendy
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### Re: Can 4D beings read our books?

For me, 4D adds the extra ana and kata directions to see things in.

A 4D being looks along a line of sight at the 2D height and width of an open page of a book and can read it just fine.

I've always liked Aale de Winkel's quote in the Flaw in Flatland thread when he said:

"I doubt very much that tetra-vision would be the same as x-ray-vision.
Tetronians will not be able to see within a trionian body, they see the lightrays reflecting off a body just in a direction more than we trionians do!"

Hugh
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### Re: Can 4D beings read our books?

Let's create a lower dimensional analogy!
So, imagine 2d being make books out of pieces of paper with dots and dashes, like morse code, we would be able to read these sheets if we understood what they meant.
Similarly, 4d beings would be able to read our books like this.

ubersketch
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### Re: Can 4D beings read our books?

ubersketch wrote:Let's create a lower dimensional analogy!
So, imagine 2d being make books out of pieces of paper with dots and dashes, like morse code, we would be able to read these sheets if we understood what they meant.

To a 2D viewpoint, those dots and dashes can only be viewed perpendicularly on a line of sight along the plane, but a 3D viewpoint could view that 1D line perpendicularly from all the way around that line, 360 degrees, like going around a flagpole.
Similarly, the 2D plane of a 3D book can only be viewed perpendicularly on a line of sight straight towards the plane one way by a 3D viewpoint, but a 4D viewpoint could view that 2D plane from a perpendicular line of sight all the way around, 360 degrees.
A 4D viewpoint can see the same 2D plane viewpoint from different perpendicular directions, and the plane would look the same, even though it's from a different perpendicular direction.

Hugh
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### Re: Can 4D beings read our books?

neverhood311 wrote:I realized that I'm making a pretty big assumption about how 4D vision systems and brains work. It would be hard for us (me, at least) to extract a 1D slice of my field of view, mentally stretch it to 2D, and "read" it in 2D. But, as Cliff Pickover suggests in Surfing Through Hyperspace, a 4D brain has so much more room for neural connections than our flat 3D ones that they could have exponentially more brainpower. Who knows what their brains are capable of?

I always assumed that 4D beings would be super-intelligent compared to humans due to the complexity of geometry increasing exponentially. The amount of disimplicial polytopes in 4D is 37 compared to the 3D amount which is 3.

ubersketch
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