Examples of the 4th Dimension

This is a thought that just popped into my head after reviewing my last post. Right off the top of my head, I picked out two candidates for the fourth dimension of space; Scale and State. The underlying principle used to distinguish them was a concept that is spatial in nature, that lies beyond the immediate scope of a volume. Technically speaking, a four dimensional space can theoretically contain an infinite number of volumes, much the way three dimensional space can potentially contain an infinite number of surfaces; what we typically experience as the expression of two dimensionality.

To illustrate, in three dimensions, you can observe a large, but presumably finite number of spheres populating space. Any given sphere can be broken down into onion layers, infinitesimally, discounting the plank limit on matter. In terms of energy shells, however, like magnetic fields, the illustration holds up. The upper limit for the size of a magnetic field is the sphere of three dimensional space itself.

Our concept of space is object oriented, dominated by the nature of vision and physical movement. That is, our perceptions are limited by the context of our bodies, which we generally think of as three dimensional. The notion of higher dimensions led us to the concept of hyperspace and objects like a hyper-sphere, the descriptions of which seem paradoxical. For example, hyperspace can be described as a place with an infinite, unbounded volume on it’s surface, and in each layer you slice it into–which you can do an infinite number of times.

It’s an expansion of the concept of a number line, where you can have an infinite number of points between any two established points. Say, zero and one. Of course, if you happen to be a point, this linear property is inconceivable. So it is for us, trying to think of four dimensions of space. Even so, we can glimpse and recognize the fourth dimension when making observations of changes in state or scale.

A dimension of scale is demonstrated by the onion layers example, and it is bi-directional, or polarized, like the three dimensions we are most familiar with. An object can be scaled up or down (in some cases you might think of it as in and out). It bends the mind a bit to imagine things scaling up or down to infinity, especially when you consider the alternative, a finite but unbounded line–a circle. In a loop, the infinitely large scale seamlessly meets up with the infinitely small scale, revealing that their differences are only apparent at a distance from each other.

Side by side, they end up being equal.

Mind boggling, isn’t it? If it isn’t, then consider the fact that the entire universe is a scaled object. The universe, and everything in it, is built to a specific measure, which we’ve identified as a plank unit. The only possibility of a universe achieving a true change in scale, would be an instance where the scale of the plank unit is higher or lower than what we are bound to. The thing is, you cannot tell from within the universe if the plank scale changes, because everything else changes relative to it–unless you observe it from outside the universe.

Like many things, the scale of a universe is best observed from another position–in this case, another universe. A change in the scale of your own universe would only become apparent if you observed a global change in scale across all observable universes, indicating that it is not their scale that is changing, but your own. Of course, by introducing the possibility of change, you have really entered the realm of things that are defined by state.

The concept of a state is one we are familiar with, because we experience change. Take into account the association between space and time, you can say that state is the particle of time; the infinitely divisible singularity with an intrinsic value of both zero and one. That is, existence cannot be reduced to less than a state. If you discount all of time, or isolate the most finite instant, you enter a state that does not change. Call it the zero state, or call it now. Or, call it eternity.

They all end up being the same thing.

Focusing in on states and change makes thinking about time easier. Time is a concept evolved from the experience of change, and it only becomes possible when you are dealing with something that can have more than one state. By thinking in terms of state, you can get over the paradoxes of loops, circles and cycles of time. As beings with more than one state, we commonly return to known states.

If you can make rational sense of something like going to sleep each night, or waking up every morning, you can cope with the possibility of revisiting a point in time. The main difficulty we have with the concept of time travel is tied to the polarity of logic; cause and effect. To return to a point in time, there has to be more than one chain of causality leading to or from any moment in time. The trick lies in finding the paths, and knowing how to enter or exit a moment on these different paths.

Things like the grandfather paradox dissolve when you account for the vectors of the moment. Assuming you found the path to sync up with your grandfather, before your birth, you would already be moving in a construct with multiple pasts and futures for any given moment. Killing your grandfather does not negate the path you followed to get there, but the moment of that killing is a deviation from that path.

