Conceptual Analysis Mathematized
Conceptual Analysis Mathematized
Frege mathematized meaning by invoking the concept of a function, the central concept in modern mathematics. Concepts are conceived as functions from objects to truth-values, etc. This enables Frege to give a systematic rigorous account of the workings of language, modelled on mathematical notation. I propose to do the same for conceptual analysis: the analysandum is viewed as a function from the elements constituting the analysans. For example, knowledge is a function from belief, truth, and justification to a propositional component (intuitively, the concept of knowledge viewed as a constituent of thought). There are several ways of constructing the arguments and values of such functions, but the important point is that the function exists: it takes us from the primitive elements of the concept to the concept itself. It operates as a kind of binding function: it unites the several elements into a conceptual whole, glues them together. Thus, the concept is not just a list or conjunction; there is a natural unity. We define the function as second-level because it takes first-level functions as arguments—since belief, truth, and justification are functions from objects to something else (truth-values or states of affairs). The idea is that complex concepts like knowledge are mappings from simpler concepts, themselves mappings from one kind of entity to another (ala Frege). There is a hierarchical structure, representable by a tree diagram, linking complex concepts to simpler concepts. Of course, the concepts used in the analysis will often have analyses of their own, so that the tree will be ramified and many-branched. We could assign a number to its complexity and compare analyses in respect of cardinality (the concept of a game, say, might be twice as complex as the concept of knowledge, computed according to the number of functions in the analysis). A whole proposition (thought) would combine several analyzable concepts (“John knows what a game is”) and this entity would contain the full analysis of all the concepts that compose it. It would be mathematically quite hairy. The structure is familiar from linguistics and descriptions of conceptual constituency; I am merely adding the Fregean apparatus of functions, arguments, and values. We view the basic concepts as inputs to a function that gives as output a complex concept containing the input concepts. Think of the concept-forming function as a binding function: it fuses the elementary concepts into a conceptual whole that is available for cognitive use. Geometrically, it is defined over a space of basic concepts (also functions) that can be assembled into complex wholes; it is not unlike atoms and molecules, or words and sentences, or organs and bodies. We have a kind of mereological mathematics applied to the conceptual domain. Concepts can share parts and hence be available for intersection—one concept may incorporate an element also possessed by another concept. Set theory may thus be brought to bear. Formal methods can be applied to the domain of concepts, because of their compositional structure. We get a mathematics of the conceptual—primitive perhaps but mathematically formulated. It will yield equations like “Knowledge equals the combination of Belief, Truth, and Justification” (K=BTJ), i.e., “The thought-content of the concept of knowledge is the value of a second-level function from first-level functions corresponding to the attributes of Belief, Truth, and Justification”. This should satisfy the ambitions of mathematically inclined analytical philosophers wedded to the project of conceptual analysis.[1]
[1] Nothing says that this is the only way to mathematize conceptual analysis; I offer it as one way to impose mathematical structure on the underlying reality—illustrative not definitive.
