Formations are Solutions

If it is tractable it can be constructed

This page has a number of concepts that all add up to something meaningful. The best way to work them is to realize that what you have been taught as mainstream science is a bunch of pronouncements with silly conclusions. For some of you, mainstream science is warped so bad it borders on conspiracy. In any case, you decided to push the reset button and see if you can come up with something better. You want to set the context to 'placement and movement' and continue on.

The first two items deal with a continuum -- what makes a continuum into continuum and what is but an overlay.

The third item is simple but it is only an intro to a more complex issue: dependence and independence of variables. This is a very new topic and "foreign" to science: it deals with reversibility. Rising temperatures may increase the consumption of ice cream but the increase in the consumption of ice cream will not increase outdoor temperature. A mainstream scientist cannot even begin to address this and probably never will.

The next two items deal with tractability. In essence, you send scientists packing every time they claim that the solution happens eventually. You see, you do not complain about some conspiracies because you want to get to another solar system in a week, and not in a million years. You do not need a scientist (or anybody else) to tell you what cannot be done because everything and anything can be done tractably.

You are now in the second section taking a second step on the track toward quantum mechanical gravitation. The previous section introduces momentum creation and it may be worth your visit there.

The book you will thoroughly enjoy:
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To move within cosmos, you will need to figure out how the universe is organizing. You will discover that certain things are formal while others are informal (associative). You realize that the associative domain (the virtual domain) actually exists in the universe and it has no distance parameter. You are on the right track.

TwoA. Distance-Time Overlay

When bodies are well defined and are far apart, they travel on a smooth path and we have no difficulty associating continuous time with their travel. Here is where we feel most comfortable because general solutions exist and we can calculate what will happen to the bodies. Time can be used to foretell the trajectory because the path (distance) has a mathematical solution. Two-body solutions are circle, ellipse, parabola, and hyperbola. Another way of looking at time is that periodicity exists and things eventually return to the same spot

If the mathematical solution exists, the path can be computed on ahead because distance and time are linked through a formula. Since the formula relates time to distance and distance to time, we can pick either one to obtain the other. We can, then, speak of distance-time linking, or a convergence (conjunction, union, synchronization, commutation) of spatial distance and time. One can also speak of distance-time continuum if the definition of continuum is weakened

Mathematical solution results in the distance and the time to be linked up through equation and distance-time overlay is a good way to describe any and all mathematical solutions of moving bodies. Time overlay signifies that time can be used to make predictions because the (polynomial) solution is available

We can also say that the periodic behavior of an atom points to high degree of computability within the atom

How far is "far apart?"
Think of some variables that are small or (almost) independent. Classically, "far apart" means that any body can be represented by a dot. In QM Gravitation this is no longer appropriate since the gravitational granularity is that of an atom. If we use a dot as representing any body, we cannot explain spin, for example. (Newton introduced the point representation for a mass body once he figured out the gravitation at the surface of a planet is the same as if the entire mass was computationally represented as a point of the same mass. This works because the gravitation measurements do not really happen below the surface of the planet. Newton's simplification works only above surface.)

Can there be time without periodicity?
Time is defined by periodicity. Or, time is a derivative of periodicity. Time is always a dependent variable -- time can only appear to be independent if a (polynomial) solution exists. Time is forever only as long as the polynomial solution is forever

What's the big deal about atomic computability?
Think stability under adverse conditions

What is computability?
When there is a mathematical solution then the embodiment is computable and tractable. Without a mathematical solution the computational methods are either approximate, irrelevant, or take so much time they are intractable (non-polynomial). Intractable "solutions" do not represent the system in real-time and, therefore, cannot emulate (model in fidelity) such systems. Intractability offers a "solution" that is not practical -- such as getting to another solar system in million years. Yes, there always exists a tractable solution because (1) all real things are finite and (2) all virtual thing (are infinite) but can be placed in superposition

TwoB. Continuum

Continuum is a meld of (usually) two variables that cannot be separated. Momentum is a product of mass and velocity, for example. Because (1) momentum is a moving energy and (2) energy is conserved, the product of mass and velocity (momentum) is also conserved. Therefore, mass-velocity product holds together in a continuum and mass cannot be classically manipulated to become zero, for example. Also, a particular amount of momentum can be composed of various masses and velocity values that multiply to the particular fixed amount. Momentum is a mass-velocity continuum

