Armen’s Rules of Abstraction

What is abstraction? Really, it's just the same thing as categorization. It is naming, and treating, a specific thing according to some bucket in which we place it. For instance, "Bobby's ball is a sphere" is an example of an abstraction. We have categorized the ball as a sphere, so that we can talk about spheres, and make the point that a particular object -- Bobby's ball -- can be used as an example of one in our discussion.

There are numerous ways to abstract something. For instance, Bobby's ball can also be categorized as a toy. The difference between saying "Bobby's ball is a sphere" and "Bobby's ball is a toy" has everything to do with the topic at hand. If we were discussing geometric objects, the first abstraction would sound natural, the second would be jarringly confusing. Yet both are true statements. Similarly, if we had asked some children to pick up all the toys off the floor, and Bobby's ball was still on the floor and hadn't been picked up, saying "Bobby's ball is a sphere" would be senseless, even though it is a totally correct statement. But saying "Bobby's ball is a toy" imparts information that any able child would immediately understand: that this particular object -- Bobby's ball -- can be abstracted to "toy" (that is, it can be referred to as "toy"); and since all toys were supposed to have been picked up, we have a little problem here. 

So, abstraction is really a new way to name something based on a carefully selected subset of its attributes. We select just the constant radius and three-dimensional aspect of Bobby's ball, forget about everything else, and those attributes alone are the attributes necessary for all spheres. Similarly, we select the attributes that indicate appropriateness for childhood play -- size, weight, material -- and forget all others, and those happen to be all the necessary ones that make up all toys. 

This selection of attributes can often be done to different degrees. The more attributes we select, the more narrow the abstraction. We can say, for instance, that "Amy's sandal is footwear" if the subject of our conversation is the requirement to wear shoes at some venue. But we would say "Amy's sandal is clothing" if our subject is the importance of protecting one's skin against UV radiation.  The topic at hand defines the validity of a given abstraction. If the choice of abstraction is not coherent with, and does not contribute to, the topic at hand, it is likely to be a non sequitor.

With this understanding, a couple of rules can be derived.


Rule 1:

Abstractions free of context express no meaning other than trivial hierarchical relationship.


Without a context: Tardigrades are Ecdysozoa.

This expresses no information other than taxonomy. There is no reason to care.


With a context: Wooden ships, small and large, were eventually replaced with ones made of metal. The last commissioned wooden ship of the British Navy was the HMS Victoria. The Victoria was a First-rate class ship.

This expresses the point, that the very last wooden ship commissioned was of the largest class. Without the topical context, simply saying that the Victoria was a First-rate class ship expresses nothing more than taxonomy.


Rule 2:

Narrower abstractions are more informative of reality. Overly broad abstractions can introduce a distorted view of reality.

Example, with a contextual first sentence:

Alexander III’s generalship was one of the most notable in history. 

1 - The Greeks were ambulatory beings.
2 - The Greeks were an expansionist people.


Here, the first sentence establishes the context: the ancient Greeks, and their famous young general, Alexander the Great, who lived in the 4th century BC. In both options for the following sentence, the abstractions are valid: they are both true, and they both contain non-trivial information. But if selecting between them, the first would be a strange one to choose. It is true that they were living creatures that could move about on their own. This would be a meaningful point if, at the time, there were nations of people that couldn't move about, or if moving around made the Greeks special in some way. But such was not the case.

Choosing abstraction #1, in this context, is arbitrary. It sits somewhere between the broadest generalizations (e.g., “The Greeks existed”) and any number of narrower, but equally uninformative ones. Selecting it is equivalent to unnecessarily eschewing information, and indirectly implying that there is something special about this. There is nothing special about the ancient Greeks having the ability to get about. Arbitrarily broad abstractions naturally result in such implications, which are then often used to dissemble.


Another example:

Human spaceflight was a long and arduous achievement involving tremendous risk to life and purse. 

1 - The first astronauts were men.
2 - The first astronauts were Navy test pilots.

There is no reason to choose the first abstraction, other than to attempt to dissemble. The man-ness of those astronauts was not essential to their being one of the first astronauts, but accidental, a result of million-year-long threads of evolution. If there had been qualified female Navy test pilots at the time, it would most likely be a false statement, yet the second would still be correct.  

Can truths be obscured, and falsehoods presented, by choosing the first abstraction? The answer depends on the model we believe to be in place. Let us consider this option:


"The newly created astronaut corps offered a new type of job to the American public -- one in which any man or woman had the potential to succeed at the time."


With such a historical model in place, the first abstraction is relevant, and contains meaningful information. It implies that there may have been an instance of sex-based discrimination at the start of the American space program.

But that model is false. There were deep developmental dependencies between the space program and the military, which itself is institutionalized inter-tribal aggression. The form of that aggression, evidenced in other primates, required the strongest participants. It is that fact that made it impossible for a woman to succeed in flying into space at the time. There was nothing that, in and of itself, required that the first astronauts be men; what was required, was that the first astronauts be experienced, elite test pilots of supersonic jets. 

A more honest historical model might look like this:


"For <biological/environmental/existential reasons x, y, and z>, certain primate societies secured limited resources through inter-tribal aggression. Success required physical strength, so this tribal function fell to the males. It was only when Man began to develop agricultural technology that civilization, and its attendant rejection of tribal norms, began to appear. (This rejection of tribal norms is so recent, that it would be impossible to visualize it on a human time line that stretched from the left to the right edge of this screen.) Civilization introduced new norms, one of which was a lifting of sex-based specialization. Slowly, in fits and starts, men began to engage in child-rearing activities, women in military activities.

Since spaceflight is such a risky and expensive endeavor, each incremental advancement was highly customized to a specific goal. The first rockets had no payloads, and the first living payloads were animals, the capsule not being large enough to fit a human. By the time rockets were able to lift humans into space, the designs of everything from the training program to the windows and flight controls were made in collaboration with the pilots of the craft's most promising precursors: Navy jet planes. Since there were no female Navy jet pilots at the time of the birth of American human space flight, and because cost, time, and safety considerations required efficiency and hyper-specialization in design, the first capsules for human habitation had the bare minimum required to support the life of a compact and highly athletic man for a few hours in a vacuum, and nothing more. If there had been qualified female Navy test pilots at the time, there is reason to believe that the first capsules would have been designed for women exclusively if it was cheaper to do so, since women were physically more suited to inhabit the limited volume."


So, the first astronauts were medium-build, extremely smart, athletic, elite US Navy test pilots with significant experience flying faster than the speed of sound. By using the abstraction "men", a false context is created -- the gendered nature of the early astronaut corps. It wasn't gendered. The genders were an accident of history that traces back to a time before humans, and not the result of anything specific to the space program itself.