YouTube Video UExQcjItRnR2MEVaOW5zeVhlbjRPNkp4WFVvVlVzbU1RQS4yMDhBMkNBNjRDMjQxQTg1 Mathematician Maggie Miller explores the strange and fascinating world of 4D topology — the study of shapes, or manifolds, that resemble flat Euclidean space when viewed up close. Four-dimensional manifolds behave in unexpectedly complex ways, pushing mathematicians to develop advanced techniques to understand them. Maggie Miller is an assistant professor in the mathematics department at the University of Texas at Austin. She was also a former Visiting Clay Fellow and Stanford Science Fellow. -------- CHAPTERS 00:00 4D topology is weird 00:45 What is topology? 01:00 Manifolds 01:33 Examples of 1D manifolds 01:48 Examples of 2D manifolds 02:26 We live in a 3D manifold 03:05 4D manifolds explained 04:09 Why 4D topologists study 4D manifolds 05:11 4-torus manifold explained by analogy 10:28 Problems unique to 4D topology 10:44 Smooth vs continuous equivalency 12:04 Big open questions --------- - VISIT our website: https://www.quantamagazine.org - LIKE us on Facebook: / quantanews - FOLLOW us Twitter: / quantamagazine Quanta Magazine is an editorially independent publication supported by the Simons Foundation: https://www.simonsfoundation.org
How to 'See' the 4th Dimension with Topology
May 15, 2025 10:14 pm
Mathematician Maggie Miller explores the strange and fascinating world of 4D topology — the study of shapes, or manifolds, that resemble flat Euclidean space when viewed up close. Four-dimensional manifolds behave in unexpectedly complex ways, pushing mathematicians to develop advanced techniques to understand them. Maggie Miller is an assistant professor in the mathematics department at the University of Texas at Austin. She was also a former Visiting Clay Fellow and Stanford Science Fellow. -------- CHAPTERS 00:00 4D topology is weird 00:45 What is topology? 01:00 Manifolds 01:33 Examples of 1D manifolds 01:48 Examples of 2D manifolds 02:26 We live in a 3D manifold 03:05 4D manifolds explained 04:09 Why 4D topologists study 4D manifolds 05:11 4-torus manifold explained by analogy 10:28 Problems unique to 4D topology 10:44 Smooth vs continuous equivalency 12:04 Big open questions --------- - VISIT our website: https://www.quantamagazine.org - LIKE us on Facebook: / quantanews - FOLLOW us Twitter: / quantamagazine Quanta Magazine is an editorially independent publication supported by the Simons Foundation: https://www.simonsfoundation.org
How to 'See' the 4th Dimension with Topology

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YouTube Video UExQcjItRnR2MEVaOW5zeVhlbjRPNkp4WFVvVlVzbU1RQS4yMDhBMkNBNjRDMjQxQTg1

How to 'See' the 4th Dimension with Topology

Gravitational waves can distort space and time, but their effects on humans are imperceptible unless the source event is catastrophic—by which point, it would already be too late to notice. The nature of time and simultaneity is relative, and the concept of "now" loses meaning at cosmic scales. From 'Answering Questions about Hubble Tension, Dyson Spheres, & Relativity': https://youtu.be/y8b93R3kfso?si=00o3TaIY9RJifycM Get the StarTalk book, 'To Infinity and Beyond: A Journey of Cosmic Discovery' on Amazon: https://amzn.to/3PL0NFn Support us on Patreon: https://www.patreon.com/startalkradio FOLLOW or SUBSCRIBE to StarTalk: Twitter: http://twitter.com/startalkradio Facebook: https://www.facebook.com/StarTalk Instagram: https://www.instagram.com/startalk TikTok: https://www.tiktok.com/@neildegrassetyson
What Gravitational Waves Reveal About the Illusion of Time

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YouTube Video UExQcjItRnR2MEVaOW5zeVhlbjRPNkp4WFVvVlVzbU1RQS5ENDU4Q0M4RDExNzM1Mjcy