The virtual electron is a continuum of spatial volume and energy. [You may want to look at de Broglie's wave equation relating momentum and frequency. Frequency is wave's energy just as momentum is moving mass energy.] Virtual electron is a pocket of space-energy continuum. The interaction of the virtual electron with its environment is a function of both the volume (shape) and the frequency of the virtual electron. Changing the shape while keeping the energy (frequency) the same yields different interactions (wavefunction changes). Spatial volume and frequency of the virtual electron are inseparable, just as mass and velocity of a real (moving) object are inseparable. Virtual electrons are also about geometric shapes, forms, structures and topologies where interactions can produce computable as well as learning (one-time) entities [advanced]

Continuum, being based on the conservation of energy, cannot be broken or destroyed but can be transformed as a whole. Space-time continuum is an often used phrase but it is not a continuum because it does not include energy that guarantees the continuum to prevail as continuum.

 To Publisher...
Only energy can form a continuum with another parameter.


How is it possible to maintain space-time continuum or speak of time as being the fourth dimension?
You are too smart to be a patsy to general relativity. If two things make a continuum then by definition they meld together and cannot be separated. Time readily separates as a variable during collisions and in all chaotic interactions. Time also cannot be an extra (independent) dimension because we cannot move (increase/decrease) time independently of other variables. Continuum remains a continuum only if energy is a part of the continuum. Spatial distance or time do not have energy components

It is easy to break or tear distance-time continuum if the distance-time continuum is not a continuum in the first place. Also note that quantum mechanics differentiates quantum vacuum (space) from spatial distance. Spatial distance deals with measured magnitudes

Much evidence exists that one can travel in time. People described visiting old places that turn out to be historically accurate.
Data or information is a form of energy (virtual energy) that is conserved. There may be some who have the talent to read the past but it is a read-only (intangible data) environment. Time can serve as a thread in the record to access other data. Time is just one of many variables in the record and, if ignored or blocked [advanced], one can retrieve an overlay of historical data. Could one create a fictitious record for someone else to find? Could one think he is accessing old records but in fact it's a fantasy? If so, you may want to validate what you get and stories that cannot be validated such as Atlantis then continue to be just that [Thera?]

If an object disappears and then reappears someplace else, does it violate space-time continuum? My guess is that it does.
Sure does. You will note that the basic definition of continuum relies on the conservation of energy. Neither spatial distance nor time contain energy and, therefore, cannot form a continuum. Discontinuous movement violates the presumption of space-time continuum but does not violate Newton's absolute distance and time because in Newton's framework the object has unambiguous trajectory even though it makes discontinuous jumps.

In this topic, continuum holds only if energy is included

TwoC. Physical Contact

Collisions happen whenever bodies come together in one place. If bodies do not crumple (crumpling dissipates momentum as heat), colliding bodies instantly recoil and instantly change direction as well as speed, all as a result of conserving the combined (total) momentum of the colliding assembly

At this point, however, we need to reevaluate our cozy feeling about time. Discontinuous effects happen because the conservation of momentum prevails. The conservation of momentum is so dominant that all other smooth aspects of velocity, trajectory and time subordinate themselves to the conservation of momentum. In fact, we do not need time when calculating the before-and-after effects of collisions because everything happens in an instant and we do not need time (continuous or discontinuous) to get correct result. Mathematically we say that the description of a collision is not a function of time

Time follows (subordinates to) the conservation of momentum and readily makes itself zero



If time follows other variables then how can time be an independent variable?
Yes. Time is not an independent variable, and cannot be or become independent.

If time cannot be moved forward independently of other variables, how can anyone make a prediction?
Leading variables continue to dominate into the future. Momentum is a leading variable and knowing its value much can be forecast. One can also build variables into independent variables that will then dominate into the future.

Time cannot be made into an independent variable. We can successfully forecast the start of the next baseball season but it is only because the organized infrastructure is in place.

