Saturday, January 27, 2024

What Does It Mean to Live in Processual Hyperdimensional Worlds?



What Does It Mean to Live in
Processual Hyperdimensional Worlds?

by R.E. Slater


How do you go about explaining hyper-dimensionality and yet make it practical. Let's try...

Mathematicians, Physicists, and Science Fiction writers have together sought to explain space and time to us through their tools and trades of knowledge and speculation.

Below is a temporal explanation of 11 connected forms of temporal dimensions including that of our own 3 dimensional space.

Once completed, think through each dimensional paradigm as describing a living organic complexity infinitely related to itself, experiencing itself, and reacting to itself as a self-aware chaotic essence continual evolving to-and-from itself as it moves through an infinite chaotic cascade of concrescing events in its present super-state in which all component parts are continually adapting, evolving and becoming more than it was before some point in time. We have now described the world of Whitehead's process-based metaphysics of the cosmos.

R.E. Slater
January 27, 2024


Firstly, our perceptions of reality are shaped by the kinds of reality we live in and experience. Many of the dimensions shown below can be experienced by ourselves, as alpha beings. We might describe such people as being wise, learned knowledgeable, prescient, well-travelled, snd so forth.

But if we think of ourselves as affected-and-affecting living elements in a vast sociological-spiritual sea of personalized communities than as "simple" beings living out our lives in whatever temporal modes of physicality we find ourselves, then as alpha beings living in 4 dimensional worlds we might effectively heal and atone, revive and redeem, translate and ascend over today's many world realities of negative conflict and debilitating consequences caused by non-perspectival living to one's self.

A process philosophy, such as Whitehead's, when coupled with a grand processal theology vision can grant all ecocosmo-civilizations the great ability to find salvation in living with one another. That the very unity of solidarity in itself can heal and disrupt the evil and wickedness created by communities not leaning into life and love.

Further, religions such as Christianity becomes better informed when adopting its own processual form of faith. Likewise Judaism, Islam, and all world religions. A process-based-abd-informed faith and/or formation of pricess-informed habits of life finds deep reflection and "raision d'etre" when placed upon a succinct process philosophy emphasizing love and respect for all beings and living things.

R.E. Slater
January 27, 2024


Envisioning 11 dimensional spacetime

by R.E. Slater


Mankind typically has five senses and a recent sixth sense as designated by scientific studies. They are taste, smell, vision, hearing, touch and… an awareness of one's body in space. Yes, humans have at least six senses, and a new study suggests that the last one, known as called proprioception, may have a genetic basis. Proprioception refers to how our brain understands where our body is in relationship to space, and perhaps to spacetime, in the more general sense of things.

d = dimensions or dimensionality

ST = space time

Alpha 3d + 1d Time = 4d ST - If using our five/six senses we humans are 3 dimensional beings living in a 4 dimensional world per our senses.. We call this four-dimensional space - "spacetime" - as Einstein referred to it in his relativity theories of the very large.

Beta 5d - The purposeful (or random) sequencing of ST. Essentially a 5d being may play-back, pause, or play-forward life modes in a any chosen random succession.

String Theories vacillating frequencies

Gamma 6d - The superpositioning + random temporality of ST = A 6d being may observe "all-at-once life modes" granting to it the ability to re-live all, or part, of one's sequentialized  lifetimes at any point and all a once (e.g., ST as a non-linear compactification of scale and sequence).

Delta 7d - Here a 7d being may experience "the plane of absolute awareness of all possible worlds". This would be a superpositional + supertemporal multimodal dimensional experience where one might see all possibilities of one's life choices all at once in order to know and chart preferred outcomes. This would not be unlike an alpha time being such as ourselves when describing a mentor as a wise sage or prescient-type of guru. Which is to say that for every dimension beyond our own we still may ascribe a parallel experience. In so many words, we have inherited the Divine's superdimensionality in likeness but not in exactness. I will explain further as we go on....

The "Many Worlds Paradigm" of Multiverses

Epsilon 8d - Here, an 8d being may randomly chose a point of origin when applying superpositionality and supertemporality. That is, by changing one's "initial conditions" one will most likely produce drastically different outcomes leading to more favorable optimal results. An 8d spacetime is one which integrates chaos theory with experientially determinative results using agency and reflection. This then will allow --> multilocality, multitemporal corporeal travel to explore, experiment and experience infinite regressive possibilities --> resulting in gaining "exterior" perspectives via experiential knowledge.

Ex. The same  8d child/adult may chose to be born to different parents, to live in different conditions, to experience different opportunities, localities, eras, etc.

By application, a living 3d alpha being may live on different continents, under differing cultures and religions, and with later applying these experiences to one's life and ministries, business or community leadership to help lead a community towards some preferred lifestyle. This is most common with military kids, refugees, or missionary kids as they experience goodness or duress, serenity or hardship. All experience can be leveraged to better one's life or help another as opportunities allow. Which is another reason we should always be sensitive to assisting and helping where we can.


