The Fourth Dimension Is Real ✨

very few subjects have captured people's imagination the idea of traveling to another dimension what was originally mere mathematical curiosity a student scientists and artists for over a century What secrets are hiding beyond the third dimension and what can we ultimately learn from them I'm Alan zukoni and faster your seatbelt because we're about to travel to the fourth dimension [Music] thank you [Music] from books to movies from Mod to games it's difficult to find a medium in which the fourth dimension in one of its many forms has now been portrayed an Asawa Society evolved so did

our understanding of higher Dimensions along with the many artifacts they contain objects so alien to us that not only do they escape our imagination but defy the very reality we live in and yet their existence has been and still is a driving force that inspires both Scholars and artists the way we think about the fourth dimension the language that we use and even the equations that we write are all the results of over 100 Years of History and that's why the Journey To The Fifth Dimension is one that runs across not just space but time

as well Charles Howard in turn was among the first to popularize the concept of a higher dimension and across the 19th and 20th Century it published several books and articles with precise instructions to construct and visualize four-dimensional cubes he also invented the word Tesseract which is still in use today alongside its more technical version hypercube but it was the French mathematician Maurice prince who introduced the subject to the Parisian artist reside in a liberal which was a workshop of some of the most creative people in the early 20th century he explained to Picasso and to

his contemporaries how from the fourth dimension we could see all aspects of our 3D Universe at once and in doing so Prince himself and know England started the art movement then is now known as cubism paintings like fantasies and they're portrayed of Daniel hurricane valer a Picasso's attempt at capturing on the canvas the perspective of a higher dimensional being looking down at us what we see in these paintings is not a singular point of view but many different ones fractured but crystallized in time these portraits are familiar yet chaotic as we dare to experience reality

as only the denizens of the fourth dimension were supposed to incidentally it was around the same time that more and more people became aware of Einstein's theory of relativity which introduced them to the idea that space and time were actually a single entity and space-time is done a stage like Rene de Carr thought when imagining his Cartesian plane it's the main protagonist and surprise surprise one that is four-dimensional as a fact of time into the equation we'll never know for sure but it's likely that some of these ideas influence Marcel Duchamp pieces like said young

man on a train and new descending a staircase are Exquisite deconstructions of space-time these paintings are captured in reality possibly for the first time in its four-dimensional Glory and of course our journey through the 20th century will now be complete without mentioning one of the most iconic portrayal of a hypercube in the entire history of art Salvador Dali crucifixion a piece that implies a metaphysical transcendental nature of Jesus Christ nailed against a four-dimensional cross of which we can only perceive a mere three-dimensional shadow eventually the fourth dimension found an even more fertile ground outside the

Hermetic boundaries of abstract art the possibility of traveling outside the constraints of our reality has been a predominant theme in the world of science fiction and thanks to books movies and TV shows the fourth dimension reached its largest audience one of the most classical examples is the British series Doctor Who the show revolves around the doctor a time traveling alien will explore space and time in a 1930s British police box which the audience is constantly reminded is bigger on the inside that's possible because the Tardis that's the name of the spaceship it's dimensionally transcendental which

means that the inside and the outside exist in two different dimensions in the 1977 episode titled the robots of death the doctor explains these with a clever analogy if you take two boxes one larger and one smaller and you place them at the right distance their perceived size will actually change same perspective trick happens inside the Tardis but in another dimension and that's indeed how it looks bigger on the inside even we're not directly at the center of the story the existence of extra Dimensions is often introduced to justify faster than light travel the distance

between stars is no pun intended astronomically large especially compared to how slow the speed of light really is and its Rockets cannot accelerate an object even close to that many sci-fi stories came up with equally sci-fi solutions to the problem of traveling Among the Stars from warp drives to Stargate science fiction offers no shortage of superluminal solutions and a lot of them if not all of them actually rely on the existence of high dimensions many faster than light drives in fact work by folding space on itself creating what is often referred to as a wormhole

chances are you might have seen this concept explain over and over again with a pencil passing through a folded piece of paper other times superluminal speeds are achieved by accessing a parallel dimension in which distances are shorter this is both the case of Isaac Asimov foundation and George Lucas's Star Wars in which spaceships can jump in and out of the so-called hyperspace more recently a cheeky Tesseract also made a few appearances in the Marvel Cinematic Universe where it's revealed to be a vessel for one of the six Infinity Stones while the stones themselves are a