What Gravitational Waves Reveal About the Illusion of Time

11 Dimensions are explained in this video. You will know what are dimensions and how many dimensions are there in the universe. All higher dimensions are explained in the video. All the dimensions from 0th dimension to 11th dimension have been covered in the video. The video discusses the super powers of the higher dimensional beings. Basics of Parallel universes and string theory are also included. 0th Dimension (Zero Dimension) A point is an example of 0th dimension that has no length, no breadth and no height. A 0 dimensional being cannot move in any direction and is fixed to a point. 1st Dimension (First Dimension) A straight line is an example of 1st dimension that has only one dimension- length. A 1 dimensional being can move only in one direction i.e. on a straight line. 2nd Dimension (Second Dimension) 2nd dimensional or 2D objects are flat shapes like squares and triangles. Motion of a 2 dimensional being is restricted to a plane surface therefore, it can't move upward or downward. 3rd Dimension (Third Dimension) 3rd dimensional objects have 3 dimensions length, breadth and height. Solid objects like Cubes and spheres are examples of 3D objects. We humans live in the 3 dimensional world. 4th Dimension (Fourth Dimension) Time is considered the 4th dimension. A four Dimensional being can move freely in time dimension and has full control over time. It would be able to move in any desired direction in time; past or future. A person living in the 4th dimension can go to a certain point in past time and change its decision. But if we consider the fourth dimension from the geometrical point of view then hypercube is a 4 dimensional object. It is also called a Tesseract. A hypercube is four dimensional analog of the cube. 5th dimension (Fifth Dimension) A 5th dimensional being can move freely in time either in past or future as per his wish and is able to be present at different locations at the same time. He can do many jobs and have different hobbies simultaneously. Actually Parallel universes exist in the 5th dimension, therefore your separate versions can exist in parallel universes having separate timelines. 6th Dimension (Sixth Dimension) In the 6th dimension you have all the powers that you possess in the 5th dimension. You can see all the presents, pasts and futures of all the parallel universes. But one limitation of the 6th dimension is that, all the parallel universes must have the same beginning (initial conditions) that is the Big Bang. In the 6th dimension your multiple versions can live their lives in parallel universes simultaneously. 7th Dimension (Seventh Dimension) All the powers of a 6th dimensional being are possessed by the being of 7th dimension. He can have infinite forms of itself and can move from one universe to any other universe. Unlike the 6th dimension, the 7th dimensional universes may have originated from different start conditions not just the big bang. 8th Dimension (Eighth Dimension) The 8th dimension has a plane of all the possible presents, pasts and futures for all the infinite number of parallel universes. According to the string theory, in the 8th dimension objects do not have any physical existence like our digital world, where we cannot touch the objects but only can see or hear them. 9th Dimension (Ninth Dimension) In the ninth dimension, universes may have their own laws of Physics and separate conditions and probabilities of their origin. In the 9th dimension many civilizations or aliens may live simultaneously at the same place. These coexisting civilizations may not see or feel the presence of each other. The superpowers of a 9h dimensional being will blow your mind. He would have no physical form and would be able to move freely in space and time in any of the universes. 10th Dimension (Tenth Dimension) The10th dimensional being would possess infinite powers that are beyond your imagination. It would be possible for him to control even the space-time and everything present in all the infinite number of universes. Because of the infinite powers of the 10th dimensional being, some researchers also suggest that the God lives in the 10th dimension. 11th Dimension (Eleventh Dimension) According to string theory, everything in the universe is made up of infinitely small one dimensional vibrating loops called strings. These strings vibrate in 11 dimensions. Even the subatomic particles like electrons, protons and neutrons are made up of Strings. Unique manner of vibration of strings is responsible for the unique characteristics of each subatomic particle. Size of a string is infinitely small. It is of the order of 10(-33) cm. 10^-33 cm is actually millionth of a billionth of a billionth of a billionth of a centimeter. Didn't get it. Let's understand it with an analogy. If we increase the size of an atom up to the size of the whole observable universe, then the size of the string would be just equal to a tree. #dimensions #HigherDimensions
11 Dimensions Explained – Higher Dimensions Explained – All Dimensions Explained – Dimensions

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YouTube Video UExQcjItRnR2MEVaOW5zeVhlbjRPNkp4WFVvVlVzbU1RQS45RTgxNDRBMzUwRjQ0MDhC