Evil Opaque
Evil Opaque
There is an interesting epistemic asymmetry between good and evil: you can be doing evil and not know it, but you can’t be doing good and not know it. You can think you are doing good and really be doing evil, but you can’t think you are doing evil and really be doing good. Goodness is transparent, but evil isn’t. You can have unconscious evil motives that you consciously represent as good, but you can’t have unconscious virtuous motives that you consciously represent as evil. For example, no one ever gives money to charity with nothing but good intentions and yet believes he is acting evilly; but plenty of people have killed other people in evil ways while not recognizing the evil of their actions. Indeed, evil acts, evilly motivated, have often been represented as especially virtuous acts—genocidal acts, racist acts, acts of religious persecution, etc. A lot of evil flies under the radar, while virtuous acts are never depicted as evil (or morally neutral) by the agent. We can think we are good when we are not, but we never think we are evil when we are not (putting aside insanity or brainwashing). Why? Because evil is bad and virtue is good—so we have to represent evil as really virtuous, or at least morally neutral. There is no similar motive to regard good acts as evil—what would be the point of that? Evil must hide itself, but virtue has nothing to hide—there is nothing good about evil, but good is good. Thus, evil is opaque, furtive, sly—while goodness is out in the open and has no reason to disguise itself as evil. No one boasts about being evil when they are actually good, but people routinely boast of their goodness when their evil is quite evident to others. If people could not hide their evil from themselves, there would be much less of it—maybe none. If all evil were conscious evil, it would be a rare commodity. Good is invariably conscious good, which is fortunate or else good acts might be smothered by self-ascriptions of evil. But evil has the ability to conceal itself by various psychological stratagems, so it can lurk unseen while the conscious mind paints it in virtuous colors. Just think how different history would be if evil had no such ability, simply revealing its presence to the conscious mind. It is much the same with intelligence and stupidity: intelligent acts reveal themselves to the subject as intelligent, but stupid acts don’t automatically reveal themselves as stupid—the subject may regard them as perfectly intelligent. There is an epistemic asymmetry here: stupidity is opaque but intelligence is transparent. People don’t go around accusing themselves of stupidity when they are models of intelligence, because stupidity is not a desirable trait; but they do ascribe intelligence to themselves no matter how stupid they really are. Again, there would surely be less stupidity if stupidity were self-intimating; but it is able to conceal itself and put on a good face. Stupidity can disguise itself as intelligence, and has reason to do so, but intelligence never presents itself as stupidity—what would be the point of that? To put it in terms of repression, self-knowledge of stupidity and evil is subject to repression, because these are not admirable traits; but self-knowledge of virtue and intelligence has no reason to be repressed, because they are admirable qualities. If such repression were impossible, stupidity and evil would be far less prevalent (though some people might revel in their stupidity and evil).[1]
[1] Imagine if there were a stupidity-evil meter in the brain that automatically went off whenever the person did something stupid or evil: surely that would deter the person in question (no-one would be deterred from being intelligent and virtuous by a similar meter). Perhaps one day such a device will be invented; the world would be a better place (or am I being naïve?). As things stand, stupidity and evil are opaque presences in the mind, shielding themselves from exposure.
Analysis and Mathematics
Analysis and Mathematics
Mathematics is an analytical discipline (a branch of it is even called Analysis). It analyzes shapes (geometry), numbers (arithmetic), populations (statistics), motion (calculus), logical relations (mathematical logic), chance (probability theory), games (game theory). The OED gives us two definitions of “analysis”: “a detailed examination of something in order to explain or interpret it” and “the process of separating something into its constituent elements”. Putting these together, we could say that analysis is the detailed examination of something in order to separate it into its constituent elements. Mathematics does this in a rigorous and precise way: it breaks entities into their parts and specifies the relations that constitute wholes. It isn’t interested in the meaning of these entities in human life, or their psychological significance, or their poetic resonance, or their historical influence; it wants to know their constituent structure, pure and simple. It takes an abstract domain and dissects it, probes it, disassembles it. It looks for primitive entities and relations and investigates how they combine to produce more complex entities. A mathematics text can always be called A Mathematical Analysis of X. But is all analysis mathematical analysis? That is by no means clear; it depends on our notion of analysis and our interpretation of “mathematical”. Chemical analysis is clearly mathematical: it uses numbers and geometric shapes, and it employs rigorous methods (the OED defines “mathematical” as “(of a proof or analysis) rigorously precise”). Economic analysis is typically quantitative and mathematically formulated (e.g., the laws of supply and demand). Anatomical analysis specifies bodily parts in numerical and geometric terms (size and shape). But what about psychoanalysis or textual analysis or conceptual analysis—are these mathematical?
