Discussion

 

 

This Discussion is the summation of a paper published in the journal, Knowledge Organization (Martin G. Channon, The Unification of Concept Representations; an Impetus for Scientific Epistemology, Vol. 40, Issue 2, pp. 83-101).  Some links load VRML files, requiring Cortona.

 

 

Introduction

This web site is devoted to the presentation of a science-related reference tool, one that takes the form of a graphics-based summation of concepts. For virtually every category of phenomena, science provides some standard schematic (e.g., diagrams for atomic orbitals, cross-section of the earth, the phylogenetic tree). The most notable exception to this rule concerns the cosmos as a whole. Project Cosmology is devoted to the presentation of such an holistic schematic. This is to be achieved by plotting the standard schematics for constituent phenomena within a three-dimensional coordinate system, time on the vertical axis. The standard schematics for lesser phenomena, then, are arranged along this time line in the order that the corresponding phenomena have typically developed. The result is a 3D graph of the schematics for the various phenomena. Position on the vertical axis reflects typical “event time” and distance on the horizontal axis reflects “size” [e.g., radius (particle phenomena), number of rRNA base sequence changes (phylogenetic tree), evolutionary change per cognate (languages)]. Plotting symbols (in this case, schematics) is not unprecedented; the Stowe periodic table is another such graph, as is the typical street map.

Alternatively expressed, this project is an attempt to provide a unification of standard scientific schematics. The individual schematics are most rigorously presented within a coordinate system, although these are often neglected in practice. The cross-section for the Earth, for example, might best be presented using polar coordinates. The effort here is to bring these schematics together, using a single Cartesian system. This approach has had the unanticipated effect of allowing, more generally, an intuitive, interactive unification of all scientific, graphical concept representations (schematics, graphs, formulae, tables, etc.). Thus, it would be more accurate to characterize the project as a unification of concept representations in general. The result is a 3D, scientific, graphical user interface (GUI); it can be characterized as a graphics approach to knowledge organization. Perhaps most fundamentally, this project can be understood as an effort to map all knowledge; it will be for scientific concepts what the Human Genome Project is to our DNA.

As might be expected for such a mapping effort, the project is having the effect of revealing unnoticed gaps in knowledge, inconsistencies among the different sciences and apparent regularities throughout and across the various disciplines. Any such regularities would be laws relating to laws (i.e., laws relating to knowledge). The project, then, may facilitate the development of scientific epistemology (something already in process). The project also seems to indicate that there are definite limits to the potential extent of knowledge; the growth of science would not be absolutely open-ended. It further suggests that the established concepts of all disciplines will eventually be presented in a collective, concise, intuitive, highly organized graphical format, providing a manageable system, conceivably capable of being mastered by anyone of normal mental capabilities. This is in contrast to the utterly overwhelming accumulation of material as presented in ordinary, expository format. This scientific GUI would be to the expository presentation of knowledge what the general computer GUI is to the command-line approach, the  radical departure from what is often an unwieldy alternative. None of this should be entirely surprising; graphs almost always reveal patterns and gaps most effectively. Furthermore, they often provide an almost immediate understanding of what would otherwise require a time-consuming review of expository discussion. This unification of concept representations is based on a cosmological perspective that provides a one-to-one correspondence between major entity (phenomenon) and aspect (discipline) classifications.

The approach used here is based on the increasingly common point of view that the cosmos is much more than stars, planets and galaxies (astronomy and physical cosmology). As is indicated by the range of scientific disciplines, the cosmos consists of space, time, particle phenomena, life and civilization (on at least one planet). A proper schematic must take all of these into consideration. There are a few important qualifications. First, the major categories of phenomena appear to be exclusively systems. Second, event times in the Unified Schematic correspond to the emergence of fully-formed systems. Thus the event time for language, for example, corresponds to the appearance of the first, fully versatile writing system, cuneiform, circa 2600 BC. These comments can be summarized in terms of the “Fully-formed Criterion”:

The standard schematics of all systems will be arranged within the 3D coordinate system in a manner consistent with fully-formed event times .

 

This criterion is made necessary by the virtual impossibility of assigning event times according to some supposed first form of a phenomenon. Consider technology, for example. The earliest stone tools date to about 2.3 to 2.6 Ma. (Kibunjia 1994; Kimbel et al. 1996; Semaw et al. 1997; Wood 1997). However, our ancestors undoubtedly used more easily worked materials prior to that date, and a stick or a bone used for any purpose is a form of technology. But these would not be specifically human tools; animals are also known to use sticks and stones (e.g., Boesch and Boesch 1984; Shuster and Sherman 1998). An even more extreme case is that of the wasp, Ammophila urnaria, known to use a pebble as a hammer . This was first noticed by  S. W. Williston (1892) and George and Elizabeth Peckham (1898) and has been widely discussed since (e.g., Frisch 1940; Brockmann 1985). There does not seem to be any clear threshold between animal and human technology. Therefore, to trace the origin of technology, we need to look back so far that we are no longer discussing the features of civilization, nor even our distant ancestors (unless we are to look back as far as insects). Similar problems appear for many other categories of phenomena; there is often no rigorous way to assign event times based on some supposed first form. 

