Et similiter in numeratione motus, quae fit per tempus, id quod distinguit prius et posterius temporis, est ipsum nunc, quod est terminus praeteriti et principium futuri. Sic igitur se habet nunc ad tempus, sicut mobile ad motum: ergo secundum commutatam proportionem, sicut tempus ad motum, ita et nunc ad mobile. In like manner, in the counting of motion (which counting is done by time), that which distinguishes the before and after of time is the now, which is the end of the past and the beginning of the future. Thus, the now is related to time as the mobile is to motion. Therefore, also, by commuting the proportion, we get that time is to motion as the now is to the mobile. Unde si mobile in toto motu est idem subiecto, sed differt ratione, oportebit ita esse et in nunc, quod sit idem subiecto et aliud et aliud ratione: quia illud quo discernitur in motu prius et posterius, est idem subiecto, sed alterum ratione, scilicet mobile; et id secundum quod numeratur prius et posterius in tempore est ipsum nunc. Hence, if the mobile remains the same as to subject throughout the entire motion—though differing in account—the same will be true of the now: it too will remain the same as to subject but will be different in account. For that by which before and after are discerned in a motion is the same as to subject but differing in account, the mobile; and that according to which before and after are counted in time is the now. 586. Ex hac autem consideratione de facili potest accipi intellectus aeternitatis. Ipsum enim nunc, inquantum respondet mobili se habenti aliter et aliter, discernit prius et posterius in tempore, et suo fluxu tempus facit, sicut punctus lineam. Sublata igitur alia et alia dispositione a mobili, remanet substantia semper eodem modo se habens. Unde intelligitur nunc ut semper stans, et non ut fluens, nec habens prius et posterius. Sicut igitur nunc temporis intelligitur ut numerus mobilis, ita nunc aeternitatis intelligitur ut numerus, vel potius ut unitas rei semper eodem modo se habentis. 586. This train of thought makes easy an understanding of eternity. For the now, insofar as it corresponds to a mobile that is continually different, distinguishes the before and after in time and, by its flow, makes time, just as a point makes a line. But, if that varying status of the mobile be removed, the substance remains always in the same state, and the now is then understood as always standing still and not as flowing nor as having a before and after. Therefore, just as the now of time is understood as the number of the mobile, so the now of eternity is understood as the number, or rather the unity, of a thing always remaining in the same state. 587. Deinde cum dicit: et notum etc., ostendit unde habeat nunc mensurare tempus. Et dicit quod hoc ideo est, quia id quod est maxime notum in tempore, nunc est; et unumquodque mensuratur per id quod est maxime notum sui generis, ut dicitur in X Metaphys. 587. Then, at this is what is (219b28), he shows from what the now derives its function of measuring time. And he says it is because that which is best known in time is the now, and what is best known in any genus is the measure of everything in that genus, as is said in Metaphysics 10. Et hoc etiam ostendit ex habitudine motus ad mobile: quia motus cognoscitur per id quod movetur, et loci mutatio per id quod localiter fertur, quasi minus notum per magis notum. He also shows this from the relation of motion to the mobile, for motion is perceived through something being moved and local motion is perceived through observing something being moved locally, after the manner of the better known manifesting the less known. Quod ideo est, quia id quod movetur est hoc aliquid, idest res quaedam per se stans; quod non convenit motui. This is so because that which is being moved is a real thing, namely, a certain thing stable in itself—a characteristic that does not belong to motion. Unde mobile est notius motu, et per mobile cognoscitur motus: et similiter tempus per ipsum nunc. Hence, the mobile is more known by us than the motion, and motion is known through the mobile object. In like manner, time is made known through the now. Et sic concludit conclusionem principaliter intentam, quod id quod dicitur nunc, semper est idem quodammodo, et quodammodo non; quia similiter est de mobili, ut dictum est. Thus, he reaches the conclusion principally intended: what is called the now is always the same in one way, and in another way not, because it is similar to the mobile, as was said. 588. Deinde cum dicit: manifestum est autem etc., assignat rationem eorum quae dicuntur de nunc; 588. Then, at clearly, too (219b33), he explains the reason for the things that are said of the now: et primo eius quod dicitur, quod nihil est temporis nisi nunc; first, why it is said that nothing of time exists but the now; secundo eius quod dicitur, quod nunc dividit et continuat temporis partes, ibi: et continuum iam etc.; second, why the now is said to separate and continue the parts of time, at time, then, also (220a3; [590]); tertio eius quod dicitur, quod nunc non sit pars temporis, ibi: et adhuc manifestum etc. third, why it is said that the now is not a part of time, at and further because (220a18; [592]). 589. Dicit ergo primo manifestum esse, quod si non sit tempus, non erit nunc; et si non erit nunc, non erit tempus. Et hoc ex habitudine motus ad mobile. Sicut enim loci mutatio et id quod fertur, sunt simul; sic et numerus eius quod fertur, simul est cum numero localis motus: sed tempus est numerus loci mutationis, ipsum autem nunc comparatur ad id quod fertur, non quidem sicut numerus (quia nunc indivisibile est), sed sicut unitas numeri. Relinquitur igitur quod tempus et nunc non sunt sine invicem. Attendendum est autem quod tempus semper comparatur loci mutationi, qui est primus motuum: tempus enim est numerus primi motus, ut dictum est. 589. He therefore says first (219b33) that it is plain that, if there is no time, there will be no now, and if no now, no time. This is explained by the relation of motion to the mobile. For just as the change of place and that which is being moved are together, so the count of that which is being moved accompanies the count of the change of place. But time is the number of a local motion, while the now is related to what is being moved not as its number (since the now is indivisible), but as the unit of number. It follows, therefore, that time and the now are always together. Notice that time is always compared to a local motion, which is the first of all motions, for time is the number of the first motion, as was said. 590. Deinde cum dicit: et continuum iam tempus etc., assignat rationem eius quod dicitur, quod tempus continuatur et dividitur secundum nunc. 590. Then, at time, then, also is (220a3), he explains why it is said that time is continued and divided according to the now. Et primo ex parte motus et mobilis; First, he explains it by considering motion and the mobile; secundo ex parte lineae et puncti, ibi: sequitur autem et hoc etc. second, by considering a line and a point, at here, too, there is (220a9; [591]). Dicit ergo primo quod iam ex praedictis patet, quod tempus est continuum ipsi nunc, idest per ipsum nunc, et dividitur secundum ipsum. Et hoc etiam consequens est ad id quod invenitur in loci mutatione, cuius numerus est tempus, et in eo quod fertur secundum locum, cui respondet ipsum nunc. He says first, therefore, that what we have already said makes clear that time is made continuous with the “now” itself—namely, by the now—and is divided by the now. This fact also follows from what is found in local motion (the number of which is time) and in the object that is being moved according to place (which corresponds to the now). Manifestum est enim quod omnis motus habet unitatem ab eo quod movetur: quia scilicet illud quod movetur est unum et idem manens in toto motu; et non est indifferenter id quod movetur, uno motu manente, quodcumque ens, sed illud idem ens quod prius incepit moveri: quia si esset aliud ens quod postea moveretur, deficeret primus motus, et esset alius motus alterius mobilis. For it is clear that every motion derives its unity from the object being moved, since what is being moved remains one and the same throughout the whole course of the motion. And it is not a matter of indifference whether that which is moved in the course of one motion be any being at all, but rather it must be that same being that first began to be moved, for if it were another being that was later moved, the former motion would have failed and there would now be another motion of another mobile. Et sic patet quod mobile dat unitatem motui, quae est eius continuitas. Sed verum est quod mobile est aliud et aliud secundum rationem. Et per hunc modum distinguit priorem et posteriorem partem motus: quia secundum quod consideratur in una ratione vel dispositione, cognoscitur quod quaecumque dispositio fuit in mobili ante istam signatam, pertinebat ad priorem partem motus; quaecumque autem post hanc erit, pertinebit ad posteriorem. Sic igitur mobile et continuat motum et distinguit ipsum. Et eodem modo se habet nunc ad tempus. So, it is clear that it is the mobile that gives unity to the motion, which unity constitutes its continuity. But it is true that the mobile is different according to account. And it is in this way that it distinguishes the prior and the subsequent part of motion, for insofar as the mobile is considered under one account or disposition, it is recognized that whatever disposition was in the mobile previous to its present state pertained to the prior part of the motion and that whatever disposition will come after this state will pertain to the subsequent part of the motion. Thus it is that the mobile both continues the motion and distinguishes its parts. And the same holds for the now in relation to time. 591. Deinde cum dicit: sequitur autem et hoc etc., assignat eiusdem rationem ex parte lineae et puncti. Et dicit quod hoc quod dictum est de tempore et nunc, consequitur quodammodo ad id quod invenitur in linea et puncto: quia punctum continuat lineam, et distinguit ipsam inquantum est principium unius partis et finis alterius. 591. Then, at here, too, there is (220a9), he explains a case of the same in the matter of line and point. And he says that the conclusion drawn about time and the now in the preceding section follows in a way from what is found in a line and a point: the point continues the line and distinguishes its parts, inasmuch as it is the beginning of one part and the end of another. Sed tamen differenter se habet in linea et puncto, et tempore et nunc. Quia punctum est quoddam stans, et linea similiter: unde potest homo accipere idem punctum bis, et uti eo ut duobus, ut scilicet principio et ut fine. But there is a difference between the case of line and point and the case of time and the now. For both the point and the line are something stationary; hence, a person can consider the same point twice and use it as two, namely, as both a beginning and an end. Et cum sic utimur puncto ut duobus, accidit quies; sicut patet in motu reflexo, in quo id quod erat finis primi motus est principium secundi motus reflexi. Et propter hoc probatur infra in octavo, quod motus reflexus non est continuus, sed intercidit quies media. When we thus use the point as two, rest occurs, as is evident in a reflected motion, where that which was the end of the first motion is the beginning of the second and reflected motion. It is on this basis that we shall prove in book 8 that a reflected motion is not continuous, but that an intermediate pause occurs. Sed ipsum nunc non est stans, propter id quod respondet mobili, quod semper fertur durante motu; et propter hoc oportet nunc esse semper alterum et alterum secundum rationem, ut supra dictum est. But the now is not stationary, for it corresponds to the mobile that is always being carried along during the motion—which also accounts for the now having to be always different in account, as was said above. Et ideo, cum tempus sit numerus motus, non hoc modo numerat motum, quod aliquid idem temporis accipiatur ut principium unius et finis alterius; sed magis numerat motum accipiendo duo ultima temporis, scilicet duo nunc, quae tamen non sunt partes eius. Et quare competat iste modus numerandi in tempore magis quam alius, quo per punctum numerantur partes lineae, inquantum est principium et finis, ratio est quae dicta est, quia secundum hunc modum utitur aliquis puncto ut duobus; et sic accidit quies media, quae non potest esse in tempore et in motu. Non tamen intelligendum est per id quod dicitur, quod idem nunc non sit principium futuri et finis praeteriti, sed quod non percipimus tempus numerando motum per unum nunc, sed magis per duo, ut dictum est: quia sequeretur quod in numeratione motus idem nunc sumeretur bis. Therefore, since time is the number of motion, it does not number motion in the sense that some same time is taken as the beginning of one and the end of another, but rather it numbers motion by taking two boundaries of time, namely, two nows that are nevertheless not parts of time. The reason that this method of counting is used in numbering time, rather than the method used when a point numbers the parts of a line (where the same point is considered both a beginning and an end), is that, as was stated, in the latter method, we use the point as two things and this brings about an intermediate pause, which cannot exist in time or in motion. Now, this does not mean that the same now is not the beginning of the future and the end of the past, but that we do not perceive time by counting motion in terms of one now, but in terms of two, as was said; otherwise, in our counting of motion, the same now would be employed twice. 592. Deinde cum dicit: et adhuc manifestum quod nulla pars etc., assignat rationem eius quod dicitur, quod nunc non est pars temporis. Et dicit manifestum esse quod nunc non est pars temporis, sicut neque id per quod distinguitur motus, est pars motus, scilicet aliqua dispositio signata in mobili; sicut etiam nec puncta sunt partes lineae. Duae enim lineae sunt partes unius lineae. Manifestat autem proprietates ipsius temporis ex motu et linea: quia, sicut dictum est supra, motus est continuus propter magnitudinem, et tempus propter motum. 592. Then, at and further because (220a18), he explains why it is said that the now is not a part of time. And he says it is plain that the now is not a part of time, just as what distinguishes a motion is not a part of the motion—namely, some disposition in the mobile itself—just as points are not parts of a line. For two lines are the parts of a line. Now, he manifests the properties of time from the properties of motion and of line because, as was said above, motion is continuous on account of the magnitude, and time on account of the motion. Concludit ergo finaliter, quod ipsum nunc secundum quod est terminus quidam, non est tempus, sed accidit tempori, ut terminus terminato: sed secundum quod tempus vel nunc numerat alia, sic etiam nunc est numerus aliorum quam temporis. Et huius ratio est, quia terminus non est nisi eius cuius est terminus; sed numerus potest esse diversorum, sicut numerus decem equorum numerus est et aliarum rerum. Sic igitur nunc est terminus solius temporis, sed est numerus omnium mobilium quae moventur in tempore. He concludes, therefore, finally, that the now, insofar as it is a certain boundary, is not time, but it is an accident of time, as a boundary does to that which is bounded; but, insofar as time or the now numbers other things, the now is the number of things other than time. The reason is that a boundary can be only of that of which it is the boundary, but a number can be applied to various things, as the number of ten horses is also that of other things. Therefore, in this way, the now is the boundary only of time, but it is the number of all mobiles that are being moved in time. Lectio 19 Lecture 19 Manifestantur quaedam quae de tempore dici solent Clarification of certain things said about time Quod quidem igitur tempus numerus motus secundum prius et posterius sit, et continuum (continui namque), manifestum est. Minimus autem numerus, qui simpliciter quidem est, dualitas est: quidam autem numerus, est qui est quidem sic, est autem tanquam non sic; ut lineae minimum multitudine quidem est duae aut una, magnitudine autem non est minimum; semper enim dividitur omnis linea. Quare similiter et tempus: minimum enim quidem est secundum numerum, unum aut duo; secundum vero magnitudinem non est. It is clear, then, that time is “the number of motion in respect of the before and after” and is continuous, since it is an attribute of what is continuous. The smallest number, in the strict sense of the word “number,” is two. But of one certain number, sometimes there is a minimum, sometimes not: for instance, of a line, the smallest in respect of multiplicity is two (or, if you like, one), but in respect of size, there is no minimum; for every line is divided to infinity. Hence, it is so with time. In respect of number, the minimum is one (or two); in point of extent, there is no minimum. Manifestum est autem propter quid tardum et velox non dicitur: multum autem et paucum, et breve et longum. It is clear, too, that time is not described as fast or slow, but as many or few and as long or short. Secundum enim quod continuum est, longum et breve dicitur; secundum autem quod numerus, multum et paucum. Velox autem et tardum non est: neque enim numerus quo numeramus, velox et tardus ullus est. For as continuous, it is long or short, and as a number, many or few, but it is not fast or slow—any more than any number with which we number is fast or slow. Et idem autem ubique simul. Prius autem et posterius non idem: quia et mutatio praesens quidem una est; facta autem et futura altera est. Tempus autem numerus est, non quo numeramus, sed quod numeratur. Huic autem accidit prius et posterius semper esse alterum: ipsa enim nunc semper altera. Est autem numerus unus quidem et idem qui est centum equorum, et qui est centum hominum: quorum autem numerus est, altera sunt; ut equi ab hominibus. Further, time is the same everywhere at once, but not the same time before and after, for while the present change is one, the change that has happened and that which will happen are different. Time is not number with which we count, but the number of things that are counted, and this is always different according as it occurs before or after, for the “nows” are different. And the number of a hundred horses and a hundred men is the same, but the things numbered are different—the horses from the men. Amplius, sicut contingit motum esse eundem et unum iterum et iterum, sic et tempus contingit, ut hiemem aut ver aut autumnum. Further, as a motion can be one and the same again and again, so too can time—for instance, a year or a spring or an autumn. Non solum autem motum tempore metimur, sed motu tempus, propterea quod definiuntur ad invicem. Tempus quidem enim determinat motum, cum sit numerus ipsius: motus autem tempus. Et dicimus multum aut paucum esse tempus, motu mensurantes; sicut et numerabilibus numerum. Numero quidem equorum multitudinem cognoscimus; iterum autem uno equo equorum numerum ipsum. Similiter autem et in tempore et motu est. Tempore quidem enim motum, motu autem tempus mensuramus. Not only do we measure the motion by the time, but also the time by the motion, because they define each other. The time marks the motion, since it is its number, and the motion the time. We describe the time as much or little, measuring it by the motion, just as we know the number by what is numbered—for instance, the number of the horses by one horse as the unit. For we know how many horses there are by the use of the number; and again, by using the one horse as unit, we know the number of the horses itself. So it is with the time and the motion, for we measure the motion by the time and vice versa. Et hoc rationabiliter accidit. Imitatur enim magnitudinem quidem motus, hunc autem tempus, eo quod quanta et continua sint et divisibilia: propter magnitudinem enim esse huiusmodi, motus haec sustinet, propter autem motum tempus. It is natural that this should happen, for the motion goes with the distance and the time with the motion, because they are quanta and continuous and divisible. The motion has these attributes because the distance is of this nature, and the time has them because of the motion. Et mensuramus magnitudinem motu, et motum magnitudine: multam enim dicimus esse viam, si processus multus; et hunc multum, si via multa. Sic igitur et tempus si motus, et motum si tempus. And we measure both the distance by the motion and the motion by the distance, for we say that the road is long if the journey is long and that this is long if the road is long—the time, too, if the motion, and the motion, if the time.