It might be said that psychoanalysis is mathematical in that it divides the psyche into precisely three parts—the id, ego, and superego. It also specifies quantitative laws of motivation expressed hydraulically. It aims for rigor and precision (it tries to be mathematical). The mathematics is crude and simple, but it is still mathematical in form—it resembles a typical scientific theory. Psychoanalysis is a bit like evolutionary science in this way: it too is concerned with quantitative structural relations—the probability of survival given certain genetic and environmental conditions. Some biology is aptly described as mathematical biology. Textual analysis can certainly be mathematical, even if not all is—word frequencies, inscriptional forms, etc. Astronomy also analyzes the physical universe mathematically, though some is not mathematically formulated. Linguistics is partly mathematical, though not wholly. Logic is certainly analytical and has attained the status of a mathematical discipline. Genetics is pretty mathematical, as is psychology. The concept of the mathematical is broad and inclusive; it doesn’t need to approximate the equations of advanced theoretical physics. The human mind is quite mathematical, thinking habitually in terms of quantity and number—counting, measuring, computing. It is perfectly possible to be mathematical about the arrangement of your room or the structure of a piece of music or the shapes in a painting. We shouldn’t overintellectualize mathematics or equate it with what we learn in school in a mathematics class. Other animals have rudiments of it, as do pre-school children. Mathematical competence is arguably innate (remember the Meno). Mathematical thought is more pervasive than might be supposed. We think in terms of sets and their relations. We recognize the magnitude of multiplicities. We add, subtract, divide, and count. We symbolize and generalize, abstract and mathematize. We have mathematical minds, and we like to impose mathematical methods on reality.
I say all this in order to prepare the ground for a somewhat startling thesis: conceptual analysis is mathematical analysis. Analytic philosophy is mathematical philosophy. In analyzing concepts, we mathematize them, as we have so much else. We can approach the matter both historically and intrinsically. Historically, we have the figures of Frege, Russell, Wittgenstein, Carnap, Tarski, Quine, Kripke, Montague, and many others—all mathematicians by training and eager to apply its methods and attitudes to philosophy. Russell wrote Introduction to Mathematical Philosophy and Montague wrote Formal Philosophy. The shape of so-called analytical philosophy was certainly influenced by mathematics, modelled on it, inspired by it. Tarski’s theory of truth is a prime example. Carnap’s Aufbau is in this tradition. These philosophers wanted philosophy to be rigorous and precise, and mathematics was their paradigm. This conception of philosophy contrasts with other conceptions prevalent in the intellectual tradition: historical and cultural (Vico and Collingwood), psychological (Locke and Hume), religious (Aquinas and many others), linguistic (Austin and later Wittgenstein). It is ahistorical, anti-psychologistic, secular, and contemptuous of ordinary speech. It likes proof not poetry, dissection not description, abstraction not particularity. It is Pythagorean not Hegelian or phenomenological. It is about logic not life, entailment not lived experience. It prefers science to stories. It deals with the form of thought not the dynamics of action (the “deed”). It is formalistic not humanistic. It prefers rigor to uplift. It reveres Plato more than Aristotle, and has no time for Nietzsche. It is pure not applied. It is anti-biological. It is above politics. It is contemplative not practical. It deals in necessities not contingencies, essences not empirical facts. It is more rationalist than empiricist (Russell’s first book was on Leibniz). Thus, analytical philosophy is mathematically oriented, mathematically imbued; it grows from mathematics.
