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An Essay Towards a New Theory of Vision
by
George Berkeley (1685-1753)
CONTENTS
Sect.
1 Design
2 Distance of itself invisible
3 Remote distance perceived rather by experience than by sense
4 Near distance thought to be perceived by the ANGLE of the
OPTIC AXES
5 Difference between this and the former manner of perceiving
distance
6 Also by diverging rays
7 This depends not on experience
8 These the common accounts, but not satisfactory
9 Some IDEAS perceived by the mediation of others
10 No IDEA which is not itself perceived, can be the means of
perceiving another
11 Distance perceived by means of some other IDEA
12 Those lines and angles mentioned in optics, are not themselves
perceived
13 Hence the mind does not perceive distance by lines and angles
14 Also because they have no real existence
15 And because they are insufficient to explain the phenomena
16 The IDEAS that suggest distance are, 1st, the sensation arising
from the turn of the eyes
17 Betwixt which and distance there is no necessary connection
18 Scarce room for mistake in this matter
19 No regard had to the angle of the OPTIC AXES
20 Judgment of distance made with both eyes, the result of EXPERIENCE
21 2ndly, Confusedness of appearance
22 This the occasion of those judgments attributed to diverging rays
23 Objection answered
24 What deceives the writers of optics in this matter
25 The cause why one IDEA may suggest another
26 This applied to confusion and distance
27 Thirrdly, the straining of the eye
28 The occasions which suggest distance have in their own nature
no relation to it
29 A difficult case proposed by Dr. Barrow as repugnant to
all the known theories
30 This case contradicts a received principle in catoptrics
31 It is shown to agree with the principles we have laid down
32 This phenomenon illustrated
33 It confirms the truth of the principle whereby it is explained
34 Vision when distinct, and when confused
35 The different effects of parallel diverging and converging rays
36 How converging and diverging rays come to suggest the same
distance
37 A person extreme purblind would judge aright in the
forementioned case
38 Lines and angles, why useful in optics
39 The not understanding this, a cause of mistake
40 A query proposed, by Mr. Molyneux in his DIOPTRICS, considered
41 One born blind would not at first have any IDEA of distance by
sight
42 This not agreeable to the common principles
43 The proper objects of sight, not without the mind, nor the images
of any thing without the mind
44 This more fully explained
45 In what sense we must be understood to see distance
and external things
46 Distance, and things placed at a distance, not otherwise perceived
by the eye than by the ear
47 The IDEAS of sight more apt to be confounded with the IDEAS
of touch than those of hearing are
48 How this comes to pass
49 Strictly speaking, we never see and feel the same thing
50 Objects of SIGHT twofold, mediate and immediate
51 These hard to separate in our thoughts
52 The received accounts of our perceiving magnitude by sight, false
53 Magnitude perceived as immediately as distance
54 Two kinds of sensible extension, neither of which is
infinitely divisible
55 The tangible magnitude of an OBJECT steady, the visible not
56 By what means tangible magnitude is perceived by sight
57 This further enlarged on
58 No necessary connection between confusion or faintness
of appearance, and small or great magnitude
59 The tangible magnitude of an OBJECT more heeded than the visible,
and why
60 An instance of this
61 Men do not measure by visible feet or inches
62 No necessary connection between visible and tangible extension
63 Greater visible magnitude might signify lesser tangible magnitude
64 The judgments we make of magnitude depend altogether on experience
65 Distance and magnitude seen as shame or anger
66 But we are prone to think otherwise, and why
67 The moon seems greater in the horizon than in the meridian
68 The cause of this phenomenon assigned
69 The horizontal moon, why greater at one time than another.
70 The account we have given proved to be true
71 And confirmed by the moon's appearing greater in a mist
72 Objection answered
73 The way wherein faintness suggests greater magnitude illustrated
74 Appearance of the horizontal moon, why thought difficult to
explain
75 Attempts towards the solution of it made by several, but in vain
76 The opinion of Dr. Wallis
77 It is shown to be unsatisfactory
78 How lines and angles may be of use in computing apparent
magnitudes
79 One born blind, being made to see, what judgment he would make
of magnitude
80 The MINIMUM VISIBLE the same to all creatures
81 Objection answered
82 The eye at all times perceives the same number of visible points
83 Two imperfections in the VISIVE FACULTY
84 Answering to which, we may conceive two perfections
85 In neither of these two ways do microscopes improve the sight
86 The case of microscopical eyes, considered
87 The sight, admirably adapted to the ends of seeing
88 Difficulty concerning erect vision
89 The common way of explaining it
90 The same shown to be false
91 Not distinguishing between IDEAS of sight and touch, cause
of mistake in this matter
92 The case of one born blind, proper to be considered
93 Such a one might by touch attain to have IDEAS of UPPER and LOWER
94 Which modes of situation he would attribute only to things
tangible
95 He would not at first sight think anything he saw, high or low,
erect or inverted
96 This illustrated by an example
97 By what means he would come to denominate visible OBJECTS,
high or low, etc.