Lamda 9d - A lambda being is presciently self-aware and their attuned to re-perspectivizing their life as it is enhanced when subsuming all possible initial condition matrices all at once. Hence, such a being may profoundly navigate the chaotic complexity of a living, processual universe with purpose, intentionality and precision. More simply, with this kind of knowledge and ability "every path becomes the right path" with knowledge, experience and perspective in which to gain optimal results for differing paths good or bad.
Ex. Essentially a 9d being is actively creating a library of all possible beginnings with all possible results. This resembles the god-like being in Star Trek Next-Gen and the cable series Picard known as "Q". A diffident, albeit obsequious, being who taunts and questions, teases, and mocks Captain Picard's human efforts to guide his crew, humanity, and alien life forms, towards a better tomorrow.

Q's younger and older selves moving
together through life events.


Q whispering into Picard's ear as either devil or angel,
Picard could never be sure.

Picard always had the choice to listen while also choosing
how to listen. Most times he never knew the end game.

     

Sigma 10d - Here, a 10d sigma being may also change their cosmological constants. That is, they are not bound to any one universe but have at their disposal all possible universes.

Similarly, we think we live in a finely-tuned creation where changing the charge of an election in the slightest degree, or the weakness of gravity by a little more or a little less, would no longer make our current universe habitable for our present species. This is not the case for a sigma being.

And though this may an argument for the strong anthropology principle I would rather not couch this observation in these terms but in terms of the weak anthropological argument which states that life resulted via evolutionary process because of that quality which God has give all living things in which to adapt and embrace one's  existing cosmological constants whatever they may be. Thus, God is not a determinative being but more of a wise being creating life with the capability to thrive wherever it may exist against all the odds that it exist at all.

Theologically, a processual cosmology allows for a positively evolving and pancessually adaptive ("many forms and modes") dimensional spacetime best described as a processually evolving creation/cosmos/cosmology.

Omega 11d - Finally, an 11d omega being has an infinite array of all possible worlds with all possible outcomes lending to an infinite array of perspectives. Importantly, one can no longer speak of "the impossible" because even the impossible exists in many infinite forms. This is the stuff of speculative science fiction, theology and philosophy. It is fun to imagined and though actually unobtainable for alpha beings it is in fact, the kind of universe we live in and are formed by, if we are beings at all. The quantum realm is the kind of playground where dimensional space may be found and where Whiteheadian process philosophy and theology demands its place.

- res

"What If You Could Access the TENTH Dimension?"
10D Explained
by Beeyond Ideas  |  Sep 29, 2023

Let’s unravel the layers of existence that redefine reality. From Alpha's linear perception of time to the unfathomable Omega, where every conceivable reality exists. 

Chapters

00:00 Opening
01:08 Time as a dimension
04:28 Multiple time dimensions
06:19 The next level of twin paradox
08:10 α-Alpha (3D)
09:55 β-Beta (4D)
11:48 γ-Gamma (5D)
14:21 δ-Delta (6D)
16:44 ε-Epsilon (7D)
19:41 λ-Lambda (8D)
22:26 σ-Sigma (9D)
24:51 ω-Omega (10D)
26:21 The existential question



11 Dimensions Explained
What are Dimensions & How Many Dimensions are there?

Posted by Lalit Vashishtha 


What you will learn here about Dimensions. Here I will tell you what we mean by dimensions and how many dimensions are there.

Get ready to experience the amazing world of 11 dimensions. I request you to read this post till the end as it is going to be more and more interesting as we proceed.

What are the First 4 Dimensions

I know most of you are aware of first three or four dimensions. The first three dimensions are dimensions of space - i.e., "Length, width, and height." While the fourth dimension is the time dimension.

You will find it interesting that we have control over the first three dimensions of space which are length, width and height. It means we can freely move in space in forward, reverse, up and down directions. But we have no control over the fourth dimension, that is the time dimension. We are only allowed to travel only in the forward direction in the time dimension.

Even if we could fully control only the first four dimensions including the time dimension, we would become a person with supernatural powers because then it would be possible for us to travel freely not only in space but also in time in both directions; I.e. past and future as per our wish.

So just imagine, how powerful a person would be if he or she could control all 11 dimensions. Believe me, that person will actually be called The God as s/he would have the potential to do the things that you cannot even imagine.

So I think, now you are ready to enter into the fascinating world of 11 dimensions.

Let's discuss each dimension one by one.

Zeroth Dimension

Any object having Zero dimension has no length, no width and no height. A point is an example of zeroth dimension as it has no length, no width and no height or depth.

Now let's discuss the first dimension.

First Dimension

An object in first dimension has only one dimension i.e. the length. If we connect two points then we get a line having only one dimension. So a line is an example of first dimension having no width and no height but only the length dimension. Someone living in one dimensional universe, will only be allowed to move in the forward and reverse directions. There will be no existence of anything like left or right for him.

Now we will know what we mean by second dimension.

Second Dimension

Flat figures like a square or triangle are two dimensional objects. These two dimensional or 2D Objects have non zero area but their volume is zero as there is no height. They have only two dimensions, length and width. So these are known as two dimensional or 2D objects. A person living in a two dimensional space can only move on a plane.In other words he or she can only move in forward, reverse and left, right directions but not in up and down directions. So his life will be limited to a plane surface. Everything will be flat with zero height in such a universe. Some daily life examples of a two dimensional world are screens of televisions and mobile phones. Although they appear to be a three dimensional World but actually this world inside these devices is confined to a flat screen having no depth or height.

