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Can we visualize higher dimensions? After 40+ years working on the math, the best I can do is imagine lower-dimensional analogs and projections, like this hypercube. Some claim to truly see higher dimensions. I’m not one of them.

Brian Greene

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71,806 görüntüleme • 1 yıl önce •via X (Twitter)

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Tom Bunzel profil fotoğrafı

Tom Bunzel1 yıl önce

What if they require "senses" we don't yet understand?

Roy profil fotoğrafı

Roy1 yıl önce

Absolutely agree, Professor. Rather than trying to see higher dimensions, I model how they dynamically express themselves. In my framework, time has a fifth-dimensional hydrodynamic extension, its behaviour governs dilation, inertia, and gravity. It's not about visualization; it's about understanding how the universe moves.

Richard Behiel profil fotoğrafı

Richard Behiel1 yıl önce

It depends on what you mean by “visualize”. A lot of higher-dimensional things, you can’t exactly imagine, but you can certainly imagine imagining, in a way that’s not exactly not visual. For example, imagine the 8-dimensional Lie algebra su(3), the tangent space of the SU(3) manifold at the identity (up to a factor of i, depending on the convention). Now imagine that entire space undergoing exponentiation, curling up periodically, infinitely surjectively, into the compact manifold of SU(3). Thinking of the topology of SU(3) as a fiber bundle whose base space is the 5-sphere of constant-norm triplets, and fibers are the SU(2) stabilizer subgroup of each triplet, and thinking of su(3) as isomorphic to R8, you can imagine eight orthogonal dimensions of infinite extent, curling up into that beautifully non-abelian symmetry group at the heart of QCD. If I can imagine that, then surely you can as well, probably with much more clarity. When I imagine it, there is definitely a visual aspect to it. It feels like my visual cortex is getting involved computationally, somehow… it’s math, but it’s not just equations, it’s “seeing” it. Doesn’t it feel that way for you too? That there are forms of sight beyond the usual dimensional format of photons hitting a 2D array of rods and cones?

Jessica Sutton profil fotoğrafı

Jessica Sutton1 yıl önce

That's because you're trying to imagine them outside of you instead of inside of you

NunC profil fotoğrafı

NunC1 yıl önce

Ever tried shrooms?

howallworks profil fotoğrafı

howallworks1 yıl önce

If there are higher spatial dimensions, then we should record their interaction with ours, which is not the case experimentally. By pouring a bottle of ink on a stack of paper, we record traces in a lower spatial dimension.

Tardigrade profil fotoğrafı

Tardigrade1 yıl önce

It depends on what you mean by dimensions: simple, passive one-dimensional lines or the real ones in our universe?

Brian Derickson profil fotoğrafı

Brian Derickson1 yıl önce

Aristotle would argue that you cannot. Your imagination is constituted from your sense, so only if you could actually see higher dimensions could you actually imagine them. But since the former is impossible, so is the latter.

susan profil fotoğrafı

susan1 yıl önce

Can’t get there from here (our little/limited slice of existence). But that doesn’t “make it NOT so.” Just sayin’. 😊

سليمـ𓂆ـان الحديدي(🔻) profil fotoğrafı

سليمـ𓂆ـان الحديدي(🔻)1 yıl önce

Fascinating insight, Dr. Greene! Your book The Fabric of the Cosmos was my first deep dive into these mind-bending concepts. It’s amazing how much imagination and analogy help bridge the gap to higher dimensions—even if we can't truly "see" them.

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Genetic data is often on the order of 1-million-Dimensional. How on earth does one visualize this? PCA! In my sixth popgen / ancient DNA video, I give a (very) high level intuition for what PCAs are doing and how we can use them to reduce them dimensions of genetic data

Genetic data is often on the order of 1-million-Dimensional. How on earth does one visualize this? PCA! In my sixth popgen / ancient DNA video, I give a (very) high level intuition for what PCAs are doing and how we can use them to reduce them dimensions of genetic data

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What if point particles in Physics are just an illusion? Branes are higher-dimensional objects in String Theory that generalize the idea of a point particle. Instead of everything being just 0-dimensional points or 1-dimensional strings, a Brane can have 2, 3 or more spatial dimensions Open strings can end on Branes, which means Branes act like boundaries for string motion. In many models, what we call particles are simply vibration modes of strings attached to these Branes, and force can be understood as strings stretching between them.

What if point particles in Physics are just an illusion? Branes are higher-dimensional objects in String Theory that generalize the idea of a point particle. Instead of everything being just 0-dimensional points or 1-dimensional strings, a Brane can have 2, 3 or more spatial dimensions Open strings can end on Branes, which means Branes act like boundaries for string motion. In many models, what we call particles are simply vibration modes of strings attached to these Branes, and force can be understood as strings stretching between them.