Viewed intrinsically, we can note that conceptual analysis is what the name implies—analytical; it breaks concepts into their more primitive elements. It reduces unity to multiplicity. This multiplicity has a number—the number of necessary conditions that constitute the concept. Thus, knowledge has three necessary conditions, according to the classical analysis—belief, truth, and justification. These conditions are recognized in their numerical dimension: this is a three-component concept. Each component is added to the others to produce the concept being analyzed. We could represent the analysis in the form of an equation: knowledge equals belief plus truth plus justification. This appeals to our mathematically inclined mind. We could say the same about the causal analysis of perception, Grice’s analysis of speaker meaning, Suit’s analysis of the concept of a game, or any other attempt at conceptual analysis. We could divide concepts into three-component concepts, two-component concepts (a bachelor is an unmarried man), and one-component concepts (primitive concepts like the good, according to Moore). That is, we could dwell on the numerical attributes of concepts. Concepts have a mathematics, according to the tenets of analytical philosophy, construed as methodologically mathematical. We already do this with regard to other points of conceptual analysis: we speak of one-place, two-place, and three-place predicates; we distinguish first- and second-order quantifiers; we call existence a second-level concept; we talk regularly of the finite and the infinite. Of course, we have a philosophy ofmathematics, as well as a generally mathematical philosophy. We are well aware that concepts have mathematical properties. Above all, we approach the task of analytical philosophy in a mathematical spirit—rigorously, precisely, as mathematically as we can. Some analytical philosophers even go so far as to apply mathematical model theory to philosophical issues (e.g., Montague). Such philosophers want philosophy to approximate to a mathematical science, and they are not wrong to be so motivated, because conceptual analysis fits the paradigm. This is why Russell’s theory of descriptions was so applauded by philosophers in the analytical tradition: it provides a mathematical analysis of the definite article (symbols, quantifiers, formality). Similarly, for Tarski’s theory of truth and Davidson’s attempt to convert it into a theory of meaning. If only we could employ calculus to resolve the problems of space and time, or the statistics of neurons to solve the mind-body problem! It is an entrancing vision. It beats windy pronouncements about the course of history, or the problematics of the text, or the puny joys of “experimental philosophy”. Mathematical philosophy sounds like the kind of philosophy a serious student might get behind. Okay, it hasn’t quite lived up to the hype, but its heart is in the right place—some distance from the actual heart (unless you are Plato or Pythagoras). It carries better credentials than merely descriptive ordinary language philosophy, which threatens to turn into a kind of localized anthropology. In any case, the analysis of concepts looks like a bona fide case of mathematical analysis: it is precise, abstract, systematic, and susceptible of proof.
How does the mathematical method arise in the human mind? We don’t know, but here is a promising suggestion: it arises from the language faculty. For the language faculty is itself mathematically structured: it consists of a finite array of primitive elements (words) that combine in a rule-governed way to generate an infinity of linguistic strings (sentences). We might plausibly regard the mathematical faculty as wholly or partially derived from the language faculty, arising at some point in evolutionary history. Without going into the matter further, we can entertain the hypothesis that our capacity to conduct conceptual analysis ultimately derives from our capacity for language; crudely, conceptual structure and composition mirror linguistic structure and composition, as seen through the lens of mathematics. The analytic-mathematical turn in philosophy owes its origin to the linguistic-mathematical turn in evolution: the human brain went linguistic and mathematical long ago and then much later it occurred to people to investigate the concepts involved in philosophical problems mathematically. Mathematics grew out of language millennia ago, developed in the course of human history, and then suggested itself as the royal road to philosophical enlightenment. According to this hypothesis, creatures without a language faculty will not develop a mathematical faculty, and will therefore not develop what we call analytical philosophy. This is a new type of “linguistic turn” in philosophy, happening perhaps millions of years ago not in the middle part of the twentieth century. First, we have the mathematical turn in philosophy that did happen in the twentieth century, but this turn depended on the prior existence of mathematics in the human mind, going back into deep evolutionary history, some time after the appearance of language in humans. From language to mathematics to analytical philosophy—the long curve of human intellectual history.
Mathematical-analytical philosophy was conceived as exclusionary—we should do that kind of philosophy and not the other kinds of philosophy. But this is not compulsory: we can let the mathematical kind of philosophy roam over its domain of operations but we can also make room for the historical, psychological, anthropological, spiritual types of philosophy. We can have existentialist philosophy as well as essentialist philosophy—the human condition and necessary and sufficient conditions. The humanistic and the formalistic. For example, we can philosophize about the role of games in human life as well as analyze the concept of a game in quasi-mathematical style. Collingwood can coexist with Russell, Sartre with Carnap. Doing analysis does not preclude investigating Dasein. We can talk about the structure of our concepts and the meaning of life. We can have analytical philosophy and the other kind (it has no accepted name)—historical, hermeneutical, humanistic, humid. We can have the dry and the moist, the desiccated and the succulent. By all means let’s take the gustatory turn! We can be both mathematical and musical (bacchanalian even). Punk philosophy is not out of bounds (it belongs with existentialist philosophy). We can talk about money and sexual perversion as well as knowledge and the form of the good. You could happily describe yourself as an analytical-humanistic philosopher. What you don’t want to be is a bullshit philosopher (either pedantically so or pretentiously so). There is more than one way of being good at philosophy.[1]
[1] Unfortunately, few people are good at both types of philosophy: if you are good at one, you tend not to be good at the other. Practically, I would encourage graduate schools in philosophy to educate students in both traditions, while allowing that students will generally be better at one sort of philosophy than the other. There is, however, no excuse for the dismal prose style of the typical product of an American philosophy graduate program. Someone should really do something about this.