Third Dimension

If we add height or depth to a two dimensional object, it becomes a three dimensional object. A Three dimensional object has non zero volume. A cube or sphere are geometrical examples of three dimensional objects. We live in a three dimensional world where we can move in any direction in space as per our wish. We are free to move in forward, reverse, up and down directions.

Fourth Dimension (Time)

Time is considered the fourth dimension. As I just told you that we live in a three dimensional world where we are free to move in any direction in space. But without the fourth dimension i.e. The time dimension, no events can take place. Without time dimension nothing will change in this world. Time is the way for three dimensions to change. It is the time dimension that allows the objects to change their position and location in space. Without time, the whole universe will look like a snapshot for ever.

As we are living in a three dimensional world, so we have no control on the fourth dimension, the time. We are forced to move only in the forward direction with time. But a person living in four dimensions will be able to go in any direction in time like past or future. He will have control over the time dimension as he is a person of four dimensions.

So these were the first four dimensions that can be perceived by humans. Now We are going to discuss higher dimensions that we can not perceive, although they exist.

So let's start with the fifth dimension

Fifth Dimension

As I just told you that we can not perceive dimensions that are higher than the fourth dimension because they exist on a subatomic level. These higher dimensions actually deal with the possibilities. But why we cannot perceive higher dimensions. Actually these dimensions are curled in on themselves in a process known as Compactification.

But how these higher dimensions are imperceptible. Let me explain it by giving you a simple example.

When we see a rope from large distance, we only observe it's one dimension that is the length. But any insect moving on that rope will also see other dimensions of the rope like its thickness. It will also observe the fine groves and roughness and circumference of the rope that could not be seen by a distant observer.

If a person were living in a world of five dimensions then he would be able to play with time in different ways. He could move either in past or in future. It would also be possible for him to be present at different locations at the same time. He would be able to do many jobs or can have many hobbies at the same time. He could be a doctor, an engineer, a cricketer, a poet and anything else at the same time, as he has full control over the time dimension.

Sixth Dimension

Sixth dimension gives more powers to a person living in this dimension. He can not Only move in any direction in time at his will but also can take many forms at the same time just like the quantum world. We know that the quantum world is the world of probabilities, where particles can be present at different places at the same time and can take different forms. So the sixth dimension gives more flexibility in comparison to the fifth dimension. In The sixth dimension we enter into the world of parallel universes I.e. The concept of multiverse. This dimension will allow us to see all possible presents, pasts and futures. But Every Universe present in this multiverse will have the same beginning as that of our universe I.e. the big bang. This is the limitation of this dimension.

Seventh Dimension

This dimension also, includes the concept of parallel universes. Seventh dimension contains infinite number of universes. So a Person living in seven dimensions can move in any universe and can have infinite forms of itself. The basic difference between the sixth and the seventh dimension is that, the infinite universes in the sixth dimension had the condition that they all must have the same beginning as of ours I.e the big bang.But the seventh dimension is free from this condition also. Seventh dimension can contain a plane of all possible universes with different start conditions. Universes present in this dimension may have originated from different possibilities.

Eighth Dimension

According to String theory, there will be no physical existence of any object that is present in the 8th dimension. So anyone living in this dimension would not be able to touch anything nor it can be touched by anything or anyone as nothing will have any physical existence. If you find it difficult to imagine, then you can understand it like the digital world that we are familiar with. The eighth dimension will contain a plane of all the possible presents, pasts and futures for all the infinite number of parallel universes that are stretching up to infinity.

Ninth Dimension

Ninth dimension is again very interesting and unbelievable. In the ninth dimension, it is possible for many civilizations or aliens to live at the same place and at the same time without seeing and feeling the presence other, I.e. being completely unaware of the presence of the other. If someone is able to see, then he might be seeing all the civilizations and Aliens living together at the same time at the same place smoothly, independent of each other.

A Person living in the ninth dimension will be able to move in any infinite number of universes, will have no physical form, will be able to move in all presents, pasts and futures of any infinite number of universes that are extending to infinity. One different thing that will happen in the universes of the ninth dimension will be, that these universes may have their own laws of physics and separate conditions and probabilities of their origin.

Tenth Dimension

This dimension will contain infinite possibilities and would be infinitely complex to understand for us. A person living in the tenth dimension will have infinite powers. That person would be so powerful that he would be no other than the God itself as he would be able to control space and time and every thing present in any infinite number of universes.He would have all the powers that are possessed by the person living in other lower dimensions that we have already discussed. The possibilities for this dimension are infinite. Even those things are possible in this dimension that are beyond your imagination.

Eleventh Dimension

Friends before describing the eleventh dimension, let me tell you that according to string theory there are 10 dimensions, while M- Theory says that there are total 11 dimensions. But According to Bosonic theory, total number of dimensions may be up to 26.

But scientists say that, because of self consistency, a universe cannot have more than 11 dimensions as they become unstable. Because of this instabilty they collapse back down into 11 or 10 dimensions.

So now let's come back to the 11th dimension.

In the eleventh dimension everything imaginable or unimaginable is possible. In other words you can say, that there is nothing that cannot happen in the 11th dimension.

