And, in this one instance, give me leave to say, you shew a manifest weakness of judgment. With relation to the following _Essay_, I shall only add that I beg your pardon for laying a trifle of that nature in your way, at a time when you are engaged in the important affairs of the nation, and desire you to think that I am, with all sincerity and respect,
SIR,
Your most faithful and most humble servant,
GEORGE BERKELEY.
An Essay Towards A New Theory Of Vision
1. My design is to shew the manner wherein we perceive by Sight the Distance, Magnitude, and Situation of objects: also to consider the difference there is betwixt the ideas of Sight and Touch, and whether there be any idea common to both senses(286).
2. It is, I think, agreed by all that Distance, of itself and immediately, cannot be seen(287). For, distance(288) being a line directed endwise to the eye, it projects only one point in the fund of the eye, which point remains invariably the same, whether the distance be longer or shorter(289).
3. I find it also acknowledged that the estimate we make of the distance of objects considerably remote is rather an act of judgment grounded on experience than of sense. For example, when I perceive a great number of intermediate objects, such as houses, fields, rivers, and the like, which I have experienced to take up a considerable s.p.a.ce, I thence form a judgment or conclusion, that the object I see beyond them is at a great distance. Again, when an object appears faint and small which at a near distance I have experienced to make a vigorous and large appearance, I instantly conclude it to be far off(290). And this, it is evident, is the result of experience; without which, from the faintness and littleness, I should not have inferred anything concerning the distance of objects.
4. But, when an object is placed at so near a distance as that the interval between the eyes bears any sensible proportion to it(291), the opinion of speculative men is, that the two optic axes (the fancy that we see only with one eye at once being exploded), concurring at the object, do there make an angle, by means of which, according as it is greater or lesser, the object is perceived to be nearer or farther off(292).
5. Betwixt which and the foregoing manner of estimating distance there is this remarkable difference:-that, whereas there was no apparent _necessary_ connexion between small distance and a large and strong appearance, or between great distance and a little and faint appearance, there appears a very _necessary_ connexion between an obtuse angle and near distance, and an acute angle and farther distance. It does not in the least depend upon experience, but may be evidently known by any one before he had experienced it, that the nearer the concurrence of the optic axes the greater the angle, and the remoter their concurrence is, the lesser will be the angle comprehended by them.
6. There is another way, mentioned by optic writers, whereby they will have us judge of those distances in respect of which the breadth of the pupil hath any sensible bigness. And that is the greater or lesser divergency of the rays which, issuing from the visible point, do fall on the pupil-that point being judged nearest which is seen by most diverging rays, and that remoter which is seen by less diverging rays, and so on; the apparent distance still increasing, as the divergency of the rays decreases, till at length it becomes infinite, when the rays that fall on the pupil are to sense parallel. And after this manner it is said we perceive distance when we look only with one eye.
7. In this case also it is plain we are not beholden to experience: it being a certain necessary truth that, the nearer the direct rays falling on the eye approach to a parallelism, the farther off is the point of their intersection, or the visible point from whence they flow.
8. (293)Now, though the accounts here given of perceiving _near_ distance by sight are received for true, and accordingly made use of in determining the apparent places of objects, they do nevertheless seem to me very unsatisfactory, and that for these following reasons:-
9. [_First_(294),] It is evident that, when the mind perceives any idea not immediately and of itself, it must be by the means of some other idea.
Thus, for instance, the pa.s.sions which are in the mind of another are of themselves to me invisible. I may nevertheless perceive them by sight; though not immediately, yet by means of the colours they produce in the countenance. We often see shame or fear in the looks of a man, by perceiving the changes of his countenance to red or pale.
10. Moreover, it is evident that no idea which is not itself perceived can be to me the means of perceiving any other idea. If I do not perceive the redness or paleness of a man"s face themselves, it is impossible I should perceive by them the pa.s.sions which are in his mind.
11. Now, from sect. ii., it is plain that distance is in its own nature imperceptible, and yet it is perceived by sight(295). It remains, therefore, that it be brought into view by means of some other idea, that is itself immediately perceived in the act of vision.
