A whole and All

Humans are the only species that create a whole from all with an intention. We call this a machine. All parts are assembled to create a machine’s function as a whole, which is not possessed by individual parts. The function is a concept associated with reproduction and repetition. In this sense, each part also has its function as a machine does. A screw is reproducibly attaching two or more pieces together. Therefore, a machine can reproduce something (i.e. things or events) using the geometry of all its parts. What does the geometry of parts do? It creates a sequence of events based on the proximity of individual parts. As a whole, this is the function of the machine. When something is reproduced, either things or events, the functions and roles emerge for the sake of reproduction.  In other words, without reproduction, there is no function or role.

Machines are human creations that reproduce their function based on properly assembled parts. Each part also has its own reproducible function for the machine to work.

“Assembling” is the issue of allocation and orientation – this is geometry. In addition, each part has its own shape. Again, this is geometry.  This indicates that a machine consists of two nested layers of geometry – the shape of individual parts at a base layer of geometry. Their allocation, including orientation, is the upper nested layer of geometry. This can also be rephrased as a machine consists of two nested layers of function.

A factory has many machines. A factory has its function and role because it reproduces something based on the sequence of machine-controlled events. The distribution of the machines coordinates the sequence of events – workflow.  The third layer of nestedness.

What is the difference between a whole and all. A whole includes the geometry of all parts. Only when a whole reproduces something based on the reproduced sequence of internal events do we recognize it as a whole. A whole is something that is greater than the sum of all. A whole is only recognized when something is reproduced, repeated or replicated. “All” is not “a whole”. “All” indicates the composition of a whole but not its geometry. All is insufficient to reproduce anything. The geometry of all parts dictates the sequence of events. This is “a whole” that permits the reproduction of things or events. 

A machine is the consequence of the top-down nestedness. The purpose/intention of humans comes first. The top-down nestedness is designed by humans to reproduce something using its mechanism inside.  The top-down nestedness is designed with a purpose.

Tools and parts are conceptually very similar. A shape that helps to reproduce things or events is called a tool. A function of a tool is equal to the purpose of the person who uses it. A tool is designed by a designer with an intention. However, the first tools for humans were likely discovered by accident. The shapes helped the reproducibility. Reproducibility is the point.  Importantly, for a tool to work properly, a person who uses it must know how to use it. In addition, there is no tool for everyone. The design of tools is tightly associated with (and strongly constrained by) the background environment and intrinsic properties of persons. This is closely linked with norms, normal, standards, ubiquity and abundance. Tools always demand pre-existing conditions to be used properly, although we now have the concept of universal design.   

Tools are the shapes that help a user reproduce things or events. Tools are the shape, which is a one-layer geometry used by humans’ ubiquitous ability to reproduce something. The orientation (i.e. angle) of a tool is an essential matter for its reproductive function, though (we call this a skill).  

When a whole emerges, individual pieces in a whole become parts. Each machine has the geometry (i.e. allocation and orientation) of all parts. Each of which has its own shape. As a whole, the nested layers of geometry secure the reproducibility.

As a whole, a machine reproduces a sequence of physical mechanical events.  Because of physical mechanical events, some energy inputs are required for a machine to work. The energy can be gravity, human or animal power, or heat. Combustion engines are a great example. Physical momentum is reproducibly transferred to the tires, and a car reproducibly moves the driver and passengers from one place to the other. All are based on the geometry of parts, which all have their own shape.

Human-made machines have a linear logic (a linear sequence of events) within a machine. Usually, no detour. If one part changes its shape, the logic is compromised. All parts are still present but dysfunctional as a whole.

On the other hand, a whole created by the bottom-up nested layers is observed in nature and human social structures. No one intends to make a whole, but it emerges. When parts gather, a reproducible whole emerges. A whole is a consequence but not an intention. A whole has risen as a reproducible, equilibrated state derived from individual local adjacent interactions of parts.  

Two material characteristics permit this type of bottom-up emerging layer formation. Self-assembly and self-organization.

The typical self-assembly is the crystallization of salts. Each unit has a shape. They align under a certain rule to form unique configurations of units. The shape of individual units is not changed, but is aligned in consistent orientations. Imagine LEGO.  Each piece has its own shape and can align with others. The shape of individual pieces does not change, but the variation of the shape of a whole is almost infinite. LEGO blocks can create a bridge, a house or an airplane.  More precisely, once YOU name the shape that you created with all connected pieces, the shape becomes something reproducible as a whole. A name allows us to recognize it as the point to be reproduced. Without it, no such thing.