According to M-Theory the smallest thing in the universe is not atoms, electron, higgs boson or quarks. The smallest thing is much smaller than all these subatomic particles. Actually the smallest thing in the universe is "Strings". You may think, why I am explaining the strings here? Actually strings vibrate in the eleventh dimension that we are going to discuss.

Everything present in every universe of every dimension is made up of Strings. All the atoms, subatomic particles, muons, quarks, Higgs bosons are made up of Strings. You will be surprised to know that according to M theory, everything in the universe originated from the 11th dimension not from the first, second or third dimension.

What are these Strings and how small they are?

In Physics, string theory is a theoretical framework in which the point like particles of particle physics are replaced by one-dimensional objects called strings.According to the string theory all fundamental particles are actually tiny vibrating loops of string. Various properties of particles like mass and charge are determined by the vibrations of the one dimensional string like entities. The String theory describes how these strings propagate through space and interact with each other.

Now let's come to the size of the string.

The size of the string is about 10^-33 cm. Let me tell you that 10^-33 cm is actually millionth of a billionth of a billionth of a billionth of a centimeter. Confused?

Ok, let me explain it to you in simple words.

To give you an Idea let's compare the size of a string with the size of an atom.

If an atom were magnified, to the size of the whole observable Universe, then a String would only be the size of a tree!!!

So friends these were the 11 dimensions according to the M theory. I hope you enjoyed this post and learned many new things.


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From Quora

Historian of theoretical physics.Updated 5y

Originally Answered:


The best way to understand dimensions is to start with smaller dimensions than three and work up very slowly so that the analogy is clear. An overage of detail is needed to eliminate confusion. Patience will pay off. Furthermore I hope to point out that a spatial version of Tarski’s undefinability exists in consideration of dimensions without any reference to formal set theory.

1) Creating a space to hold things and defining the relationships.

A zero dimensional object is called a point but a single dimensional “array” used to store it can have infinite points. The array is the actual "dimension" which contains the point objects. (an array in programming looks like this: arrayname[#]) Given that a point has no dimension and is not measurable, it is a bit misleading to insist that a collection of dimensionless points is somehow measurable. In fact, the relationship of the points to each other is utterly undefined until another dimension is defined. An infinite number of them could all be in the same place or they could be randomly arranged in some higher dimensional space. The point is that the dimension or array is a "space" which is kind of like an infinite set of containers. If a higher dimension does not exist, however, our concept of arrangement between them is something we add via imagination because of our concept of a linear arrangement of a number line that we label those boxes with, but that relationship cannot exist in a 1D reality. In a 1D reality there is no spacial relationship between points. Just like higher dimensions, our pre-conceived notions accidentally add things to lower dimensions as well. There’s no collision or direction because there’s no way to define a direction without something for the “line” to traverse. Therefore the following is visualization is misleading without higher dimensions. What it does convey is that we use sets of containers called arrays to store and label things like bits of empty space of whatever size we decide to use for a unit size.

Once the higher dimension is defined, however, (two dimensions) then the relationship of the points (places or bits of space) in that higher dimensional structure is also somewhat automatically defined by cartesian coordinate systems. Suddenly, because there is an external reference, measurability becomes more meaningful. If they were labelled in numerical order then they now exist in a line. There are also now unlimited number of possible locations along a line that a point can exist and the relationship between the points in this higher dimensional reality is numerically labelled in a two dimensional array. (arrayname[x][y]) This is to say that what we think of as lines, can now actually exist since there is some higher dimensional reference. Our labeled boxes for holding points may be labeled along x because that’s what we do for cartesian coordinates, but a general line can go across both x and y axis. The habit of cartesian coordinate systems adds something that isn’t really there for a 1D reality. Without that y axis, the “line”(or collection of bits of space) could be thought of as piled up in one place or tied in a knot and there’d be no way to differentiate because the relationship is undefined. It would all be imagination without that higher dimensional reality to contain and define it.

This means that going from one dimension to two defines a real structure which, filled or not, has unlimited "slots" for the lower dimension. To restate it, while unlimited number of points could have existed in the single dimensional structure before the extra dimension was added to view it from, no relationship between them could be clearly defined. IE The relationships of a dimensional structure we use to keep up with things, cannot have real relationships unless there is a (somewhat hidden or intimated) higher dimensional reality to view it from. We should think of the one dimensional array as the "space" of one dimension and while we might think of it as an infinite line, that straight structure called a line cannot exist without the next dimension. It is arbitrary that we would usually stuff the previous single dimension into the two-dimensional array at the bottom and lay in out orthogonal to the y axis. (arrayname[x] gets put into arrayname[x][0])

Consequently, once a second dimension is added, the "space" of two dimensions now exists whether or not you fill it with lower dimensional objects such as points. Or same-dimensional (2-dimensional) objects such as lines. (unlimited x and unlimited y) This additional dimension now allows us the very first "shape", a line, but it also simultaneously allows numerous lines to exist upon different axes.

A crucial digression on the borderline between dimensions: Above it looks as though I’ve called a line a 2-dimensional object by mistake. A line is conventionally considered a 1-dimensional object. I find this convention to be misleading because points are called zero dimensional. This is a little like timekeeping in that the spaces between divisions can cause a little oddness. So long as one has lives 10 years and 2 seconds that lifetime can span 3 different decades.