Perhaps needless to say, this is an extremely ambitious endeavor, one that is far beyond the capabilities of one person. What we have here at present, then, is little more than the illustration of a potential; only a very limited catalog of concepts is included at this time. This site, then, is currently very much a work in progress. The concepts included are lopsided in favor of physics, simply due to that being the portion of science with which the author is most familiar. Otherwise, the reader will undoubtedly find errors of various kinds, both in the graphics and this Discussion. Some of the schematics are cartoon-like. Others are grievously superficial. Some may be dead wrong. Most are missing. (Please let me know of any errors that you find.)

In itemizing and arranging the primary categories of phenomena, a gradually emerging set of rules is being used. It is a tentative list, perhaps better characterized as working assumptions (some of which are obviously problematic for civil categories).

 

·      There are three primary categories of systems: physical, life and civil. This appears to be an emerging consensus among cosmologists and system theorists (e.g., Bertalanffy 1968; Laszlo 1996; Harrison 2000)

·      Each of these categories breaks down into ten subcategories (the heading counted as one).

·      The other phenomena develop in hierarchical order (at least for the physical and life sciences).

·      An elemental unit is the first item in each of the three main categories (at least for the physical and life sciences).

·      The uppermost item in each category is the all-inclusive phenomenon (metacluster, biosphere, civilization).

·      The systems are perfectly nested in that (a) the phenomena for each category (physical, life, civil) are hierarchical and (b) the three all inclusive phenomena (metacluster, biosphere, civilization) are nested; civilization is a feature of the biosphere and the biosphere is found within the metacluster. See Table 1. (The civil science phenomena do not clearly constitute an hierarchical association.)

 

 

TABLE 1. Primary phenomena (systems).

Physical science

 

Life science

 

Civil science

 

Metacluster          

Biosphere                     

Civilization

Galaxy Systems

Ecosystems

Religion

Galaxies

Complex multicellularity

Science

Ellipsoid systems

Organ systems

Institutions

Ellipsoids

Organs

Technology

Molecules

Tissues

Language

Atoms

Populations

Art

Atomic  nuclei

Cells

Communities

Hadrons

Organelles

Law

Elem. particles

Polymers

Mind

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The standard schematic for the gravitational field, the embedding diagram, is included as the zero event. Otherwise, force separations will be treated in connection with the associated particles (bosons). The gravitational field is apparently not mediated by an associated particle, and, therefore, requires a separate treatment. (Actually, the gravitational field is simply a feature of space; it does not represent a separate category of phenomena; this fact will be developed in future drafts of the Unified Schematic.)

Above the embedding diagram, the schematics for particle phenomena are plotted. Notice that there are ten of these under the category of "Metacluster," i.e., physical cosmos. (The count includes the heading.) Notice also that this list is comprehensive; the major categories of all particle phenomena are included. Event times are as cited in textbooks on introductory astrophysics.

As to the life- and civil-science events, the policy followed here is that of the so-called “principle of mediocrity,” the belief that earth and human civilization are typical examples of such phenomena. This notion has been justifiably criticized (Deutsch 2011; Kukla 2010), but it does appear to at least articulate the apparent, intuition-based consensus among astrobiologists. The reasoning behind it is partly motivated by the well-established Copernican principle, according to which, we cannot attribute to ourselves any special position in the universe. Further still, various biological principles would probably apply to life regardless of where it develops; natural selection, for example, seems likely to be universal, as do the operations of biogeochemical cycles. These considerations are admittedly speculative, but this is about the best we can do for now. In any case, it is intuitively more sensible to assume that we are not special, rather than otherwise. Furthermore, while we have no experience with life elsewhere, we have had plenty of experience in analyzing a wide diversity of phenomena (atoms, stars, etc.); our intuition is well informed. The opposing principle, “the rare earth hypothesis,” has also been subject to extensive criticism, most notably an inconsistency with the constantly increasing number of observed exoplanets. (See, for example, Jean Schneider’s Exoplanet.eu, CNRS/LUTH - Paris Observatory.) Another principle commonly cited in this connection is Nick Bostrom’s (2002) “self-sampling assumption,” according to which we should think of ourselves as random observers from a “suitable reference class.”  Revisiting the Principal of Mediocrity, it is worth mentioning, as noted by Guillermo Lemarchand (2006) that “From a Lakatosian epistemological point of view, this hypothesis is within the ‘hard core’ of the research programs which main purpose is the search for life in the universe (e.g., exobiology, bioastronomy, astrobiology, SETI).” Imre Lakatos (1970) has argued that the ‘hard core’ of a research program includes any hypothesis that is widely viewed by the experts as valid, despite the possible lack of real supporting evidence. On the basis of these various considerations, we can cautiously assume that life and civilization will develop on any Earth-like planet very much as they have here. The evolution of life on this planet is commonly thought to be an aimless diversification. This supposition does not actually follow from evolutionary theory; it is, at least at present, unsubstantiated speculation.

