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.
English Christian theologian, and mathematician (1630-1677)
Isaac Barrow (October 1630 – 4 May 1677) was an English Christian theologian, and mathematician who is generally given credit for his early role in the development of ; in particular, for the discovery of the .
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It cannot be justly inferr'd... We do not perceive the Thing, therefore there is no such Thing, that is a false Illusion, a deceitful Dream, that wou'd cause us to join together two remote Instants of Time. But nevertheless this is very True... That is, for as much Motion as there was, so much Time seems to have been elapsed; nor, when we mention such a Quantity of Time, do we merely mean any Thing else, than the Performance of so much Motion, to the continued successive Extension of which we imagine the Permanency as Things is co-extended.
As Magnitudes themselves are absolute Quantums Independent on all Kinds of Measure, tho' indeed we cannot tell what their Quantify is, unless we measure them; so Time is likewise a Quantum in itself, tho' in Order to find the Quantity of it, we are obliged to call in Motion to our Assistance as a Measure... and thus Time as measurable signifies Motion; for if all Things were to continue at Rest, it would be impossible to find out by any Method whatsoever how much Time has elaps'd; and the several Ages wou'd roll on imperceptibly and undistinguish'd. Do I say we shou'd not perceive how Time flows? No indeed, nor any Thing else, but remain like Stocks or Stones in a continual Insensibility. We perceive nothing, unless so far as we may be instigated by some Change affecting the Senses, or that our Souls are mov'd and excited by the internal Operation of the Mind. We esteem the Quantities and different Degrees of Things according to the Extension or Intension of Motions striking upon us either interiorly or exteriorly. So that the Quantity of Time so far as we can observe; depends upon the Extension of Motion.
But you may perhaps wonder why I explain Time without Motion, and will say, does not Time imply Motion? I answer no, as to its absolute and intrinsic Nature; any more than it does Rest. The Quantity of Time, in itself, depends not on either of them; for whether Things move on, or stand still; whether we sleep or wake, Time flows perpetually with an equal Tenor.
But perhaps you may ask, whether Time was not before the World was created? And if Time does not flow in the Extramundane Space, where nothing is: A mere Vacuum? I answer, that since there was Space before the World was created, and that there now is an Extramundane, infinite Space, (where God is present)... Time existed before the World began, and does exist together with the World in the Extramundane Space, because 'tis possible that some Thing might have existed long before the World was made; and there may now be something in the Extramundane Space, capable of such a Continuance: Some Sun might have given Light long before; and at present this, or some other like it, may diffuse Light thro' Imaginary Spaces. Time therefore does not imply an actual Existence, but only the Capacity or Possibility of the Continuance of Existence; just as Space expresses the Capacity of a Magnitude contain'd in it.
Now pray tell me what Time is? ...Time (to speak abstractedly) is the continuance of any Thing in its own Being. But some Things continue longer in their Beings than others... Time absolutely... is Quantity, as admitting in some Manner the chief Affections of Quantity: Equality, Inequality, and Proportion...
Among these Ways, or any other whatever, of generating Magnitudes, the Primary and Chief is, that perform'd by local Motion, which all of them must in some Sort suppose, because without Motion, nothing can be generated or produced and therefore this must first be considered. The following Axiom of Aristotle concerning Motion is famous... He that is ignorant of Motion, must necessarily know nothing of Nature... in Nature every Thing created is produc'd by Motion, or certainly not without Motion.
I... chose rather to publish... in puris Naturalibus, or as they were produced as first, than be at the Trouble of reducing them into any other Form... I could not bear the Pains of reading over again a great Part of these Things; either from my being tired with them, or not caring to undergo the Pains and Study in new modelling them. But I have done in this as weakly Mothers, who give up their Offspring to the Care of their Friends, either to Nurse and bring up, or abandon to the wide World. One of which is Mr. Isaac Newton, my Collegue, a Man of great Learning and Sagacity, who revised my Copy and noted such Things as wanted Correction, and even gave me some of his own, which you will see here and there interspersed with mine, not without their due Commendations. The other is Mr. John Collins (who may be deservedly called the Mersennas of our Nation, Born to promote this Science, both with his own Labours, and those of others. Who with much Trouble took care of the Edition.