Trump Squared
Trump Squared
I don’t think Trump is going far enough in his immigration policies. He wants all the illegal migrant criminals out—good, we don’t want criminals in our midst. No criminal, no crime. But the same argument applies to allcriminals—we want them gone, so they won’t commit crimes on us. We could send them all to Mexico but that might prove difficult politically. The solution is to send them somewhere empty and far away, like the British did with Australia. That worked out pretty well in retrospect. True, Australia today might not want planeloads of American criminals deported there, but I have an answer to that: send them to Greenland! All we have to do is buy Greenland, or just take it, and then send all of our criminals there. Bingo, problem solved. This has the added advantage that Greenland is a cold desolate place, unlike Australia, so no one can accuse us of going easy on our criminals. This will solve the crime problem in America. Trump just needs to get tough on crime.
A Proof of Simulation
A Proof of Simulation
I have come to the conclusion that we are living in a simulation. We have the proof to hand: a character named Donald J. Trump has become president of the United States—twice. It is impossible to believe; and what is impossible cannot be true—therefore, it is not true. But all the evidence points to it being true, so there must be a massive effort at deception underway; hence, we are living in a simulation. Someone is manipulating our minds to persuade us that this fictional character is running the country. Clearly, no such thing can be true—it is just too crazy to believe. Think about it: he even looks fake, as if made of synthetic material. He is like an Alice in Wonderland character: a speaker of nonsense, completely irrational, a cartoon villain. He isn’t real. Donald Trump does not exist. He is a fiction. That is the only way to explain it, because such a man couldn’t become president of a great country. It is beyond the bounds of possibility. It must all be an alien plot to mess with our minds. Thus, we are living in a simulation.
A Puzzle Regarding Color
A Puzzle Regarding Color
Color has long intrigued philosophers and others. Is it objective or subjective, or something in between? Is an inverted spectrum possible? What is the nature of logical truths about color? I will raise a different question: do things have the colors they have contingently or necessarily? Is color arbitrary or grounded in facts of nature? For example, could the sky have been green and plants blue? Could blood have been yellow, snow black, coal white, the earth red? I mean by this could things have looked that way; I am not concerned with whether objects could have had different reflectance properties. Things look a certain way color-wise to humans and other animals, but could they just as easily have looked a different way? Is it like driving on the right: could we just as easily have driven on the left (as some other countries do)? Is it completely contingent what colors we bathe the world in? Or is it that specific colors naturally belong to some things and could not be changed without some sort of loss or disruption? If we saw plants not as green but as blue or red or yellow, would there be any loss of accuracy or utility? Are plants naturally seen as green—is this the color they ought to be seen as? I think we are confronted by conflicting intuitions on this question: on the one hand, we feel that plants are correctly seen as green; on the other, there would be no error in seeing them as a different color. Thus, if Martians inverted our color perceptions, they could not be convicted of error or perversity or sub-optimality—they would be as right as we are. The reason is that each color presents the same range of variations and hence distinctions: the same visual information can be presented in blue as in green—and that is all that matters (biologically, intellectually). The color itself is just an arbitrary label, like a proper name. The function of color perception is to allow for visual discrimination, but this can be achieved in a variety of ways; perceivers are not tied down to one color. It would be a form of color prejudice to insist that seeing plants as green is the only viable and veridical way of seeing them; blue would do just as well. Seeing blood as yellow is just as reasonable as seeing it as red. And yet we observe that no such variation obtains: as far we can tell, all animals see the colors of objects the same way, i.e., plants as green and blood as red. The color receptors in the eyes are universal in seeing creatures on Earth: but this seems surprising from an evolutionary perspective, since it would have been just as sensible to evolve blue perception for plants as green perception. We find variation in which side of the road people drive on, which is only to be expected given that this is entirely arbitrary; but we find no variation in what colors are attributed to the world despite the apparent arbitrariness of a given selection. Why? That is the puzzle: why is it theoretically feasible to invert colors and yet this doesn’t happen? Moreover, why does it feel wrong to see plants as anything other than green? Why is seeing plants as green universal and intuitively appropriate, while logically it could have been otherwise without loss or error? Something has to give.