One branch of reality accounts for the events leading up to your birth. Another branch accounts for the untimely death of your grandfather. You end up with two instances of reality that are co-equal, even though they may become radically different because of the consequences of moving through time. Reality becomes entirely relative, dictated by choices and actions the participants in any situation make, regardless of how they got there. Because they exist, the have the potential to be alive or dead in what might outwardly seem to be the same time.

This last part is where much of the difficulty of temporal thought lies. Our participation in the universe is both objective and subjective. Our actions have consequence, and our lives are shaped by the consequences of our actions. Some kind of relative distance is involved; a bit like being in or out of phase with particular events. Taken together, phase and state are both spatial aspects of time, which remains discrete from, but inextricably involved with space. Account for our involvement, and you have a universe with three distinct media; things we conceive of as space, time and mind.

You really don’t get a viable existence without the integration of all three aspects. They blend together into a single continuum, with seamlessly smooth transition gradients in one direction, and hard, high-contrast boundaries with exclusive domains in another. In our three dimensional world, they seem to stand apart. Perhaps in the fourth dimension, they all blend together into the same thing. If you really stop and think about it, asking where is space? and when is time?

For us, it’s all in our heads.

Musings On Physics & Metaphysics

A lot of time has passed since I had the impulse to post anything; that does not mean I stopped writing my thoughts down! I came across the following on a buried tab in my Notepad++ application. I have tons of random notes like this, and often do nothing with them. I mean, they’re not really intended for the average reader. You might not be able to follow it, and I don’t really know what parts need further elaboration for you to grok them. Even so, I can still throw them out there and hope that you will comment or request explanations if you need them. I can preface this text by saying it’s things that have been on my mind long enough to move me to jot my thoughts down. This is stuff I want to follow up on, and some of it references other notes I’ve made or published. If you’ve caught up on the Eye of Paradox posts, you should be able to follow much of this.

Thoughts

Before delving into my record of study, there are a few thoughts I need to put down concerning my interests at the moment. Several topics have been on my mind, ranging from a desire for a better understanding of existence, through several concepts that keep returning to mind and on into an interest in seeing if my weird inspirations may come of anything. Things I think I need to study include the hierarchy of mathematic concepts–the things you need to know, in the order you can best learn them, to understand the hard sciences, the modern concepts of dimensions and media in practical use–as well as a summation of my own take on those topics, and a more general review of concepts in practice versus my own ad-hoc usage.

Recent thoughts have included (but are not limited to):

Divide by Zero, which piqued my interest way back to the first time someone said it can’t be done. I played with the idea, in the abstract, as a question of perspective, but I come back to the little experiment I did with a calculator, taking a given number and dividing by increasingly small orders of magnitude between 1 and 0. The calculator promptly spits out results (in comparable orders of magnitude) of increasing value. Presumably, the ultimate result confirms the opinion (I don’t have a specific citation) that any number, divided by zero, becomes infinite. Which takes me back to one of my first assumptions, and my later conclusion that existence encompasses absolutes.

Dividing by zero doesn’t really break mathematics, it just points to interesting things that bear further consideration. One case in point, is that even in the universe, infinite values can make sense provided you address (interpret) them properly. Take a distance between two points (arbitrarily of any length) and divide it by zero; an infinite result seems counter-intuitive, but it’s an infinite number of parts with zero length. An infinite number of points are possible in any line, mathematically, or in space, dimensionally. To follow up on the real-world implications, I would need to find out what theoretically (or experimentally) happens when a real world value is divided by a plank unit, in a conventional scale (probably time or distance, since those are infinitesimal numbers). [This is where it’s really helpful to have a subject matter expert to converse with; then I could just ask if (and how) physicists deal with massive values resulting from division by infinitesimal values.]