feel Rouge that connects most of the movies together the Tesseract is little more than a megaphin which exists only to advance the stories of the main characters over the past 70 years however audience expectations have gone up and the portrayal of extra dimensions are shifted towards a more scientifically accurate one and honorable mention goes to the Japanese animecado the right answer which tells the story of a high dimensional being landed in Tokyo of all places with a giant fractal Cube but possibly the most spectacular representation of the fourth dimension in the whole history of Cinema

goes to Interstellar with a tesseract fold in both space and time while the movie was an inspiration for many it definitely prefer a more dramatic tone over a scientific one the reality is that most movies and TV shows are presenting extra Dimensions as a mere device to further their plot and rarely have an incentive to portray them accurately so we should not be surprised to hear that the place where they really play a role is video games because only video games these extra Dimensions can actually be explored and experienced through core mechanics after all games

often provide the best playground to test not just new gameplays but entirely new realities unbothered and unconstrained by the laws of our physics a gun that creates portals check a new euclidean puzzle game check a hyperbolic Adventure check the game industry is now shy of mind-banding titles and over the years many games have flirted with the idea of high dimensions similarly to what happened to books and movies the majority are only Loosely inspired by these ideas but sometimes some games are really able to let us experience higher dimensions for what they really are one such

title is fast a 2d puzzle game set in a 3D world where its inhabitants are unable to perceive the third dimension only the main character can thanks to a magical fast which grants him the ability to switch the perspective he sees the word from the game heavily plays with the concept of Dimension so much so that our companion is literally a floating hypercube called Dot what Fez ultimately offers is the perfect analogy for all the viewers who are struggling and marveling a hidden mind-bending beauty of the fourth dimension Monument Valley is another brilliant example of

that and a technical achievement both in terms of gameplay and art Direction similarly to Fez Monument Valley plays on the idea of perspective if two platforms appear next to each other the player is able to cross them even if they are far apart in 3D space neither game is technically 4D but they can both help us to imagine what it would feel like to experience a new dimension when it comes to actual four-dimensional games there aren't that many titles that reach the mainstream audience among the first ones to ever be made with Magic Cube 4D

a game originally developed in 1988 that challenges plays with a fully version of the traditional Rubik's Cube obviously I've saved the most well-known title for last migakur as well gameplay revolves around the fourth dimension and is one of the very few games which accurately portrays it at least from a mathematical and geometrical point of view the developer also released an educational game called 4D toys which lets everyone play around with hypercubes hyperspheres and all sort of hyper objects that are only to be found in higher dimensions up to the stage 4D toys is possibly the

only title which correctly simulates rigid body physics in 4D although a close Contender is the anticipated 4D golf which are the hyper twist to a well-known and beloved genre [Music] chances are the most representation of high Dimensions that you have ever seen were either artistic interpretations or only add the sole purpose of entertaining the audience what does it mean for an object to be four-dimensional what determines if something is one two three four or even 10 dimensional as it turns out the number of Dimensions is directly linked to the concept of coordinates a line is

a one-dimensional object as every point along its path can be uniquely identified with one single chord in it like the distance from a given origin likewise a square is two-dimensional because we need at least two coordinates for every point it contains and it doesn't really matter how these coordinates are measured both Cartesian and Polar Systems for example require two independent numbers and we live in a 3D world because we need at least three coordinates now it might be counter-intuitive at first but a surface of a 3D object is generally 2D even though it exists in

a 3D space every point on the surface of a sphere can be addressed using just two coordinates like latitude and longitude and that's what makes it 2D the definition of Dimensions is obviously much more Technical and complex than these but there are mathematical objects which are effectively one-dimensional but which points cannot be identified with just one coordinate one such monstrosity is the so-called curve which has a dimension somewhere between one and two this class of mathematical objects are called fractals and they are so interesting that they are endless complexity deserves a documentary of its own

in the future if you reach this far in the video first of all thanks second perhaps you should subscribe but seriously if you reach this far in the video you might wonder is the fourth dimension even real at all and the answer is more complicated than you might expect what does even mean for something to be real the definition tells more about ourselves than it does about the very concept of reality let me show you an example are numbers real well they are a tool that we can use to measure things that are definitely real

like counting how many apples I have but there's no such thing as a negative amount of apples so does it mean the negative numbers themselves don't exist that's actually what western Scholars thought for a long time of Alexandria a Greek mathematician for the third Century describe negative numbers as absurd something that even Michael Stiefel did when writing his arithmetic Integra in the 16th century for most of our history negative numbers were not just considered not real they were thought to be completely absurd yes there is no such thing as a negative amount of apples unless

