Random Vortexes

 

Alexander Liss

 

07/15/04

 

 

 

There is some similarity between turbulence in a stream of water, whirlwinds in the air, and person's thoughts and feelings.

An observer of these phenomena briefly discerns some local pattern and this pattern disappears; eventually a different pattern is observed and so on.

One could say that these patterns are figments of imagination, remnants of working of the mind, which tries different patterns until it finds an appropriate one. However, there is no consistent theory describing these phenomena and it makes sense to provide a theory, which could use our ability to describe local patterns of motion of water, air, or thought and feeling, even when these patterns can't be extended to describe the entire phenomenon.

 

Water

 

We start with the stream of water, because it benefits from our intuition the most.

To describe a vortex (a whirlpool) in a stream, one should describe a segment in a stream, where water moves in a pattern different from surrounding patterns, and one has to describe this pattern (direction of rotation, speed, etc.). A real stream is three-dimensional; hence, a segment is three-dimensional. However, we could work with two-dimensional models as well.

A segment could have a neighboring segment with a different pattern of motion, it could be inside a large segment, it could have smaller segments, etc.

A segment could move in the stream. One could observe a localized vortex-wave (segment) moving in a river.

Eventually, the vortex breaks into many smaller vortexes and disappears. In the description of this phenomenon, one describes changing in time segmentation. Instead of one set of boundaries, the other set of boundaries emerges. Inside each new segment, a new pattern is discerned. When vortex disappears, all boundaries disappear.

The change in segmentation is a flipping of the system from one state to another. Such flipping is caused by numerous small factors, which are not possible to enumerate or to measure. Hence, we are left with a model, where such flipping is assumed random. Moments of time and new segmentation are random.

Changing in time random segmentation with own pattern in each segment is a major element of the model.

"Random" does not mean that there is no information about the dynamic of change of this "segmentation with patterns". This dynamic is restricted and the restriction is described with a probability to flip from one "segmentation with patterns" into another.

Following are observations, which allow defining of this probability.

Higher temperature (local or overall) should create more events, which could cause such flipping of the state. Lower temperature should cause less frequent flipping and stable segmentation and vortexes. Stable segmentation and vortexes are observed in super-cooled liquids.

If the water moves in a segment in one direction and in an adjacent segment in another direction, then there is a higher degree of traction near corresponding area of a boundary between segments and there is higher probability that this boundary disappears in the next segmentation.

However, if there is some feeding of energy into a vortex, then it does not slow down because of traction and the boundary persists. A vortex could take energy from the stream and be stable. In calm water, there is nowhere to get energy and vortexes and boundaries between them quickly disappear.

If there is a "hard" boundary in the stream (for example, there is a body in the stream or there is a limit of the stream), then a boundary of segmentation (a "soft" boundary) could start from the hard boundary and extend into the stream. This start of soft boundary could move along the hard boundary.

A stream with vortexes has more internal traction and hence dissipates more energy into heat. Different forms of segmentation cause different degree of energy dissipation. It should be a pattern of segmentation, which causes minimal energy dissipation in given conditions.

Vortexes could cancel each other and an existing bound disappears. This is a predictable event.

Instead of a bound between two vortexes an entire new segmentation could appear, with smaller segments between original large segments. This way large vortexes break down into smaller ones. This event is only partially predictable.

A new segment - a small ball in midstream or a half-ball adjacent to a hard boundary, could randomly appear and grow. Water rotates inside it. These events are random, but the probability of appearance of a new segment only depends on current state of the stream (does not depend on history of segmentation).

Movement of the bounds of segmentation in relation to the stream or to hard bounds has a component, which could be predicted and it has a random component.

These observations provide a foundation for creation of a stochastic model describing dynamic of segmentation. It is reasonable to assume in this model that (soft) bounds of segmentation are smooth, except where they meet.

Temporary vortexes are broadly used for locomotion. Fish creates them with its tail and pushes against them. One could observe use of vortexes in row boating.

Sea creatures have scales or special skin texture, which creates a special segmentation pattern of the stream around them; this reduces resistance of water when they swim.

 

Air

 

Whirlwinds are usual in the air. They are visible, when they touch the ground. Their stability is assured either by a horizontal wind, by rising air or by downdraft from a cloud or along the slope of a mountain. A tornado is such stable vortex in the air supported by a downdraft from a cloud.

Vortexes in the air could be described using approach developed for vortexes in the water: segmentation of the space, pattern of movement of the air inside a segment, which does not cross segment's boundaries and random flipping from one segmentation with patterns to another.

Patterns of movement of the air in a segment are different from patterns of movement of the water, because air could be squeezed, but this is irrelevant to the construction of the model's foundation.

Random flipping of the segmentation in this model reflects an essential fact of too many factors affecting this flipping. This could be an explanation of notorious difficulty of the problem of tornado prediction.

Structured by feathers surface of birds create predictable vortexes in the air, which reduce traction and make flight steadier. Vortexes created by insects and birds in-flight provide lift and flight control. Vortexes created by control surfaces of airplanes improve flight control. New golf balls have dimples to cause predictable vertexes around them, which reduce traction and make ball's flight steadier.

 

Space

 

Gas in Space acts as air. It should be vortexes in it; we describe them the same way as vortexes in air.