For the life sciences, there seem to be another ten events, the list seems comprehensive and the phenomena seem to have developed, once again, in hierarchical order. As it turns out, there appear to be another ten events from the civil sciences. The list of civil science events has been produced as the result of a careful review of the Propedia (Outline of Knowledge) for the Encyclopedia Britannica. This is, in effect, a comprehensive survey of the literature, one prepared by a team of well-regarded professionals. (These lists of phenomena, however, are very much in need of a careful review.)

The event times for phenomena have been listed in column four of  Table 2. Column five transposes the scientific notation into purely logarithmic numbers. Given that the total time interval is measured in billions of years, the short intervals between civil science events necessitates very fine discriminations. However, as we look downward in the list, this becomes progressively less important. Hence, the values in Column 6 are truncated below event 20 (Biosphere). The numbers above event 20 are abbreviated as illustrated here: . The abbreviation scheme provides a count without having to squint. Not incidentally, there is good reason for using years instead of years for the total time interval. To remain consistent with the Copernican Principle, we need to use an interval that would be typical for observes past, present and future.

The first part of the unified schematic to develop must be the timeline itself, and this is not quite straightforward. Consider Figure 1 (typical timeline of physical science events). This uses a logarithmic scale starting at about and ending at  seconds, a future time, logarithmically just past the present. Now, the intent is to produce an essentially similar timeline, but one that includes events other than just those studied in astrophysics, i.e., those of the life and civil sciences. But if we are to include a reference to these other phenomena, the simple logarithmic scale becomes hopelessly problematic. At the high end, numerous events are bunched together in an unreadable manner, and at the low end, things are spread out more than they need to be. To remedy this, the timeline needs to be adjusted; we need some variation of the logarithmic scale. Ideally, the events would be spread out in a uniform manner. When spread out this way, the events describe an exponential arc, as illustrated in Figure 2. The following equation models this graph.

 

 

 

 

 

The use of this equation, in lieu of something such as a logarithmic scale, is unsatisfactory (too complicated). The simple logarithmic scale will not work, but it would be preferable to find some variation that will.

 

Building the Unified Schematic

The Frame. Consider a two-dimensional space-time frame. If we are to place something such as the two-dimensional cross-section for the earth within this (normal oriented vertically), we immediately encounter a problem: the frame has only one spatial dimension. The correction is simple enough: we add a second. This, however, has the effect of also adding a second dimension to the timeline (or it can be interpreted as doing such). This is convenient because it allows us to incorporate the standard, 2D schematic for time, the geologic time-scale (modified here to include astrophysical and archeological increments). Click on the link “Time log(yr)” in the upper left corner of the Unified Schematic to view this unified time-scale. The time-scale includes borders on all sides. This suggests that we use the same for the rest of the 3D space-time frame, producing a cube overall. The bottom panel of the Unified Schematic has spatial dimensions in both directions, and, therefore, can only be used to present the standard schematic for two-dimensional (Euclidean) space, the usual x-y grid. (Click on “Space |log(m)|” to bring this panel out. You will then find buttons to transform the schematic to render spherical and hyperbolic space.) The rear face has a spatial dimension in one direction and time in the other. This suggests that it be used to present the standard, two-dimensional schematic for space-time. The right side face involves no obvious requirement; temporarily, it will be used to present graphs for the primary cosmological parameters (temperature, density, radius and energy). The overhead face has yet to be developed. Likewise, the front face is undeveloped. (It could be used for something that appears only when the cube is rotated by, revealing the face from the rear. VRML allows scenes that are transparent when viewed from one side but not the other.)

Unified Time-Scale. As mentioned, the left side panel is used to incorporate the geologic time-scale. However, for present purposes, this time-scale is not complete; it begins only at about the six-billion year mark. In order to use it for the entire period of time since the big bang, we need to supplement it with cosmological increments of time. We also need to break down the uppermost increments (the Pleistocene and Holocene) to incorporate the archeological time-scale. Clicking on text shapes will cause the view to zoom in, where necessary. (If a text shape turns blue, it will produce a zoom effect.) In some future draft, this time scale will include the degenerate (heat death) increment; it would then be fully complete.