Within the conventional terminology, there is the acknowledgement that an arrangement of 0 dimensional objects is 1 dimensional but involves two dimensions. (0th and 1st)

When I called a line 2-dimensional, it was not my intent to confuse, but to bring to mind the reliance upon the second dimension for a line to be in any way line-like. It is crucial to understand this borderline between dimensions and keep it in mind when attempting to grasp the real meaning of dimensions.

Recapping: In the case of going from one dimension to two, simply adding one additional dimension not only defined relationships between 0th dimensional objects like points but also allowed for relationships between conventional two dimensional objects like triangles and one dimensional arrays (lines) can now be curved and have an additional relationship to themselves. We gained not only lines but other shapes such as triangles etc. This idea of additional new relationships between different parts of a line is an important concept moving forward.

Let’s simplify for a moment and just consider dimensions without all the requirements and dependencies and in-between things.

If we intend to extend from dimension to dimension in a way that makes sense, then we can use our first concept of the first dimensional space as an infinite number of points leading to an infinite length straight line as one dimensional space to see that an infinite stack of these lines creates the second dimensional space.

EG: Think of making a line along the very bottom of a page from tiny points and knowing you can do this forever on a page that has no side edge. Now think of making the next line on top of this one and the next on top of that etc. You know you can keep doing this forever and you have now described an infinite plane or two dimensions. (bear with me, while obvious, you'll want to hold this idea in your head for going from the third dimension to the fourth)

This infinite stack which is called two dimensions can now also be stacked. Though two-dimensional space is an infinite plane, sometimes it's easier to conceive of as a sheet of paper. With this concept it becomes easy to think of a stack of paper that can be infinite.

We now have infinite points stacked into an infinite line for the first dimension, infinite lines stacked into an infinite sheet for the second dimension, infinite sheets stacked into an infinite cube for the third dimension. (and you're seeing where this is going)

What we must now realize is, that upon adding a second dimension, it became easier of us to think of a whole universe that is 2-dimensional. An infinite plane is a two dimensional universe and the infinite cube is a 3-dimensional universe.

Just like when we added the second dimension we created a new form of relationship between one-dimensional objects, upon adding a third dimension we have created a new form of relationships between two dimensional objects. Previously with only one dimension we had only one line constrained to be in a stack but then with the second dimension there could be multiple lines with multiple relationships.

When there were only two dimensions there was only a single sheet constrained to be in a plane. Upon adding a third dimension multiple sheets could exist with not only relationships to each other but with relationships to themselves. IE A sheet not only has a rotational orientation but it can now be curved back upon itself.

If we now add a fourth dimension we have created a space with room for infinite three dimensional universes. Consequently we have now also created new relationships between these three dimensional universes such that they can have an orientation and additional relationship to each other. They can now be curved back upon themselves.

This idea of creating an infinite set of sets (adding another dimension) continuously allows new types of relationships to appear (or be defined) with each additional dimension added. An additional dimension allows a set to be bent back upon itself.

Simplifying the 4th dimension.

Given that time is conjoined with space in special relativity, there are some strange conventions that have to be employed to represent rearrangements of the 4th dimension, so lets just start with collapsing spatial dimensions.

We can think of a 2D plane at a sheet of paper with it’s various points and shapes being swept down to the bottom of the page and squashed flat along the bottom line and we’ve compressed 2D into 1D. We can think of doing this for a whole stack of papers and we’ve compressed 3D into 2D.

Now it is crucial to note that when we think of a 3D universe we are thinking of a single moment in time and therefore the universe we think of is already 4D. A 3D array can only hold the information for one single moment of time and would require a 4th dimension to store all the copies of the universe that exist moment after moment.

So, now with our 3D universe compressed to a sheet, we can stack these sheets together to represent a 4D universe. Just like a sheet shape within a 3D plane is not constrained to one axis, we can now define a moment as a slice through that 4D (multiple compressed 3D) universe.

So far this is all pretty easy until we add relativity.


The illusion of time:
past, present and future all exist together



Now, however, upon adding relativity there is a requirement of a 5th dimension.

This is not apparent in the video above, but before relativity the universe was already 4D. A single moment was 3D and there were multiple moments. Upon adding relativity, however, a single moment is fundamentally 4D. One cannot speak about space without mentioning time. Location is dependent upon time.

What this means for the discussion in the video above is that the “loaf” of spacetime they show is only one possible configuration of all the moments. Modern interpretations of relativity state that there is no preferred frame of reference therefore entirely different versions of that loaf are equally valid as the one presented.

When we consider the alien on the bike and the man on the park bench we think of them as definitely directly across spacetime from each other. This relationship, however, cannot be established since another frame’s idea of simultaneous would place them at an angle to one another across the loaf in one direction while another would place them at the opposite angle.

That is to say, there are multiple valid arrangements of the loaf such that if we consider forward time to be x, in one case the alien starts out in front of the man on the bench (further along x) and in another valid arrangement, the man on the bench is in front.

So if we try to think of being simultaneous with another location’s future, how do we determine where the starting point to move forward from is? The relationship is undefined. If there is no singular true and valid arrangement we are actually slicing from then another dimension is required to store all the various but valid alternative configurations of our 4D loaf of the universe.

To cut across a 4D universe a 5th dimension must be added just like to have a line, a second dimension must be added.