A function is quite similar to a name. A structure of connected pieces without a name can become a bridge by connecting two separated sides of a river, and some use it to communicate between the two sides. For example, a tall apartment building on the bank of a river.  Whatever the reason, the building had fallen and crossed over the river. Now, it is a bridge for squirrels and deer. Or in a disparate situation, even for humans. No intention is needed, but its shape consequently creates reproducible functions. Functions and roles are the concepts within reproduction.

When reproducibility is created by several parts, each part has its function and role within the reproducibility of the whole. In the case of self-assembly, no instruction is needed, but each piece interacts and attaches with other pieces. Each piece does not change its shape but gets connected to its direct neighbours. Individual pieces have no idea beyond their direct neighbours.  But they keep connecting. Then, if something is reproduced, the aggregate becomes a whole, and each piece has roles and functions to produce reproducibility.   

Self-organization is quite similar to this.  The fundamental difference between self-organization and self-assembly is that, in self-organization, each part changes its shape through interaction with its direct neighbours. The shape before and after the interaction is different. I would call this sharing or compromising with each other.  What this means is that something new in terms of the shape that did not exist before the interaction emerges, even at the individual level.

An example is soap bubbles. Individual soap bubbles are always spherical. If two are connected, the individuals are no longer spheres, but as the two, they create a consistent two-attached structure as a whole. With multiple bubbles, it is possible to make a cubic bubble within a structure that never exists as an isolated bubble. Why is this possible? Because they share the force called surface tension when they attach to each other. This force permits a spherical shape in individual bubbles. Although they share the surface tension, they do not share the air inside.  They are in two separate compartments but share the force holding them.

How about two water droplets? As soon as they touch each other, they coalesce and become one drop. They share the surface tension as well as share the space, permitting the intermingling of water molecules.  How about two metal balls or two ice balls? They can touch each other, but no change happens in their shape. How about two LEGO pieces? They can fit each other, but no change in their shape.

Self-organization is not full mixing. Not giving away or taking away. Sharing and maintaining the sharing.  Individuals in the self-organized whole maintain their individuality. However, the individual property in a whole is different from the property shown in isolated individuals. In a whole, the property shown in isolation is compromised/shared/modulated based on the direct neighbour interactions, but not beyond.  

Self-organization is highly robust and scalable. The variation at the entry stage converges at one or a few stable equilibrated states. However, this robustness and scalability have their range limits, not limitless.

In addition, a whole created by self-assembly can become a part of self-organization or vice versa. Self-organization or assembly as a whole can be nested above parts created by self-organization or assembly. Our physical world consists of nested layers of self-organization and assembly – elementary particles, atoms and molecules in physics and chemistry  – cells and organisms in biology  – families, tribes, villages/towns/cities, provinces/states, and countries in human society.

“All” does not exist without a whole unless someone defines “all”.  All is the concept within a whole, but without the geometry. A whole is the consequence of reproducibility or repetitiveness. Before this repetitiveness, there is only chaos that is represented with every.  Chaos has everything but nothing. When a cyclic circuit of connectiveness emerges (this is the first reproducibility) from chaotic everything, a whole emerges. A whole defines “all” from the infinite and creates its functions and roles. Logic is a sequence of events within a whole that permits the reproducibility of a whole.

A whole is not created bit by bit. Not like artifacts humans create. A whole happens as chaotic everything. A whole comes first. After a whole emerges as a cyclic circuit, trimming occurs. Trimming permits to reduce the risk of errors that disrupt the circuit. Along with trimming, “all” changes, so do functions and roles. Think about a river delta. It forms at the river mouth, connecting the point with the water current (i.e. river) to the no current (i.e. lake or ocean). Many routes to reach the ocean. In a dry season, water runs in one major route. Humans like to constrain them into one.

Another analogy is the relationship between a full sports game telecast and its digest. Without the completion of a game, its digest is hardly possible to make. Each game is not designed to have highlight scenes. Each scene becomes a highlight based on the final consequence. Even after the game, the selection of scenes in the digest could vary.  Importantly, without knowing the end, the collection of scenes cannot be a meaningful digest that can reproduce the result of the game.

A whole created by the top-down has one route within it to conduct one series of events. On the other hand, a whole created by the bottom-up starts from multiple routes (i.e., a lot of detours) and then trims/constrains them to one or a few routes. This type of whole often implicates detours and permits flexibility (i.e. plasticity) in route choices.

A whole comes from nothing, but everything in the case of bottom-up. All does not exist before a whole emerges. Everything is nothing but the infinite.  A cyclic reproducibility takes a whole excised part out of chaos. Life is a whole. Life is a whole that conducts growth, replication and reproduction. Life is a circuit that behaves like a perpetual motion under the energy of the Sun, which provides the surrounding environmental foundation for the conditionally perpetual circuitry reproduction.