The Definition in the Elements, according to Clavius, is this: Magnitudes are said to be in the same Reason [ratio], a first to a second, and a third to a fourth, when the Equimultiples of the first and third according to any Multiplication whatsoever are both together either short of, equal to, or exceed the Equimultiples of the second and fourth, if those be taken, which answer one another.... Such is Euclid’s Definition of Proportions; that scare-Crow at which the over modest or slothful Dispositions of Men are generally affrighted: they are modest, who distrust their own Ability, as soon as a Difficulty appears, but they are slothful that will not give some Attention for the learning of Sciences; as if while we are involved in Obscurity we could clear ourselves without Labour. Both of 300 which Sorts of Persons are to be admonished, that the former be not discouraged, nor the latter refuse a little Care and Diligence when a Thing requires some Study.
They [mathematicians] only take those things into consideration, of which they have clear and distinct ideas, designating them by proper, adequate, and invariable names, and premising only a few axioms which are most noted and certain to investigate their affections and draw conclusions from them, and agreeably laying down a very few hypotheses, such as are in the highest degree consonant with reason and not to be denied by anyone in his right mind. In like manner they assign generations or causes easy to be understood and readily admitted by all, they preserve a most accurate order, every proposition immediately following from what is supposed and proved before, and reject all things howsoever specious and probable which can not be inferred and deduced after the same manner.—Barrow, Isaac.
It may be observed of mathematicians that they only meddle with such things as are certain, passing by those that are doubtful and unknown. They profess not to know all things, neither do they affect to speak of all things. What they know to be true, and can make good by invincible arguments, that they publish and insert among their theorems. Of other things they are silent and pass no judgment at all, choosing rather to acknowledge their ignorance, than affirm anything rashly. They affirm nothing among their arguments or assertions which is not most manifestly known and examined with utmost rigour, rejecting all probable conjectures and little witticisms. They submit nothing to authority, indulge no affection, detest subterfuges of words, and declare their sentiments, as in a court of justice, without passion, without apology; knowing that their reasons, as Seneca testifies of them, are not brought to persuade, but to compel.
Now as to what pertains to these Surd numbers (which, as it were by way of reproach and calumny, having no merit of their own are also styled Irrational, Irregular, and Inexplicable) they are by many denied to be numbers properly speaking, and are wont to be banished from arithmetic to another Science, (which yet is no science) viz. algebra.
These Disciplines [mathematics] serve to inure and corroborate the Mind to a constant Diligence in Study; to undergo the Trouble of an attentive Meditation, and cheerfully contend with such Difficulties as lie in the Way. They wholly deliver us from a credulous Simplicity, most strongly fortify us against the Vanity of Scepticism, effectually restrain from a rash Presumption, most easily incline us to a due Assent, perfectly subject us to the Government of right Reason, and inspire us with Resolution to wrestle against the unjust Tyranny of false Prejudices. If the Fancy be unstable and fluctuating, it is to be poised by this Ballast, and steadied by this Anchor, if the Wit be blunt it is sharpened upon this Whetstone; if luxuriant it is pared by this Knife; if headstrong it is restrained by this Bridle; and if dull it is roused by this Spur. The Steps are guided by no Lamp more clearly through the dark Mazes of Nature, by no Thread more surely through the intricate Labyrinths of Philosophy, nor lastly is the Bottom of Truth sounded more happily by any other Line. I will not mention how plentiful a Stock of Knowledge the Mind is furnished from these, with what wholesome Food it is nourished, and what sincere Pleasure it enjoys. But if I speak farther, I shall neither be the only Person, nor the first, who affirms it; that while the Mind is abstracted and elevated from sensible Matter, distinctly views pure Forms, conceives the Beauty of Ideas, and investigates the Harmony of Proportions; the Manners themselves are sensibly corrected and improved, the Affections composed and rectified, the Fancy calmed and settled, and the Understanding raised and excited to more divine Contemplation. All which I might defend by Authority, and confirm by the Suffrages of the greatest Philosophers.