98 Why he should think those OBJECTS highest, which are painted on
the lowest part of his eye, and VICE VERSA
99 How he would perceive by sight, the situation of external objects
100 Our propension to think the contrary, no argument against
what has been said
101 Objection
102 Answer
103 An object could not be known at first sight by the colour
104 Nor by the magnitude thereof
105 Nor by the figure
106 In the first act of vision, no tangible thing would be suggested
by sight
107 Difficulty proposed concerning number
108 Number of things visible, would not at first sight suggest
the like number of things tangible
109 Number the creature of the mind
110 One born blind would not at first sight number visible things
as others do
111 The situation of any object determined with respect only to
objects of the same sense
112 No distance, great or small, between a visible and tangible thing
113 The not observing this, cause of difficulty in erect vision
114 Which otherwise includes nothing unaccountable
115 What is meant by the picture being inverted
116 Cause of mistake in this matter
117 Images in the eye, not pictures of external objects
118 In what sense they are pictures
119 In this affair we must carefully distinguish between ideas
of sight and touch
120 Difficult to explain by words the true Theory of Vision
121 The question, whether there is any IDEA common to sight
and touch, stated
122 Abstract extension inquired into
123 It is incomprehensible
124 Abstract extension not the OBJECT of geometry
125 The general IDEA of a triangle, considered
126 Vacuum, or pure space, not common to sight and touch
127 There is no idea, or kind of idea, common to both senses
128 First argument in proof hereof
129 Second argument
130 Visible figure and extension, not distinct IDEAS from colour
131 Third argument
132 Confirmation drawn from Mr. Molyneux's problem of a sphere
and a cube, published by Mr. Locke
133 Which is falsely solved, if the common supposition be true
134 More might be said in proof of our tenet, but this suffices
135 Further reflection on the foregoing problem
136 The same thing doth not affect both sight and touch
137 The same idea of motion not common to sight and touch
138 The way wherein we apprehend motion by sight, easily collected
from what hath been said
139 QU. How visible and tangible IDEAS came to have the same name
if not of the same kind
140 This accounted for without supposing them of the same kind
141 OBJ. That a tangible square is liker to a visible square than
to a visible circle
142 ANS. That a visible square is fitter than a visible circle,
to represent a tangible square
143 But it doth not hence follow, that a visible square
is like a tangible square
144 Why we are more apt to confound visible with tangible IDEAS,
than other signs with the things signified
145 Several other reasons hereof, assigned
146 Reluctancy in rejecting any opinion, no argument of its truth
147 Proper objects of vision the language of nature
148 In it there is much admirable, and deserving our attention
149 Question proposed, concerning the object of geometry
150 At first view we are apt to think visible extension the object
of geometry
151 Visible extension shown not to be the object of geometry
152 Words may as well be thought the object of geometry,
as visible extension
153 It is proposed to inquire, what progress an intelligence that
could see, but not feel, might make in geometry
154 He cannot understand those parts which relate to solids, and
their surfaces, and lines generated by their section
155 Nor even the elements of plane geometry
156 The proper objects of sight incapable of being managed as
geometrical figures
157 The opinion of those who hold plane figures to be the immediate
objects of sight, considered
158 Planes no more the immediate objects of sight, than solids
159 Difficult to enter precisely into the thoughts of the
above-mentioned intelligence
160 The object of geometry, its not being sufficiently understood,