It may be said that this is a case of simple prejudice—custom, what we are used to. We have always seen plants as green and blood as red, so we mistakenly think there is something necessary about this; we are like people who think that driving on the right is the God-given correct way of driving. We have a color superiority complex (prejudiced Martians would have the opposite prejudice). Alternatively, evolution just happened to make an arbitrary choice millions of years ago and has seen no reason to change its mind, even locally. It could have chosen blue or red for plants, but it settled on green and has stuck in its ways. I think neither of these views is plausible: there is something more deep-seated about the way color is perceived. But it is hard to discern what it is exactly—nothing immediately suggests itself. To put it crudely, plants really are green, so it is preferable to see them that way. Compare: it is really better to drive on the right, because actually the sun is less blinding that way. But what is this hidden factor? Could it be that green is actually better suited to encoding subtle differences in things than blue? That would appear to be true of black and white, but on the face of it blue admits of the same degree of variation as green. Is it that things would be more confusing if plants were blue given that the sky is blue—animals would see no sharp distinction? But then why not see the sky as green by way of contrast? Why is blue better for the sky than green? Both can vary in degree of lightness; both can allow clouds to be equally visible. It would be different if we asked why the sky isn’t seen as bright red, because then it would be more limited in its potential variations. So, the puzzle remains: every color seems as good as any other from an informational point of view. Nor does it seem any harder for the brain to produce blue than green perceptions; the colors are equally available and equipotential. Nothing in nature favors one over the other—and yet nature seems determined to stick with a single color-scheme. It is as if it wants animals to see plants as green, even though it has no reason to want that. The colors seem functionally identical, but nature sticks religiously to one scheme rather than another, puzzlingly.
Perhaps we are looking in the wrong place—the informational powers of color perception. What about the emotional and pragmatic connotations of color—the psychology of color? For it does seem true that colors vary in their psychological associations—and not just by habit or custom. Green really is a soothing restful peaceful color, while red is not. Yellow is a joyful light-hearted color. Blue is an attractive charming color (blue eyes). Black is a doom-laden sinister color. White is an optimistic open color. Why this is, we don’t know; it just is. There is a psychology of color—affective, even moral. Orange is felt to be tacky and in poor taste; brown is rather blah. We have favorite colors and least favorite colors. We are not indifferent to color, as if it is nothing but a neutral medium for conveying information. Nature wants us to have good feelings about plants, so it makes us see them as green. Why? Because we have to live with them every day, eat them, lie down on them, or up them. Nature needs to make them a color we are not put off by; it needs to make our brain receptive to them. In the case of blood, it needs to make us wake up and take notice, because the sight of blood is a bad sign. Thus, the colors of nature are designed to mesh with our emotions, desires, and practical decisions—to be psychologically right. Nature (evolution) is cunning in this way: it designs animals to be the best they can be in the circumstances—the most efficient, survival-oriented. All this is carefully planned: the plant world is bathed in green because that is what works best psychologically. Green is inherently likeable, even loveable, so evolution sees to it that we see plants as green. Of course, this is rather mysterious: how can a color be inherently emotional (compare shapes)? And yet it appears to be so: we are hardwired to react to green in certain ways that are conducive to survival, because green intrinsically has a certain affective character. Colors have logical relations built into them, but they also have psychological dispositions built into them. Neither of these things is easy to understand, but they appear to be facts: green is essentially affect-positive, and in a specific way. Not scintillating perhaps (unlike blue) but easy on the eye and brain; not attention-grabbing but mellow and relaxing. When we see green, as with a country landscape, our soul breathes a sigh of relief, a feeling of security and tranquility—unlike a blaze of red flowers or a gorgeously blue sky (too much uplift). The painter chooses his colors carefully, aware of their affective potential; nature chooses its color palette with equal care, properly sensitive to the needs and desires of the creatures living within it. It just wouldn’t feel right to see plants as blue or red, even if this would entail no loss of informational content—it would send the wrong emotional message. Likewise, the bright red of blood delivers a message of alarm and danger—act now! Red is the color of emergency; green of contentment; blue of transcendence (heaven above, piercing blue eyes). Colors are actually very clever, ingeniously designed, magically effective. Natural selection knew what it was doing when it selected the colors of the rainbow, right down to the last detail. Colors are carefully designed adaptive devices not merely dispensable means of conveying objective information. They are not bland. Thus, they are not arbitrarily assigned and interchangeable.