Infinite Values in Finite Systems, which is clearly a derivative line of interest that I started to address with the automatic inclusion of a dimensional reference in any system. It’s been while since I thought about dimensional concepts in detail, but I can still grok the general breakdown of systems into finite-bounded-unbounded-infinite contexts at varying levels of dimensional complexity. I still maintain the practice of distinguishing between media when applying dimensionality to concepts and models. I find the distinction of media essential, though it becomes necessary to address the difference in application when addressing the universe, as my practice is different conceptually and interpretively from the established practices in math and physics. I used to waste time arguing that time is not the fourth dimension, which runs to an entirely different topic.

The point is, a more articulate and rigorous definition of dimensions is needed. In general, the dimensions of an expression can be thought of as the number of coordinates of equivalent measure necessary to account for any object or the intrinsic framework of that expression. In space, three-dimensions are sufficient for the expression of a volume, which can be measured according to height, width and depth–all three measures equivalent to a measure of length or distance in one-dimensional units on perpendicular axes. The spatial example of dimensionality presents an (implicit?) argument that the next dimension up from a given dimension overlies and extends ninety-degrees outside that dimension. A zero-dimensional space is a point (and carries the property of position). A one-dimensional space is a line (and measures distance). A two-dimensional space is a plane (or a surface, and measures area). A three-dimensional space is a volume (also measurable as a depth).

To continue in this manner, a four-dimensional space would be a depth or volume extending beyond (perpendicularly, “above” and “below” or “in” and “out”) from the working volume. The concept of dimensions is applicable to more than just space, however. The reason for introducing the distinction of media can be made clear, along with other applications of the concept of dimensions in other contexts (and maybe replacing the use of media with context is more explicit?), together with the implications and potential of interactions between different media… well, there’s always something churning through my mind on this. As far as infinite values in finite systems go, I still have this intuitive/instinctive sense that it’s a huge, blinding sign of a dimensional transition; sort of where things take a step up (maybe a step down–or perhaps in/out) from the established (select) frame of reference. [I have got to do a brain dump on dimensions; it’s really overdue.]

New Modeling Methodology, which is presently a quantum-cloud of notions derived from my eclectic pursuits. I dumped a rough hash of the idea on the Filter Forge forums, positing a unification of things like multi-domain, multi-dimensional coordinate systems with intrinsic properties (hidden dimensions) suitable for rendering, rigging and animating models with the addition of vector traits controlling curvature, gradients, volumetrics, etc., with material properties necessary for a truly physics-based modeling and rendering system. It’s sort of a fusion of modeling and programming that features hyper-dynamic meshing and massively-multidimensional data arrays to produce objects with virtually infinite mesh resolution, in both curvature and gradients, possessing intrinsic simulation characteristics, limitless modeling flexibility and morphology through the implementation of proportionality frameworks. The list goes on. Call it Virtual Body Dynamics. It’s the sort of project I can keep dumping new ideas into as I pursue other interests. A lot of work, but it could often be fun!

Conjunction Engines, Etc., or what can be accomplished combining…. This is a relatively new pursuit, though it’s driven by a long practice of pondering fantastic mechanical notions. At this moment, I’ve been wondering if a practical engine (or motor or generator) can be designed that combines principles of thermo-dynamics, thermo-electrics, piezo-electrics, photo-electrics, cryonics, magnetics, super-conductors, or even zero-point energy in ways that would make for a more powerful and portable solution to a number of inefficient technologies we use today. This is more a pool of questions that need to be asked, than a pointer to any particular project. I just can’t help wondering about things, and musing about what could be possible if some of these questions could be answered.

Some of the recent queries include: What kind of energy could be pulled out of a system that used atmospheric nitrogen in a cryogenics driven cycle (methods?) and thermo-electrics? What happens to magnets at ultra-low temperatures (rare-earth or electromagnetic) and what happens to the force itself (changes in strength?)? Can cellular magnetic bottles be constructed? How strong/granular can they be? Could you build circuits using super-conductive material (and or use them in a cryo-reservoir of nitrogen)? What if you generated an ionic breeze across the top surface of a wing? Is liquid nitrogen compressible? How would you filter pure nitrogen out of the atmosphere? Are virtual particles the same type/variety as real particles? Do real particles ever trade places with virtual particles? Can that explain the motion of real particles at the zero-point?

