Reddit mentions of Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

> "Hidden Dimensions" by Lisa Randall.

Just for clarity, I think you mean:

Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions, by Lisa Randall.

https://amzn.com/0060531096

Physicists take the idea of additional unknown dimensions seriously. I think the implication is that some unusual phenomena share a common physical mechanism that isn't very well understood but that science is at least aware of. It's interesting to consider that some religious or spiritual phenomena might have an actual physical basis. I think we're culturally conditioned to believe that some supernatural phenomena are non-physical but increasing evidence points in the opposite direction.

http://www.amazon.com/Warped-Passages-Unraveling-Mysteries-Dimensions/dp/0060531096/ref=sr_1_4?ie=UTF8&qid=1375151231&sr=8-4&keywords=Lisa+Randall

To build on doc_daneeka's answer, I'll try to recollect an explanation I read about 4D objects in 3D space.

An object existing in n dimensions may be represented in n-1 dimensions. This representation may be called a shadow.

So, a 2D representation of an object existing in 3 dimensions is called a shadow (and is a shadow as we know it). Looking at a 2D representation alone, one might be able to reconstruct what the original object looks like in 3D.

Say, you see the shadow of a clear glass vase. If you know where the light source is placed, you might be able to ascertain what the vase looks like based solely on its shadow. Spin the vase, and the shadow will show some movement as well.

What we're looking at is a 3D representation of an object that exists in 4 dimensions. For a moving object in 3 dimensions, its shadow would also show movement albeit only in two axis. Similarly, objects in 4 dimensions would show movement along three axis.

From what I gather, we haven't yet developed a sophisticated way to think or even explain (to the layman at least) what an object might look like in 4D. Most of our brains aren't wired to think that way. Kinda like the characters in Flatland - really nice read, BTW.

You know...I may have come across this explanation while attempting (and failing miserably) to read and understand Lisa Randall's Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions.

If this interests you, you might enjoy warped passages by Lisa Randall. It’s a few years old now, so I’d bet the science has evolved, but she does a great job of explaining these kinds of concepts in lay-terms.

I've been exploring this recently. I'm not an expert, but I'll do my best to explain it.


The shape or object represented in the gif you posted is called a tesseract or a hypercube. You can search for these terms for more information.


To explain this, some basics about 2D and 3D must first be established to understand how to continue the explanation to 4D.


A super-brief explanation of the gif above as the four dimension object (spatially) is that it is a representation or projection of viewing a 4D object/shape in a 2D view. (That gif as displayed on our computer screens is 2D because our screens are 2D and it's not encoded as 3D to be viewed with 3D glasses) and a 4-D object or shape actually appears to us to be 3D objects inside of 3D objects, just as if we look at a 2D object - say a square drawn on a piece of paper - we are able to see inside of the 2D object and see additional objects drawn inside of it and just as we are only able to draw a 3D object on a piece of paper if it is drawn as a transparent outline, this gif shows the 4D object drawn as a transparent outline in which we only see the many sides folding in and outside of itself. A being that is capable of seeing four spatial dimensions would be able to look at you and see inside of you. The following demonstrates this concept pretty well:


Fourth Spatial Dimension 101 (video, 6:27)



To better understand the concept of the fourth dimension, read on. I also included more videos below, including an excellent one by Carl Sagan.


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First, some facts / definitions:

• 0D (zero spatial dimension) is simply a point. It either exists or does not exist. There is no concept of a point moving in 0 dimensions because there is no space for it to move.
  
  
• 1D (one spatial dimension) is simply a line. It has length. A point can move along the line from side to side, left or right.
  
  
• 2D (two spatial dimensions) is a plane. It has length and width. A point can exist and/or move from side to side lengthwise and side to side width-wise, left or right, and (if we imagine the plane as a flat surface that's level to the ground,) then we can call the width direction either forward and back, if we imagine looking at the plane on a wall, we might call it up or down. Either is fine. Two dimensions.
  
  
• 3D (three spatial dimensions) is technically called "3-dimensional Euclidean space" but since it's what we commonly perceive, we often just refer to it as "space." It has length and width and height. Other words can be used for these directions, as long as it's three separate directions not in the same plane, such as left-right, up-down, and forward-back.
  