11 Dimensions Explained – Higher Dimensions Explained – All Dimensions Explained – Dimensions

All Dimensions Explained here from Zero Dimension (0 dimension) to the Eighth Dimension (8th dimension) by Drawing the dimensions. In this video I will show you, How you can draw all the dimensions on a sheet of paper, starting from the zero dimension to the eighth dimension. This video explains 0 dimension, 1st dimension, 2nd dimension, 3rd dimension, 4th dimension, 5th dimension, 6th dimension, 7th dimension and 8th dimensions. Let's begin our journey of explaining and drawing from zero dimension to eighth dimension. We will start with the Zero (0) dimension. Here on the screen we have a single point having no length, no width and no height. As it has no dimension, it is called as the zero dimension. Now if we double the number of points then we enter into a one dimensional (1st dimension) world having only 1 dimension i.e. length. So in the first dimension we only get a straight line having no width or height. Now let's double the points again and this is, what we call as the second dimension (2nd Dimension). Observe here it has only two dimensions length and width. So it is a plane surface having no height or depth dimension. To enter into the third dimension (3rd dimension) let's again double the points and we get the third dimension. As you can see here, the third dimension contains 3 dimensions which are length, width and height. On adding third dimension I.e. height to the second dimensional plain object, they become the third dimensional solid objects. We all live in a three dimensional world. Now to draw and understand the fourth dimension (4th Dimension) we again need to double the points and here we are in the fourth dimension. Observe carefully that to draw fourth dimension we need to join respective points of both the cubes which are three dimensional objects. Now let's repeat the process of doubling the points to enter into the next higher dimension. So to draw the fifth dimension (5th Dimension) all you need to do is just double the number of points that we used to draw the fourth dimension and join the similar points respectively as shown here in the video and you will know how would the fifth dimensional space look like. By continuing the same process of doubling the points of a dimension, we can draw the next higher dimensions. Although the concept of drawing the next higher dimension is easy but as you can see here, it becomes more and more complex as we continue. So here for drawing the Sixth dimension (6th dimension), Seventh dimension (7th dimension) and Eighth dimensions (8th Dimensions) . I am just showing you the doubling of points only without joining the lines as it would be too complicated and messy for me to draw and also for you to understand. As you now know how to do it so You can do it by yourself for fun. So friends I hope you enjoyed learning how to draw any dimension just by following a simple rule of doubling the points. #Dimensions #VisualizeDimensions #DrawDimensions #Universe #EngineeringMadeEasy
How to Visualize Higher Dimensions – Dimensions Explained – How to Draw Dimensions

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YouTube Video UExQcjItRnR2MEVaOW5zeVhlbjRPNkp4WFVvVlVzbU1RQS41QTY1Q0UxMTVCODczNThE

How to Visualize Higher Dimensions – Dimensions Explained – How to Draw Dimensions

This video explains 4 Dimensions of energy. These dimensions are "physical energy, emotional energy, mental energy and spiritual energy. These dimensions refer to different aspects of a person's well-being and vitality. Physical dimension of energy is associated with the quantity of the energy we have. Emotional dimension of energy indicates the quality of our energy. Mental dimension of energy is linked to the focus of our energy. And the Spiritual dimension of energy tells us about the force of our energy. Here the physical dimension is the most fundamental source of energy and the most significant dimension of energy is the spiritual dimension. Now let's know more interesting things about these different dimensions of energy. 1. Physical Energy: This dimension is related to our physical health, vitality and overall physical wellness. Factors like exercise, sleep and nutrition are included in the physical dimension of energy. We have plenty of physical energy when we exercise regularly, get enough sleep and nutritious diet. This dimension is considered the most fundamental source of energy. 2. Emotional Energy: Emotional energy covers our feelings and emotions. It is about understanding and learning, how to manage our emotional state. Let me tell you that emotions like love or joy which are positive emotions can boost our emotional energy, while negative emotions like anxiety or stress can deplete it. It is possible to maintain healthy emotional energy level by taking care of our emotional well-being through practices like self-care and building positive relationships. 3. Mental Energy: This dimension of energy is associated to our cognitive abilities and clarity of mind. Mental energy involves our capacity to focus, think creatively, solve problems, and make decisions. To enhance mental energy we must practice focusing the energy in the right direction. This can be achieved by engaging in activities that sharpen our mind. Meditation techniques like mindfulness can control our distracting mind. Do one task at a time with full concentration. To reduce stress and anxiety, try to live in the present moment most of the time instead of dwelling in the past or future. 4. Spiritual Energy: Spiritual energy refers to a sense of our connection with the universe. This energy gives us inner fulfillment and the ultimate purpose of our life beyond our self-interest. To nurture our spiritual energy we should spend more time in nature. Engaging in practices like meditation or prayer can also help us in alleviating spiritual energy. Friends, please keep it in mind, these four dimensions of energy are interconnected. So it is necessary to take care of each dimension of energy for our overall well-being. #energy #dimensions
4 Dimensions of Energy – Physical Energy, Emotional Energy, Mental Energy and Spiritual Energy

