Isomorphism

Isomorphism is an information preserving transformation of a pattern between different media (mediums). I will quote in italics Douglas R. Hofstadter, who covers this concept thoroughly in his book Gödel, Escher, Bach: The Eternal Golden Braid:

The word "isomorphism" applies when two complex structures can be mapped onto each other, in such a way that to each part of one structure there is a corresponding part in the other structure, where "corresponding" means that the two parts play similar roles in their respective structures. The usage of the word "isomorphism" is derived from a more precise notion in mathematics. The perception of an isomorphism between two known structures is a significant advance in knowledge -- and I claim that it is such perceptions of isomorphism which create meanings in the minds of people...it is not always totally clear when you really have found an isomorphism. Thus, "isomorphism" is a word with all the usual vagueness of words -- which is a defect but an advantage as well.

An example of isomorphism is the relationship between records, music and record players...a record contains the same information as a piece of music, because of the existence of record players, which can "read" records and convert the groove-patterns into sounds. In other words, there is an isomorphism between groove-patterns and sounds, and the record player is a mechanism which physically realizes that isomorphism.

Patterns which are isomorphic can transmit meaning between media. The Greek word persona had in its original meaning simply the mask that an actor wore during his performances. Carl Jung revived the term to mean that set of images or ideas that normal people use to face society. It is the set of ideas that we desire others to know us as. Our persona that is this set of ideas that we use exactly as an actor performing Greek tragedies would. Every part of the mask has a corresponding part in the idea of the persona each fulfilling the same purpose in their respective medium or environments. The mask covers the actor's face with a fake skin,shape,and color to affect the eye. The persona covers up a person's psyche and true nature with images and ideas to affect the understanding.

Within our body after stimulation of the senses messages travel through our body literally. Images and ideas are electrical patterns which dance across pathways of brain cells, neurons. These waves of neural activity set off waves of molecular chemical hormonal flow which can be felt traveling through the body. These chemical patterns affect more complicated organizations of proteins which effect cells which affect the general attitude and positioning of the one whole wave that is called our body.

Meaning steps down through many graduated levels of organization in our bodies via isomorphic patterns.

Example of Isomorphism: Human Hive

I will attempt here to draw an isomorphic mapping between an ant colony and the structure of human society.

Ants are amazing creatures. This type of insect forms complex collections of individuals which acting in unison accomplish goals which one ant alone could never accomplish. The first mapping of characteristics between ant colonies and human societies is this: that ant colonies are societies of ants in the same way that human society is a collection of individual humans acting in concert toward goals which no one individual could accomplish alone.

All the ants in the world do not cluster into one gigantic colony and similarly humanity on Earth historically forms itself into many separate tribes, cultures, and societies. Humanity does trend toward creating ever larger scale organizations and this is not observed in ants. If one were to look at humanity in say 10000BC one may have found only scattered tribes and assumed that higher organization was not possible. It may because of some ability to create new forms of communication and organization the Earth as a whole will become one giant anthill of humanity.

One might think that most be smarter than other insects somehow. Otherwise how could they form a complex organization structure? The truth is that ants are dumb. The average ant is not any more intelligent than any other insect, in fact there are several reasons to suppose they are less so. An individual ant as little chance of survival on its own. Most ants have poor vision. They respond to a limited set of triggered stimuli and have a limited repertoire of behavior. In fact it can be said that ants have evolved into dumber individual creatures as the higher organization of ant colonies has evolved what seems to us as more intelligent behavior.

In fact it will begin to be seen that an ant colonies overall constructive behavior is a consequence of the completely random and purposeless lives of the individual ants. Perhaps purposeless is a bit harsh. Ants are free beings. They freely wander about, find bits of food, interact with other ants, and work on trails. Nonetheless they never step out of their small ant-world life. They do not have the mentality to imagine even the relatively simple overall pattern and behavior of the entire ant colony. They cannot objectify their world, their colony. They cannot step outside and look at it as an object, and then improve it. They do not debate amongst each other and offer practical suggestions for improvement. We think we do although it is debatable how far the common man mentally steps outside his world, the pattern of human society.

Hofstadter: ...even though ants as individuals wander about it what seems a random way, there are nevertheless overall trends, involving large numbers of ants, which can emerge from the chaos...ant trails are a perfect example of such a phenomenon. There, you have really quite unpredictable motion on the part of any single ant--and yet, the trail itself seems to remain well-defined and stable...There is some degree of communication among the ants, just enough to keep them from wandering off completely at random. By this minimal communication they can remind each other that they are not alone but are cooperating with teammates. It takes a large number of ants, all reinforcing each other this way, to sustain any activity--such as trail building.