Godel and mutual dependencies.

This problem above is an expression of Godel incompleteness and Tarski’s undefinability in yet another form. There are many structures such as lines that we do not think of as actually a comparison or interaction between things and we therefore lose sight of the need for another “thing” to compare or interact with.

Imagine if there was nothing in the universe but two people. Each can say of the other “you are above me” and they might both be considered correct or incorrect because the answer is undefined without an external reference.

What we think of as a river cannot exist if we remove the water. That’s just a dry depression. It cannot exist as water alone. That could be a cloud or an ocean. It is only by the interaction of the water and the depression that a river arises.

There are many instances in which we metaphorically attempt to keep the concept of a river while removing one of the components it is made of. This leads to various problems in logic and attempts to make judgement about things which are undefined.




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WIKIPEDIA

Dimension

From left to right: a square, a cube and a tesseract. The square is two-dimensional (2D) and bounded by one-dimensional line segments; the cube is three-dimensional (3D) and bounded by two-dimensional squares; the tesseract is four-dimensional (4D) and bounded by three-dimensional cubes.
The first four spatial dimensions, represented in a two-dimensional picture.
  1. Two points can be connected to create a line segment.
  2. Two parallel line segments can be connected to form a square.
  3. Two parallel squares can be connected to form a cube.
  4. Two parallel cubes can be connected to form a tesseract.

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.[1][2] Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces.

In classical mechanicsspace and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism. The four dimensions (4D) of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an observerMinkowski space first approximates the universe without gravity; the pseudo-Riemannian manifolds of general relativity describe spacetime with matter and gravity. 10 dimensions are used to describe superstring theory (6D hyperspace + 4D), 11 dimensions can describe supergravity and M-theory (7D hyperspace + 4D), and the state-space of quantum mechanics is an infinite-dimensional function space.

The concept of dimension is not restricted to physical objects. High-dimensional spaces frequently occur in mathematics and the sciences. They may be Euclidean spaces or more general parameter spaces or configuration spaces such as in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space.

In mathematics

In mathematics, the dimension of an object is, roughly speaking, the number of degrees of freedom of a point that moves on this object. In other words, the dimension is the number of independent parameters or coordinates that are needed for defining the position of a point that is constrained to be on the object. For example, the dimension of a point is zero; the dimension of a line is one, as a point can move on a line in only one direction (or its opposite); the dimension of a plane is two etc.

The dimension is an intrinsic property of an object, in the sense that it is independent of the dimension of the space in which the object is or can be embedded. For example, a curve, such as a circle, is of dimension one, because the position of a point on a curve is determined by its signed distance along the curve to a fixed point on the curve. This is independent from the fact that a curve cannot be embedded in a Euclidean space of dimension lower than two, unless it is a line.

The dimension of Euclidean n-space En is n. When trying to generalize to other types of spaces, one is faced with the question "what makes En n-dimensional?" One answer is that to cover a fixed ball in En by small balls of radius ε, one needs on the order of εn such small balls. This observation leads to the definition of the Minkowski dimension and its more sophisticated variant, the Hausdorff dimension, but there are also other answers to that question. For example, the boundary of a ball in En looks locally like En-1 and this leads to the notion of the inductive dimension. While these notions agree on En, they turn out to be different when one looks at more general spaces.

tesseract is an example of a four-dimensional object. Whereas outside mathematics the use of the term "dimension" is as in: "A tesseract has four dimensions", mathematicians usually express this as: "The tesseract has dimension 4", or: "The dimension of the tesseract is 4" or: 4D.

Although the notion of higher dimensions goes back to René Descartes, substantial development of a higher-dimensional geometry only began in the 19th century, via the work of Arthur CayleyWilliam Rowan HamiltonLudwig Schläfli and Bernhard Riemann. Riemann's 1854 Habilitationsschrift, Schläfli's 1852 Theorie der vielfachen Kontinuität, and Hamilton's discovery of the quaternions and John T. Graves' discovery of the octonions in 1843 marked the beginning of higher-dimensional geometry.

The rest of this section examines some of the more important mathematical definitions of dimension.

Vector spaces

The dimension of a vector space is the number of vectors in any basis for the space, i.e. the number of coordinates necessary to specify any vector. This notion of dimension (the cardinality of a basis) is often referred to as the Hamel dimension or algebraic dimension to distinguish it from other notions of dimension.

For the non-free case, this generalizes to the notion of the length of a module.

Manifolds

The uniquely defined dimension of every connected topological manifold can be calculated. A connected topological manifold is locally homeomorphic to Euclidean n-space, in which the number n is the manifold's dimension.

For connected differentiable manifolds, the dimension is also the dimension of the tangent vector space at any point.

In geometric topology, the theory of manifolds is characterized by the way dimensions 1 and 2 are relatively elementary, the high-dimensional cases n > 4 are simplified by having extra space in which to "work"; and the cases n = 3 and 4 are in some senses the most difficult. This state of affairs was highly marked in the various cases of the Poincaré conjecture, in which four different proof methods are applied.

Complex dimension

The dimension of a manifold depends on the base field with respect to which Euclidean space is defined. While analysis usually assumes a manifold to be over the real numbers, it is sometimes useful in the study of complex manifolds and algebraic varieties to work over the complex numbers instead. A complex number (x + iy) has a real part x and an imaginary part y, in which x and y are both real numbers; hence, the complex dimension is half the real dimension.

