Divisible Quotes
In every human being one or the other of these two instincts is predominant: the active or positive instinct to offer hospitality, the negative or passive instinct to accept it. And either of these instincts is so significant of character that one might as well say that mankind is divisible into two great classes: hosts and guests.
Max Beerbohm
Nature is a wary wily long-breathed old Witch, tough-lived as a Turtle and divisible as the Polyp, repullulative in a thousand Snips and Cuttings, integra et in toto! She is sure to get the better of Lady MIND in the long run, and to take her revenge too - transforms our To Day into a Canvass dead-colored to receive the dull featureless Portait of Yesterday.
Samuel Taylor Coleridge
Time is composed of time-atoms, i.e., of many parts, which on account of their short duration, cannot be divided. The Mutakallemim undoubtedly saw how Aristotle proved that time, space, and locomotion are of the same nature. ...They, therefore, knew that if time were continuous and divisible ad infinitum, their assumed atom of space would of necessity likewise be divisible. Similarly, if it were supposed that space were continuous... the time-element... could also be divided. This has been shown by Aristotle in... Acroasis [Aristotelis stagyritae acroases physicae]. ...An hour is, e.g., divided into sixty minutes, the second into sixty parts and so on; at last after ten or more successive divisions by sixty, time-elements are obtained which are not subjected to division, and in fact are indivisible.
Maimonides
As a Line, I say, is looked upon to be the Trace of a Point moving forward, being in some sort divisible by a Point, and may be divided by Motion one Way, viz. as to Length; so Time may be conceiv'd as the Trace of a Moment continually flowing, having some Kind of Divisibility from an Instant, and from a successive Flux, inasmuch as it can be divided some how or other. And like as the Quantity of a Line consists of but one Length following the Motion; so the Quantity of Time pursues but one Succession stretched out as it were in Length, which the Length of the Space moved over shews and determines. We therefore shall always express Time by a right Line; first, indeed, taken or laid down at Pleasure, but whose Parts will exactly answer to the proportionable Parts of Time, as its Points do to the respective Instants of Time, and will aptly serve to represent them. Thus much for Time.
Isaac Barrow
Since... nature is a principle of motion and mutation... it is necessary that we should not be ignorant of what motion is... But motion appears to belong to things continuous; and the infinite first presents itself to the view in that which is continuous. ...[F]requently ...those who define the continuous, employ the nature or the infinite, as if that which is divisible to infinity is continuous.
Aristotle
Business cycles are a type of fluctuation found in the aggregate activity of nations that organize their work mainly in business enterprises: a cycle consists of expansions occurring at about the same time in many economic activities, followed by similarly general recessions, contractions, and revivals which merge into the expansion phase of the next cycle; this sequence of changes is recurrent but not periodic; in duration business cycles vary from more than one year to ten or twelve years; they are not divisible into shorter cycles of similar character with amplitudes approximating their own.
Arthur F. Burns
I have never proceeded from any Genus supremum of the actual infinite. Quite the contrary, I have rigorously proved that there is absolutely no Genus supremum of the actual infinite. What surpasses all that is finite and transfinite is no Genus; it is the single, completely individual unity in which everything is included, which includes the Absolute, incomprehensible to the human understanding. This is the Actus Purissimus, which by many is called God.
I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author. Thus I believe that there is no part of matter which is not - I do not say divisible - but actually divisible; and consequently the least particle ought to be considered as a world full of an infinity of different creatures.
Georg Cantor