The Map of Physics: Language and Reality

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    To what extent does language mimic Reality? Underlying the Map of Physics we have an assumed proposition that the objects and actions of language exist in a perfect (or almost perfect) intimacy with the corresponding objects and actions of Reality. Do we have any justification for making that assumption?

    To answer that question we need to explore the relationship between language and Reality and, in particular, explore how humans create language out of their interactions with Reality. That latter particularity brings us into contact with General Semantics, the part of linguistics concerned with the origin of language in a process of abstraction.

    Devised in the 1920's by Alfred Korzybski (1879 Jul 03 - 1950 Mar 01), General Semantics takes as its central goal the raising in the human mind a full consciousness of the origin of language in a process of abstraction. Korzybski represented that process in a diagram that he called the Structural Differential, which has three basic components.

    Korzybski called the first component the Event and represented it by a parabolic segment whose base appears as a jagged line to indicate that the parabola extends to infinity. Holes drilled into the segment represent the indefinite number of characteristics of the Event. We cannot apprehend the Event directly, so, as an absolute, the Event corresponds to what philosophers call the thing-in-itself, the modern version of Plato’s Forms.

    Korzybski called the second component the Object and represented it by a circular disc. Holes drilled into the disc represent percepts obtained from the Event by an observer: the Object represents the set of those percepts and not an actual physical object. The physical object, the source of our percepts, lies within the Event and strings passing from holes in the paraboloidal segment to holes in the disc represent the process of perception.

    And the third component, represented by a rectangle, got the name Label and Korzybski asserted that these could extend, as links in a chain, as far as we could take them. Here words, as mental phenomena, enter the picture. The first rectangle suspended from the Object contains the names of the percepts to which the strings connect them. Thus we get words such as green, straight, cold, sweet, etc.

    Here we encounter one of the two rules made famous by Samuel Ichiye Hayakawa (1906 Jul 18 - 1992 Feb 27) in his classic work, "Language in Thought and Action" (1949). That rule states that "the map is not the territory; the word is not the thing defined." That means that we use arbitrary noises (words) to organize percepts into concepts, the objects of our thinking. But it also means that no magic connection exists between words and the concepts that they denote. I can exemplify that proposition with an anecdote that the physicist Richard Feynman told of his childhood:

    While out for a walk with his father, he reported, his father pointed out a bird and said, "See that bird? It’s a Spencer’s warbler. Well, in Italian, it’s a Chutto Lapittida. In Portugese, it’s a Bom de Peida. In Chinese, it’s a Chung-long-tah, and in Japanese, it’s a Katano Takeda. You can know the name of that bird in all the languages of the world, but when you’re finished, you’ll know absolutely nothing whatever about the bird. You’ll only know about humans in different places and what they call the bird. So let’s look at the bird and see what it’s doing – that’s what counts."

    Whatever sound we associate with a given concept as its name, whenever we hear that sound we will have an example of that concept brought into consciousness. So whenever I hear the sound "bird" an example of a bird comes to mind. But the sound does nothing else: it has no other powers.

    We find our basic object-action vocabulary in a second rectangle hanging from the first. Here we organize basic percepts into objects from which we receive them. Thus, for example, we organize green, flat, flexible, and roundish into the concept to which we apply the word leaf. And here we also begin our encounter with the Sapir-Whorf hypothesis.

    Also called the principle of linguistic relativity, the Sapir-Whorf hypothesis asserts that the form of a language affects the way in which its speakers conceive the world and thereby influences the thought and behavior of those speakers. To paraphrase Whorf, we can say that

    We divide up the phenomena of nature along lines laid down by our native language. We do not find the categories and types that we isolate from the world of phenomena because they stand out as obvious to every observer; on the contrary, the world comes to us in a kaleidoscopic flux of impressions which our minds must divide up and organize into concepts, a task that our minds accomplish largely through language. We divide up nature, organize it into concepts, and ascribe significance as we do, as parties to a tacit agreement to organize it in this way. That agreement, codified in the patterns of our language, holds throughout our speech community, the people with whom we share a language. The same physical evidence does not lead all observers to the same picture of the world, unless those observers have the same linguistic background or they can, in some way, calibrate their respective languages.

    That proposition obliges us to modify Korzybski’s Structural Differential in several minor ways.