Particle Phenomena. Within the 3D “frame,” and above the embedding diagram, the cross-sectional schematics for particle phenomena are stacked, one on top of another, in the order in which the corresponding phenomena developed. Sizes are according to the absolute values of the logarithms of the radii (meters). These schematics for particle phenomena are called out to a face-on position by first loading a classification table to the right frame. Clicking on “The Atom,” for example, loads the periodic table to the right frame. Clicking on symbols in the periodic table will call out the schematics for atoms. (At the present time, only hydrogen has been developed, although data is available for the other atoms.) Classification tables are now available for many, if not most categories of physical science phenomena, although most of these are still in a developmental stage [e.g., elementary particles, hadrons (VRML), Table of Nuclides, Stowe Periodic Table (VRML), Vaucouleur’s System in VRML (galaxies), Friedmann Universes.]. This suggests that all major categories of phenomena may eventually have classification tables. Indeed, at least some efforts are being made toward the development of classification tables for biological and civil phenomena (e.g., Ajtay, Ketner, and Duvigneaud 1977). There is also some indication that these different tables would be developed according to a set of epistemic rules (Channon 2011). In this case, the Unified Schematic could be developed in a highly systematic fashion; each label (e.g., “Atoms”) would call a classification table to the right HTML frame, and, from there, schematics for corresponding phenomena can be called from the left frame. Note that text shapes often have both mouse-over and on-click events. For example, a mouse-over event for “The Atom” will bring out spatial and temporal scales. These have blinking indicators for event time and radius.

Phylogenetic Tree. In addition to the schematics for particles and particle systems, we need to include some reference to organic phenomena. The primary schematic in biology is probably the phylogenetic tree, now referred to as the cladogram. This can be brought out by clicking on the term "Biosphere." The phylogenetic tree is, of course, not the only biology-related schematic; over time, additional biology schematics will be included. At this time, only the cross-sectional schematic for the protocell (Organelles   Protocell) and ecosystem are included.

Civilization. The next issue concerns the need to provide a schematic for civilization. Apparently, no such schematic exists, so an effort is made here to develop one. We can follow the same principle as is used for the Unified Schematic: combine the existing schematics for subordinate phenomena. It appears that these phenomena (e.g., languages, law, knowledge) are usually represented using branching diagrams reminiscent of the phylogenetic tree. Hence the tree-like schematic for civilization. This is placed within the upper region of the cladogram.

Lettering. The lists of terms on the right of the Unified Schematic (“Elementary Particles.” etc.), were originally motivated by the desire to label the various individual schematics. However, these have since been given the various secondary and tertiary functions that they now have (mouse-over and on-click events). Most importantly, they are intended to call classification tables to the right frame. The on-click event for “The Atom,” for example, will call a new version of the periodic table to the right frame. For some categories of phenomena, such classification tables already exist. The rest, presumably, will come over time.

The lettering on the left side is intended to compliment the lettering on the right; as presently conceived, each discipline corresponds to one of the primary classes of phenomena. These left-side terms are to be developed such that each will call a list of subdisciplines to the right side frame. These, in turn, will be broken down into more subordinate categories, then into topic areas and, finally, into summations of concepts. Meanwhile, the sub-disciplines serve as links to introductory Wikipedia articles. (Not all of the text shapes on the left have this functionality.) In time, these lists will be developed as three-dimensional discipline and concept maps. (The lists arguably constitute one-dimensional maps.)

 

An Example: the Hydrogen Atom

This completes the outline of the Unified Schematic, all of which might be interesting, but it does not tell us if it will accommodate any significant level of detail. Perhaps needless to say, such detail cannot be provided at this time for all categories of phenomena; that is something that would require proper funding and a team effort. However, it would be helpful to at least illustrate any such potential. The hydrogen atom has been chosen for this illustration. (This will exclude the atomic nucleus, something treated as a separate category of phenomena, a different level in the hierarchy of particle phenomena.)

From the list of terms on the right in the Unified Schematic, click on “The Atom.” This loads the Stowe periodic table to the right frame. Then in the table, click on “H” (hydrogen). This will bring up the schematic for the 1s state. It will also displace the Stowe Table and load the hydrogen energy level diagram to the right frame. The energy level diagram doubles as a classification table for excited states. Clicking on any of the energy level terms (e.g., “2p”) will cause the view to zoom in on the fine structure. There you will find buttons for bringing out schematics for the various excited states (e.g., “m = -1, 0, 1”). There is also an option for the Zeeman Effect, although this has not been fully developed. When an excited state is loaded to the left frame, there is a “slider” that allows the user to view particular values of . There is another slider for scale.

This is nearly a comprehensive graphical treatment of details relating to the hydrogen atom, although there are an infinite number of excited states. Also, some of the allowed transitions may have been neglected, and some of the fine structure might be missing. In a future draft, improvements will be made. Nevertheless, we have here enough detail to illustrate that this Unified Schematic can accommodate all of the details of the hydrogen atom. Hopefully, this is an indication as to how well it will handle other phenomena.

 

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