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4 Dimensions of Energy – Physical Energy, Emotional Energy, Mental Energy and Spiritual Energy

In this video, you will understand- What we mean by a 5 dimensional space and How we can visualize the 5 dimensional space geometrically. The video also answers, Why the researchers think that there must be a 5th dimension and why they needed the 5th dimension. After watching the video you will know, why the fifth dimension cannot be observed directly by humans. And most importantly, What is the scientific evidence for the existence of the fifth dimension? You will also get familiar with the supernatural powers that a person living in the fifth dimension would have and What are the limitations of the fifth dimensional world that are not present in the dimensions higher than the 5th dimension. What we mean by a 5 dimensional space. A five dimensional space is a space having five dimensions. Actually Dimension of a point is defined as the minimum number of coordinates that are needed to specify that point in it. So to represent a 5 dimensional object we need 5 coordinates. How we can represent a 5 dimensional space geometrically. On the Screen you are seeing a single dot. This is the geometrical representation of the zeroth dimension. 0th dimension does not have any length, width or height. To get the next higher dimension all we need to do is to double the number of points. Therefore by doubling the number of points we have now two points. And this is the geometrical representation of the first dimension. Now again double the number of points to get to the next higher dimension i.e. the second dimension. Therefore In the second dimension we have four points and by joining these 4 points, we get a plane surface which is a two dimensional object. Now on doubling the number of points again we enter into the next higher dimension i.e. the 3rd dimension. Here we have 8 points. To go to the Fourth dimension double the number of points once again. This time we have 16 points. As you can see here, this 4 dimensional structure is created by joining the respective points of two, 3D structures. Now if we double the number of points, that are present in the four dimensional structure, we get a structure of next higher dimension i.e. the 5th dimension. You can count that this five dimensional structure has 32 points. On joining these points as indicated in the video we get a 5 dimensional structure. Why the researchers believe in the presence of the fifth dimension and why they needed the 5th dimension. Actually researchers wanted to develop a theory that unifies the four fundamental forces in nature which are electromagnetism, gravity, strong and weak nuclear forces. For this they needed a five dimensional space. In 1921, A German mathematician Theodor Kaluza and Swedish physicist Oskar Klein independently developed a theory known as the Kaluza-Klein theory. The Kaluza-Klein theory used the 5th dimension for unifying two fundamental forces in nature; gravity and electromagnetic force. But later it was found that their approaches were partially inaccurate. Why the fifth dimension cannot be observed directly by humans. Klein suggested that the fifth dimension would be rolled up into a tiny and compact loop and this loop is on the order of 10(-33cm). Although the gravity and electromagnetic forces seem unrelated but introduction of the fifth dimension can help in finding connection between these forces. Actually according to the superstring theory, everything in this universe is made up of tiny vibrating loops, known as strings which vibrate in 11 dimensions. Therefore it made the scientists believe that there are at least 11 dimensions in the universe. Hence Kaluza-Klein theory suggesting 5 dimensions of space was supported by the superstring theory. Now I will discuss, what is the scientific evidence for the existence of the fifth dimension? Although We cannot directly observe the fifth dimension but it is possible to record indirect evidence of existence of the 5th dimension. It has been made possible by the Large Hadron Collider (LHC). When the subatomic particles collide in the Large Hadron Collider, new particles are produced including graviton. It was found that the graviton escapes from the fourth dimension and leaks off into a 5 dimensional bulk. Next we will see the supernatural powers that a person living in the fifth dimension would possess. A being of 5 dimensions would be able to control time as per his wish and be present at different locations simultaneously. The 5th Dimensional being would be able to choose different career paths or job at the same time. Now we will discuss the limitations of the fifth dimensional world One major limitation of this dimension is- there are no shortcuts between the timelines. You cannot jump directly from a point on one timeline to another point on other timeline. All 11 dimensions explained (Advanced) https://youtu.be/UxubeeSqSmk
5th Dimension Explained – 5th Dimension – 5 Dimension – Fifth Dimension – The 5th Dimension

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5th Dimension Explained – 5th Dimension – 5 Dimension – Fifth Dimension – The 5th Dimension