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Appendix to Part V.
ОглавлениеConcerning the methods which nature hath afforded for computing time and space.
I Introduce here the subject proposed, because it affords several curious examples of the power of passion to adjust objects to its gratification; a lesson that cannot be too much inculcated, as there is not perhaps another bias in human nature that hath an influence so universal, and that is so apt to make us wander from truth as well as from justice.
I begin with time; and the question shortly is, What was the measure of time before artificial measures were invented? and, What is the measure at present when these are not at hand? I speak not of months and days, which we compute by the moon and sun; but of hours, or in general of the time that runs betwixt any two occurrences when there is not access to the sun. The only natural measure we have, is the train of our thoughts; and we always judge the time to be long or short, in proportion to the number of perceptions that have passed through the mind during that interval. This is indeed a very imperfect measure; because in the different conditions of a quick or slow succession, the computation is different. But however imperfect, it is the only measure by which a person naturally calculates time; and this measure is applied on all occasions, without regard to any occasional variation in the rate of succession.
This natural measure of time, imperfect as it is, would however be tolerable, did it labour under no other imperfection than the ordinary variations that happen in the motion of our perceptions. But in many particular circumstances, it is much more fallacious; and in order to explain these distinctly, I must analize the subject. Time is generally computed at two different periods; one while time is passing, another after it is past. I shall consider these separately, with the errors to which each of them is liable. It will be found that these errors often produce very different computations of the same period of time. The computation of time while it is passing, comes first in order. It is a common and trite observation, That to lovers absence appears immeasurably long, every minute an hour, and every hour a day. The same computation is made in every case where we long for a distant event; as where one is in expectation of good news, or where a profligate heir watches for the death of an old man who keeps him from a great estate. Opposite to these are instances not fewer in number. To a criminal the interval betwixt sentence and execution appears miserably short; and the same holds in every case where one dreads an approaching event. Of this even a schoolboy can bear witness: the hour allowed him for play, moves, in his apprehension, with a very swift pace: before he is thoroughly engaged, the hour is gone. A reckoning founded on the number of ideas, will never produce computations so regularly opposite to each other; for a slow succession of ideas is not connected with our wishes, nor a quick succession with our fears. What is it then, that, in the cases mentioned, moves nature to desert her common measure for one very different? I know not that this question ever has been resolved. The false reckonings I have suggested are so common and familiar, that no writer has thought of inquiring for their cause. And indeed, to enter upon this matter at short hand, without preparation, might occasion some difficulty. But to encounter the difficulty, we luckily are prepared by what is said above about the power of passion to fit objects for its gratification. Among the other circumstances that terrify a condemned criminal, the short time he has to live is one. Terror, like our other passions, prone to its gratification, adjusts every one of these circumstances to its own tone. It magnifies in particular the shortness of the interval betwixt the present time and that of the execution; and forces upon the criminal a conviction that the hour of his death approaches with a swift pace. In the same manner, among the other distresses of an absent lover, the time of separation is a capital circumstance, which for that reason is greatly magnified by his anxiety and impatience. He imagines that the time of meeting comes on very slow, or rather that it will never come. Every minute is thought of an intolerable length. Here is a fair and I hope satisfactory account, why we reckon time to be tedious when we long for a future event, and not less fleet when we dread the event. This account is confirmed by other instances. Bodily pain fixt to one part, produceth a slow train of perceptions, which, according to the common measure of time, ought to make it appear short. Yet we know, that in such a state time has the opposite appearance. Bodily pain is always attended with a degree of impatience and an anxiety to be rid of it, which make us judge every minute to be an hour. The same holds where the pain shifts from place to place; but not so remarkably, because such a pain is not attended with the same degree of impatience. The impatience a man hath in travelling through a barren country or in bad roads, makes him imagine, during the journey, that time goes on with a very slow pace. We shall show afterward that he makes a very different computation when his journey is at an end.
How ought it to stand with a man who apprehends bad news? It will probably be thought, that the case of this man resembles that of a criminal, who, in reckoning the short time he has to live, imagines every hour to be but a minute, and that time flies swift away. Yet the computation here is directly opposite. Reflecting upon this difficulty, there appears one capital circumstance in which the two cases differ. The fate of the criminal is determined: in the case under consideration, the man is still in suspense. Every one knows how distressful suspense is to the bulk of mankind. Such distress we wish to get rid of at any rate, even at the expence of bad news. This case therefore, upon a more narrow inspection, resembles that of bodily pain. The present distress in both cases, makes the time appear extremely tedious.