    First we need to look at how we attach the strings between the components of the Structural Differential. The Event represents the Absolute, so we have no control over its connections to the Object. Except for people with sensory disabilities (such as deafness), everyone senses the same connections between the Event and the Object. But those connections make up an almost infinite set, whereas the human mind can only attend to a finite (if large) number of things at any given time.

    In going from the Object to the first level of Labels we create a finite set of words. Each community of humans originally created its own basic vocabulary, which then evolved into a proper language. The German philosopher Ernst Cassirer (1874 Jul 28 – 1945 Apr 13) described, in his 1925 treatise "Language and Myth", a process by which humans created their first words. Cassirer asserted that words denote concepts that we conceive through an emotional process of noticing: our remote ancestors created words for things that they had noticed as having some importance for them.

    That assertion explains how different speech communities devised completely different sets of words to denote essentially the same phenomena. Consider, as an example, the human linguistic response to collections of frozen-water flakes.

    In the temperate zone the cold fluff comes during the winter as a nuisance that people avoid as much as possible, primarily by staying indoors. It has no importance for those people beyond that fact, so the languages of temperate-zone cultures have only one word to denote the stuff – sheleg in Hebrew (the stuff does appear occasionally in the Judean Hills), khioni in Greek, nieve in Spanish, and snø in Old Norwegian, which became snow in English.

    In the arctic zone, on the other hand, snow represents a resource as much as it represents a nuisance. Consequently the cultures of that region thus make finer distinctions than temperate-zone cultures do. The Iñupiak of Northern Alaska, for example, use about a dozen different denotations, where English uses only one, based on the mechanical properties of snow. The Iñupiak hunter thus conceives a given snowscape differently from the way in which a native speaker of English conceives it: in a certain respect the Iñupiak actually exist in a different world. We can see the reason behind that fact in the understanding that an Iñupiak hunter standing on an expanse of powdery-dry snow as a storm approaches will likely die, unless he can go to a large enough patch of hard-packed snow, so that he can cut the snow into blocks with his snow knife and build an apudyak, the stereotypical dome-shaped igloo, in which he can wait out the storm in relative comfort and safety.

    Furthermore, the Iñupiak language has a single word that denotes "glare on the horizon indicating the presence of sea ice". English has no such word; it takes ten English words to express the concept. In that fact we see Cassirer’s assertion reflected yet again. The first of the Iñupiak noticed the phenomenon, saw that it held some importance for them, and gave it a single name, which they passed down as a linguistic heritage to their descendants. Even after they became aware of the phenomenon, the English never felt that it held enough importance to warrant the creation or adaptation of a single word to denote it.

    Thus we can envision the evolution of language as a positive-feedback process. As Cassirer asserted, what the people of a community notice in their environment shapes the language that they speak. And as the Sapir-Whorf hypothesis maintains, the shape of the language determines how people conceive their world and form expectations pertaining to their interactions with it.

    And the second change that we make in the Structural Differential consists of threads that we extend, more-or-less horizontally, from a Label in one chain of abstraction to Labels in other chains of abstraction. Just as the strings running vertically down each chain of abstraction represent the denotations that organize percepts into concepts, so the threads represent connotations, a set of concepts associated with a primary denotation.

    Consider, for example, the word "horse". That word denotes a concept that contains percepts emanating from a certain animal, the concept providing the abstraction of those percepts. But in addition to abstraction we have a process of association. Thus, hearing the word horse will evoke in the mind of the average American the concepts denoted by "cowboy" (a man who rides a horse to do his job, primarily moving herds of cattle across a prairie), "Kentucky Derby" (horses racing around an oval track), "cavalry" (soldiers fighting while riding horses), and so on.

    In the end we have the Structural Differential displaying how abstraction and association prompted by human emotional reactions to an inchoate and evolving environment have created our primary means of communicating with each other about that environment. We have arbitrariness upon arbitrariness, so how can we possibly believe that, using language alone, we can infer the rules by which Reality operates? On what basis can we claim that language gives us the ability to take a small set of axioms and deduce the fundamental laws of physics, which we do not perceive directly?

    Can we answer those questions? To do so we must use the very language whose use in deducing the laws of physics we have called into question. Of course, we can’t avoid it, so we press ahead and see what we can find. The answer to the above questions comes in several parts.