TwoD. Chaos

When three or more bodies come close together and interact gravitationally, the conservation of momentum again prevails. Bodies begin to move in ways that are not computable and their paths are not predictable. Time appears (and is) continuous because the body's trajectory is continuous, but there is no general solution to the gravitational interactions of three or more bodies. Mathematically we say that there exists no function that can be computed (anytime we want and as fast as we want) to give us answers ahead of real-time. We can also say that there exists no embodiment or that the situation is intractable. Time is useless because if we insist on applying time, the calculated and the actual trajectories forever diverge. [Question: Does chaotic system have periodicity?] Things get a bit dizzy here and calling it chaos makes sense. Since we do not find chaotic structures in the cosmos, it is a good guess that QM Gravitation provides for solutions (provides for systems) that have certain organized outcomes or topologies

In chaotic environment the distance and time are not and cannot be linked through a formula. In chaotic context the distance-time overlay (space-time "continuum") does not exist

Classical physics has no mechanism that would diminish chaos. This is because in the classical mindset the non-polynomial problem, while solvable in principle, is not solvable for all practical purposes -- the Traveling Salesman problem being a good example. QM allows solutions to non-polynomial problems in a practical timeframe but the timeframe itself is not guaranteed


If time is a derivative of a periodic system, can we create periodic system by manipulating time?
Can you move an object by moving its shadow?

What really determines if a problem does or does not have a solution?
Think degrees of freedom. Very ancient and fertile though unexploited arena. (Pythagoreans accomplished much here.)

If there is no general solution then the outcome is not a given. If it is not a given that organization prevails over chaos, why isn't there more chaos in the universe?
Think QM's unbounded concurrency

If there exists no formula linking distance and time in a chaotic context, then how can nature compute what it does and man cannot?
Present computer cannot perform instantaneous (nonlocal) operations -- quantum computing is yet to come. Nature's own "limit" is at Planck's constant, which is a construction construct. This is a gateway question

We have a page on chaos, which is really about three-body instability. It also includes a new definition of the scientific method

TwoE. Completeness

Nonpolynomial problem presents a good example of intractability. For such problem in general, when we increase the number of members in a system by one, the new member relates to every other member in a system and to completely describe such new system becomes practically impossible. If there is a system that takes one year to describe, then for every 1,000 fold increase in processing speed, for example, the size of the system we can completely describe in a year may increase by a scant 10 percent. Moreover, even though the size of the fully described system increases, the number of members is nowhere near the number we need for practical-size systems. It makes sense to call nonpolynomial problems intractable: Relationships within the system can be so numerous that relationships cannot be tractably processed to obtain a solution or an update. In summary, arbitrary addition of a new member can change the composition of the system to such extent that we must start from scratch rather than build upon the results obtained from previous systems descriptions

To guarantee a solution of a nonpolynomial problem is to attack it systematically and exhaustively. Starting from scratch and leaving no stone unturned is the price of a guarantee. But, even though we know there is a solution, we also know we cannot get the solution soon enough. Yet we need a solution. Whoever can process practical quantities of influencing variables in practical timeframe will not only be able to come up with a solution, but will also be able to come up with a better solution

Scientific concepts use the property of completeness without hesitation. If intractability arises with the completeness construct, and it often does, further development of such concepts becomes limited or impractical. To the classical scientist system completeness is something that is achievable and something that can be repeatedly and predictably measured. Classical scientist, however, ignores the fact that completeness can take forever to formulate. Because the measurement is the scientist's tool for achieving completeness, classical scientist cannot accept the possibility that measurement could be impossible, unpredictable, or detrimental (when the superposition of states is affected). This is the core of the mystery of irrational numbers. Irrational number's magnitude (mantissa) is infinite and, therefore, intractable. Ignoring intractability leads to "good enough" truncation but then the irrational number is no longer irrational.

Study of quantum mechanics leads to the conceptualization of the real and the virtual. In the real domain we measure. In the virtual we compare and relate -- that is, we relationally compute. The measurement results in one answer whereas relational computing (reputing) results in a list of all possible outcomes. Such list can then be prioritized based on relevancy. When possible outcomes reduce to one, we have a solution

Reputing is not about the consensus of ways and means toward accomplishing a desired outcome because reputing is about many and various influences that are relevant to the situation at hand. Reputing quantifies the relevant negative (detracting) and positive (supporting) influences we are subject to. Reputing also quantifies relevant influences that issue from us (outfluences) and that support and detract others. Reputing does not exclude the accomplishment of an objective and reputing does have a purpose. Reputing allows the review of all possible outcomes and if the outcomes are not close to the desired ones the influences need some work

If some method leads to intractability then we should abandon it. QM formalism is intractable, so let's toss it.
Quite so. QM becomes intractable if we try to describe it with real methods such as the if-then method. We should distinguish between a solution that is polynomial and a solution that is not. The existence of a solution as such is not sufficient because nonpolynomial solution is useless. [If you have a problem with "solution per se is not sufficient," then differentiate and come up with two new words: one that stands for a polynomial solution and one for non-polynomial.]