12. But those lines and angles, by means whereof some men(296) pretend to explain the perception(297) of distance, are themselves not at all perceived; nor are they in truth ever thought of by those unskilful in optics. I appeal to any one"s experience, whether, upon sight of an object, he computes its distance by the bigness of the angle made by the meeting of the two optic axes? or whether he ever thinks of the greater or lesser divergency of the rays which arrive from any point to his pupil?
nay, whether it be not perfectly impossible for him to perceive by sense the various angles wherewith the rays, according to their greater or lesser divergence, do fall on the eye? Every one is himself the best judge of what he perceives, and what not. In vain shall any man(298) tell me, that I perceive certain lines and angles, which introduce into my mind the various ideas of distance, so long as I myself am conscious of no such thing.
13. Since therefore those angles and lines are not themselves perceived by sight, it follows, from sect. x., that the mind does not by them judge of the distance of objects.
14. [_Secondly_(299),] The truth of this a.s.sertion will be yet farther evident to any one that considers those lines and angles have no real existence in nature, being only an hypothesis framed by the mathematicians, and by them introduced into optics, that they might treat of that science in a geometrical way.
15. The [_third_ and(300)] last reason I shall give for rejecting that doctrine is, that though we should grant the real existence of those optic angles, &c., and that it was possible for the mind to perceive them, yet these principles would not be found sufficient to explain the phenomena of distance, as shall be shewn hereafter.
16. Now it being already shewn(301) that distance is _suggested_(302) to the mind, by the mediation of some other idea which is itself perceived in the act of seeing, it remains that we inquire, what ideas or sensations there be that attend vision, unto which we may suppose the ideas of distance are connected, and by which they are introduced into the mind.
And, _first_, it is certain by experience, that when we look at a near object with both eyes, according as it approaches or recedes from us, we alter the disposition of our eyes, by lessening or widening the interval between the pupils. This disposition or turn of the eyes is attended with a sensation(303), which seems to me to be that which in this case brings the idea of greater or lesser distance into the mind.
17. Not that there is any natural or necessary(304) connexion between the sensation we perceive by the turn of the eyes and greater or lesser distance. But-because the mind has, by constant experience, found the different sensations corresponding to the different dispositions of the eyes to be attended each with a different degree of distance in the object-there has grown an habitual or customary connexion between those two sorts of ideas: so that the mind no sooner perceives the sensation arising from the different turn it gives the eyes, in order to bring the pupils nearer or farther asunder, but it withal perceives the different idea of distance which was wont to be connected with that sensation. Just as, upon hearing a certain sound, the idea is immediately suggested to the understanding which custom had united with it(305).
18. Nor do I see how I can easily be mistaken in this matter. I know evidently that distance is not perceived of itself(306); that, by consequence, it must be perceived by means of some other idea, which is immediately perceived, and varies with the different degrees of distance.
I know also that the sensation arising from the turn of the eyes is of itself immediately perceived; and various degrees thereof are connected with different distances, which never fail to accompany them into my mind, when I view an object distinctly with both eyes whose distance is so small that in respect of it the interval between the eyes has any considerable magnitude.
19. I know it is a received opinion that, by altering the disposition of the eyes, the mind perceives whether the angle of the optic axes, or the lateral angles comprehended between the interval of the eyes or the optic axes, are made greater or lesser; and that, accordingly, by a kind of natural geometry, it judges the point of their intersection to be nearer or farther off. But that this is not true I am convinced by my own experience; since I am not conscious that I make any such use of the perception I have by the turn of my eyes. And for me to make those judgments, and draw those conclusions from it, without knowing that I do so, seems altogether incomprehensible(307).
20. From all which it follows, that the judgment we make of the distance of an object viewed with both eyes is entirely the result of experience.
If we had not constantly found certain sensations, arising from the various disposition of the eyes, attended with certain degrees of distance, we should never make those sudden judgments from them concerning the distance of objects; no more than we would pretend to judge of a man"s thoughts by his p.r.o.nouncing words we had never heard before.