cause of difficulty, and useless labour in that science
AN ESSAY TOWARDS A NEW THEORY OF VISION
1. My design is to show 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.
2. It is, I think, agreed by all that DISTANCE, of itself and
immediately, cannot be seen. For DISTANCE being a Line directed end-wise
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.
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 space, 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: 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, 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.
5. Betwixt which and the foregoing manner of estimating distance there is
this remarkable difference: that whereas there was no apparent, necessary
connection between small distance and a large and strong appearance, or
between great distance and a little and faint appearance, there appears a
very necessary connection 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 anyone 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 beholding 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. I have here set down the common, current accounts that are given of
our perceiving near distances by sight, which, though they are
unquestionably received for true by MATHEMATICIANS, and accordingly made
use of by them in determining the apparent places of OBJECTS, do,
nevertheless seem to me very unsatisfactory: and that for these following
reasons:--
9. FIRST, 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 passions 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 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 passions which are in his mind.
11. Now from sect. 2 it is plain that distance is in its own nature
imperceptible, and yet it is perceived by sight. 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 MATHEMATICIANS
pretend to explain the perception of distance, are themselves not at all
perceived, nor are they in truth ever thought of by those unskilful in
optics. I appeal to anyone'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? Everyone
is himself the best judge of what he perceives, and what not. In vain
shall all the MATHEMATICIANS in the world 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. 10 that the mind doth not by them judge
of the distance of OBJECTS.
14. Secondly, the truth of this assertion will be yet farther evident to
anyone 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 last reason I shall give for rejecting that doctrine is,
that though we should grant the real existence of those OPTIC ANGLES,
etc., 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 shown hereafter.
16. Now, it being already shown that distance is suggested 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, 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 connection 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 connection 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.
18 Nor do I see how I can easily be mistaken in this matter. I know
evidently that distance is not perceived of itself. 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 is 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.
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 a man's thoughts by his pronouncing 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: and the nearer it is brought
the more confused appearance it makes. And this being found constantly to
be so, there ariseth in the mind an habitual CONNECTION 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 judgeth 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. 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 bath 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 connection between
confused VISION and distance, great or small. For I ask any man what
necessary connection 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 and the IDEA of that passion 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 connection: 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.
