By Basil Gala, Ph.D.
In Search of Meaning
Thesis: Abstract thought is more powerful than concrete thinking in solving general problems; but concrete thinking is better for solving practical problems and experiencing life.
Concreteness has more emotional impact; it’s used in story telling. Story telling can convey an abstract message so that the message is clear and sharp in the minds of the people as in the case of biblical parables.
Abstraction is the process that leads to higher-level thinking and expressing ideas. Abstract thinking appears to be unique to humans, differentiating them from other animals. Many animals use tools, especially chimpanzees, but these animals are unable to think in abstract terms, plan, and follow a road map in what they do.
With complex brains, humans are animals capable of abstract thinking. We pay a price for our outsize brains which give us this ability. When we believe that our mental constructs are part of the outside world, we become irrational.
Humans are irrational animals with two legs. Other animals are more rational than humans in mating, acquiring food, shelter, and defending their territory. Animals naturally do what is best for survival, following instincts encoded in genes without interference from a large cortex.
Beasts rarely overeat, kill their own kind, or sell sex; they commit no crimes, although they have no concepts for good or evil. Animals don’t smoke, drink alcohol, or do drugs. Our dumb animal relatives act virtuously to survive as individuals, families, tribes, and species.
Abstracting is recognizing a higher-order pattern, which is useful and powerful in solving problems, or example, algebra over arithmetic, calculus over algebra.
Making something concrete, specific, and detailed is the opposite of abstracting. Physics tends to abstract; engineering is geared to concrete objects, so concepts from physics can be put to practical use.
Abstraction can be taken to ever higher levels; specificity can be reduced to sense impressions and feelings. Abstraction, a process in the neo-cortex, tends to detach us from feelings and emotions, allowing for better control of our actions. But we lose some of our spontaneity.
Children tend to deal with specific objects; educated adults are apt to think more abstractly. Those of higher intelligence think and talk in terms of concepts and general truths; others chit chat about trivial matters.
Civilized people are more abstract thinkers than savages.
Stories and novels involve concrete images to recreate an experience.
Mathematicians and physicists tend to be abstract; engineers tend to deal with the concrete, because they need to design things that work.
At the lowest level of abstraction the brain receives sense impressions from the skin which are simple conversions of electromagnetic signals from the environment to nerve impulses. Nerve impulses from the eyes are organized automatically by the occipital lobe into elementary patterns, such as lines, surfaces, textures, and colors. We fit elementary or primitive patterns into objects, a first level of classification by means of syntax.
A perceived object can be, for example, a single grape–a green, yellow, red, or black spherical thing on a vine. The animal sees a grape, a grape, and a grape, and if it can count, three grapes. In the next level of abstraction, we humans assign the number three in sounds or writing to a collection of three objects of any kind.
We follow that by assigning letters to rational or decimal numbers that we can compare with equalities or inequalities containing unknown and known quantities, as in algebra.
Newton and Leibniz progressed to calculus using the infinite and infinitesimal in calculating changes in quantities. Partial differential equations cover many more cases than simple equations, parameters supplying additional information after integration.
Abstract concepts of algebra, analytic geometry, calculus, and other mathematics, not only enable us to solve classes of problems, but also allow us to solve problems that would be virtually impossible to solve without these tools.
In formulating theories, we use abstraction; when we apply theory to practice, we turn to concreteness, employing specifics to solve problems.
Abstracting to a higher level concept, the genus, from a lower one, the species, is common in all sciences and arts. This process can continue indefinitely, where we make the genus into a species and find a genus over all the species in the same category. A category is a group or set of related objects, related by a quality or characteristic, which differentiates them from the objects in other categories.
The objects in a category are close to each other if we have devised a metric based on measurements on the object; the objects are distant from objects in other categories by the same metric.
More commonly, we classify an object by specifying a characteristic which it shares with other objects in its category or genus. We identify or define an object by specifying its genus and the traits which differentiate it from other members in its class.
The opposite of classification or abstraction is analysis, decomposing things into their component parts, like reverse engineering. We decompose by breaking relations, ties, or associations, among the members of the group. When we acquired optics to see into objects, we found molecules and atoms. Then we found atoms to be composed of electrons, protons, and neutrons. Now we know even protons and neutrons are made up of quarks.