The reader probably will not be displeased, to have this branch of the subject illustrated in a pleasant manner, by an author acquainted with every maze of the human heart, and who bestows ineffable grace and ornament upon every subject he handles.
Rosalinda. I pray you, what is’t a clock?
Orlando. You should ask me, what time o’ day; there’s no clock in the forest.
Ros. Then there is no true lover in the forest; else, sighing every minute, and groaning every hour, would detect the lazy foot of Time, as well as a clock.
Orla. Why not the swift foot of Time? Had not that been as proper?
Ros. By no means, Sir. Time travels in diverse paces with diverse persons. I’ll tell you who Time ambles withal, who Time trots withal, who Time gallops withal, and who he stands still withal.
Orla. I pr’y thee whom doth he trot withal?
Ros. Marry, he trots hard with a young maid, between the contract of her marriage, and the day it is solemnized: if the interim be but a se’ennight, Time’s pace is so hard that it seems the length of seven years.
Orla. Who ambles Time withal?
Ros. With a priest that lacks Latin, and a rich man that hath not the gout: for the one sleeps easily, because he cannot study; and the other lives merrily, because he feels no pain: the one lacking the burden of lean and wasteful learning; the other knowing no burthen of heavy tedious penury. These Time ambles withal.
Orla. Whom doth he gallop withal?
Ros. With a thief to the gallows: for though he go as softly as foot can fall, he thinks himself too soon there.
Orla. Whom stays it still withall?
Ros. With lawyers in the vacation; for they sleep between term and term, and then they perceive not how Time moves.
As you like it, act 3. sc. 8.
Reflecting upon the natural method of computing present time, it shows how far from truth we may be led by the irregular power of passion. Nor are our eyes immediately opened when the scene is past: the deception continues while there remain any traces of the passion. But looking back upon past time when the joy or distress is no longer remembered, the computation we make is very different. In this situation, passion being out of the question, we apply the ordinary measure, viz. the course of our perceptions; and I shall now proceed to the errors that this measure is subjected to. In order to have an accurate notion of this matter, we must distinguish betwixt a train of perceptions, and a train of ideas. Real objects make a strong impression, and are faithfully remembered. Ideas, on the contrary, however entertaining at the time, are apt to escape an after recollection. Hence it is, that in retrospection, the time that was employed upon real objects, appears longer than the time that was employed upon ideas. The former are more accurately recollected than the latter; and we measure the time by the number that is recollected. I proceed to particulars. After finishing a journey through a populous country, the frequency of agreeable objects distinctly recollected by the traveller, makes the time spent in the journey appear to him longer than it was in reality. This is chiefly remarkable in a first journey, where every object is new and makes a strong impression. On the other hand, after finishing a journey through a barren country thinly peopled, the time appears short, being measured by the number of objects, which were few and far from interesting. Here in both instances a reckoning is brought out, directly opposite to that made during the journey. And this, by the way, serves to account for a thing which may appear singular, that in a barren country the computed miles are always longer, than near the capital, where the country is rich and populous. The traveller has no natural measure of the space gone through, other than the time bestowed upon it; nor any natural measure of the time, other than the number of his perceptions. These being proportioned to the number of visible objects, he imagines that he hath consumed more time on his day’s journey, and accomplished a greater number of miles, in a populous than in a waste country. By this method of calculation, every computed mile in the former must in reality be shorter than in the latter.
Again, the travelling with an agreeable companion produceth a short computation both of the road and of time; especially if there be few objects that demand attention, or if the objects be familiar. The case is the same of young people at a ball, or of a joyous company over a bottle. The ideas with which they have been entertained, being transitory, escape the memory. After all is over, they reflect that they have been much diverted, but scarce can say about what.
When one is totally occupied in any agreeable work that admits not many objects, time runs on without observation; and upon an after recollection must appear short, in proportion to the paucity of objects. This is still more remarkable in close contemplation and in deep thinking, where the train, composed wholly of ideas, proceeds with an extreme slow pace. Not only are the ideas few in number, but are apt to escape an after-reckoning. The like false reckoning of time may proceed from an opposite state of mind. In a reverie, where ideas float at random without making any impression, time goes on unheeded and the reckoning is lost. A reverie may be so profound as to prevent the recollection of any one idea: that the mind was busied in a train of thinking, will in general be remembered; but what was the subject, has quite escaped the memory. In such a case, we are altogether at a loss about the time: we have no data for making a computation. No cause produceth so false a reckoning of time, as immoderate grief. The mind, in this state, is violently attached to a single object, and admits not a different thought. Any other object breaking in, is instantly banished, so as scarce to give an appearance of succession. In a reverie, we are uncertain of the time that is past: but in the example now given, there is an appearance of certainty, so far as the natural measure of time can be trusted, that the time must have been short, when the perceptions are so few in number.
The natural measure of space appears more obscure than that of time. I venture however to enter upon it, leaving it to be further prosecuted, if it be thought of any importance.
The space marked out for a house, appears considerably larger after it is divided into its proper parts. A piece of ground appears larger after it is surrounded with a fence; and still larger when it is made a garden and divided into different copartments.
On the contrary, a large plain looks less after it is divided into parts. The sea must be excepted, which looks less from that very circumstance of not being divided into parts.
A room of a moderate size appears larger when properly furnished. But when a very large room is furnished, I doubt whether it be not lessened in appearance.
A room of a moderate size, looks less by having a ceiling lower than in proportion. The same low ceiling makes a very large room look larger than it is in reality.
These experiments are by far too small a stock for a general theory. But they are all that occur at present; and without attempting any regular system, I shall satisfy myself with a few conjectures.
The largest angle of vision seems to me the natural measure of space. The eye is the only judge; and in examining with it the size of any plain, or the length of any line, the most accurate method that can be taken is, to run over the object in parts. The largest part that can be taken in at one stedfast look, determines the largest angle of vision; and when that angle is given, one may institute a calculation by trying with the eye how many of these parts are in the whole.
Whether this angle be the same in all men, I know not. The smallest angle of vision is ascertained; and to ascertain the largest angle, would not be less curious.
But supposing it known, it would be a very imperfect measure; perhaps more so than the natural measure of time. It requires great steadiness of eye to measure a line with any accuracy, by applying to it the largest angle of distinct vision. And suppose this steadiness to be acquired by practice, the measure will be imperfect from other circumstances. The space comprehended under this angle, will be different according to the distance, and also according to the situation of the object. Of a perpendicular this angle will comprehend the smallest space. The space will be larger in looking upon an inclined plain; and will be larger or less in proportion to the degree of inclination.
This measure of space, like the measure of time, is liable to some extraordinary errors from certain operations of the mind, which will account for some of the erroneous judgements above mentioned. The space marked out for a dwelling-house, where the eye is at any reasonable distance, is seldom greater than can be seen at once without moving the head. Divide this space into two or three equal parts, and none of these parts will appear much less than what can be comprehended at one distinct look; consequently each of them will appear equal, or nearly equal, to what the whole did before the division. If, on the other hand, the whole be very small, so as scarce to fill the eye at one look, its divisions into parts will, I conjecture, make it appear still less. The minuteness of the parts is, by an easy transition of ideas, transferred to the whole. Each part hath a diminutive appearance, and by the intimate connection of these parts with the whole, we pass the same judgement upon all.
The space marked out for a small garden, is surveyed almost at one view; and requires a motion of the eye so slight, as to pass for an object that can be comprehended under the largest angle of distinct vision. If not divided into too many parts, we are apt to form the same judgement of each part; and consequently to magnify the garden in proportion to the number of its parts.
A very large plain without protuberances, is an object not less rare than beautiful; and in those who see it for the first time, it must produce an emotion of wonder. This emotion, however slight, tending to its own gratification, imposes upon the mind, and makes it judge that the plain is larger than it is in reality. Divide this plain into parts, and our wonder ceases. It is no longer considered as one great plain, but as so many different fields or inclosures.
The first time one beholds the sea, it appears to be large beyond all bounds. When it becomes familiar, and raises our wonder in no degree, it appears less than it is in reality. In a storm it appears larger, being distinguishable by the rolling waves into a number of great parts. Islands scattered at considerable distances, add in appearance to its size. Each intercepted part looks extremely large, and we silently apply arithmetic to increase the appearance of the whole. Many islands scattered at hand, give a diminutive appearance to the sea, by its connection with its diminutive parts. The Lomond lake would undoubtedly look larger without its islands.
Furniture increaseth in appearance the size of a small room, for the same reason that divisions increase in appearance the size of a garden. The emotion of wonder which is raised by a very large room without furniture, makes it look larger than it is in reality. If completely furnished, we view it in parts, and our wonder is not raised.
A low ceiling hath a diminutive appearance, which, by an easy transition of ideas, is communicated to the length and breadth, provided they bear any sort of proportion to the height. If they be out of all proportion, the opposition seizes the mind, and raises some degree of wonder, which makes the difference appear greater than it really is.