“We are mainly interested in the processes… not… in presenting mathematics in its most abstract form. …we will often begin with concrete forms and then exhibit the process of abstraction.”

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)

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Richard Hamming 90
American mathematician and information theorist 1915–1998

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“Universal History exhibits the gradation in the development of that principle whose substantial purport is the consciousness of Freedom. The analysis of the successive grades, in their abstract form, belongs to Logic; in their concrete aspect to the Philosophy of Spirit.”

Here it is sufficient to state that the first step in the process presents that immersion of Spirit in Nature which has been already referred to ; the second shows it as advancing to the consciousness of its freedom. But this initial separation from Nature is imperfect and partial, since it is derived immediately from the merely natural state, is consequently related to it, and is still encumbered with it as an essentially connected element. The third step is the elevation of the soul from this still limited and special form of freedom to its pure universal form ; that state in which the spiritual essence attains the consciousness and feeling of itself. These grades are the ground-principles of the general process; but how each of them on the other hand involves within itself a process of formation, constituting the links in a dialectic of transition, to particularise this must be preserved for the sequel. Here we have only to indicate that Spirit begins with a germ of infinite possibility, but only possibility, containing its substantial existence in an undeveloped form, as the object and goal which it reaches only in its resultant full reality. In actual existence Progress appears as an advancing from the imperfect to the more perfect; but the former must not be understood abstractly as only the imperfect, but as something which involves the very opposite of itself the so-called perfect as a germ or impulse. So reflectively, at least possibility points to something destined to become actual; the Aristotelian δύναμιςis https://en.wiktionary.org/wiki/%CE%B4%CF%8D%CE%BD%CE%B1%CE%BC%CE%B9%CF%82 also potentia, power and might. Thus the Imperfect, as involving its opposite, is a contradiction, which certainly exists, but which is continually annulled and solved; the instinctive movement the inherent impulse in the life of the soul to break through the rind of mere nature, sensuousness, and that which is alien to it, and to attain to the light of consciousness, i. e. to itself.
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“And from the point of view of art there are no concrete or abstract forms, but only forms which are more or less convincing lies. That those lies are necessary to our mental selves is beyond any doubt, as it is through them that we form our aesthetic point of view of life.”

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