How many colors are there? Estimates vary: I would say basically four: blue, green, red, and yellow (plus black and white). We are told that some animals see colors we don’t see. Let’s say there are ten basic colors on planet Earth. But how many logically possible colors are there—a hundred, a million, infinitely many? Let’s say a lot. Then evolution selected a small subset from the full range, presumably because these are the best ones given the conditions on Earth. They are assigned to objects according to criteria involving psychological requirements (as well as informational requirements). We can assume that this choice was well-motivated—these are the optimal colors for evolutionary purposes. It wasn’t haphazard, random, arbitrary. We thus have a carefully curated world of colors to feast our eyes on (good metaphor)—the best of the best. We should feel good about this: our eyes and brains are recipients of the finest class of colors that money can by—the Rolls-Royces of colors. When you see green you are seeing a finely crafted chromatic machine lovingly perfected over millions of years. You should feel privileged to be privy to such a marvelous spectacle, to live with it day in and day out. Aesthetically speaking, our colors are probably the most beautiful of all (it’s nice to think so anyway); they are not second-rate goods selected by a careless middle man. And each belongs in its proper place. Our visual world is a lot more resplendent and fine-tuned than we might have supposed. We should be thankful.[1]
[1] I almost want to say that colors are a minor miracle—but perhaps I should say that they are major (natural) miracle. They are wonders of the world, demigods, great works of art. We have no idea how they came to be, from what they evolved; but they are with us all the time, glowing like so much pale fire. They came into existence many billions of years after the big bang, themselves flaring into being, and entered the minds of terrestrial creatures. Whenever you see a color, you are seeing a miracle of nature, a veritable show-stopper. I am surprised they have never been used to prove the existence of God! They are much more miraculous than the standard biblical miracles, and we can witness them all the time just by opening our eyes (again, I am speaking of perceived color not the physical basis of color in objects.) They have a kind of intelligence. They evolved but have never gone extinct (that we know of), thus demonstrating their adaptive value. They have helped many a species live to fight another day.
Medical Update
Medical Update
I was driving over to Eddy’s today for a game of tennis. I had just been reading my friend Oliver Sacks’ wonderfully revealing Letters (2024) and had reached nearly the end when cancer had invaded his body. It began as a small melanoma in his right eye, depriving him of some vision in that eye. It was treated with radiation and had responded, but it proved “persistent” and needed extra doses. Then he discovered that it had spread to his liver and would be terminal. Soon, it was. Of course, I couldn’t help thinking of the melanoma in my right ear, which had spread to my neck and then to my lungs—for which I had received the standard treatments. As I drove, on a fine Miami day, I received a phone call from my oncologist’s office from his nurse, Yvonne, telling me that the doctor had reviewed my latest CT scan and that there was no evidence of melanoma in my upper body. This means, pretty much, that I am now cancer-free. I enjoyed a game of tennis.