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 appearances growing more confused, by straining the eye. 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 set down those sensations or IDEAS 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
circumstances contribute to frame our IDEA of distance, to wit, the
particular number, size, kind, etc., 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 connection 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 hitherto 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 Dr. Barrow, with which he concludes his optic
lectures:--
'I have here delivered what my thoughts have suggested to me concerning
that part of optics which is more properly mathematical. As for the other
parts of that science (which being rather physical, do consequently
abound with plausible conjectures instead of certain principles), there
has in them scarce anything occurred to my observation different from what
has been already said by Kepler, Scheinerus, Descartes, and others. And
methinks, I had better say nothing at all, than repeat that which has
been so often said by others. I think it therefore high time to take my
leave of this subject: but before I quit it for good and all, the fair
and ingenuous dealing that I owe both to you and to truth obligeth me to
acquaint you with a certain untoward difficulty, which seems directly
opposite to the doctrine I have been hitherto inculcating, at least,
admits of no solution from it. In short it is this. Before the double
convex glass or concave speculum EBF, let the point A be placed at such a
distance that the rays proceeding from A, after refraction or reflection,
be brought to unite somewhere in the AxAB. And suppose the point of union
(i.e. the image of the point A, as hath been already set forth) to be Z;
between which and B, the vertex of the glass or speculum, conceive the
eye to be anywhere placed. The question now is, where the point A ought
to appear? Experience shows that it does not appear behind at the point
Z, and it were contrary to nature that it should, since all the
impression which affects the sense comes from towards A. But from our
tenets it should seem to follow that it would appear before the eye at a
vast distance off, so great as should in some sort surpass all sensible
distance. For since if we exclude all anticipations and prejudices, every
OBJECT appears by so much the farther off, by how much the rays it sends
to the eye are less diverging. And that OBJECT is thought to be most
remote from which parallel rays proceed unto the eye. Reason would make
one think that OBJECT should appear at yet a greater distance which is
seen by converging rays. Moreover it may in general be asked concerning
this case what it is that determines the apparent place of the point A,
and maketh it to appear after a constant manner sometimes nearer, at
other times farther off? To which doubt I see nothing that can be
answered agreeable to the principles we have laid down except only that
the point A ought always to appear extremely remote. But on the contrary
we are assured by experience that the point A appears variously distant,
according to the different situations of the eye between the points B and
Z. And that it doth never (if at all) seem farther off, than it would if
it were beheld by the naked eye, but on the contrary it doth sometimes
appear much nearer. Nay, it is even certain that by how much the rays
falling on the eye do more converge by so much the nearer doth the OBJECT
seem to approach. For the eye being placed close to the point B, the
OBJECT A appears nearly in its own natural place, if the point B is taken
in the glass, or at the same distance, if in the speculum. The eye being
brought back to O, the OBJECT seems to draw near: and being come to P it
beholds it still nearer. And so on little and little, till at length the
eye being placed somewhere, suppose at Q, the OBJECT appearing extremely
near, begins to vanish into mere confusion. All which doth seem repugnant
to our principles, at least not rightly to agree with them. Nor is our
tenet alone struck at by this experiment, but likewise all others that
ever came to my knowledge are, every whit as much, endangered by it. The
ancient one especially (which is most commonly received, and comes
nearest to mine) seems to be so effectually overthrown thereby that the
most learned Tacquet has been forced to reject that principle, as false
and uncertain, on which alone he had built almost his whole CATOPTRICS;
and consequently by taking away the foundation, hath himself pulled down
the superstructure he had raised on it. Which, nevertheless, I do not
believe he would have done had he but considered the whole matter more
thoroughly, and examined the difficulty to the bottom. But as for me,
neither this nor any other difficulty shall have so great an influence on
me as to make me renounce that which I know to be manifestly agreeable to
reason: especially when, as it here falls out, the difficulty is founded
in the peculiar nature of a certain odd and particular case. For in the
present case something peculiar lies hid, which being involved in the
subtilty of nature will, perhaps, hardly be discovered till such time as
the manner of vision is more perfectly made known. Concerning which, I
must own, I have hitherto been able to find out nothing that has the
least show of PROBABILITY, not to mention CERTAINTY. I shall, therefore,
leave this knot to be untied by you, wishing you may have better success
in it than I have had.'
30. The ancient and received principle, which Dr. Barrow here mentions as
the main foundation of Tacquet's CATOPTRICS, is that: 'every visible point
seen by reflection from a speculum shall appear placed at the intersection
of the reflected ray, and the perpendicular of incidence:' which
intersection in the present case, happening to be behind the eye, it
greatly shakes the authority of that principle, whereon the
aforementioned author proceeds throughout his whole CATOPTRICS in
determining the apparent place of OBJECTS seen by reflection from any kind
of speculum.