  
• 4D (four spatial dimensions) is known simply as four-dimensional space, probably because we don't use it in conversation enough to have a nifty, shorter term for it. There is also a non-spatial version of four dimensions commonly referred to as "spacetime" which is a combination of 3D space and time.
  
  
  
• A special note about the fourth dimension... Space vs time as a fourth dimension are differentiated as such: time as the fourth dimension is referred to as the Minkowski continuum, known as spacetime, and the spatial-only dimensions are referred to as Euclidean space or dimensions. Spacetime is not Euclidean space; it is not only spatial. (The gif you linked above is a representation of the spatial fourth dimension. ..yes, it includes time to show it rotating. If you were to consider it as a spacetime dimension then it would be 5 dimensions: 4 spatial plus time, but it is commonly referred to simply as spatial in my understanding.)
  
  
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  Conceptualizing the limitations and advantages of dimensional perception:
  
  
  
• Beings that can perceive in 2D can see inside of objects that are 1D.
  
  
• Beings that can perceive in 3D can see inside of objects that are 2D.
  
  
• Beings that can perceive in 4D can see inside of objects that are 3D.
  
  
• Beings that can perceive in 1D can only see representations or projections of 2D objects.
  
  
• Beings that can perceive in 2D can only see representations or projections of 3D objects.
  
  
• Beings that can perceive in 3D can only see representations or projections of 4D objects.
  
  
  
  
  
  We are able to perceive objects spatially in 3 dimensions (3D). By spatially, we mean that we're interpreting the environment or world's space, and not considering the fourth dimension as something other than space, such as time. (The gif linked above is of a four-dimensional object of which the fourth dimension is also space.) When we look at a drawing of a square on a piece of paper, we are able to see not only its length and width, but also inside of it because we are viewing it from above - from height. If we look down at it and draw a triangle inside of it, we can see both at the same time. We are able to see inside of 2D objects. A 3D object is comprised of several layers of 2D objects stacked upon one another. So imagine the 2D drawing, and stacking many papers on top of each other until it's several inches or centimeters tall. That's a 3D object now. Then, shape it into a square at each sheet of paper (so cut through all sheets) and you will end up with a cube of paper. Shape it into a triangle and it will be a triangular, pie-like shape. Angle it more narrow on the way up and it will be a pyramid-like shape. With any of these shapes, we cannot see inside of it. But now imagine this: just as we in the 3rd dimension looking at a shape in the 2nd dimension can see inside of it, a being in the 4th dimension looking at a shape in the 3rd dimension can see inside of the 3D object. That is because just like there is only length and width in the 2nd dimension, but no height; in the third dimension we have length width and height, but no __. I'm unaware of whether there is a name for the additional direction that would exist in the fourth dimension.
  
  
  I also don't know whether a 4th spatial dimension actually exists or is just an abstract concept, nor do I know whether it is possible or known to be possible to detect. As far as I am aware, the fourth spacial dimension is only known of abstractly, meaning that there is no evidence for it actually existing.
  
  
  ------------------------------------
  
  
  These videos explain how to understand what the 4th dimension would look like:
  
  
  Dr. Quantum explains the 4th dimension (video, 5:09)
  
  An oversimplified explanation from the movie "What the bleep do we know: down the rabbit hole" in which the character, Dr.Quantum, first explains what an (imagined) 2D world (flatland) would look like to us - who are able to see the 3D world, as a way of understanding (or extrapolating) how a being that could see in the 4D world would be able to see through and inside of 3D objects. (note: I've been warned that this is part of a video that goes on to some cult-like recruiting, so please be forewarned about the video's conclusion and entirety.)
  
  
  Cosmos - Carl Sagan - 4th Dimension (video, 7:24)
  
  Carl Sagan explains how to imagine what the 4th dimension looks if we were able to see it and how it would allow us to see inside 3D objects. An important part of this video is explaining and showing exactly how and why we can only see a distorted version of 4D objects since we only see in 3D
  
  
  4th Dimension Explained By A High-School Student (video, 9:05)
  
  An excellent description of the first through fourth dimension and how we can perceive them.
  
  
  Unwrapping a tesseract (4d cube aka hypercube) (video, 1:39)
  
  
  Hypercube (video, 3:18)
  
  Watch the above two videos to see how we can conceptualize a 4D object in 3D space.
  