Taking a closer look at the concept of Space-time, does that concept imply a conversion between space and time? That question arose from the implications of a conversant coordinate system you would expect from a proper application of dimensionality. From recent reading, I’ve confirmed that the four-dimensional continuum of General Relativity consists of three-dimensions of space and one-dimension of time, so the distinction I make between media is upheld to an extent. The curvature of space presented in physics is observed in the three-dimensions of space, with the included context of time, as evidenced by the paths taken by light near very massive celestial objects. I’ve struggled with some of the illustrations of this principle, which in some cases imply that space curves in toward massive objects; in which case the path of light would return to it’s original heading as it passed back into relatively flatter space. The case that seems to exist is that space curves around a massive object, so a light source appears to shift out from behind a massive object as it is actually passing behind it, within the limits of the gravity-lens and the alignment of the light source and massive body.

The curvature of space remains an interesting notion, to me. I want to be clear if and how the curvature of space is actual or apparent. In true curved space, as evident in two dimensions, a line within a plane remains straight by one-dimensional rules even if the line curves within the plane, by two-dimensional rules–or even if the plane containing it is bent in three-dimensions. The curvature of the line requires at least one higher dimension into which the line is projected. So, the curvature of space associated with gravity indicates that a fourth spatial dimension (at least) is in use. Three-dimensional perceptions would record effects with no obvious three-dimensional explanation, with only volumes and their surfaces apparent in open, flat, volumetric space that is perceivable by three-dimensional rules. The bending of light at the interface between the vacuum and matter is another case of a possible dimensional effect. Is it another example of curvature, viewed as bending by virtue of the scale of the object (properly, the zone of influence)?

Related reading on the mass-energy equivalence has also touched on the assertion that the energy in an object-system contributes to the gravity associated with it. If mass is viewed as a measure of energy bound in the structure of particles and atoms of the object-system, the focus shifts to the questions of precisely what is structured, and the balance of energy distributed in the bindings and components of that structure. The creation of the balanced system that is matter must consist of something more than just the energy invested in the process; something besides energy goes into the system, even accounting for the fact that matter is composed mostly of empty space. The substance of that structure is registered through the interaction of the forces present in (or represented by) the particles within the matter. A general assumption is that the particles arise from the quantum foam, precipitated out to some point where they survive the perpetual flux. The question shifts to the underlying fabric; the volume in which the fundamental forces present and interact. So, is it all about space?

Another implication that bears further investigation is that of virtual particle precipitation at the quantum level. A few related questions are: How do they create anti-mater? How is space created, whether in the Big Bang, through Inflation, and in the case of Expansion?

Our understanding represents a variable limit to the true extents of existence. Courtesy of the use of language and mathematics, individual understanding can extend beyond our experience, so we tend to operate withing the limits of human understanding. Instinct, in animals (and even in people) can also allow for action that exceeds understanding or comprehension, while intuition can highlight possibilities worth exploring. Physics is framed in the context of science, through methods of formulating and testing ideas held under the pretext of knowledge, providing us with a core of practical understanding to counterbalance the unrestrained scope of imagination, which is what truly takes humanity to the furthest limits of understanding experienced in our individual and collective minds.

The origin of properties need to be addressed fairly early in my reading. I need to understand how physics defines and describes the origin of all fundamental properties, whether they are forces or attributes. Energy, which can neither be created nor destroyed (as a conserved quantity, and merely changing form or state), stands out as a true fundamental property. It provides for the possibility for change. As for the possibility for something that is, and what it is that would be changed, the next, immediate fundamental property would be some expression of state.

