The FIRST REASON given for studying paths is that different paths may have identical origins.

Thus there might be reason for researching the exact and complete phylogenetic (or cladistic) history of different species, or even quite remote taxa, of organisms, to discover whether singular events in the history of the earth- ice ages, perhaps, or volcanic episodes, or the infall of asteroids-may have cooriginated, or rectilinearly codirected, such different organisms or their subsequent evolutionary paths.

The same question arises in the historical study of mankind: in recent centuries democracy and high industry have become common over the earth and a question that needs to be answered about both is whether, in effect, they derived from a single point (locus) in space, or instead had multiple spatial origins encouraged by connected conditions (or perhaps by their very synthesis)?

Conceivably by retracing the ancient genotypal or phenotypal paths of modern, seemingly unrelated or disparate diseases, common evolutionary origins of pathogens may be discovered, This would not necessarily have to mean that when these diseases or their pathogenic entities split off from one another on a common evolutionary tree, they bore marked or any phenotypal or genotypal similarity: possibly instead they originated as miscellaneous fragments of some fundamentally-or merely accidentally and temporarily-united mass of genetic or quasi-genetic material.

Thus there are many senses in which different paths may have identical origins, some of which are:

Unrelated paths may spring up from single events

Or from general events

Or shared conditions (perhaps subsequently extinguished);

At some point in the past (or in the present or future) two or any number of paths may interact (symmetrically or asymmetrically) and as a result undergo a change of character or direction;

Chronologically unrelated paths may nonetheless be identical in the type, form, or nature of their origin;

Paths of unlike form may actually or potentially have one or many identical (or equivalent) -simpler or more complex forms from which they are mutually-or perhaps reciprocally -derivable morphogenetically or morphodynamically;

Even the phenomena (or topics) of different sciences (or

subjects) may have like paths or paths with like, homologous, or self-identical origins.

A SECOND REASON for treating paths is that it may aid the construction of artificial paths.

The paths that are to be treated may be ones to be found in physical nature, or simply discoverable by imagination, or that already exist artificially but in some different form or situation or for some different reason or purpose.

Microbiologists are studying the existing catabolic pathways of microorganisms in order to confer upon them unnatural abilities to degrade toxic wastes. The scientists would achieve this either by restructuring existing pathways or by assembling entirely new ones (that nonetheless retain parts of, or bear analogy to, old ones).

The paths that historically led to different inventions may upon study reveal generic or abstractable properties that would be of use in furthering new innovations in the future; or modifications, extensions, or generalizations of these paths may have such value.

Paths that through genetic recombination, mutation, or speciation lead to novel phenes, phenotypes, or species-or to revolutionary genotypes- in nature, need to be studied and understood, for eventually they will suggest new and novel paths that can or must be followed by tomorrow's biological engineers.

The paths of electrons traversing molecules, of water molecules constructing or transforming a watershed, or of command or data sets in a computer, may have a general form, or certain qualities, that are relevant to the design of road structures and networks, or that could improve their efficiency or capacity.

A THIRD REASON for investigating paths is that it may disclose the peculiarities of phenomena.

Paths are subtle telltales of the laws, nuances, and sensitivities of phenomena. They can reveal what nature is otherwise reluctant to reveal, or would keep hidden. They can be the integral, structured handwriting of her interrelated events or coordinated processes, or a decipherable equivalent of the brain's electrical waves.

Comparisons of the daily paths of different animals cohabiting a forest may suggest through contrast the differing mentalities of those animals.

Studies of the anomalous paths taken on occasion by bolts of lightning may clarify more than merely the kinematic peculiarities of lightning.

Paths taken to the workplace-or exhibited in the search for a wife-by various persons may manifest the differences of character of those persons. The rate of development, directness, variational dispersion or clustering, randomness or methodicalness, efficiency, errancy, experimentalism, etc of such paths may have a wealth to say about the psychology of Homo sapiens and of individual human beings.

A FOURTH REASON why paths should be researched is that it may enable them to be more efficient or direct.

That this is so can be suggested by analogy. In recent years the great advances that have occurred in computer hardware, software, and algorithms have enormously augmented man's power to simulate aircraft and ocean vessels and their dynamic interactions with the environment, with the result that it has been discovered that the 'intuitive' design of traditional vehicles is often astonishingly wrong, or that vehicles of truly optimal design would involve innovations that would seem to us bizarre and ridiculous.

Almost certainly a corollary of this is that what we presently think of as being paths of maximal or optimal efficiency or directness, are in reality quite otherwise; and that for many familiar things the most direct or efficient paths possible are ones so far from being imagined that upon first being proposed or glimpsed they would strike us as horrendous mistakes or decidedly queer.

We remain ignorant of the most efficient way in which to send telephone messages over a network, or for a traveling salesman to make his way between a set of cities.

In fundamental physics the optimal paths between different physical events may be equivalent to the laws of those events, or the interactions between the paths of different particles may be paradoxically equivalent to the existence of those very particles or imply that other, undiscovered particles exist. This highlights the potential importance of optimizing paths, in theory or fact.

Yet a FIFTH REASON for treating paths is that it may help man to distinguish one path from another.

Unquestionably many phenomena presently thought of as traversing or generating the same or an equivalent path or route, actually involve two or more partly or wholly distinct or disparate ones.

Knowledge or perception of existing paths must be blinding our perception or imagination of other paths that are possible. Indeed, since possible paths are probably infinitely many, diverse, ranging, transcendent, and encompassing, whereas the set of all known paths is finite and small, it might be said of current hodological knowledge that it is infinitesimal in amount, but infinite in cost.

One could easily have the impression nowadays that all nations on earth are basically following the same political, economic, and cultural path and will eventually become so unified as to be indistinguishable, This may be an illusion, however, and careful historical studies of the individual paths of, say, the United States and China might enable us to distinguish different but easily confused, or quasi-analogous, paths governing the past and future history of these peoples.

Moreover, the path taken by the world 'to date' may one day change radically, and the beginnings of this divergent path may be immanent-hidden discoverable- in the present course of things.

A SIXTH REASON for treating paths is that it may help one to quantify phenomena.

By studying the fine structure of Mars' orbit, for example, and relating it to perturbations caused by other bodies, one can quantify the mass and long-term dynamical history of that planet.