Conversely, in algebraically unconstrained contexts, a single complex coordinate system may be applied to an object having two real dimensions. For example, an ordinary two-dimensional spherical surface, when given a complex metric, becomes a Riemann sphere of one complex dimension.[3]

Varieties

The dimension of an algebraic variety may be defined in various equivalent ways. The most intuitive way is probably the dimension of the tangent space at any Regular point of an algebraic variety. Another intuitive way is to define the dimension as the number of hyperplanes that are needed in order to have an intersection with the variety that is reduced to a finite number of points (dimension zero). This definition is based on the fact that the intersection of a variety with a hyperplane reduces the dimension by one unless if the hyperplane contains the variety.

An algebraic set being a finite union of algebraic varieties, its dimension is the maximum of the dimensions of its components. It is equal to the maximal length of the chains  of sub-varieties of the given algebraic set (the length of such a chain is the number of "").

Each variety can be considered as an algebraic stack, and its dimension as variety agrees with its dimension as stack. There are however many stacks which do not correspond to varieties, and some of these have negative dimension. Specifically, if V is a variety of dimension m and G is an algebraic group of dimension n acting on V, then the quotient stack [V/G] has dimension m − n.[4]

Krull dimension

The Krull dimension of a commutative ring is the maximal length of chains of prime ideals in it, a chain of length n being a sequence  of prime ideals related by inclusion. It is strongly related to the dimension of an algebraic variety, because of the natural correspondence between sub-varieties and prime ideals of the ring of the polynomials on the variety.

For an algebra over a field, the dimension as vector space is finite if and only if its Krull dimension is 0.

Topological spaces

For any normal topological space X, the Lebesgue covering dimension of X is defined to be the smallest integer n for which the following holds: any open cover has an open refinement (a second open cover in which each element is a subset of an element in the first cover) such that no point is included in more than n + 1 elements. In this case dim X = n. For X a manifold, this coincides with the dimension mentioned above. If no such integer n exists, then the dimension of X is said to be infinite, and one writes dim X = ∞. Moreover, X has dimension −1, i.e. dim X = −1 if and only if X is empty. This definition of covering dimension can be extended from the class of normal spaces to all Tychonoff spaces merely by replacing the term "open" in the definition by the term "functionally open".

An inductive dimension may be defined inductively as follows. Consider a discrete set of points (such as a finite collection of points) to be 0-dimensional. By dragging a 0-dimensional object in some direction, one obtains a 1-dimensional object. By dragging a 1-dimensional object in a new direction, one obtains a 2-dimensional object. In general one obtains an (n + 1)-dimensional object by dragging an n-dimensional object in a new direction. The inductive dimension of a topological space may refer to the small inductive dimension or the large inductive dimension, and is based on the analogy that, in the case of metric spaces, (n + 1)-dimensional balls have n-dimensional boundaries, permitting an inductive definition based on the dimension of the boundaries of open sets. Moreover, the boundary of a discrete set of points is the empty set, and therefore the empty set can be taken to have dimension -1.[5]

Similarly, for the class of CW complexes, the dimension of an object is the largest n for which the n-skeleton is nontrivial. Intuitively, this can be described as follows: if the original space can be continuously deformed into a collection of higher-dimensional triangles joined at their faces with a complicated surface, then the dimension of the object is the dimension of those triangles.[citation needed]

Hausdorff dimension

The Hausdorff dimension is useful for studying structurally complicated sets, especially fractals. The Hausdorff dimension is defined for all metric spaces and, unlike the dimensions considered above, can also have non-integer real values.[6] The box dimension or Minkowski dimension is a variant of the same idea. In general, there exist more definitions of fractal dimensions that work for highly irregular sets and attain non-integer positive real values.

Hilbert spaces

Every Hilbert space admits an orthonormal basis, and any two such bases for a particular space have the same cardinality. This cardinality is called the dimension of the Hilbert space. This dimension is finite if and only if the space's Hamel dimension is finite, and in this case the two dimensions coincide.

In physics

Spatial dimensions

Classical physics theories describe three physical dimensions: from a particular point in space, the basic directions in which we can move are up/down, left/right, and forward/backward. Movement in any other direction can be expressed in terms of just these three. Moving down is the same as moving up a negative distance. Moving diagonally upward and forward is just as the name of the direction implies; i.e., moving in a linear combination of up and forward. In its simplest form: a line describes one dimension, a plane describes two dimensions, and a cube describes three dimensions. (See Space and Cartesian coordinate system.)

Graphics of Dimensional 3d Space


temporal dimension, or time dimension, is a dimension of time. Time is often referred to as the "fourth dimension" for this reason, but that is not to imply that it is a spatial dimension. A temporal dimension is one way to measure physical change. It is perceived differently from the three spatial dimensions in that there is only one of it, and that we cannot move freely in time but subjectively move in one direction.

The equations used in physics to model reality do not treat time in the same way that humans commonly perceive it. The equations of classical mechanics are symmetric with respect to time, and equations of quantum mechanics are typically symmetric if both time and other quantities (such as charge and parity) are reversed. In these models, the perception of time flowing in one direction is an artifact of the laws of thermodynamics (we perceive time as flowing in the direction of increasing entropy).