    First, we require that our reasoning use only denotation and that we exclude the connotations of words from our logic. When people first began to create science they assumed a magical connection between the denotations and connotations of words. Thus we got primitive sciences, such as astrology and alchemy. As people made more discoveries natural philosophers began to remove the assumed magic from their consideration. Using Francis Bacon’s empirical-inductive Scientific Method, they transformed astrology and alchemy into the modern sciences of astronomy and chemistry. Likewise, Aristotelian physics evolved into modern Newtonian physics.

    In addition, we want to use denotations to which we can assign numerical values, either directly or through the labeled blanks of algebraic formulae. We carry out that assignment through the process of measurement, by which process we organize certain percepts into the concept of magnitude, which we then absorb into our Label as part of its denotation. We understand what that means if we consider a small body moving along a ruler that we have put next to a clock. The percepts consist of images of the body at two different places along the ruler and two different views of the clock associated with those images. From those images we abstract two numbers – distance crossed and time elapsed – to whose ratio we give the denotation "speed". We then associate that denotation to the denotation of the body under consideration, not as a connotation, but as a property, something which properly belongs to "body of mass M". We might represent properties on the Structural Differential as additional holes drilled into the rectangle denoting the thing possessing those properties.

    Here we begin to get our first glimmerings of a special relationship between a kind of basic language and Reality. Recall that when we went from the statement that "the motions of all the bodies in the Universe always add up to a net zero" to an explicit description of what constitutes the amount of motion carried by a body, the body’s linear momentum, we used a series of purely imaginary experiments involving collisions among clusters of identical bodies. From those experiments, in which we imagined the clusters of bodies doing nothing different from obeying the rule that we had established, we saw a new property of bodies emerge, which property we associated with the number of identical standard bodies in a cluster and which we denote by the phrase "inertial mass" or, more commonly, simply "mass". That new property corresponds precisely to what Isaac Newton called quantity of matter. Thus, we have the linear momentum of a body as the product of the body’s mass and its velocity (speed manifested in a specific direction).

    That analysis raises a question about the relationship between mathematics and General Semantics: How does mathematics fit into the Structural Differential? It seems clear that we can gather together percepts from the Object and abstract from them the concept of manyness. That abstraction may also include specific kinds of manyness, such as fourness, sevenness, twentyness, and so on. From all of the kinds of manyness we then abstract the fixed sequence of names that we call the set of the natural numbers.

    Through manipulations of that set we get the basics of arithmetic. We get three basic synthetic processes – addition, multiplication, and raising to powers – and their inverses, three basic analytic processes – subtraction, division, and extraction of roots. Those last three processes necessitate the conception of three new kinds of numbers – negative numbers, fractions, and imaginary numbers respectively – which combine with the natural numbers to form a complete set, one fully closed under the six basic processes of arithmetic. All subsequent mathematics emanates from that numerical-arithmetic core.

    Another feature of mathematics may offer additional perspective on our question. To those not adept in its use mathematics seems hard (like rock or manual labor), dry (like a desert), cold (like ice), or all three. Such connotative descriptions of mathematics in terms of discomfort remind me of Mephistopheles’ advice to a young student in Goethe’s "Faust":

"My friend, ‘tis gray all theories be,

and green alone Life’s golden tree."

Connotations of bleakness typify most people’s reaction to mathematics, which tells us that mathematics confounds normal processes of human reasoning. That happens because mathematical logic uses only denotation, which means that mathematical logic gives us a perfect model of theoretical physics.

    Indeed, we think of mathematics as the hallmark of physics, the hardest of the "hard" sciences. We express a bewildering array of laws in an arcane symbolism that seems to have no relation to plain English and we deduce those laws themselves from fundamental principles by way of that same esoteric language. In that language numbers, in their various arrays, provide the vocabulary while binary-valued logic provides the grammar.

    Now we come to the second part of the answer to the questions posed above. To carry out proper deductions we must use binary-valued logic, reasoning based on pairs of mutually exclusive either-or statements. To see how that process works and to understand the role that different levels of abstraction can play in our reasoning consider the following two imaginary experiments:

    Imagine that we have a deck of cards. Each card has a letter on one side and a number on the other. Someone gives us a rule which states that every card bearing a vowel has an odd number on its opposite side. That someone then deals out four cards which show A, M, 5, and 8. Which two of those cards must we turn over to ensure that all four obey the rule?