the real interpretation is that perhaps you owe a positive amount to someone else as a society with pretty much assimilated these ideas by now but there are other Concepts that have now been around long enough for us to properly Digest like imaginary numbers which while being very well understood are still somewhat difficult to grasp for many as they lack a physical counterpart then we can touch and the same goes for high Dimensions as well ultimately asking whether or not something mathematical is real is a dangerous business because it links our understanding of something metaphysical to

a human-centric experience perhaps a better way to fix this question would be to ask a more practical one do we live in a four-dimensional universe but how can we even answer that when we have no way to cross the boundary between dimensions the answer is now by searching for 4D objects in our 3D universe but by finding 3D objects escaping into the fourth dimension it is theorized that some high energy collisions might project particles into high dimension in a process node is similar to how Billet balls can sometimes jump off the table when you hit

them too hard but as far as we know we have no reason to believe or even to suspect that to be the case for our universe and yes there are indeed mathematical theories that suggest that we live in either a 10 11 or even 26 dimensional universe to this day there have been no proposed experiments to confirm any of that and while fascinating the remain just that theories for a video on covering the hidden secrets of the fourth dimension that sounded quite anticlimactic if the universe is likely not four-dimensional why are we even discussing hypergeometry

well the answer is that regardless of the nature of the universe we live in there are many problems that cannot be expressed with just three numbers in computer graphics for example rotations are usually encoded using quaternions which as the name suggests a four-dimensional object yes phone numbers are used to define rotations in three dimensions and if that sounds weird well there are techniques to compute rotations using three by three matrices which are effectively nine-dimensional objects as they only contain nine independent numbers so high dimensions are all around us literally and they are very real even

if they're minor be physical after all [Music] it is undeniable that what makes hyperdimensional objects so fascinating and incidentally so misunderstood is their inherent mystery a mystery that lies not so much in their own nature but in our inability to grasp them within the boundaries of our imagination us creatures that evolved in a 3D World we are very ill-equipped to visualize 4D shapes in our head and something as intuitive as rotating a cube can suddenly becoming comprehensible when that very same rotation take place in the fourth dimension so what does a hypercube actually look like

well as we live in a 3D Universe we can only perceive a fraction of its complexity but this doesn't mean that we don't have any tools to understand it after all the monitor you're watching this video on is effectively two-dimensional but this doesn't stop you from rendering three objects like this Cube and as long as our brain can pick up some Clues like depth and shadows it's able to reconstruct the missing dimension fortunately the same doesn't come as natural for hypercubes as our brain never really evolved to do that so let's see the three main

different techniques that are used to visualize for the objects best way to render a four-dimensional object is to not render it in full Dimensions every vertex of a tesseract for example has four coordinates but we can simply decide to ignore one of them the resulting shape is indeed three-dimensional and while this sounds like an arbitrary Choice it is one that is actually pretty common in the field of 3D modeling dropping a coordinating 4D is the equivalent of an autographic projection and since there are four possible coordinates that can be dropped there are four projection for

any given for the object to be fair orthographic projections are rarely used to visualize for the objects as they collapse too much of their complexity and lack any sense of depth objects usually look smaller the further away they are from the camera and this is what helps our brain to infer depth even when looking at a picture we can use the same perspective projection to render hyper objects so that the vertices appear further away the deeper they are into the fourth dimension this technique introduces significant deformations but gives enough Clues to trick our brain into

perceiving some sort of hyper depth and most importantly it does so in a single object not full perspective projections are effectively Shadows that hyper objects cast into our own world and they appear 3D in the same way a 3D object leads to the Shadows behind both autographics and perspective projections are invaluable tools that allow us to peer into the fourth dimension but they fail to capture what hyper objects actually look like in 3D before we can finally answer this question it helps to go down one dimension and ask what a three object would look like

to two-dimensional beings they would only be able to perceive the parts of the cube intersecting their reality only the points with that coordinate equal to zero would manifest well all the other would simply be invisible as they reside somewhere else in the Z dimension from their perspective what they would see is effectively a square that suddenly appears and disappears this is known as a cross-section but as the cube rotates its cross-section becomes more complicated and can manifest as a single point a line segment a triangle a parallelogram a pentagon or even a hexagon to the