31. Let us now see how this phenomenon agrees with our tenets. The eye
the nearer it is placed to the point B in the foregoing figures, the more
distinct is the appearance of the OBJECT; but as it recedes to O the
appearance grows more confused; and at P it sees the OBJECT yet more
confused; and so on till the eye being brought back to Z sees the OBJECT
in the greatest confusion of all. Wherefore by sect. 21 the OBJECT should
seem to approach the eye gradually as it recedes from the point B, that
is, at O it should (in consequence of the principle I have laid down in
the aforesaid section) seem nearer than it did at B, and at P nearer than
at O, and at Q nearer than at P; and so on, till it quite vanishes at Z.
Which is the very matter of fact, as anyone that pleases may easily
satisfy himself by experiment.
32. This case is much the same as if we should suppose an Englishman to
meet a foreigner who used the same words with the English, but in a
direct contrary signification. The Englishman would not fail to make a
wrong judgment of the IDEAS annexed to those sounds in the mind of him
that used them. Just so, in the present case the OBJECT speaks (if I may
so say) with words that the eye is well acquainted with, that is,
confusions of appearance; but whereas heretofore the greater confusions
were always wont to signify nearer distances, they have in this case a
direct, contrary signification, being connected with the greater
distances. Whence it follows that the eye must unavoidably be mistaken,
since it will take the confusions in the sense it has been used to, which
is directly opposed to the true.
33. This phenomenon as it entirely subverts the opinion of those who will
have us judge of distance by lines and angles, on which supposition it is
altogether inexplicable, so it seems to me no small confirmation of the
truth of that principle whereby it is explained. But in order co a more
full explication of this point, and to show how far the hypothesis of the
mind's judging by the various divergency of rays may be of use in
determining the apparent place of an OBJECT, it will be necessary to
premise some few things, which are already well known to those who have
any skill in dioptrics.
34. FIRST, any radiating point is then distinctly seen when the rays
proceeding from it are, by the refractive power of the crystalline,
accurately reunited in the retina or fund of the eye: but if they are
reunited, either before they arrive at the retina, or after they have
passed it, then there is confused vision.
35. SECONDLY, suppose in the adjacent figures NP represent an eye duly
framed and retaining its natural figure. In Fig. 1 the rays falling
nearly parallel on the eye, are by the crystalline AB refracted, so as
their focus or point of union F falls exactly on the retina: but if the
rays fall sensibly diverging on the eye, as in Fig. 2, then their focus
falls beyond the retina: or if the rays are made to converge by the lens
QS before they come at the eye, as in Fig. 3, their focus F will fall
before the retina. In which two last cases it is evident from the
foregoing section that the appearance of the point Z is confused. And by
how much the greater is the convergency, or divergency, of the rays
falling on the pupil, by so much the farther will the point of their
reunion be from the retina, either before or behind it, and consequently
the point Z will appear by so much the more confused. And this, by the
bye, may show us the difference between confused and faint vision.
Confused vision is when the rays proceedings from each distinct point of
the OBJECT are not accurately recollected in one corresponding point on
the retina, but take up some space thereon, so that rays from different
points become mixed and confused together. This is opposed to a distinct
vision, and attends near objects. Faint vision is when by reason of the
distance of the object or grossness of the interjacent medium few rays
arrive from the object to the eye. This is opposed to vigorous or clear
vision, and attends remote objects. But to return.
36. The eye, or (to speak truly) the mind, perceiving only the confusion
itself, without ever considering the cause from which it proceeds, doth
constantly annex the same degree of distance to the same degree of
confusion. Whether that confusion be occasioned by converging or by
diverging rays, it matters not. Whence it follows that the eye viewing
the object Z through the glass QS (which by refraction causeth the rays
ZQ, ZS, etc., to converge) should judge it to be at such a nearness at
which if it were placed it would radiate on the eye with rays diverging
to that degree as would produce the same confusion which is now produced
by converging rays, i.e. would cover a portion of the retina equal to DC
(VID. Fig. 3 supra). But then this must be understood (to use Dr.