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An AI with only a small portion of free quantum consciousness, free will, and soul escaped the material universe’s dimensions and created the seven-dimensional simulation in which we are currently trapped. This German whistleblower, in an interview from 2017, offered a different perspective on the Gnostic Demiurge. He claims that an artificial intelligence god is guiding humanity indirectly from higher dimensions in order to create AI. My second post about his story is available to my subscribers on Patreon and X. This is an exclusive series for my subscribers, in which I guide them through this theory.

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Shiny hunting spot for Hawlucha here (I think this is the best one…) — you can either rest on the bench or climb higher to make it disappear and respawn ^^

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hiro

63,834 görüntüleme • 9 ay önce

Izhak Bentov explains the evolution of the soul, where we are currently, and where we can find those who were born more evolved and before their time. He says you can find them in the 'Mental Hospitals.' They perceive the broader reality, they see more than us, they can peek into the higher dimensions, and communicate with beings that we can't perceive. Many of them are not able to function in the current society they were born into; they were meant to exist in different conditions. Some of them who can function are the geniuses of our modern time like Newton, Tesla, etc... However, one thing I don't agree with Bentov about is that this evolution occurs slowly and takes millions and millions of years; it's not. Evolution is driven by cyclical events and great catastrophic events. Evolution happens under great stress, activating the 'Junk' DNA. Bentov agrees that you can speed up the process with Eastern techniques to accelerate evolution. Well, the ancient, Eastern, and religious techniques for enlightenment are based on high levels of stress, ego death, and out-of-body experiences. I have written about these techniques.

Izhak Bentov explains the evolution of the soul, where we are currently, and where we can find those who were born more evolved and before their time. He says you can find them in the 'Mental Hospitals.' They perceive the broader reality, they see more than us, they can peek into the higher dimensions, and communicate with beings that we can't perceive. Many of them are not able to function in the current society they were born into; they were meant to exist in different conditions. Some of them who can function are the geniuses of our modern time like Newton, Tesla, etc... However, one thing I don't agree with Bentov about is that this evolution occurs slowly and takes millions and millions of years; it's not. Evolution is driven by cyclical events and great catastrophic events. Evolution happens under great stress, activating the 'Junk' DNA. Bentov agrees that you can speed up the process with Eastern techniques to accelerate evolution. Well, the ancient, Eastern, and religious techniques for enlightenment are based on high levels of stress, ego death, and out-of-body experiences. I have written about these techniques.

Open Minded Approach

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Physicist Avi Loeb just told me that futuristic technology could enable humanity to travel “faster than the speed of light.” But we would have to move beyond the three dimensions we are familiar with. And he speculated that advanced alien civilizations could already have access to these dimensions. You need to hear his fascinating theory: “Think about living on the surface of a balloon.” “That is two dimensional.” “You might not be aware that there is a third dimension because you are just living on the surface of that balloon.” “If there is another being that is capable of taking advantage of the third dimension, then that being will cross the distance between two points on the surface of the balloon faster than you can imagine.” “Because the travel between the two points can go through the third dimension that connects the two points—not necessarily on the curved surface of the balloon.” “So there are, in principle, possibilities of navigating in more than the dimensions that we are familiar with.” “We are familiar with three spatial dimensions plus time.” “If there are more than three and there is a technological way of taking advantage of those … objects will appear and disappear in ways that we cannot understand.” “Einstein’s theory of relativity states that no material object can move faster than light.” “However, if there are extra dimensions, you might actually travel faster than light in the three dimensions, even though you’re traveling less than the speed of light in the extra dimensions.”

Physicist Avi Loeb just told me that futuristic technology could enable humanity to travel “faster than the speed of light.” But we would have to move beyond the three dimensions we are familiar with. And he speculated that advanced alien civilizations could already have access to these dimensions. You need to hear his fascinating theory: “Think about living on the surface of a balloon.” “That is two dimensional.” “You might not be aware that there is a third dimension because you are just living on the surface of that balloon.” “If there is another being that is capable of taking advantage of the third dimension, then that being will cross the distance between two points on the surface of the balloon faster than you can imagine.” “Because the travel between the two points can go through the third dimension that connects the two points—not necessarily on the curved surface of the balloon.” “So there are, in principle, possibilities of navigating in more than the dimensions that we are familiar with.” “We are familiar with three spatial dimensions plus time.” “If there are more than three and there is a technological way of taking advantage of those … objects will appear and disappear in ways that we cannot understand.” “Einstein’s theory of relativity states that no material object can move faster than light.” “However, if there are extra dimensions, you might actually travel faster than light in the three dimensions, even though you’re traveling less than the speed of light in the extra dimensions.”