    Most people say that they would flip the cards bearing A and 5. But the correct answer tells us to flip the cards bearing the A and the 8: turning over the A-card tells us whether the opposite side bears an odd number (as the rule demands) and turning over the 8-card tells us whether the opposite side does not bear a vowel. If either card does not conform to the rule, then we must discard the deck as flawed. Note that we did not have to flip the 5-card because it doesn’t matter whether its opposite side bears a vowel or a consonant: the rule says nothing about the relationship between consonants and even or odd numbers. For the same reason we don’t have to flip the M-card.

    For our second imaginary experiment imagine that we have gone into a bar and we see four young men sitting at a table. One of the men has a glass of beer, the second has a can of soda pop, the third just celebrated his twenty-fifth birthday, and the fourth is sixteen years old. We all know the rule – no one under the age of eighteen may drink alcoholic beverages – so, to ensure that the four men have complied with the rule, which two of them must the bouncer interrogate?

    People rarely get this wrong. The bouncer has to interrogate the beer drinker to ensure that he is over eighteen and interrogate the sixteen-year-old to ensure that he is not drinking an alcoholic beverage. He doesn’t need to interrogate the other men, because the twenty-five-year-old can drink either alcoholic or non-alcoholic beverages and the soda drinker can be any age at all.

    In both experiments we see the binary-valued logic. Our cards or bar patrons either conform to the rule or they don’t. The two possibilities are mutually exclusive and we have no third alternative, so if we falsify one possibility, we necessarily verify the other possibility. Symbolically, if we represent two mutually exclusive statements as P and Q, we have our rule as P or Q but not both, so if we falsify Q in the realm of our discourse, then we necessarily verify P in that realm of discourse.

    As an example of how we exploit either-or logic consider the most fundamental binary relation, that of existence. We have two and only two sets – the set of all things that exist and the set of all things that do not exist. We assert that in order for a thing to exist it must have an existent relationship with other things that exist: if that statement did not stand true to Reality, then some object could exist in absolute isolation from all other things that exist. But absolute isolation, lacking any possibility of affecting things that exist, defines nonexistence, so anything absolutely isolated from the other things that exist necessarily belongs to the set of things that do not exist. Thus the set of all things that exist must constitute a Universe in which every object has the possibility of communion with any other object.

    The existent relationship among the things that exist adds two more elements to the set of all things that exist – space and time. Empirically we know that those elements exist because they conform to a statement made by Einstein to the effect that, "No answer can be admitted as epistemologically satisfactory, unless the reason given is an observable fact of experience. The law of causality has not the significance of a statement as to the world of experience, except when observable facts ultimately appear as causes and effects." In the case of space and time we use rulers and clocks to obtain our observable facts, as Einstein required. But rationalistically, we must conceive space and time differently. That existent relationship among existing objects must have the ability to change without in any way changing the existing objects (because it is not part of those objects), it must have maximum simplicity (because complexity requires separable and rearrangable parts, which space cannot have), and it must have maximum flexibility (because it must encompass all things that exist). Whatever form space takes in itself, we can mimic that form linguistically by assigning numbers (which we call coordinates) to objects. Differences between pairs of coordinates give us the concept and measure of distance.

    Here we see how we can match concepts derived by abstraction from the concept of manyness with concepts derived from pure logic analyzing the concept of existence. On the Structural Differential we have the rectangle labeled manyness suspended from the Object and from it we suspend a rectangle labeled Numbers. We also have suspended from the Object a rectangle labeled Space, which we have connected horizontally to the rectangle labeled Numbers, using a wire instead of a thread to make the connection. The connection looks like that of a connotation, but Space and Number do not, either of them, connote the other. But neither do we obtain one of them by abstraction from the other. We associate Space and Number through analogy: Number consists of an endless, ordered sequence of names and Space consists of a presumably endless, ordered sequence of places or points. The wire thus represents a logical connection.

    But we also deduced the concept of Space from the concept of Existence. In this instance we have the rectangle labeled Existence suspended from the Object, as with any other concept directly abstracted from our perception of Reality, but in this case we have abstracted a fundamental property of Reality itself and not some minor feature of it. Rather than abstracting an element of contingency from the Object (as with, say, horse or bird), we have abstracted an element of necessity: we cannot possibly obtain other than what we got, thus we have an axiom, a self-evident truth that we cannot deny, from which we can deduce other truths. And among those truths we find the existence and fundamental properties of space, again found necessarily, not contingently.