Organized systems follow a hierarchical order; the top of the hierarchy holds all of the members; at the bottom are elements, which cannot be reduced further, each element a class with one member, itself. A society is such an organization with the owners at the top, managers further down, and workers at the bottom, each worker controlling only his or her own output.
Not all abstract or concrete thinking is hierarchical. Probability theory allows us to deal with chaotic or random phenomena, using statistical tools, essentially averages. An average is an abstract concept, but not derived from a species collection. It names the mathematical of operation of collecting a series of measurements, adding them up, and dividing the sum by their number.
We use probability theory and statistics to understand the behavior of particles in quantum mechanics, a behavior contrary to common sense: a particle can be in more than one place at the same time; it can entangle with another particle and affect that other particle instantaneously regardless of the distance separating them.
Justice, freedom, equality, fraternity, soul, and God are all abstract concepts in the social sphere which stand outside hierarchies. These are operational concepts which guide the behavior of people.
Abstractions often derive from first principles or axioms, self evident truths, such as those of logic, geometry, and other mathematical disciplines. We use those abstract concepts that we find useful in deriving further truths using a logical sequence of statements.
First principles cannot be deduced from other principles; we accept the truth of first principles if they are consistent with each other and if we firmly believe they are true. We have to question the validity of any principle if it leads to erroneous conclusions, that is, if observations contradict the conclusions.
The links from statement to statement need to be logically strong; weak links may allow the whole argument to collapse. Logical linkage is intriguing. In mathematics strong linkages establish rigor in theoretical results.
Abstractions from first principles are employed in all sciences; we derive these abstractions using deductive thinking as Euclid did in his Geometry. Descartes stated that first principles are truths that we clearly, without doubt, know to be true.
What we consider as indubitably true relies on common sense, which is sometimes wrong. The truth of first principles is upheld when derived results agree with observations. Common sense tells us that the earth is flat and that the sun revolves around the earth. More astute observations have shown us that these assumptions are incorrect.
In the sciences, such as physics, first principles are called ab initio, which derive from established knowledge without new assumptions.
Any statement is open to doubt. Euclid’s axioms gave rise to classical geometry, a very useful discipline for flat surfaces; when surfaces are curved, Riemann’s geometry is more fruitful. Einstein used Riemann’s geometry in developing general relativity. In Euclidean space, the shortest distance between two points is a straight line; that’s a common notion and it works for us ordinarily; but this notion is incorrect in a different kind of space.
Objects do not change their shape or mass because they are in motion says common experience. But we observe such changes in particles that move close to the speed of light. In a cyclotron, particle shape shortens and mass increases (or requires more energy to accelerate) near the speed of light. That is so because the particle is also a wave, as every object is a wave, with larger objects having shorter waves. Thus an electron microscope can penetrate matter better than a light microscope. The entire universe is a wave on an immense scale, reaching peaks of expansion and collapsing into points.
The sun appears unchanging and eternal; it will rise tomorrow and forever, according to common knowledge. We know today, however, that the sun has vast but finite energies which eventually will be spent and the sun will cease to exist as we know it. We can count on the common notion the sun will rise tomorrow, given our short life span compared to the sun’s billions of years.
First principles or axioms are also known as a priori knowledge; statements we know are true simply by reasoning and without reference to the physical world outside our minds. A priori concepts have no referents. We accept their truth on faith, as most of us accept the concepts the soul and of God.
You can come up with new concepts and theorems by making up definitions, posing basic assumptions, and working with common notions (a priori truths, axioms, or first principles). If you just want to do mathematics, you’re done; if you want to describe a physical phenomenon or engineer a system, you look to the usefulness of your new theories.
Concepts derived from observations and experiences belong to a posteriori knowledge. A posteriori knowledge is the domain of scientists who conduct experiments and collect observations. Yet, scientists organize and interpret observations using a priori concepts. What is the source of axioms or first principles?
We may form abstractions by taking away information from objects in a classification and retaining only those features we need to perform a particular operation.
Mapping or modeling takes away information from an object, reducing the salient features of an object on paper or other medium, a simple representation, easy to perceive for study and action. No map is like the actual terrain.
Maps, however, are very useful in planning and designing. Military campaigns use plans showing rivers, hills, mountains, valleys, and other geographical features important in laying out troops and defenses. The plans for a development include enough detail for engineers and contractors with specific skills, tools, and materials to actually build it, but the plans lack many details of the final product.
Many abstract concepts in mathematics and computer science are based on operations, like names of program subroutines.
Every word or concept has referents: things to which it refers. When a term is too far removed from its referents, it is likely to break its moorings, and may turn into academic nonsense, losing its usefulness.
What are the advantages of thinking abstractly? One advantage is the capability to solve a class of problems, rather than one problem. Therefore, when a problem from the same class faces us we can apply the same proven method to solve it quickly. Moreover, by assigning a unique symbol to the concept and manipulating it like an object to develop further results.
Suppose we set up the definition of an enemy as someone who has injured us or threatens to do so. We can immediately go into a defensive posture or proactively into an offensive position and action.
Prejudice works the same way to make it easy for us to avoid someone who belongs to a class we have set up in our minds representative of certain undesirable characteristics in people. Prejudice makes it easier for us to deal with an encounter that may displease us in the future.
On the hand, treating others as individuals, more concretely, has advantages also. In any group that we form conceptually, there exist individuals distinct in many ways from other members of the group; when doing a practical task it is often necessary to deal with the individual in concrete terms, like the stone mason using natural stones to build a structure. The stonemason picks up the right stone to position in his wall, maybe hammers it a little to adjust it, and places it in the structure.
Aesthetically, concrete things have an appeal to the senses that abstract objects lack. Artists use specific items for their compositions. Story tellers describe characters, interesting places, and plots to entertain and edify us. They engage our emotions with their stories about people, or even animals with human traits.
Maxwell’s equations describing electromagnetic fields, including light, are beautiful, but a rainbow in the sky stirs our emotions more deeply.
Poems and stories provide intellectual second-hand experiences; they don’t engage our senses directly, rather by association. When we read aloud a poem or story, even more so when we sing it or act out on a stage, we impact the senses of the audience more directly. The experience we render continues to be vicarious.
Well chosen words or symbols can evoke strong feelings; yet, an elegant sonnet or a mathematical equation is far from being an elegant statue. We love Shelley’s “Ode to a Grecian Urn,” but a beautiful urn we actually see and touch is closer to the senses and holds far more complexity than the poem.
The world is not simple and cannot be fully described in simple terms. Einstein’s E = mc² is simple indeed, but it does not describe the process of building a nuclear power plant; that is left up to engineering detail and ingenuity.
It is helpful to have a theory, a plan, a strategy, but to accomplish anything in the world outside our minds we need to deal with execution, tactics, and nitty-gritty details.
The direct experiences we obtain interacting with the world with our senses and other organs may give rise to new concepts. We pick up a strange object with our hands, look at it closely, lift it up, touch it, smell it, taste it even, and put it next to our ears to hear any sounds emanating from it. Now we name it, compare it to similar or dissimilar objects, and categorize it. We have formed a new concept, different from others described in books or in school for us. We have advanced science instead of simply regurgitating knowledge stuffed into us.
We note that the sun rises and sets daily, we may infer it will rise again tomorrow morning. Inferences are drawn from experiences; they make up experiential knowledge. By comparison, abstract knowledge like mathematics is mental; as useful as it may be in calculating and predicting events, mental objects have a tenuous relationship with the outside world. By means of experiments outside the mind, scientists periodically revise or scrap the mathematical “laws” of nature, advancing the frontiers of knowledge.
Intellectuals tend to think in terms of abstract terms and are often at a disadvantage in dealing with day to day challenges, getting lost in the details.
Our human powers to abstract events have allowed us to master the world and also to destroy it. Our brains are complex, perhaps too complex for our own good. As a rule, increasing complexity in a system causes more breakdowns. We learn and adapt more easily to changing circumstances; but our skills at ideation often lead us to insanity, because we tend to think our ideas and what we imagine to be objects outside our minds in nature. Animals are saner than we are and more direct in their behavior in sex, accumulation of goods, and relations with their own kind.
Still, abstract thinking can give us the ability to control our emotions (even love if it is destructive) and our reactions to pain and pleasure, allowing us to do what is needed for our survival. We rise above our hatred or fear, beyond our pain or pleasure to react to challenges of existence in ways impossible for animals.
The world of ideas can be so rich, so elevating, some judge this ideal world to be the real one, and the world of ordinary experience with our senses only a shadow of the ideal one. This kind of thinking is madness of a sort, but a divine madness.