Meanwhile, keep on looking. QM's property of superposition (inclusiveness), which is not possible in the real (exclusive) world, is very much a helper in QM because the concurrency is unbounded and ..

Alchemical Note:
The meaning of a reduction in Alchemy is to reduce the potential set of solutions by increasing the quantity (and/or range) of relationships rather than by member exclusion because exclusion yields no solution. When engaging computers instead of flasks, a more appropriate term for reduction is reputation (n.) or repute (n., v.) since we seek to quantify any and all influences. Reputing is, technically, Relational computing

Condensate is the solution if solution is the condensate. If you say you will know it's a solution when you see it, you need more work. Solutions must be sought to be seen

TwoF. Organization

Our solar system (Oss) is indeed one of the multi-body solutions that for the most part is not chaotic. Real solution is a solution that is computable in polynomial fashion. We can also say that real methods are applicable because all computational resources (parameters) become localized and can be measured. In addition to spatial distance, localization includes periodicity and, therefore, another time reference is born

Without a topological solution the multi-body system is intractable. We can now say that the reason there exists no function that would describe the chaotic system is because more than one solution is possible – that is, chaotic system contains multiple solutions. Because no one solution is clearly indicated the system is not computable. Moreover, chaotic system contains more than one solution and does not have zero solutions. Entering a new territory, we no longer lament our inability to describe the chaotic environment, for other computing methods besides intractable methods can become available

All classical scientists start at the point of the organized assembly (problem is already solved) and describe moving or orbiting systems as they found them. HyperFlight takes advantage of the organizing knowledge and to get to HyperFlight, we will need to understand how matter organizes from potentially chaotic to specifically organized assemblies

To diminish chaos, one solution of QM Gravitation calls for large planetary separation and a massive central body forming two-body (sub)systems with each planet. The goal is to minimize three-body chaotic systems. (Also consider particular orbital ratios in helping to merge many bodies into one -- think harmonics in general and the octave in particular.) Another solution calls for a dual-sun system which, again, is a computable two-body system. One-body solution is also computable in a polynomial fashion and this solution applies to a "piece of rock" moving in a straight line in the absence of other bodies, and also applies to other single-body geometries where (if) plurality of bodies move as one body

It is obvious to some that every star is a component of an organized system and, with our propensity to name things, it is curious we refer to our solar system as 'our solar system' while all other suns (solar systems) have names. It then makes perfect sense to call our solar system The Oss ["The Awesome"]

How can we localize something that is local already? Distance is local and it cannot be localized!
Think duality. In the virtual domain, spatial distance does not exist as a variable. If an entity materializes in a context of a reduction (or a solution), spatial distance becomes one of the variables we must contend with. Localization of spatial distance, then, happens during (or as a result of) a transition from virtual to real.
Spatial distance indeed is and remains local. Consider that the real and the virtual are separated by a discontinuity and exist side-by-side (and are always engaged)


TwoG. Disappearing Body

The conservation of momentum is not violated if, for example, one body disappears instantly and two or more other bodies instantly appear in the same system with their combined momentum matching the one that disappeared. Similarly, several bodies can instantly disappear and many other bodies appear bearing the equivalent momentum of all disappeared bodies. The idea of disappearing bodies seems preposterous, yet it can and does happen with particles the size of the electron. What the possibility of disappearing bodies suggests is that real mass subordinates to the conservation of momentum as well. (Real mass is our everyday mass with measurable properties.) What is happening here is that if a reversible transformation happens in the context of energy conservation, interesting things happen

Here is a good example of the mechanics of reputation (relational computation). We observe the dominance of the conservation of momentum so many times under so many different circumstances that we can postulate the subordination of real mass to momentum conservation. No equation can bring you here because we were reputing, but an equation can possibly start here (if we have a solution)

Real matter does not disappear when it subordinates to the conservation of momentum. Rather, matter can transition from the real to the virtual domain, and back again. We can also add that the transition of matter from virtual to real is none other than localization within the framework of a reduction (reputation) or a final reduction (condensate) of a solution. It is a good guess that localization of matter is not arbitrary because reputation decreases chaos. Real matter can, however, be destroyed if its atomic constituents cannot remain in a computable (reputable) state