    If we can extract from the Event via the Object a concept that necessarily stands true to Reality, then we can use binary-valued logic to derive from that concept other concepts that necessarily stand true to Reality. Binary-valued logic, the logic of either-or, enables us to use the process of reductio ad absurdum, in which we assert two mutually exclusive propositions from some axiom or theorem, show that one of those propositions necessarily stands false to our realm of discourse, and thereby necessitate that the other proposition stand true to the realm of discourse.

    Reality consists solely of Existence (the set of all things that exist) and Nonexistence. We assert that the two sets have a relationship with each other analogous to touching, that in some sense they have contact with each other. Either that statement stands true to Reality or it doesn’t. If it doesn’t, then Reality must contain a third entity to come between Existence and Nonexistence. That third entity does not and cannot exist; therefore, our original statement stands true to Reality.

    If any thing has a contact-like relationship with Nonexistence, then it doesn’t exist. If that statement did not stand true to Reality, then the set of all things that do not exist would contain as an element a thing that exists. That cannot happen, so the statement that leads this paragraph stands true to Reality.

    Now we seem to have a serious contradiction. On one hand we have the fact that Existence must have a contact-like relationship with Nonexistence and on the other hand we have the fact that anything that touches Nonexistence does not exist. Here our either-or logic seems to have failed, but the fundamental property of Reality prevents it from supporting contradictions, so if we truly have a tight connection between language and Reality, then logic can give us a way in which to dissolve the contradiction. To find that way, let’s look again at the possibility of putting something between Existence (aka the Universe) and Nonexistence.

    The concept of between-ness denotes a property of space, whose existence we have already deduced. Space comes between things that exist. Strangely enough, in working out the relationship between Existence and Nonexistence we can represent Nonexistence as a thing that exists. That fact necessitates that we ask whether any part of space can both exist and not exist. A fundamental property of space leads us to answer that question in the affirmative.

    Because of the analogy between space and numbers, the real numbers in particular, space possesses a property that we call measure, which encodes the concept of size. Where space touches Nonexistence no measure can exist. Where that same part of space touches Existence it must have the same measure, but instead of no measure, it has zero measure, the existent analogue of no measure. That boundary between Existence and Nonexistence thus has the character of a mathematical point, a geometric entity of zero measure. Then, just as the numbers on the number line increase away from zero, space increases its measure as it extends away from the boundary.

    In addition to space, Existence includes time as an existent relationship. But unlike space, which provides a relationship between different objects, time provides a relationship between different arrangements of the same objects. However, like space, time bears an analogy to the set of the real numbers and, like space, time must have zero measure on the boundary with Nonexistence (as we have seen in other essays, that fact necessitates that the boundary of space move away from each and every point in space at the speed of light in all directions). As space enables difference, so time enables change: those two concepts, taken together, enable motion.

    We know that the Universe, the set of all things that exist, can have no motion. In order for that statement to stand false to Reality the Universe would need to have a full spatial relationship with Nonexistence, instead of the single unique point that we inferred above: something like space would have to exist outside the set of all things that exist and we dismiss that concept as a logical impossibility and a physical one as well. But motion exists inside the Universe. The existence of both space and time allows the distances among objects to change as time elapses, allows the distance from one object to another to change as time elapses.

    To devise a concept that reconciles the two mutually exclusive statements above consider a potter’s wheel, which displays motion but does not move. That example shows us clearly that we can produce the equivalent of a system having no motion if all of the component motions in our system add up to a net zero. Thus we infer that, in order for the Universe to have no motion, Reality, the thing-in-itself, must have such a structure that all of the motions of all of the objects in the Universe always add up to a net zero.

    Here, again, we have used the concept of necessity along with simple language to deduce a valid description of another feature of Reality. In addition we clarified our reasoning by referring to a relatively familiar, human-scale object, a potter’s wheel, and, tacitly introducing the concept of likeness, we reasoned by analogy: as the potter’s wheel does not move and yet has motions within itself, so the Universe, which has no motion, has motions within itself. As long as we use only denotation and as long as the rules incorporated into the as-so likeness have the same structure, then for so long will our reasoning by analogy yield valid results.