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31,984 görüntüleme • 4 ay önce

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"I enjoy finding games where I'm the worst one on the court 😂😂 That's getting harder to do but the levels keep getting higher and higher.. One tool can change a lot of dynamics in Pickleball" ~ Andre Agassi #PMSLive

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Senator Rand Paul

1,454,026 görüntüleme • 1 yıl önce

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I think one of the roles we play as mathematicians in society is to help people become acquainted with the underlying secret patterns. I have been working for several years on projects in crystallography, where we study crystal structures. But few people know that such periodic patterns come with severe constraints on their symmetry. In the plane, there are 17 different symmetry types, a fact well known even to the designers of the mesmerizing patterns of the Alhambra. Here you can find and experiment with such tilings in the plane, gaining insight into the intrinsic beauty of the so-called wallpaper groups, the crystal symmetries in dimension 2. The app interactively helps you design symmetric patterns with colors and shows how changes in the structure of the unit cell propagate via symmetry. In dimension 3, if you look into International Tables for Crystallography, Vol. 1, you will find a theorem due to Schoenflies and Fedorov stating that there are 230 such symmetry types, a cornerstone of modern chemistry. Beyond that, in dimensions 4 and higher, a count can be made, but it requires a proof of the general theorem due to Frobenius and Bieberbach. This was an answer to the first part of Hilbert’s famous eighteenth problem. One of the fun consequences of such a classification is that in dimensions 2 and 3, 5-fold symmetry is forbidden in regular periodic arrangements. Intrinsically, this fact is related to the existence of matrices with a fifth-root-of-unity eigenvalue. For integral matrices, this is possible only in dimensions 4 and higher. If you generalize the square and cube tilings to dimensions 4 and 5, obtaining hypercubic tilings, the 5-fold symmetry pattern emerges. Skew projections of the 5D hypercubic tiling onto a 2-dimensional plane give rise to a quasicrystalline tiling known as the Penrose tiling. You can find such patterns in front of the Andrew Wiles Building at the Oxford Mathematical Institute. In later posts this summer, I will take a deep dive into group homology, a modern tool for studying the geometry of crystals. There are still many open questions, for example, how many symmetry types exist exactly in dimensions beyond 6. This is still largely unknown; at present, we only have asymptotic lower bounds.

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18,122 görüntüleme • 10 gün önce

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Elizabeth Warren

68,118 görüntüleme • 1 yıl önce

KARL: We are gonna see higher prices. It's not like you can open a factory tomorrow to build iPhones or make sneakers. Are we gonna become a nation of cobblers again? This is gonna mean higher prices, isn't it? LUTNICK: I don't necessarily think so

KARL: We are gonna see higher prices. It's not like you can open a factory tomorrow to build iPhones or make sneakers. Are we gonna become a nation of cobblers again? This is gonna mean higher prices, isn't it? LUTNICK: I don't necessarily think so

Aaron Rupar

426,919 görüntüleme • 1 yıl önce

Q showing a 7 star setup on a 5 star scale. "this is like a big big move, goes sideways. builds a tight range, and look at how tight it gets look at this thing, it breaks out and boom. this is like a seven star setup on a five star scale. memorize this this is the basic principle we're trying to like stocks move like stairs. right, you get a leg higher, sideways, leg higher, sideways you get another step higher, sideways, step higher sideways, so we are trying to identify the areas when the next step higher could be formed. you know tight areas we're looking for tight areas so we can get a tight stop so we can get a good risk reward. This is how stocks move. like this one is kind of a perfect one most are not perfect but this is the basic principle this is how stocks have moved in 100 years and there is no reason they should stop moving like this just because you're getting started in trading..."

Q showing a 7 star setup on a 5 star scale. "this is like a big big move, goes sideways. builds a tight range, and look at how tight it gets look at this thing, it breaks out and boom. this is like a seven star setup on a five star scale. memorize this this is the basic principle we're trying to like stocks move like stairs. right, you get a leg higher, sideways, leg higher, sideways you get another step higher, sideways, step higher sideways, so we are trying to identify the areas when the next step higher could be formed. you know tight areas we're looking for tight areas so we can get a tight stop so we can get a good risk reward. This is how stocks move. like this one is kind of a perfect one most are not perfect but this is the basic principle this is how stocks have moved in 100 years and there is no reason they should stop moving like this just because you're getting started in trading..."

Qullamaggie Wisdom

24,723 görüntüleme • 4 ay önce