1/25/2024 0 Comments Rotating hypercubePeople are free to challenge your ideas, do not be defensive if your ideas are dismissed or proven wrong. Beware to post if you do not know what a Lagrangian is.īe polite and civil: Follow the reddiquette, be polite and civil. This sub does not fear maths, so mathematical physics discussions are appreciated. Professional or amateur theories and models are welcome as long as they are backed up by actual research. Remember to always back up your posts with reliable information, clear argumentation and verifiable sources. The astrophysicist Carl Sagan explains nicely this in this classic video.Post and discuss any commentaries, opinions or external links related to advanced research in physics. There are some interesting thought experiments about how we would perceive 4D objects entering our 3D world that we consider as our reality. This is the closest we can get right now to a 4D object. If you are fascinated by the tesseract, you can now interact with this four-dimensional object in 3D space using virtual reality simulations. What you are seeing is a 4D object in a 3D world shown on a 2D screen! Far from what it really is. We are simply seeing a projection (or shadow) of a tesseract on a 2D surface. Remember that this is not how a tesseract would actually look like. You will see different perspectives of a tesseract when viewed from different angles. Just as you would see a square if you look directly at a face of a solid cube, you would see a cube if you look straight at a tesseract cell. This might not be intuitive as the rotating cube, and our brains have a hard time understanding 4D object like this. Just as the rotating cube, we would see a rotating tesseract like this: We will see different projections depending on the angle we look at. Just like the cube, we can cast a shadow of a tesseract on to a 2D surface. Just like the square and cube, all edges in a tesseract are of the same length, and all angles are right angles. We get a tesseract when a cube is protruded along the fourth dimension on the w axis. A tesseract is not an easy object we can easily comprehend, but it is the same as moving from 2D to 3D. It is easier for our brain to decipher this 2D drawing as a cube when its rotating.Įxtrapolating these concepts to the next dimension, we will be able to understand 4D objects and its behavior.Ī cube extruded perpendicular to the third dimension yields a tesseract (also called a hypercube). Depending on the angle you look at it, the 2D projection will differ, but here is an angle we all are familiar with: What we are actually seeing is a shadow (or projection) of a wireframe cube cast on a 2D surface. Really, this is how our brains are taught to understand a representation of the cube projected to 2D surface. We are all quite familiar with a drawing of a 3D cube on paper or on a computer screen. A similar concept applies for other dimensions as well. It is interesting to note that when a cube is expanded to infinity, it encompasses the entirety of the 3-dimensional space. In other words, extruding the square to the z axis makes up a 3D cube. The square extruded perpendicular to the 2D plane will make up a cube. A line moved perpendicular by the same length will make up a square. The only thing that differs between objects in 1D are the differences in their length.Ī line extruded perpendicular to the first dimensional direction brings you to the second dimension. It has no dimensions no width, no length, and no height. Lets start from 0D and walk our way up to 4D. Although we can explain higher dimensions with mathematics, I will try to keep things simple in this post. This is hard for us to understand because we cannot visualize the fourth dimension, but we can deduce some interesting properties by walking our way up from lower dimensions. Similarly, the fourth dimension is a direction w perpendicular to all three x, y, z dimensions. In the third dimension, the z axis is perpendicular to both x, y dimensions. In mathematics, we know that a 2D plane has two perpendicular directions x, y in a cartesian coordinate system. It is our brains that construct our world to be seen in 3D. We live in a three-dimensional world, and we perceive our world in 3D.
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