However, the huge distances in Space and numerous unaccounted factors cause an assumption, that movement of gas in a segment is random.

If the Universe expands, than this expansion should support creation of stable vortexes. From the other hand, the presence of observed stable vortexes gives some support for the idea of expansion of the Universe.

These vertexes are precursors of galaxies, planetary systems, and planets with satellites.

Near an axel of a vortex, the speed of movement of molecules relative to each other is the slowest. This creates a bias, which favors random coalescence of molecules in this area. When coalescence reaches some level, forces of gravity, which effect was negligible in a uniformly distributed gas, start playing larger role.

The process of coalescence and the gravity field in the vortex are random, because there are many factors, which we can't account.

In a situation with so many unaccounted factors, we opt for observation and analysis of stable states. The bias in a vortex gradually forces a vortex into a stable state.

To describe formation of galaxies, stars, etc., we focus on vortexes, where inside a large vortex segment there are segments of smaller vortexes. An axel of a smaller vortex could be far from an axel of a vortex containing it, or it could intersect.

When axels are far from each other and a large vortex creates a large body and a small vortex creates a small body, then the gravitational field forces a large body to be in the plain of rotation of small body and into the center of smaller body trajectory. This explains the mystery of the Sun's planets having trajectories in the same plane.

Different "cylinders" of rotating gas in the vortex have different speeds. The "cylinder" of the vortex, which has speed of rotation in concert with the emerging gravitation field become accumulators of coalesced material. This material is forced into the same plane, where all trajectories lay. This explains the mystery of belts: a belt of asteroids, belts around Saturn, a belt at outer regions of solar system.

Effects of gravitation field in a complex systems, as young not spiral galaxies, could be difficult to compute - there is a gravitational pull by many bodies in different directions, which we only model as random force. Motion of a body in this system (a star) is defined by original vortexes and this random gravitational force. This makes prediction of the speed of bodies difficult. This partially explains the deviation of speed of stars in some young galaxies from the pattern found in a solar system.

 

Thoughts

While there are many examples of vortexes in liquid or gas, which provide support for intuition in modeling of these phenomena, there only a few in are of analysis of thoughts. We use the entire models of vortexes to support our intuition in modeling of thoughts.

Thoughts, emotions, and feelings are termini describing functioning of a human body as an information system. They ride on hormonal changes and activity of neurons, but this is a lower layer of the system, which we do not take in consideration in this analysis.

We define:

        thoughts as patterns of internal activity,

        emotions as patterns of body's experimentation used exclusively to update its internal model of reality (including the model of oneself),

        feelings as stable combinations of emotions and thoughts.

They are vortexes in a body viewed as an information system processing a stream of sensory information coming from outside and inside.

The situation is complicated by a fact that vortexes themselves could cause emotions adjusting internal model and creation of internal events, but we ignore it for this initial analysis.

Based on analogy with vortexes in water, we arrive to a few important conclusions, which are supported by observations of human psychic activity: Thoughts as vortexes appear randomly and in large they reflect neither state of the body nor state of its surroundings.

However, some vortexes-thoughts are defined by reality, as some vortexes in a water stream are caused by real hard bounds without any random soft bounds. These vortexes reappear after they are destroyed.

Somewhere, such phenomenon of numerous random acting objects is called shoretz. Hence, we have a shoretz of thoughts, some of which cause actions and affect information stream.

In brainstorming, this is explicitly modeled and utilized: a group of people flush out their thoughts on a subject without any restriction or guidance, acting as a base of a shoretz of thoughts. These thoughts are registered. They are logically analyzed later.

If one could fashion complete isolation for a period, then one could try an exercise of quieting the shoretz of thoughts (meditation). It consists of quieting of the stream of external and internal sensations (sitting comfortably) and focusing on one unimportant thought.

In life of a person as in life of a society, the problem is associated not with erroneous thoughts and ideas, which come and quickly go away, but with stable ideas disconnected from reality. There is even a word for behavior controlled by this kind of ideas - insanity. Perpetual destruction of these stable erroneous ideas is an art, learning of which is more important.

Stability is the main problem with insane thoughts. Even quieting the stream of sensations does not destroy them, just the opposite - they emerge among a few winners. Vortexes in liquid dissipate sooner, when liquid is viscous - there is a lot of traction. Adding traction to the thought process should help dissipation of insane thoughts.

Logical analysis, self-critique and critique by others works as traction in the world of thoughts. A person and a society having culture embracing such critique have tools allowing destruction of insane ideas. Societies, where critique is suppressed, where there is no free discussion, are prone to numerous stable illusions.

Even when critique is present, illusions could be stable, if there is a strong stream of new information. While critique serves as traction, the stream of information provides a vortex-illusion with perpetual support. This could be observed in teenagers, in societies with rapid economic growth or in societies with rapid growth of population, etc. The cause is similar to feeding of vortexes in water by energy of a stream.

A Large number and diversity of thoughts is the main feature of thoughts - shoretz of thoughts. They compete with each other, cause some actions and are compared based on results of these actions, and eventually a winning thought emerges. Hence, critique, experimentation, recognition of mistakes and discarding results of "dead end" experiments, is a part of normal thought process for an individual, a group or for a society as a whole.