Simple chemical signposts act for the ant as communication. As an ant walks along he leaves a chemical trail. This chemical trail triggers other ants to follow and as many ants walk the trail the chemical scent is reinforced. The ant does not "decide" to follow the chemical scent but it is hardwired into his rudimentary nervous system to respond thus. Many times single ants will travel about and no other ant may detect the chemical signature. Where food is near many ants will have traveled back and forth reinforcing the trail and signaling to other ants.

Similarly human trails and roads build up along routes that lead to destinations that many humans seek. The more humans that travel to a destination, the wider and better built is the road. Interstate highways connect large cities where state roads and county roads connect smaller cities, towns, and villages. Our "food" is more complex and varied and our communication is visual and spoken but the analog is compelling. Towns form and grow in locations near where many humans simultaneously have been able to live successfully off the land. The town is common place where people can communicate, trade, and store food and other supplies. After a time a critical mass is reached where the town itself becomes a place where people can successfully survive and prosper.

Group phenomena which have coherence--trail-building, for example--will take place only when a certain threshold number of ants get involved. If an effort is initiated, perhaps at random, by a few ants in some locale, one of two things can happen: either it will fizzle out after a brief sputtering start...or a critical mass of ants is present, and the thing will snowball, bringing more and more ants into the picture. In the latter case, a whole "team" is brought into being which works on a single project. That project might be trail-making, or food-gathering, or it might involve nest-keeping. Despite the extreme simplicity of this scheme on a small scale, it can give rise to very complex consequences on a larger scale.

Ants colonies involve the interaction of several different types of ants which are divided into castes so to speak. There are one or more queen ants which lay the eggs, male ants which inseminate the eggs, soldier ants to protect the colony, and types worker ants which in many species are differentiated further. Naturally, human societies have evolved caste structures often with a few people regarded as royal, noble, or elite. These people ensure the consistency of the direction of the society as a whole. The human queen's eggs are not little humans, but the visions and ideas that the other castes will work to create and manifest. Warrior castes are crucial for defending the manifestations or expanding the societies space for gathering raw materials.

The worker types have evolved specializations just has humans have evolved many thousands of different specializations which serve the society in unique ways. The human hive is complex in structure and requires people of many skills such as engineers, technicians, plumbers, electricians, mathematicians, teachers, carpenters, etc...No one person could build a state of the art airplane but many different skilled people working together can build many. In most societies people are free to choose what specialization they will develop. Society does not directly determine what specialization, or sometimes even what caste, an individual should develop. What we call free-market forces can guide an individual's development. If there is a shortage of electricians the demand will be high and consequently the pay for electricians will be high. As more and more people become electricians to earn the higher pay the shortage will be satisfied and the pay will eventually achieve equilibrium with all other specializations. This equilibrium occurs even though each person randomly chooses his own specialization. That is no one ruler decides what an individual will become. There is no overall plan detailing each individual's role in advance yet the overall pattern develops. Each individual's role is determined by their starting point and how the satisfaction of their needs and desires can be accomplished.

There are all sorts of tasks which must be accomplished in a [ant] colony, and individual ants develop specializations. Usually an ant's specialization changes as the ant ages. And of course it is also dependent on the ant's caste. At any one moment, in any small area of a colony, there are ants of all types present...one caste may be very sparse in some places and very dense in others...there evolves, over a long period of time, a very delicate distribution of castes inside a colony...the constant to-ing and fro-ing of ants inside the colony...adapts the caste distribution to varying situations, and thereby preserves the delicate caste distribution...the caste distribution cannot remain as one single rigid pattern; rather, it must constantly be changing so as to reflect, in some manner, the real-world situation with which the colony is dealing, and it is precisely the [random] motion inside the colony which updates the caste distribution, so as to keep it in line with the present circumstances facing the colony.

When individual ants detect an anteater's proximity they go into a panic...which means, of course, that they begin running around completely different from the way they were before [the anteater] arrives...[the anteater] is feared by all the individual ants in the colony...[therefore] you see that the ant's action in response to [it's] arrival changes the internal distribution of ants...the new distribution reflects [the anteater's] presence. One can describe the change [of distribution] as having added a "piece of knowledge" to the colony.

Different specializations can be regarded as sub-castes.