Moving body has real momentum and if such body disappears on its own (without system consideration) then body's momentum must be conserved by transformation [advanced]

How can one possibly come up with a solution that governs a periodic and synchronous movement of billions of solar systems in a galaxy?
Think two separate yet connected domains. One real and periodic and the other virtual with infinite concurrency. You may want to rethink the Aristotelian view of infinity

What gives a system the property that momentum can be conserved within a system rather than insisting that each body conserves momentum of its own, on its own?
Consider that two bodies make the smallest workable system -- workable in terms of momentum conservation. Momentum cannot be created without adhering to momentum conservation and at least two bodies are needed thus forming a system of at least two bodies. This is also a good question because there is a tendency to use 'action-at-distance' as the "proof" of the existence of ether. Hold off on that and think of ether as passive (homogeneous) entity.

Why, if momentum dominates, there is so little information about it?
Overall, there is much information available about planets being in line-of-sight alignment with earth but there is not much data showing how planets altogether line up with respect to sun, which is a topology of greater dominance. Planetary visualization with respect to sun would yield most stable (in-line) and least stable (three-body) positions. Momentum of planets are not available right now from any simulation programs but a teen-age publication Odyssey published planetary-moon (secondary) momentum directions. Also, much insight can be gained if planetary orbits are considered as ratios of our musical (Pythagorean) octave

TwoH. Accelerating Body

We can see that if momentum appears within the system such that the total momentum of the system remains the same, we will also subscribe to the conservation of momentum. Momentum appears as a moving energy. In other words, objects can accelerate or decelerate and thus their own momentum increases or decreases (mutual momentum changes). While the sudden and ongoing appearance of acceleration fits well into the framework of the conservation of momentum, this postulate is clearly technical. If we think about the way of actually implementing the instant appearance of momentum in the context of the total momentum conservation, we will also need certain knowledge that keeps the account of the energy and where it is located and under what circumstances is the energy easily released. We will also require the increase and decrease of momentum to be instantaneous across the system because we need to conserve momentum at every conceivable instance of time within such system. When a unit of momentum appears, identical and opposite unit must appear at the very same instance someplace else within the system.

Total momentum is conserved within the system but then the idea of transforming into virtual domain offers the opportunity to move rapidly in a logical fashion. The conservation of momentum continues to hold in the virtual domain but the conservation now must hold computationally


You may have noticed that QM Gravitation always deals with two or more bodies. A single lone body cannot begin to move or spin because it needs other bodies to exchange momentum with, and do so in a way that conserves momentum.

QM Gravitation provides for solutions that result in several formations or topologies. There are eleven major topologies such as planet in orbit, planetary (multi)ring, barred galaxy, and galactic superclusters. All topologies result from dominance of certain variables and this site calls the topologies HyperStates

If you feel comfortable with the preceding topics, there is another, more intense compendium of topics regarding gravitation and the outcome (or purpose) of gravitation -- organization. It has more references, too.

"Can you reduce this to practice? You are in a spaceship as a real entity and are accelerating at a rapid rate. The real momentum you are just gaining must have been realized someplace else and must be happening in the opposite direction of your own. If the other momentum was realized at another planet, such planet would hardly move but you could be accelerating at 100 Gs or more as every atom in your body and your spaceship is receiving the same momentum."


"Hi, Geo."

    "Why isn't the universe composed of just two bodies?"

"Nice. There is something to it. Why do you think it would be only two?"

    "Or just one body. One giant hollow sphere in 3D."

"As in 'Bigger is better?'"


"Georgie, the sun at the center strives to be bigger and bigger because sun wants to have more and more orbiting planets."

    "Why more planets?"

"Orbiting planets give the solar system angular momentum or spin."

    "Does the solar system then have greater .. staying power, like the spinning top?"


    "But you did not answer my first question, Daad."

"Sun is composed of atoms that themselves are organized with electrons and protons. When the sun gets too large, atoms cannot remain organized and the whole sun blows up in a supernova."

    "You are kidding."

"I wish I could."

    "So what happens next?"

"Solar systems, instead of growing bigger on their own, collect into even larger and organized assemblies."


"Take a peek at Concept Three."

    "But wait. Are you saying that sun can figure out it is getting too big?"

"You said it just right. Sun can figure it out but it is not a given."

    "But how, Dad? Tell me how!"

"We've got to get the move on."

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Last update March 1, 2010