2D denizens living on the X Y plane a rotating Cube would appear as a 2d polygon constantly changing shape the cube itself is not changing but its cross-section is for something that is asymmetrical as a sphere instead its cross-section would appear as a circle expanded and Contracting regardless of its orientation we can apply the exact same principle to for the objects and take their cross-section at the pass through the real plane which we can imagine being the one with the w coordinate as equal to zero as a hypercube moves and rotates its cross-section appears a

series of morphine polyhedra you can also see how they are all contained almost caged inside the convex Hull of the perspective projection scenes wrapping your head around rotating hyper objects can be challenging games like 4D golf are rendering on top of the 3D cross-section their entire 4D projection disappears like a semi-transparent 3D Shadow which helps to better understand directions in the dimensions we cannot see foreign [Music] that 3D objects can be rotated independently around their X Y and Z axes so it would only be normal to think that a 4D object would also be able

to rotate around its W axis but that is not really the case one of the most common misconceptions in fact is that there is a rotation axis associated with each dimension and a simplest example to disprove that is 2D there are two axes X and Y but only one possible axis of rotation which incidentally is neither of them one better way to imagine rotations one that actually works in any Dimension is to imagine them on a plane rather than around an axis a rotation can change the position of a point but the point itself will

remain bound to its rotation plane so let's recap in 2D there is only one plane x y and so there is only one possible rotation in 3D there are three possible plane why is that X said and x y which correspond to the X Y and Z rotations axis you are familiar with when it comes to 4D well there are six possible axes the three seen before plus x w y w and z w in total there are six independent ways to rotate objects in four dimensions so what does it look like to rotate let's

say a 4D Cube around one of its three hyperplanes well it looks like flipping the cube Inside Out along one of the three main axes but don't let this fool you rotations no matter the dimension do not change the shape of an object and so a hyper rotation doesn't really flip the cube inside out it looks like that's what's happening because the rotation is taking place in a dimension that we cannot actually see the exact same illusion happens when we project the shadow of our traditional 3D cube because its shadow is 2D it actually looks

like even this 3D cube is flipped inside out but that's not what's happening in the same way that's not what happens to our hypercubes our journey into the fourth dimension would not be complete without one final lesson how to conjure four-dimensional objects into existence many familiar geometrical shapes can be generalized in any Dimension a square and a box are both 2D and 3D instances of this generalized idea of an n-cube and so are a point a line segment and a tesseract a generic n cube is constructed by extruding a N1 Cube into a new dimension

a tesseract is a cube extruded along the W axis in the same way a cube is a x y Square extruded along the z-axis with the same principle we can extrude a tesseract in the 5 Cube and so on before dimensions are more than enough for this documentary hyperspheres are constructed in a different way yes you can extrude the 3D sphere into the fourth dimension but that will not be a foodie sphere in the same way extrude in a circle doesn't then turn it into a sphere what you would obtain is a sphere in there

instead a spherical cylinder if you want which is the loose equivalent of a 4D capsule a property of a true folding sphere is that all of its points are at a given distance from its Center which can be obtained by rotating a 3D sphere on one of its hyperplanes all cross-sections of a 4D sphere are 3D spheres while the cross-sections of a sphere in there can be spheres cylinders or any shape in between extrusions and rotations are two of the most common ways to create new shapes including hyperdimensional ones but even more shapes can be

constructed by combining existing ones with an operator known as the Cartesian product these unlocks exotic shapes that extrusions and rotations alone cannot construct such as dual cylinders and Tigers the last pin one of the four possible 4D toride and even that is barely scratching the surface as there are many more objects waiting to be discovered or perhaps it would be better to say constructed in the fourth dimension [Music] Plato in a wonderful allegory speaks of some men living in such a condition that they were practically reduced to be denizens of a Shadow Wood these were

the words that Charles Howard interviews back in 1912 to introduce the fourth dimension to its readers and what are we if not Tennesse could be a mere shadow of a four-dimensional universe that we are so desperately trying to understand there is so much more that I could simply not fit into this documentaries and so much more yet to discover entire new geometries hiding in plain sight waiting for us to just reach our hand far enough into the fourth dimension to uncover their hidden Beauty perhaps this is the biggest secret that's hiding in the fourth dimension

Beauty the beauty is so rare that transcends three dimensions and perhaps exactly for this reason a beauty that only three-dimensional beings can truly appreciate [Music] foreign [Music] [Applause] thank you [Applause] [Applause] thank you foreign [Applause] [Music] [Applause] [Music] [Applause] [Music] [Applause] [Music] thank you thank you [Music]