A Quote by Alfred North Whitehead
Algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world.
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So much of western self-perception and intellectual worldview has been shaped by the moral rhetoric of the Cold War, the discourse in which communism featured as a clear enemy, determined to rule the world.
And I think detente had manifestly failed, and that the pursuit of it was encouraging Soviet expansion and rendering the world more dangerous, and especially rendering the Western world in greater peril.
Are there quantitative aspects to the phenomena of war that can be counted? Evidently!
We may always depend on it that algebra, which cannot be translated into good English and sound common sense, is bad algebra.
Numeracy: 1. The art of putting numbers to things, that is, assigning amounts to variables in order that practical decisions may be reach. 2. That aspect of education (beyond mere literacy) which takes account of quantitative aspects of reality.
If things are not going well with you, begin your effort at correcting the situation by carefully examining the service you are rendering, and especially the spirit in which you are rendering it.
Unlike the position that exists in the physical sciences, in economics and other disciplines that deal with essentially complex phenomena, the aspects of the events to be accounted for about which we can get quantitative data are necessarily limited and may not include the important ones.
The loss of quality that is so evident at every level of spectacular language, from the objects it glorifies to the behavior it regulates, stems from the basic nature of a production system that shuns reality. The commodity form reduces everything to quantitative equivalence. The quantitative is what it develops, and it can develop only within the quantitative.
But in the intellectual world, there is room for all opposing forces: even that which never appears victorious in the real world continues to be effective as a dynamic force (in the intellectual world) and precisely the unfulfilled ideals prove to be the most invincible.
They have the idea that non-commutative algebra should remind one of commutative algebra, but the former is more sophisticated. I believe that non-commutative algebra is just as simple, but it is different.
Yes, I took a remedial algebra course in college. I struggled in math in high school and didn’t have confidence to plunge in with a for-credit algebra course. The remedial course gave me a lot of confidence so that when I took the for-credit algebra course it was fairly easy and I got a ‘B,’ of which I remain proud today!
Drawing instruction is a training towards perception, exact observation and exact presentation not of the outward appearances of an object, but of its constructive elements, its lawful forces-tensions, which can be discovered in given objects and of the logical structures of same-education toward clear observation and clear rendering of the contexts, whereby surface phenomena are an introductory step towards the three-dimensional.
Most, probably, of our decisions to do something positive, the full consequences of which will be drawn out over many days to come, can only be taken as the result of animal spirits-a spontaneous urge to action rather than inaction, and not as the outcome of a weighted average of quantitative benefits multiplied by quantitative probabilities.
When we find ourselves unable to reason (as one often does when presented with, say, a problem in algebra) it is because our imagination is not touched. One can begin to reason only when a clear picture has been formed in the imagination. Bad teaching is teaching which presents an endless procession of meaningless signs, words and rules, and fails to arouse the imagination.
To image the being of God towards the world, to be the priest of creation, is to behave towards the world in all its aspects, of work, and of play, in such a way that it may come to be what it was created to be, that which praises its maker by becoming perfect in its own way. In all this, there is room for both usefulness and beauty to take their due place, but differently according to differences of activity and object.
Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras (jabbre and maqabeleh) are geometric facts which are proved by propositions five and six of Book two of Elements.
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