Of course, to really fix the state of energy, some kind of structure is necessary. Space-time has an origin, in practical terms, in the Big Bang. Some kind of place is implicit as a fundamental property, if only for the fact that space-time occupies a place in existence, even if it is impossible to be explicit about where a fundamental place actually is. As humanity exists primarily in a subjective state, we’re inclined to posit an objective state as fundamental to reality. Our perspective is seated firmly within our individual minds, through the lenses of our bodies and brains. As objects in and of the fabric of reality, the only certain place we can reduce existence to is the flow of information across the threshold of brain and mind.

As far as we’re concerned, the mind is the place where existence happens. Physics points us at the structure underlying the transaction between each mind and the universe it is accessing. In any case, there is a reason I view space, time and mind as the essential media for the expression of the implicit fundamental place. To be clear, I am addressing the mind apart from the neurophysics at play in the brain underlying the conscious state. In general, I have been fascinated by the subjective states we call the mind, particularly the awareness present in the resolved field connecting conscious thoughts, imaginings, perceptions, emotions and information, et al, of the gestalt.

The universe may exist independently of us, but for us, there is no universe without the presence of the mind. Though we are small-scale participants, we are large-scale observers. Most of the universe lies outside our personal scope of perception, so we can’t really say that our observations are required for something to exist–for an event to occur. We do, however, exploit processes by which the universe resolves itself. Our existence, dependent on the property of awareness as it is, points out–at the very least–that awareness is a property fundamental to us. It’s not a huge stretch to guess that it could be a property fundamental to the universe or existence itself. The big picture implicit in a universe rendered in infinite detail has to resolve somewhere.

Reading & Clips

In physics, mass–energy equivalence states that anything having mass has an equivalent amount of energy and vice versa, with these fundamental quantities directly relating to one another by Albert Einstein’s famous formula:

Given the equivalence of mass and energy expressed by Einstein’s E = mc^2, any point in space that contains energy can be thought of as having mass to create particles. Virtual particles spontaneously flash into existence at every point in space due to the energy of quantum fluctuations caused by the uncertainty principle. Modern physics has developed quantum field theory (QFT) to understand the fundamental interactions between matter and forces, it treats every single point of space as a quantum harmonic oscillator.

According to QFT the universe is made up of matter fields, whose quanta are fermions (i.e. leptons and quarks), and force fields, whose quanta are bosons (e.g. photons and gluons). All these fields have zero-point energy.[2] Recent experiments advocate the idea that particles themselves can be thought of as excited states of the underlying quantum vacuum, and that all properties of matter are merely vacuum fluctuations arising from interactions of the zero-point field.[10]

Zero-point energy (ZPE) or ground state energy is the lowest possible energy that a quantum mechanical system may have. The term zero-point energy (ZPE) is a translation from the German Nullpunktsenergie.[9] The terms zero-point radiation or ground state energy are also sometimes used interchangeably. The term zero-point field (ZPF) can be used when referring to a specific vacuum field, for instance the QED vacuum which specifically deals with quantum electrodynamics (e.g. electromagnetic interactions between photons, electrons and the vacuum) or the QCD vacuum which deals with quantum chromodynamics (e.g. color charge interactions between quarks, gluons and the vacuum).

A vacuum can be viewed not as empty space but as the combination of all zero-point fields. In quantum field theory this combination of fields is called the vacuum state, its associated zero-point energy is called the vacuum energy and the average energy value is called the vacuum expectation value (VEV) also called its condensate.

In quantum field theory, the vacuum state is the quantum state with the lowest possible energy; it contains no physical particles, and is the energy of the ground state. This is also called the zero point energy; the energy of a system at a temperature of zero. (Aug 3, 2011) Many physicists believe that “the vacuum holds the key to a full understanding of nature” [Davies (1985), p. 104]

Davies, P. C. W. (1985). Superforce: The Search for a Grand Unified Theory of Nature. New York: Simon and Schuster. ISBN 0-671-47685-8. LCCN 84005473. OCLC 12397205.