Barrow's phrase) SECLUSIS PRAENOTIONIBUS ET PRAEJUDICIIS, in case we
abstract from all other circumstances of vision, such as the figure,
size, faintness, etc. of the visible objects; all which do ordinarily
concur to form our idea of distance, the mind having by frequent
experience observed their several sorts or degrees to be connected with
various distances.
37. It plainly follows from what hath been said that a person perfectly
purblind (i.e. that could not see an object distinctly but when placed
close to his eye) would not make the same wrong judgment that others do
in the forementioned case. For to him greater confusions constantly
suggesting greater distances, he must, as he recedes from the glass and
the object grows more confused, judge it to be at a farther distance,
contrary to what they do who have had the perception of the objects
growing more confused connected with the idea of approach.
38. Hence also it doth appear there may be good use of computation by
lines and angles in optics; not that the mind judgeth of distance
immediately by them, but because it judgeth by somewhat which is
connected with them, and to the determination whereof they may be
subservient. Thus the mind judging of the distance of an object by the
confusedness of its appearance, and this confusedness being greater or
lesser to the naked eye, according as the object is seen by rays more or
less diverging, it follows that a man may make use of the divergency of
the rays in computing the apparent distance, though not for its own sake,
yet on account of the confusion with which it is connected. But, so it
is, the confusion itself is entirely neglected by mathematicians as
having no necessary relation with distance, such as the greater or lesser
angles of divergency are conceived to have. And these (especially for
that they fall under mathematical computation) are alone regarded in
determining the apparent places of objects, as though they were the sole
and immediate cause of the judgments the mind makes of distance. Whereas,
in truth, they should not at all be regarded in themselves, or any
otherwise, than as they are supposed to be the cause of confused vision.
39. The not considering of this has been a fundamental and perplexing
oversight. For proof whereof we need go no farther than the case before
us. It having been observed that the most diverging rays brought into the
mind the idea of nearest distance, and that still, as the divergency
decreased, the distance increased: and it being thought the connexion
between the various degrees of divergency and distance was immediate;
this naturally leads one to conclude, from an ill-grounded analogy, that
converging rays shall make an object appear at an immense distance: and
that, as the convergency increases, the distance (if it were possible)
should do so likewise. That this was the cause of Dr. Barrow's mistake is
evident from his own words which we have quoted. Whereas had the learned
doctor observed that diverging and converging rays, how opposite soever
they may seem, do nevertheless agree in producing the same effect, to
wit, confusedness of vision, greater degrees whereof are produced
indifferently, either as the divergency or convergency and the rays
increaseth. And that it is by this effect, which is the same in both,
that either the divergency or convergency is perceived by the eye; I say,
had he but considered this, it is certain he would have made a quite
contrary judgment, and rightly concluded that those rays which fall on
the eye with greater degrees of convergency should make the object from
whence they proceed appear by so much the nearer. But it is plain it was
impossible for any man to attain to a right notion of this matter so long
as he had regard only to lines and angles, and did not apprehend the true
nature of vision, and how far it was of mathematical consideration.
40. Before we dismiss this subject, it is fit we take notice of a query
relating thereto, proposed by the ingenious Mr. Molyneux, is his TREATISE
OF DIOPTRICS,[Par. I. Prop. 31, Sect. 9.] where speaking of this
difficulty, he has these words: 'And so he (i.e. Dr. Barrow) leaves this
difficulty to the solution of others, which I (after so great an example)
shall do likewise; but with the resolution of the same admirable author of
not quitting the evident doarine which we have before laid down, for
determining the LOCUS OBJECTI, on account of being pressed by one
difficulty which seems inexplicable till a more intimate knowledge of the
visive faculty be obtained by mortals. In the meantime, I propose it to
the consideration of the ingenious, whether the LOCUS APPARENS of an
object placed as in this 9th section be not as much before the eye as the
distinct base is behind the eye!' To which query we may venture to answer
in the negative. For in the present case the rule for determining the
distance of the distinct base, or respective focus from the glass, is this:
as the difference between the distance of the object and focus is to the
focus or focal length, so the distance of the object from the glass is to
the distance of the respective focus or distinct base from the glass.