21. _Secondly_, an object placed at a certain distance from the eye, to which the breadth of the pupil bears a considerable proportion, being made to approach, is seen more confusedly(308). And the nearer it is brought the more confused appearance it makes. And this being found constantly to be so, there arises in the mind an habitual connexion between the several degrees of confusion and distance; the greater confusion still implying the lesser distance, and the lesser confusion the greater distance of the object.
22. This confused appearance of the object doth therefore seem to be the medium whereby the mind judges of distance, in those cases wherein the most approved writers of optics will have it judge by the different divergency with which the rays flowing from the radiating point fall on the pupil(309). No man, I believe, will pretend to see or feel those imaginary angles that the rays are supposed to form, according to their various inclinations on his eye. But he cannot choose seeing whether the object appear more or less confused. It is therefore a manifest consequence from what has been demonstrated that, instead of the greater or lesser divergency of the rays, the mind makes use of the greater or lesser confusedness of the appearance, thereby to determine the apparent place of an object.
23. Nor doth it avail to say there is not any necessary connexion between confused vision and distance great or small. For I ask any man what necessary connexion he sees between the redness of a blush and shame? And yet no sooner shall he behold that colour to arise in the face of another but it brings into his mind the idea of that pa.s.sion which hath been observed to accompany it.
24. What seems to have misled the writers of optics in this matter is, that they imagine men judge of distance as they do of a conclusion in mathematics; betwixt which and the premises it is indeed absolutely requisite there be an apparent necessary connexion. But it is far otherwise in the sudden judgments men make of distance. We are not to think that brutes and children, or even grown reasonable men, whenever they perceive an object to approach or depart from them, do it by virtue of geometry and demonstration.
25. That one idea may suggest another to the mind, it will suffice that they have been observed to go together, without any demonstration of the _necessity_ of their coexistence, or without so much as knowing what it is that makes them so to coexist. Of this there are innumerable instances, of which no one can be ignorant(310).
26. Thus, greater confusion having been constantly attended with nearer distance, no sooner is the former idea perceived but it suggests the latter to our thoughts. And, if it had been the ordinary course of nature that the farther off an object were placed the more confused it should appear, it is certain the very same perception that now makes us think an object approaches would then have made us to imagine it went farther off; that perception, abstracting from custom and experience, being equally fitted to produce the idea of great distance, or small distance, or no distance at all.
27. _Thirdly_, an object being placed at the distance above specified, and brought nearer to the eye, we may nevertheless prevent, at least for some time, the appearance"s growing more confused, by straining the eye(311).
In which case that sensation supplies the place of confused vision, in aiding the mind to judge of the distance of the object; it being esteemed so much the nearer by how much the effort or straining of the eye in order to distinct vision is greater.
28. I have here(312) set down those sensations or ideas(313) that seem to be the constant and general occasions of introducing into the mind the different ideas of near distance. It is true, in most cases, that divers other circ.u.mstances contribute to frame our idea of distance, viz. the particular number, size, kind, &c. of the things seen. Concerning which, as well as all other the forementioned occasions which suggest distance, I shall only observe, they have none of them, in their own nature, any relation or connexion with it: nor is it possible they should ever signify the various degrees thereof, otherwise than as by experience they have been found to be connected with them.
29. I shall proceed upon these principles to account for a phenomenon which has. .h.i.therto strangely puzzled the writers of optics, and is so far from being accounted for by any of their theories of vision, that it is, by their own confession, plainly repugnant to them; and of consequence, if nothing else could be objected, were alone sufficient to bring their credit in question. The whole difficulty I shall lay before you in the words of the learned Doctor Barrow, with which he concludes his _Optic Lectures_(314):-
[Ill.u.s.tration]
"Haec sunt, quae circa partem opticae praecipue mathematicam dicenda mihi suggessit meditatio. Circa reliquas (quae f?s???te?a? sunt, adeoque saepiuscule pro certis principiis plausibiles conjecturas venditare necessum habent) nihil fere quicquam admodum verisimile succurrit, a pervulgatis (ab iis, inquam, quae Keplerus, Scheinerus(315), Cartesius, et post illos alii tradiderunt) alienum aut diversum. Atqui tacere malo, quam toties oblatam cramben reponere. Proinde receptui cano; nee ita tamen ut prorsus discedam, anteaquam improbam quandam difficultatem (pro sinceritate quam et vobis et veritati debeo minime dissimulandam) in medium protulero, quae doctrinae nostrae, hactenus inculcatae, se objicit adversam, ab ea saltem nullam admitt.i.t solutionem. Illa, breviter, talis est. Lenti vel speculo cavo _EBF_ exponatur punctum visibile _A_, ita distans, ut radii ex _A_ manantes ex inflectione versus axem _AB_ cogantur. Sitque radiationis limes (seu puncti _A_ imago, qualem supra pa.s.sim statuimus) punctum _Z_.