    Look again at our bar-patrons/marked-cards experiment. We can combine the two rules through a statement of analogy: as under eighteen years must only drink non-alcoholic beverages, so a vowel-card must have an odd number on its reverse side. Through that analogy we can associate the bar patrons with the appropriate marked cards; the beer drinker with the 8-card, the soda drinker with the 5-card, the 25-year-old with the M-card, and the 16-year-old with the A-card. That analogy enables us to determine quickly and easily the correct two cards that we must turn over to see whether the cards obey the rule.

    Can an object in the Universe change its motion? Either it can or it can’t, so again we have an application of double-valued logic before us. In this case, though, let’s assume that we cannot find a logical necessitation that a negative answer to that question stand false to Reality; thus, we cannot use reductio ad absurdum to necessitate that a positive answer therefore stand true to Reality. In this case, then, we must introduce the concept of If in order to carry our analysis forward.

    If no object in the Universe can change its motion, then we can go no further with our logic. If, on the other hand (and if we had three hands, would we have triple-valued logic?), all objects in the Universe can change their motions, we want to determine the criteria that such changes must meet. We see readily that maintaining the absolute zero-sum of all of the motions in the Universe necessitates that any change in the motion of one object must produce, at the same time and the same place, an equal and oppositely directed change in the motion of another object or set of objects. We base that statement on the simple algebraic fact that adding +P and -P yields zero, so that if P represents a change, then we get no net change in whatever that change alters. The criterion thus inferred corresponds to Isaac Newton’s first and third laws of motion (the second law defines force in terms of the rate at which motion changes).

    At this point we make an observation. We look at the Universe to see whether we can find at least one object that can undergo a change in its motion. Upon finding that object we know that at least one other such body must exist in order to manifest the equal and oppositely directed change in motion. If that statement did not stand true to Reality, then the first body would have no opportunity to change its motion, which means that it would effectively have no ability to change its motion. If we extend that reasoning further, we infer that many, if not all, of the objects in the Universe can undergo a change in their motions. Then we take that empirical datum and the knowledge induced from it, we take the results of applying the standard Scientific Method, and use them to bridge the logical gap in the Map of Physics as it exists up to this point: we hope to replace that bridge later with a proper theorem obtained through the axiomatic-deductive method.

    In the interim we carry on with our analysis, assuming that the bridge will carry the weight of the theorems that we rest upon it. The next step that we take will tell us what motion looks like mathematically. We want to deduce the basic description of linear momentum.

    Imagine that two bodies collide in front of us and stick to each other. Assume that prior to their collision the bodies move at the same speed, one body coming from our left and the other coming from our right. If, in this circumstance, the two-body cluster comes out of the collision with zero velocity, we say that the two bodies are dynamically equivalent to each other. By repeating that imaginary experiment we can build up a set of dynamically identical bodies that we can use in further imaginary experiments. From those experiments we derive the rule which states that the amount of motion (linear momentum) possessed by a body equals the product of that body’s velocity and the number of dynamically equivalent bodies that correspond to the body (which number we call mass).

    Those imaginary experiments seem to come somewhere midway between the marked-card and bar-patron experiments. The use of algebra in the analysis of the experiments mimics the abstract aspect of the marked-card experiment. And the experiment itself has the story-like nature of the bar-patron experiment. More precisely, the imaginary experiment works like a game. We play a simple make-believe in accordance with the rules that we have already inferred. As long as our make-believe conforms to the rules, then we can accept as valid any new rules that emerge from the game. We see that fact reflected in the mini-stories used to illustrate the deduction of the features of the Lorentz Transformation from Einstein’s two postulates of Special Relativity.

    In those thought experiments (as Einstein called them) we imagine making observations and conducting experiments on or around trains in a world in which light flies at one hundred miles per hour. Once we have obtained, in algebraic form, the rules that apply in our imaginary world, we need only insert into the equations the correct value of the speed of light to obtain the rules as they apply to the real world. Through the rules that we assert as the premises of the game we make our imaginary world mimic the real world in the appropriate realm of application.

    Thus we see that language, derived from our percepts by abstraction, when applied to phenomena close to the most fundamental parts of existence, can yield up the laws of physics. That fact bears witness to the utter simplicity in which Existence manifests the rules of Reality and to the power of the human mind.

Appendix:

A Platonic Perspective

    "I believe, but cannot prove, that reality exists independent of its human and social constructions." - Michael Shermer.

    "I can prove almost nothing I believe in. ... (my beliefs) are on faith in a community of knowledge whose proofs I am willing to accept...." - Mihaly Csikszentmihalyi.

    Start with Plato. He taught his pupils that ultimate Reality consists of a set of eternal Forms or Ideals, of which the world we perceive shows us a crude reflection. To explain this notion he used the metaphor of prisoners in a cave watching shadows projected onto a wall. In that metaphor the only light in the cave comes from a bonfire at the rear of the cave, in a place where the prisoners can’t see it directly. Creatures, also out of sight of the prisoners, carry objects back and forth in front of the fire and thus cast shadows on the wall that the prisoners can see. Those creatures and their loads correspond to the Forms and the shadows correspond to our perceptions of them. This basic idea has persisted in natural philosophy for twenty-four centuries now.

    Plato’s theory rests on the tacit assumption that one and only one entity that we can call Reality exists and that it exists as an objective absolute. Because Reality exists independent of any perceiver’s consciousness, desires, or feelings, we can only perceive, not create, Reality, using abstractions to integrate our perceptions into the concepts that we call knowledge.

    Mind creates concepts by naming and organizing percepts. It does so by associating the percepts with other percepts, the sounds that we call words, which have two aspects that we call denotation and connotation. In our minds denotation represents the thing-in-itself and connotation represents a purely imaginary connection between one denotation and another. With concepts and words we strive to comprehend Reality.

    We live in a world of Platonic Forms, in which world everything that we perceive is merely the shadow of an ideal Reality that we can only perceive "through a glass darkly". But we also know that language and thought consist of the manipulation of symbols to which the people of a culture and only the people of a culture assign meaning, so that we also know that reason provides no more than a conceptual tool, a product of the human mind. The interplay among ideas, mediated by reason, creates knowledge, which may or may not mimic Reality.

    Mathematics and logic give us purely conceptual tools of thought. By taking a little care, we conceive them as pure denotation. Applying them to the denotations that we associate with certain percepts enables us to devise a Map of Physics, which matches the concepts that we derive from other percepts. Thus we infer that the Map of Physics mimics Reality.

    But Plato’s theory has come under challenge. In the Eighteenth Century Anglican Bishop George Berkeley revisited the Platonic idea that our perceptions give us only shadows and whispers of an underlying perfect Form. He accepted the empirical doctrine that we can only know ideas, which can only come from perception or reflection. That doctrine led him into the problem that he wanted to solve.

    If all that we can possibly know consists only of our thoughts, then how can we know that an absolute Reality exists outside ourselves? On what basis can we assert the existence of an external world of matter, the modern equivalent of the Platonic Forms, from which we obtain our percepts? In attempting to answer those questions we must reach the conclusion that, because we cannot get outside ourselves to examine the realm of the Platonic Forms directly, we cannot possibly know anything about that realm. What then can we say about the realm whence we get our percepts?

    In fact, we can say nothing about the realm of the Forms: we can know nothing of that realm. Berkeley took the next step in that chain of reasoning and claimed that matter actually does not exist as a thing-in-itself. We can only verify the existence of percepts, so Berkeley took perception as the foundation of his doctrine of idealism, which he summed up by saying that "to be is to be perceived". In that doctrine a material object exists solely as a collection of percepts, to which we give names like "bush", "tree", and so on. But the stability of those collections raises a famous question about Berkeley’s doctrine: "If a tree falls in the forest and no on hears it, does it make a sound?"

    Nothing can exist apart from a perceiving mind, so we may well wonder whether something ceases to exist when we no longer look at it. But, on the other hand, when we resume looking at that something it comes back into existence in a way that matches our memory of it. Now we must ask how something can cease to exist and then come back into existence in its original form: how do we explain the continuity? Berkeley did so by asserting that nothing ceases to exist, because someone perceives it continuously. Berkeley identified that someone as God. Because God exists everywhere at all times, It can hold all collections of percepts in the Divine Mind and thereby ensure their continuous existence within the regularity of Nature.

    By thus asserting a necessary connection between existence and perception, Berkeley sought to prove and verify the existence of God. The following pair of limericks sums up Berkeley’s proof quite nicely:


There was a young man who said, "God,
Must think it exceedingly odd
If he finds that this tree
Continues to be
When there's no one about in the Quad."

To which the young man received the reply:


"Dear Sir: Your astonishment's odd:
As I am always about in the Quad.
And that's why the tree
Continues to be,
Since perceived by, Yours faithfully, God."

    Berkeley conceived his doctrine as a matter of simple, straightforward logic. But others found it as disturbing as modern thinkers would find Relativity and the quantum theory when they first came into public consciousness. Famously, among those critics we find Dr. Samuel Johnson (1709 Sep 18 (O.S. Sep 07) – 1784 Dec 13), one of the first compilers of an English dictionary. As James Boswell described it in book 3 of his Life of Samuel Johnson:

    "After we came out of the church, we stood talking for some time together of Bishop Berkeley's ingenious sophistry to prove the nonexistence of matter, and that every thing in the universe is merely ideal. I observed, that though we are satisfied his doctrine is not true, it is impossible to refute it. I never shall forget the alacrity with which Johnson answered, striking his foot with mighty force against a large stone, till he rebounded from it -- ‘I refute it thus."

    Unfortunately, that incident merely shows that Johnson, like many critics, missed Berkeley’s point. Berkeley’s doctrine does not imply that the stone or the sensations of kicking it do not exist: it says that the stone does not exist apart from the perceptions of the stone’s appearance, texture, and of the pain felt by someone kicking it. A thing exists only to the extent that someone perceives it, but it does, nonetheless, exist.

    But doesn’t Berkeley’s God merely give us a synonym for Plato’s Forms? Asserting that everything that exists does so as thoughts in a Divine Mind doesn’t, on further reflections, seem so different from the assertion that everything that exists does so as a collection of entities from which all of our percepts emanate.

    In the Købnhavn Interpretation of the quantum theory we essentially have the statement that to be is to be measured. In that view Reality exists in an indeterminate state until someone makes a measurement. We can conceive that measurement as a contrived perception, so in a sense the Købnhavn Interpretation gives us a version of Berkeley’s doctrine. Thus we conceive Reality as a kind of inchoate swirl of patterns from with the act of observation picks out one for realization. But how can the determinate Reality of our perceptions rest on an indeterminate foundation?

    Again we must confront the region where the quantum theory segues into Newtonian dynamics. I am reminded of Impressionism, in which a close look at a painting shows only monochromatic strokes of paint but a farther look shows a full subtly-hued picture. We don’t have a clearly defined border between an array of paint dabs and a picture and we don’t have a clearly defined border between the quantum theory and classical physics.

    Our descriptions of the world necessarily work as does classical physics, but the world itself seems to defy logic. Note that we deduce features of the Map (e.g. Relativity, quantum theory, etc.) that we cannot infer from direct observation of Reality. Contra Bacon, we can imagine or suppose what Nature does and actually get it right. And we do that through the use of language, especially mathematics. Mathematics, beginning with numbers, is purely conceptual, so why does Reality conform to mathematical rules?

    Note that mathematics evolved from a simple sequence of names and the simplest methods of manipulating them. From such a simple beginning this example of pure language has evolved into a vast, elaborate structure of concepts. By using simple statements involving words that represent only denotation, mathematicians extend lines of reasoning that automatically connect to other lines of reasoning to constitute Mathematics as an endlessly expanding web of deductions and the theorems that emerge from them.

    Starting with the pre-Socratics, philosophers have accepted the belief that the Universe consists of a single, continuous, mechanical flux of matter, of which the human mind has no direct apprehension. By taking the simplest possible description of material Reality, using only denotations in that description, natural philosophers have worked out a means to apply mathematics to the most fundamental facts of nature. We have discovered that, as Rene Descartes suspected, that if we apply mathematical logic to those facts, we can infer patterns that actually match Reality. That fact tells us that no magical connections exist among real objects, that the associations among objects and their actions exist in the same way as do the associations in the classical syllogism. In that way we see Reality mimicking language.

    Reason reflects the human capacity for memory, reflection, and judgement. Because reason alone makes us human, in reason alone must lie the means of finding human happiness. Thus we find that Man is a rational animal whose happiness consists in the contemplation of a truth that infinitely transcends him and enables him to transcend his animal nature.

    So we come back to the Platonic vision of ultimate goodness. The Platonist conceives human life as an ascent within the flux of gross matter toward an ætherial and eternal ideal. We take it as a matter of faith that reason gives us the means of ultimately freeing ourselves from the demands of our animal nature and bringing ourselves into a life of dream and play. That statement gives us a no less compelling vision of human happiness than does the pursuit of metaphysical causes.

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