Euclidean Space: a Paradoxical Dimension Where Bilingual, Geometrical Spectral Elements Might Linger
By Maria Anna van Driel, www.nexttruth.com
From prehistory to this day, we have been haunted by our memories, the past itself, by inklings of the future, by events playing outside our lives, and by ourselves. Hence the lure of ghost stories throughout history and presumably prehistory. But, if you wish to be considered a scientific-minded person, you probably know that you should not believe in the occurrence of events commonly referred to as ‘supernatural’. Because, if there was something to that sort of thing, surely the greats of science such as Newton, Bacon, Boyle, the Curies and Einstein would have told us. Right?
Science, so many state, has been a great destroyer of myth and superstition. But, what might surprise you is that each of the scientific icons named above, and many others of similar standing, took reports of those phenomena occurring beyond the scope of normal scientific understanding, quite seriously.
But, even though many believe in the existence of ghosts, spirits, demons and angles, there is still a lot of confusion over what actually is lurking in these dim and elusive realms. An extra- or intra-dimensional entity like that of a poltergeist or aliens perhaps?
“I like your sneakers!”
A poltergeist, some say, is a spirit, a ghost or even a demon that is throwing things around in your home. Others say it is the manifestation of a person’s own psychokinetic energy or PK activity that is acting out. So which is it?
The word German word poltergeist simply means “rumbling spirit” and most modern scientists would probably relegate them to the realm of fairy tales without thinking twice. And yet, history, mythology, physics, among others, are offering surprising insights in the worlds of those spirits who are generally causing a ruckus in a household. But just because a candle falls off your mantel does not mean you have a clumsy demon in the house. It doesn’t even necessarily mean you have a poltergeist who has a crush on your new sneakers. But if this is followed up by similar activity of other things falling or being thrown around, then it might be possible.
One of the characteristic features of a poltergeist, besides throwing things around, is that it piles up objects in a way that, to us, appears to be un- or supernatural. In the case of alien species, an advanced way of them using telepathy and antigravity is being reported during an encounter. Now why is that?! Are these intra-dimensional entities communicating with us in a geometric and mathematical manner like we are trying to do with species from the animal kingdom by means of sign language?
When thinking about it … piling up furniture like that looks a bit like a chaotic reflection of Euclidean geometry that listens to well-defined rules which points in the direction of the algorithms in mathematics and computer science.
Okay, okay, this is indeed a very crazy comparison. So, let’s step into the time machine of H. G. Wells, travel through a wormhole and rip up some of the fabrics of space-time and enter an, hidden to the naked eye, area in the universe were familiar objects are acting highly strangely…let’s explore the three-dimensional space, and time, of the Euclidean geometry.
What is Euclidean space?
Scrolling through internet we find that Euclidean space is a special case of Hilbert space what generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions. In other words, it is the fundamental space of classical geometry.
We can also read that it originally was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any nonnegative integer dimension, including the three-dimensional space and the Euclidean plane. In mathematics, the Euclidean distance between two points in Euclidean space is a number, the length of a line segment between the two points. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and is occasionally called the Pythagorean distance.
Um…yeah, nice try Wikipedia but let’s slow down a bit. Simply said, Euclidean space can be thought of space containing infinitive small “rank 3 Tensors” or several big ones which are in, on top, underneath, next, in front and behind each other. Think of a huge amount of 3D cubes in space of which their position is both everywhere and nowhere. Or the Matryoshka dolls for a smaller image. In this weird and odd looking space the geometry is all about shapes, lines, and angles and how they interact with each other. Oh, and it has billions and billions of points which we call “space-time coordinates” or simply written as “X”.
Entering a neighbor dimension
Okay, now we have an image of what Euclidean space looks like, but where do these extra- or intra-dimensional entities, like a poltergeist or an alien, fit in? And more interesting, how do they enter our dimension?
Let’s take a flat length of paper and put a half twist in it and then connect the ends. This is a mobius strip what is a very famous shape in the field of topology. When you cut it right down the middle and go all the way around…you are still left with one piece what is not a mobius strip as it has more than a half twist in it. Now let’s put one, two, three half twists in this strip and then cut it down the middle. Now you have a knot what is almost looking similar to the images you find on internet when searching for the “String Theory”.
As soon as you move into these higher dimensions, you will see there are a lot of unsolved problems there actually. But let’s stay with the mobius strip for a while and answer another question. What shape would you get if you could sew two mobius strips together? Well, the answer is a “Klein bottle” which is a shape that only exists in four dimensions.
That means, if you really did connect two mobius strips you only get a 3D representation of the Klein bottle. To make a real Klein bottle you need access to a fourth spatial dimension. And if you are wondering why…it is because it appears the Klein bottle to intersect with itself. But a true Klein bottle does not self intersect. That is only possible if this is embedded in a higher dimension.
Peeking around the corner of four spatial dimension
However, the Klein bottle is still a two dimensional manifold meaning close up, or locally, it looks like a two dimensional plane. It is just like the surface of the earth. To something that small, like us, standing on that surface, it does look flat and two-dimensional. But when you get to relativity space-time and the curvature of the universe, you move into those three and four dimensional manifolds.
How to think about a four spatial dimension? To do that we should first imagine a two-dimensional object ‘living’ in flatland that can only ‘see’ along this completely flat surface. If a three-dimensional sphere entered that world, all the ‘flat creature’ would see is the two-dimensional cross-section or a circle. I mean if there were some two-dimensional worlds living on a piece of paper laying in front of you, you could see everything that is going on and there is nothing these flat creatures could do to hide for you. And what is even more weirder, if you wanted to, you could enter their world but all they would see is the two-dimensional cross-section of you.
And this is exactly how it would be for us when we watch a four-dimensional being visiting our reality in the moment they are using a combination of three-dimensional Euclidean space and time into a four-dimensional manifold. In other words, time-travel by using a dimensional portal.
It seems that these extra- or intra-dimensional entities, when ‘living’ in these dimensions, have the ability to see our three-dimensional world and there is nothing we could do to hide from them. They can enter our dimension (classical reality) at any coordinate and we only would see a three-dimensional cross-section of them appearing out of nowhere…getting bigger and bigger and then smaller and smaller and eventually disappear into nothing.
Now whether or not the universe is a Euclidean space is a question that science finds hard to answer because science can only make models and test those models against the reality we are most familiar with…classical reality.
Even after billions and billions of centauries of evolution, our brains are still not evolved enough to understand how any object, or a creature, is moving through that higher dimension nor how it is communicating.
