Quotes About Abstraction

The Romanticists did not present a hero as a statistical average, but as an abstraction of man's best and highest potentiality, applicable to and achievable by all men, in various degrees, according to their individual choices.

In learning, we draw an abstraction from concrete objects and events. In creating, we make our own concrete objects and events out of the abstraction; we bring the abstraction down and back to its specific meaning, to the concrete; but the abstraction has helped us to make the kind of concrete we want the concrete to be. It has helped us to create—to reshape the world as we wish it to be for our purposes.

He slipped the sketch to the bottom of the pile. "Architecture is primarily a utilitarian conception, and the problem is to elevate the principle of pragmatism into the realm of esthetic abstraction. All else is nonsense.

If I were independent, physically, I could pretty well make it on my own. Mentally, I could think my own thoughts, I could move from one level of abstraction to another. I could think creatively and analytically and organize and express my thoughts in understandable ways. Emotionally, I would be validated from within. I would be inner directed. My sense of worth would not be a function of being liked or treated well.

I were independent, physically, I could pretty well make it on my own. Mentally, I could think my own thoughts, I could move from one level of abstraction to another. I could think creatively and analytically and organize and express my thoughts in understandable ways. Emotionally, I would be validated from within. I would be inner directed. My sense of worth would not be a function of being liked or treated well.

The most challenging part of programming is conceptualizing the problem, and many errors in programming are conceptual errors. Because

Another good reason to create a class is to model an abstract object—an object that isn't a concrete, real-world object but that provides an abstraction of other concrete objects. A good example is the classic Shape object. Circle and Square really exist, but Shape is an abstraction of other specific shapes.

Encapsulation says that, not only are you allowed to take a simpler view of a complex concept, you are not allowed to look at any of the details of the complex concept. What you see is what you get—it's all you get!

Keep Your Design Modular Modularity's goal is to make each routine or class like a black box: You know what goes in, and you know what comes out, but you don't know what happens inside.

Object-Oriented Design Heuristics (1996), Arthur Riel

One indication that a routine needs to be broken out of another routine is deep nesting of an inner loop or a conditional. Reduce the containing routine's complexity by pulling the nested part out and putting it into its own routine.

If a class contains more than about seven data members, consider whether the class should be decomposed into multiple smaller classes (Riel 1996). You might err more toward the high end of 7±2 if the data members are primitive data types like integers and strings, more toward the lower end of 7±2 if the data members are complex objects.

Classes and routines are first and foremost intellectual tools for reducing complexity. If they're not making your job simpler, they're not doing their jobs.

When we know something well, we don't realize how abstractly we think about it. And we forget that other people, who have lived their own lives, have not gone through our idiosyncratic histories of abstractification.

Abstract ideas are connected in a systematic way to more concrete experiences.

language often allows us to express that aspect as a noun, whether or not it is a physical object. For example, when we say I have three reasons for leaving, we are counting reasons as if they were objects (though of course we do not literally think that a reason can sit on a table or be kicked across a room).

Thinking can not trade in metaphors directly. It must trade in a more basic currency that captures the abstract concepts shared by the metaphor and its topic […] while sloughing off the irrelevant bits.

Behavior is imitated, then abstracted into play, formalized into drama and story, crystallized into myth and codified into religion—and only then criticized in philosophy, and provided, post-hoc, with rational underpinnings

The noble savage Rousseau described, however, was an ideal—an abstraction, archetypal and religious—and not the flesh-and-blood reality he supposed.

Mathematics is the extension of common sense by other means.

Knowing mathematics is like wearing a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world. Math is a science of not being wrong about things, its techniques and habits hammered out by centuries of hard work and argument. With the tools of mathematics in hand, you can understand the world in a deeper, sounder, and more meaningful way.

the mathematical approach is a formalized version of our natural mental reckonings, an extension of common sense by other means.

That's the dirty little secret of advanced geometry. It may sound impressive that we can do geometry in ten dimensions (or a hundred, or a million...), but the mental pictures we keep in our mind are two-or at most three-dimensional. That's all our brains can handle. Fortunately, this impoverished vision is usually enough.

not every curve is a line.