Quotes About Abstraction

It's the same sort of block some people get with the Mean-Value Theorem. Or in Optics when we get to color fields. At a certain level of abstraction it's like the brain recoils.

One of the great Greek contributions to the very concept of mathematics was the conscious recognition and emphasis of the fact that mathematical entities are abstractions, ideas entertained by the mind and sharply distinguished from physical objects or pictures.

Chesterton above is wrong in one respect. Or at least imprecise. The danger he's trying to name is not logic. Logic is just a method, and methods can't unhinge people. What Chesterton's really trying to talk about is one of logic's main characteristics—and mathematics'. Abstractness. Abstraction.

The way in which mathematicians and physicists and historians talk is quite different, and what a physicist means by physical intuition and what a mathematician means by beauty or elegance are things worth thinking about.

Fiction is life with the dull bits left out

You can not apply mathematics as long as words still becloud reality.

Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold.

By refraining from reducing multiplication to addition we are enabled through these axioms to banish continuity, which is so difficult to fix precisely, from the logical structure of geometry.

Or, we may use Cartesian co-ordinate systems from the outset:

We must here follow the first course so as to be able to pass on later to generalisations which extend beyond the limits of Euclidean geometry.

The more minimal the art, the more maximum the explanation.

My point is that things become weird and pointless if you examine them for too long.

When editing begins it is on 'large chunks' – paragraphs or a series of related paragraphs perhaps – and their relationship to one another. She moves them around as a way of answering her structural questions. More specific editing processes are involved too, like those we saw in the example from Woolf's work: deletion, insertion, and attention to repetition and abstraction

All I hear is mathematics. All I see is music.

Mathematics is an ambiguous way to prove or disprove ideal behaviors of objects.

I've always thought abstractly - through theme and variations rather than narrative.

The difficult part of knowledge is not stating a fact, but representing that fact in a useful way.

Even a novel drawn from reality, faithful to it, is not the truth, just as the image in the mirror is not a person in flesh and blood. It remains, that is, an abstraction, no matter how realistic, how close to the facts.

That's just the way people's brains work. If you want to talk about something, you have to reduce it to a form that can be understood. That's one of the reasons I'm not good about boiling down music.

Every work of art is an abstraction from time; it denies the reality of change and decay and death.

When I told my son that I had to give a talk about my work to non-mathematicians, he warned me that regular people don't think like mathematicians.

Agnes Martin is a big influence in my work actually, when I first saw her, these fine grids.

Mathematicians do not study objects, but relations between objects.

It is easy to study the rules of overloading and of templates without noticing that together they are one of the keys to elegant and efficient type-safe containers.