  
  Videos mentioned elsewhere in this comment:
  
  
  Fourth Spatial Dimension 101 (video, 6:27)
  
  
  Flatland (video, 1:39:56)
  
  
  --------------------------------------
  
  
  Videos, Books and Links mentioned by other redditors:
  
  
  Flatland: a romance of many dimensions (Illustrated) by Edwin Abbott Abbott (book, free, ~230kb)
  
  Amazon description & reviews
  
  hat-tip to /u/X3TIT
  
  
  "Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions" by Lisa Randall (Amazon book page)"
  
  Looks interesting.
  
  hat-tip to /u/karoyamaro
  
  
  
  -----------------------------------
  
  (Edited: 1- to add video lengths; 2- added book links, 3 - readability more videos, 4 - a warning about the Dr. Quantum video.)
  

Einstein: His Life and Universe

The Black Hole War

The Trouble With Physics

Parallel Worlds

The Red Limit: The Search for the Edge of the Universe

Warped Passages

The Singularity is Near

I love this question, and "to where?" is definitely one of those things where people a lot smarter than me say "I have no idea."

I read a book about it once that covered this at one point, Warped Passages if you wanted to know the name.

Anyway, she presented a few options for what the universe might be "shaped" like, in terms of curvature. Since we're talking about multiple dimensions here, i'm going to use a more understandable 3d version first.

In a shape that's (uniformly) positively curved, you get a sphere. At every point on the sphere, no matter which way you look, the surface always bends down (or up, if you're on the inside of it.) More importantly, if you travel in a straight line along its surface, you'll end up exactly back where you started, travelling all the way around the sphere. Another interesting property of being on a sphere is that there are no parallel lines, any straight line will have to intersect at two points. with any other straight line you can draw along the surface of the sphere. In this picture, the red line isn't straight, that's a circle. The green and black lines are straight. So if we're on the surface of a higher-dimensional universe that is a hypersphere, then if we travel in a straight line for long enough, we'd end up back right where we started. The "no parallel lines" thing ends up being "no parallel planes" they'd intersect at two. . . Lines? At opposite ends of the 4-sphere? This is where I get lost.

If the curvature of the surface were 0, then we'd have a large, flat, plane. It wouldn't curve. This is the realm of geometry that we all know and love. We have exactly one line that passes through a point and is parallel to another line. It doesn't matter how big a shape you draw, the sum of the angles of their sides will always add up to the same number, and the ratio between the diameter and circumference of a circle is constant. Lines don't roll back to themselves, they just go off to infinity. It's also boring.

The third option is negative curvature. And you end up with. . . Hyperbolic surfaces. As you'd expect, this is pretty much the exact opposite of positive curvature. There are two lines that pass through a given point and are parallel to each other, and an infinity of them that don't remain a constant distance away, but still never intersect (these have the fancy status of being "ultraparallel"). For example all of these lines are straight if you were to draw them on a hyperbolic plane, and none of the black ones would intersect the blue one. Bring this up to 3d, and you have an infinite number of planes that (pass through a given point and are) parallel to a given plane. And way more that are ultraparallel.

So. . . Yeah, these are the simpler ways that the universe might be configured, and i'm already in way over my head. Most of this information was from that book, some googles and some guesses. Randall Munroe recently gave a nice overview of dimensions, too.

excellent recent "progress to date" science book on implications of hidden dimensions in the universe
<a href="http://www.amazon.com/gp/product/0060531096?ie=UTF8&tag=reddit0e-20">Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions</a>

Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions

(Simplification and semi-mediocre understanding of a high-school student)
Essentially, it's a particle that, through fundamental interactions with other particles such as leptons and quarks and the so called "Higgs Field" cause inertia (mass) to arise. I would consult Wikipedia if I were you and would check out some readings.

Warped Passages by Lisa Randall
A Brief History of Time+The Universe in a Nutshell - Stephen Hawking
The Elegant Universe - Brian Greene

Personally, I'd recommend the first because, if a little bit dry, Randall explains the Higgs theory better. (The second book was what got me obsessed in science two or three years ago.) Happy Trails!

Did you happen to learn this reading Warped Passages? Because I just learned it yesterday!