The best-known treatment of time as a dimension is Poincaré and Einstein's special relativity (and extended to general relativity), which treats perceived space and time as components of a four-dimensional manifold, known as spacetime, and in the special, flat case as Minkowski space. Time is different from other spatial dimensions as time operates in all spatial dimensions. Time operates in the first, second and third as well as theoretical spatial dimensions such as a fourth spatial dimension. Time is not however present in a single point of absolute infinite singularity as defined as a geometric point, as an infinitely small point can have no change and therefore no time. Just as when an object moves through positions in space, it also moves through positions in time. In this sense the force moving any object to change is time.[7][8][9]

Additional dimensions

In physics, three dimensions of space and one of time is the accepted norm. However, there are theories that attempt to unify the four fundamental forces by introducing extra dimensions/hyperspace. Most notably, superstring theory requires 10 spacetime dimensions, and originates from a more fundamental 11-dimensional theory tentatively called M-theory which subsumes five previously distinct superstring theories. Supergravity theory also promotes 11D spacetime = 7D hyperspace + 4 common dimensions. To date, no direct experimental or observational evidence is available to support the existence of these extra dimensions. If hyperspace exists, it must be hidden from us by some physical mechanism. One well-studied possibility is that the extra dimensions may be "curled up" at such tiny scales as to be effectively invisible to current experiments.

In 1921, Kaluza–Klein theory presented 5D including an extra dimension of space. At the level of quantum field theory, Kaluza–Klein theory unifies gravity with gauge interactions, based on the realization that gravity propagating in small, compact extra dimensions is equivalent to gauge interactions at long distances. In particular when the geometry of the extra dimensions is trivial, it reproduces electromagnetism. However at sufficiently high energies or short distances, this setup still suffers from the same pathologies that famously obstruct direct attempts to describe quantum gravity. Therefore, these models still require a UV completion, of the kind that string theory is intended to provide. In particular, superstring theory requires six compact dimensions (6D hyperspace) forming a Calabi–Yau manifold. Thus Kaluza-Klein theory may be considered either as an incomplete description on its own, or as a subset of string theory model building.

In addition to small and curled up extra dimensions, there may be extra dimensions that instead are not apparent because the matter associated with our visible universe is localized on a (3 + 1)-dimensional subspace. Thus the extra dimensions need not be small and compact but may be large extra dimensionsD-branes are dynamical extended objects of various dimensionalities predicted by string theory that could play this role. They have the property that open string excitations, which are associated with gauge interactions, are confined to the brane by their endpoints, whereas the closed strings that mediate the gravitational interaction are free to propagate into the whole spacetime, or "the bulk". This could be related to why gravity is exponentially weaker than the other forces, as it effectively dilutes itself as it propagates into a higher-dimensional volume.

Some aspects of brane physics have been applied to cosmology. For example, brane gas cosmology[10][11] attempts to explain why there are three dimensions of space using topological and thermodynamic considerations. According to this idea it would be since three is the largest number of spatial dimensions in which strings can generically intersect. If initially there are many windings of strings around compact dimensions, space could only expand to macroscopic sizes once these windings are eliminated, which requires oppositely wound strings to find each other and annihilate. But strings can only find each other to annihilate at a meaningful rate in three dimensions, so it follows that only three dimensions of space are allowed to grow large given this kind of initial configuration.

Extra dimensions are said to be universal if all fields are equally free to propagate within them.

In computer graphics and spatial data

Several types of digital systems are based on the storage, analysis, and visualization of geometric shapes, including illustration softwareComputer-aided design, and Geographic information systems. Different vector systems use a wide variety of data structures to represent shapes, but almost all are fundamentally based on a set of geometric primitives corresponding to the spatial dimensions:[12]

  • Point (0-dimensional), a single coordinate in a Cartesian coordinate system.
  • Line or Polyline (1-dimensional), usually represented as an ordered list of points sampled from a continuous line, whereupon the software is expected to interpolate the intervening shape of the line as straight or curved line segments.
  • Polygon (2-dimensional), usually represented as a line that closes at its endpoints, representing the boundary of a two-dimensional region. The software is expected to use this boundary to partition 2-dimensional space into an interior and exterior.
  • Surface (3-dimensional), represented using a variety of strategies, such as a polyhedron consisting of connected polygon faces. The software is expected to use this surface to partition 3-dimensional space into an interior and exterior.

Frequently in these systems, especially GIS and Cartography, a representation of a real-world phenomena may have a different (usually lower) dimension than the phenomenon being represented. For example, a city (a two-dimensional region) may be represented as a point, or a road (a three-dimensional volume of material) may be represented as a line. This dimensional generalization correlates with tendencies in spatial cognition. For example, asking the distance between two cities presumes a conceptual model of the cities as points, while giving directions involving travel "up," "down," or "along" a road imply a one-dimensional conceptual model. This is frequently done for purposes of data efficiency, visual simplicity, or cognitive efficiency, and is acceptable if the distinction between the representation and the represented is understood, but can cause confusion if information users assume that the digital shape is a perfect representation of reality (i.e., believing that roads really are lines).

More dimensions

List of topics by dimension

See also


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