Inter hoc autem et inflectentis verticem _B_ uspiam positus concipiatur oculus. Quaeri jam potest, ubi loci debeat punctum _A_ apparere? Retrorsum ad punctum _Z_ videri non fert natura (c.u.m omnis impressio sensum afficiens proveniat a partibus _A_) ac experientia reclamat. Nostris autem e placitis consequi videtur, ipsum ad partes anticas apparens, ab intervallo longissime dissito (quod et maximum sensibile quodvis intervallum quodammodo exsuperet), apparere. c.u.m enim quo radiis minus divergentibus attingitur objectum, eo (seclusis utique praenotionibus et praejudiciis) longius abesse sentiatur; et quod parallelos ad oculum radios projicit, remotissime positum aestimetur: exigere ratio videtur, ut quod convergentibus radiis apprehenditur, adhuc magis, si fieri posset, quoad apparentiam elongetur. Quin et circa casum hunc generatim inquiri possit, quidnam omnino sit, quod apparentem puncti _A_ loc.u.m determinet, faciatque quod constanti ratione nunc propius, nunc remotius appareat? Cui itidem dubio nihil quicquam ex hactenus dictorum a.n.a.logia responderi posse videtur, nisi debere punctum _A_ perpetuo longissime semotum videri. Verum experientia secus attestatur, illud pro diversa oculi inter puncta _B_, _Z_, positione varie distans, nunquam fere (si unquam) longinquius ipso _A_ libere spectato, subinde vero multo propinquius adparere; quinimo, quo oculum appellentes radii magis convergunt, eo speciem objecti propius accedere. Nempe, si puncto _B_ admoveatur oculus, suo (ad lentem) fere nativo in loco conspicitur punctum _A_ (vel aeque distans, ad speculum); ad _O_ reductus oculus ejusce speciem appropinquantem cernit; ad _P_ adhuc vicinius ipsum existimat; ac ita sensim, donec alicubi tandem, velut ad _Q_, const.i.tuto oculo, objectum summe propinquum apparens in meram confusionem incipiat evanescere. Quae sane cuncta rationibus atque decretis nostris repugnare videntur, aut c.u.m iis saltem parum amice conspirant. Neque nostram tantum sententiam pulsat hoc experimentum, at ex aequo caeteras quas norim omnes: veterem imprimis ac vulgatam, nostrae prae reliquis affinem, ita convellere videtur, ut ejus vi coactus doctissimus A. Tacquetus isti principio (cui pene soli totam inaedificaverat _Catoptricam_ suam) ceu infido ac inconstanti renunciarit, adeoque suam ipse doctrinam labefactarit? id tamen, opinor, minime facturus, si rem totam inspexissit penitius, atque difficultatis fundum attigissit.
Apud me vero non ita pollet haec, nec eousque praepollebit ulla difficultas, ut ab iis quae manifeste rationi consentanea video, discedam; praesertim quum, ut his accidit, ejusmodi difficultas in singularis cujuspiam casus disparitate fundetur. Nimirum in praesente casu peculiare quiddam, naturae subtilitati involutum, delitescit, aegre forta.s.sis, nisi perfectius explorato videndi modo, detegendum. Circa quod nil, fateor, hactenus excogitare potui, quod adblandiretur animo meo, nedum plane satisfaceret.
Vobis itaque nodum hunc, utinam feliciore conatu, resolvendum committo."
_In English as follows_: