Inventing the Elements


Simplicity

 

'Tis the gift to be simple, 'Tis the gift to be free;
'Tis the gift to come down where we ought to be;
And when we find ourselves in the place just right,
'Twill be in the valley of love and delight.
When true simplicity is gain'd,
To bow and to bend we shan't be asham'd
To turn, turn will be our delight,
'Til by turning, turning, we come round right.
Elder Joseph Brackett (1797-1882) Simple Gifts c.1875

 

The odd dichotomy

This wonderful old Shaker song seems so at odds with the real world, much as the Shaker's themselves were with the rest of 19thcentury America. The world is complex, broad, and multifaceted. We expect theories to be complicated and large. Our disciplines are driven by great organizations - numerous practitioners jointly sign new works, large scale funding is required to advance the state of the art, and we have the belief that significant new knowledge will come out of massive collaborations, “Manhattan Projects." And while we may yearn for simpler times, as did the Shakers, we are generally unshaken in our belief in the complexity of our world.

Yet there are a few bits and pieces which should cause us to pause. When we listen to those who worked with the great thinkers, Einstein, Bohr, Fermi, we are told of their most special qualities, the ability to ask simple questions. We love the child-like nature of Picasso, of Richard Feynman, of Linus Pauling. And when we describe people as child-like we are most often describing their essential simplicity. It does seem odd that often the deepest quality of great inventors should be described in these ways. Just maybe, that old Shaker prayer really does express something truly profound.

Simplicity- An Auto Example

We can get a better sense of this by looking at our most prominent physical artifacts, automobiles. The Model A Ford, introduced in 1928, was wonderfully simple, indeed it was much simpler and easier to use than its predecessor the Model T. Perhaps the first truly modern car - it was manufacturable, had all of the same components as today's cars, and was designed to be cheap and easy to assemble. When we try to restore one, we see all of the parts that are still fundamental to today's cars. Compared to our automobiles, its parts were much simpler, but it was actually more complex to construct. Despite the great strides we have made in the sophistication of our automobiles, we have actually made them simpler to put together. The roof of the Model A was fabric, covering metal cross bars, screwed, clipped, nailed, and hooked into the body. Compared to a modern car with a single stamped welded roof, it was very complex with many parts.

Starting my son's Model A requires turning on the gas valve, setting the spark advance, the choke, and the idle speed, pumping the gas petal, turning on the key, holding in the clutch, and pressing the starter button with your foot. Starting my Saab requires turning the key.

We no longer make a separate body and frame (chassis) of a car, but instead mold them together in giant presses of the same steel. We no longer make the floorboards of the car from multiple pieces of plywood carefully cut to shape, but of a single sheet of molded steel. The parts of a modern car are certainly much more sophisticated than those of the Model A, they are no longer machinable or fixable by a home mechanic, but the overall construction is actually simpler. The automobile companies make it easier and cheaper to put together.

The history of the automobile is a mirror of the history of knowledge. The first horseless carriages were very simple affairs, equivalent to a golf cart. As they became automobiles, they grew more and more complex with new parts added year after year, lights, brakes, doors, locks, transmissions, reverse, electric starters, fuel pumps, heaters, automatic transmissions, and on and on. At first, each of these new parts was just added on, effectively bolted onto the machine. Thus the trunk was actually a wooden "truck" that could be found in any home, strapped to the rear of the car. Then came an integration, when separate parts were collected into a new part or anew whole. The car looked different, worked differently, and was manufactured in a new way. The Model A was such a car. The pattern follows an increasing complex collection being replaced by more complex and sophisticated elements and more highly integrated wholes. The automobile industry has just been through another such cycle, today producing a car that is much better built and much more satisfying to drive then those of the 1970's and '80's.

Simplicity and Knowledge

It is the same with conceptual artifacts and the Pattern of Knowledge. We start simply, build complexity taking in more and more parts and more and more experience. The sites and fasteners become complicated. We then invent new fundamental elements greatly simplifying the sites and fasteners.

Simplicity is the answer to an interesting question about the elements of knowledge.

This is exactly what happens when a new element of knowledge is invented. It can hold much more, and it can contain a much wider variety of experience. It enables us to greatly simplify our constructions, the building of other artifacts. Simplicity is the answer to an important question. Why do so many, but not all, of the greatest ideas appear at the biggest changes in the "Pattern of Knowledge?" Why did the revolutions of the 7th century, of the 1500's and the 1860's produce so many new and fundamental works? It is because such new fundamental elements enable great simplifications in our knowledges.

The new element is more powerful, more sophisticated, capable of holding much more. And the fasteners are so much simpler. It makes our world look simple and understandable. Once such an element is fashioned, it creates the potential for such vast simplification that it opens the floodgates to invention and with lightning speed passes from discipline to discipline.

While at first blush, we may think of a new element, as complicated, as difficult, as sophisticated, as hard to create; as we come to understand it, we see it as profoundly simple. We stop seeing what it took to construct this element and begin to see it as our essential building block. It is more abstract, and harder to get our arms around initially, but as we do learn to understand it, we see its essential simplicity and how it simplifies the world around us.

We thus do treasure simplicity as the Shakers did.

 

Parsimony

 

One comes nearer to the most superior scientific goal, to embrace a maximum of experimental content through logical deduction from a minimum of hypotheses
(Albert Einstein) 

Uniqueness implies rarity, which explains why parsimony is so important in knowledge.

The search for simplicity is fundamental to the work of our scientists and philosophers. It is described as parsimony. The quest for parsimony seems to be at the heart of the invention of knowledge by its greatest inventors. Over and over again they have told us that they follow Ockham's Razor, the fewer the propositions and the simpler the foundations, the closer knowledge comes to the "truth." Nearly unanimously they viewed their task as the creation of unity using the fewest assumptions.

Unique Artifacts turns this personal philosophy into a fundamental postulate - a general philosophical principle. For the very essence of uniqueness is parsimony. To be unique is to be rare, and we postulate that the invention of human knowledge is the fashioning of unique artifacts. Therefore, unique artifacts must indeed be very rare. Parsimony is the essence of our belief that a construction is in fact unique, that another artifact cannot be built which will have fewer assumptions and unite the same experience. Parsimony gives us great confidence that our fastening artifacts are rare and thus unique. That is why our greatest thinkers use the fewest possible assumptions. That is why it is futile to try to devise a new field theory of gravitation to replace General Relativity. If the assumptions are few then we have a high level of certainty that the idea is unique.

Fastening artifacts are very precious. We invest great effort and energy into them. We reorganize our cognitive world based on them. We concentrate research on them. We extend them, building an entire scaffolding of knowledge upon them. And we teach them to our children with proper diligence. We humans are knowledge conservative; we do not change our knowledge or belief systems readily - it takes too much effort. It is thus very important that the fastening artifacts we choose be unique, that we will not have to reorder our knowledges, particularly our fundamental concepts, very often. Therefore, we search for parsimony as a powerful vector to uniqueness. It is this drive for uniqueness that motivates the search for the fewest and the simplest set of assumptions upon which to build works. This demand for uniqueness underlies the greatest of our theories, the best of our art works, as well as the most beautiful of our physical artifacts.

Parsimony, a simplicity of assumptions, the use of the fewest possible foundation concepts, is the expression of uniqueness in thought. We love simplicity and parsimony because we crave uniqueness and we believe that fastening artifacts are unique when they are simple.

 

Abstraction

Uniqueness explains the shifts between the Elements - symbols, universals, objects, environments, artifacts.

Abstraction has proven to be a very powerful and yet very elusive idea. While we use it all of the time to describe thought, we never seem to get a full grasp of it. Uniqueness provides a measure of clarity. The abstractness and uniqueness of artifacts are clearly connected. The more abstract an artifact is, the broader its reach and the more likely it is to be unique. When we think, we try to construct the largest idea that we can to hold our experiences, for that idea will necessarily be rarer, more unique. It will also be more abstract. We are always trying to replace many entities with fewer entities, many sites with fewer sites, many fasteners with fewer fasteners. We try to make larger artifacts that will replace a multiplicity of smaller ones. Such larger artifacts, further from individual experiences because they encompass greater quantities, are more abstract. Our drive to uniqueness is necessarily a drive toward abstraction.

We often confuse and denigrate the abstract, when we are given a generalization as an explanation. It is common for people to say - "It is the environment. “It is human nature." - and for us to feel that we have been told nothing useful. This is no more mysterious than the difference between a complete physical artifact and one that is just beginning to take shape. The unfinished project may appear wonderful to the artisan, because their finished vision is clear. But for the rest of us that vision must be fully constructed. So it is, for the artifacts of our imaginations. They must be fully constructed for us to appreciate and accept them. Thus a broad generalization is not necessarily an abstract artifact, unless it is complete.

Abstraction explains the differences between the artifacts developed by children and adults, even when they are based on the same unique entities. The adult's artifacts, generally richer in experience, are more abstract than the child's. They are thus more unique and more powerful. While superficially the artifacts seem the same, upon closer examination they will show substantial differences in abstraction. As our minds grow stronger and our experience increases, we seek artifacts that are more abstract for they are more unique as vessels for larger quantities of experience.

In this same vein, abstraction helps us to better understand the differences between everyday artifacts and the great human artifacts. They differ in abstraction, in the quantity of experience they can hold. The great human artifacts are abstract; they are models for other artifacts. Of course, they must be finished, and they must be complete. The difference in abstraction is thus the difference in uniqueness. Abstraction is a measure of uniqueness.

Now, finally, we return to those artifacts that started our quest, the unique entities (symbols, universals, objects, environments, and now artifacts). These elements of knowledge are also the greatest abstractions that we have. And it is of great interest that our most powerful abstractions should only come in these few forms. At its most fundamental, abstraction must then not continuous. It must have discrete levels. We build abstraction on the broadest scale in large and singular steps. Symbols, universals, objects, environments, and now artifacts are the most abstract and the most unique ideas that we have. Each is the next largest idea that encompasses the previous one. We can make environments bigger and bigger, more and more abstract; but if we are to construct an element that is different, that enables simplification and not just greater abstraction, then our invention jumps a significant level of abstraction. Each of these Unique Elements is fundamentally different from the other. Each is a new stage of abstraction.

Here we come to a crucial point. There are two great engines driving thought, simplification and abstraction. We seek to construct ideas that are simpler and thus more unique. And we seek to construct ideas that are more abstract and thus more unique. Artifacts are unique when they are different and when they are the same. When we seek simplicity we are searching for difference. When we seek abstraction we are looking for sameness. The essential tools for the construction of knowledge, sameness and difference are also the essential tools that drive thought. To simplify is to group together, to fashion sameness in our artifacts. To abstract is to differentiate, to separate, to define a difference from other artifacts.

This combination of simplification and abstraction is the basis for the unique entities. Each is more abstract that the previous one. Each produces a great simplification. Without simplification, abstraction only leads to complexity. And without abstraction, simplification leads to triviality. These ideas are the heart of thought because they are the fundamental unique elements of thought in the construction of singular artifacts.

Incredible as this may seem, it provides us with an explanation for the unique entities. We commonly think of concrete to abstract as a continuum, but when artifacts are most fundamental, their abstractness comes in very discrete packages. Abstraction also helps us to understand the shifts in the unique entities from symbols, to universals, to objects, to environments, and now to artifacts in the Pattern of Knowledge. The sequence is growth in abstractness of our fundamental elements. Each is the next level of uniquely abstract entity. Each element allows a new level of abstraction, a new unique step in the capacity of our artifacts to hold experience. And each brings with it a new level of unity.

And here, finally, we return to the beginning of this work, where we found the fundamental elements that produced the great periods of knowledge. These elements - Symbols, Universals, Objects, Environments, and now Artifacts- are the basis for knowledge, the templates upon which we design the artifacts we use, the forms for the entities and thus the forms for all of the artifacts. They are the very essence of our knowledge, the most fundamental building blocks. We have already said that each is unique, fundamentally different from the others. And now we can say why.

Each new element is unique because it is different from the one that came before it. Each element is unique because it is a union of the one that came before it, collecting all of those that came before it as the same. Each is unique because it is different, fundamentally different from those that came before it.

Thus we can fashion ever increasingly complex environments, adding more and more, larger and larger environments together, but we fail to produce increased uniqueness or even increased abstraction. For to create fundamentally new uniqueness we have to construct a new kind of artifact, a new element. It must be different from those that came before and yet include them. Such are the unique elements.

Now, since we have made one, why can't we construct others? We have the formula! We have the formula - but unlike singular, plural, parts, wholes, and connections, relations, transformations - the unique entities do not form a regular, repetitive pattern that we can apply an algorithm to. The unique entities are free inventions, we cannot imagine the next one until we have used, fully explored the current one. We make a new one by fashioning a union of the old ones and then creating something fundamentally different. That is what makes them unique. This last is an invention, an act of creation, and we have been witness to a history of new invention that cannot leapfrog the pattern.

We can thus predict the pattern of knowledge in broad brush for the artifact period, but we cannot construct it out of sequence. And we shall have to wait until this period is complete before we will find what it is that will govern the knowledge building of the next. We need not at all fear that we can see the end of our construction of knowledge. Indeed it is just beginning. And it remains, as it has always been, an act of profound and wonderful invention.