When ants need to get something done, the form little "teams", which stick together to perform a chore...small groups of ants are constantly forming and unforming. Those which actually exist for a while are the teams, and the reason they don't fall apart is that there really is something for them to do...in food-gathering if there is an inconsequential amount of food somewhere which gets discovered by some wandering ant who then attempts to communicate its enthusiasm to other ants, the number of ants who respond will be proportional to the size of the food sample--and an inconsequential amount will not attract enough ants to surpass the threshold [required to form a team]...these teams are one of the levels of structure falling somewhere in between the single-ant level and the colony level...There exists a special kind of team, which I call a "signal"--and all the higher levels of structure are based on signals. In fact, all the higher entities are collections of signals acting in concert. There are teams on higher levels whose members are not ants, but teams on lower levels. Eventually you reach the lowest-level teams--which is to say, signals--and below them, ants...The effect of signals is to transport ants of various specializations to appropriate parts of the colony. So the typical story of a signal is thus: it comes into existence by exceeding the threshold needed for survival, then it migrates for some distance through the colony, and at some point it more or less disintegrates into its individual members, leaving them on their own...a signal loses its coherency just at some spot in the colony where ants of that type were needed in the first place..one would be inclined to characterize the signals' behavior as being oriented towards filling a need, and to call it "purposeful". But you can look at it otherwise...Once a signal is formed, there is no awareness on its part that it should head off in any particular direction...here, the delicate caste distribution plays a crucial role. It is what determines the motion of signals through the colony, and also how long a signal will remain stable, and where it will "dissolve." Let's say a signal is moving along. As it goes, the ants which compose it interact, either by direct contact or by exchange of scents, with the ants of the local neighborhoods which it passes through. The contacts and scents provide information about local matters of urgency, such as nest-building, or nursing, or whatever. The signal will remain glued together as long as the local needs are different from what it can supply; but if it CAN contribute, it disintegrates, spilling a fresh team of usable ants onto the scene...From an ant's point of view, a signal has NO purpose. The typical ant in a signal is just meandering around the colony, in search of nothing in particular, until it finds that it feels like stopping. Its teammates usually agree, and at that moment the team unloads itself by crumbling apart, leaving just its members but none of its coherency. No planning is required, no looking ahead; nor is any search required, to determine the proper direction. But from the COLONY'S point of view, the team has just responded to a message which was written in the language of the caste distribution. Now from this perspective, it looks very much like purposeful activity. If the caste distribution were entirely random...the colony would not last long, due to the meaninglessness of the caste distribution.

The individuals in a [ant colony] signal sometimes break off and get replaced by others of the same caste, if there are a few in the area. Most often, signals arrive at their disintegration points with nary an ant in common with their starting lineup.

One can draw a parallel to human society. When humans have their needs met they tend to stay put. When external conditions such as drought, famine, or in modern times depression and lack of work occur many individuals or groups of people are forced to migrate to find means of meeting their survival needs. Individual people making only selfish decisions will move in mass to new locations where food, resources, or jobs are available. As a mass of people moves overland some people will find what they need and stop and others who are not finding necessities will join the mass. Upon reaching a location with abundant food or resources the people will stop and begin to create homes, farms, towns etc...Similarly many people will settle in locations where there is a shortage of labor or particular skills. From the point of view of the entire society locations of abundant resources but lacking in human labor and skills receive the "signal" of groups of people even though no higher organizational plan was implemented. Groups of people naturally head to where they are needed by only attending to their personal needs for survival and fulfillment. Society as a whole reacts to external conditions not with a overall plan implemented by a ruler but because pattern develops naturally from the summation of many, many individuals' decisions to satisfy their personal needs. Although human society is much more graduated and complex than ant colonies it is clear that almost every aspect of ant colonies can be paralleled in human society.

I hope that this example shows the meaning of isomorphism and reveals the powerful information revealing capabilities of the concept.

With the basis of isomorphism I think it is possible to to get a grip on the general concepts of intelligence and meaning. In a future essay I will attempt to draw isomorphic parallels between evolution of complex informational structures and the evolution of species and societies. The human brain/mind system can be viewed as an extremely complex "society" of neurons similar in formation to ant colonies. Intelligence is then an isomorphic mapping machine, and the ever expanding meanings which intelligence recognizes are bottom-up structures whose formation is due to the summation of many lower-order properties and events. A further quote from Hofstadter may pique your interest:

Higher level teams form similarly as ant "signal" teams. Teams of signals can be referred to as "symbols". Mind you, this sense of the word has some significant difference from the usual sense. My "symbols" are ACTIVE SUBSYSTEMS of a complex system, and they are composed of lower-level active subsystems...They are therefore quite different from PASSIVE symbols, external to the system, such as letters of the alphabet or musical notes, which sit there immobile, waiting for an active system to process them.

We can draw isomorphic parallels between his use of the words signal and symbol and their common usage.

Achilles: Now just a cotton-picking minute. Are you insinuating that my brain consists of, at bottom, just a bunch of ants running around?
Anteater: Oh, hardly. You took me much too literally. The lowest level may be utterly different. Indeed, the brains of anteaters, for instance, are not composed of ants. But when you go up a level or two in a brain, you reach a level whose elements have exact counterparts in other systems of equal intellectual strength--such as ant colonies.
Douglas R. Hofstader
Gödel, Escher, Bach: The Eternal Golden Braid