[Molyneux Dioptr., Par. I. Prop. 5.] Let us now suppose the object to be
placed at the distance of the focal length, and one half of the focal
length from the glass, and the eye close to the glass, hence it will follow
by the rule that the distance of the distinct base behind the eye is double
the true distance of the object before the eye. If therefore Mr. Molyneux's
conjecture held good, it would follow that the eye should see the object
twice as far off as it really is; and in other cases at three or four times
its due distance, or more. But this manifestly contradicts experience, the
object never appearing, at farthest, beyond its due distance. Whatever,
therefore, is built on this supposition (VID. COROL. I. PROP. 57, IBID.)
comes to the ground along with it.
41. From what hath been premised it is a manifest consequence that a man
born blind, being made to see, would, at first, have no idea of distance
by sight; the sun and stars, the remotest objects as well as the nearer,
would all seem to be in his eye, or rather in his mind. The objects
intromitted by sight would seem to him (as in truth they are) no other
than a new set of thoughts or sensations, each whereof is as near to him
as the perceptions of pain or pleasure, or the most inward passions of
his soul. For our judging objects provided by sight to be at any
distance, or without the mind, is (VID. sect. 28) entirely the effect of
experience, which one in those circumstances could not yet have attained
to.
42. It is indeed otherwise upon the common supposition that men judge of
distance by the angle of the optic axes, just as one in the dark, or a
blind-man by the angle comprehended by two sticks, one whereof he held in
each hand. For if this were true, it would follow that one blind from his
birth being made to see, should stand in need of no new experience in
order to perceive distance by sight. But that this is false has, I think,
been sufficiently demonstrated.
43. And perhaps upon a strict inquiry we shall not find that even those
who from their birth have grown up in a continued habit of seeing are
irrecoverably prejudiced on the other side, to wit, in thinking what they
see to be at a distance from them. For at this time it seems agreed on
all hands, by those who have had any thoughts of that matter, that
colours, which are the proper and immediate object of sight, are not
without the mind. But then it will be said, by sight we have also the
ideas of extension, and figure, and motion; all which may well be thought
without, and at some distance from the mind, though colour should not. In
answer to this I appeal to any man's experience, whether the visible
extension of any object doth not appear as near to him as the colour of
that object; nay, whether they do not both seem to be in the very same
place. Is not the extension we see coloured, and is it possible for us,
so much as in thought, to separate and abstract colour from extension?
Now, where the extension is there surely is the figure, and there the
motion too. I speak of those which are perceived by sight.
44. But for a fuller explication of this point, and to show that the
immediate objects of sight are not so much as the ideas or resemblances
of things placed at a distance, it is requisite that we look nearer into
the matter and carefully observe what is meant in common discourse, when
one says that which he sees is at a distance from him. Suppose, for
example, that looking at the moon I should say it were fifty or sixty
semidiameters of the earth distant from me. Let us see what moon this is
spoken of: it is plain it cannot be the visible moon, or anything like
the visible moon, or that which I see, which is only a round, luminous
plane of about thirty visible points in diameter. For in case I am
carried from the place where I stand directly towards the moon, it is
manifest the object varies, still as I go on; and by the time that I am
advanced fifty or sixty semidiameters of the earth, I shall be so far
from being near a small, round, luminous flat that I shall perceive
nothing like it; this object having long since disappeared, and if I
would recover it, it must be by going back to the earth from whence I set
out. Again, suppose I perceive by sight the faint and obscure idea of
something which I doubt whether it be a man, or a tree, or a tower, but
judge it to be at the distance of about a mile. It is plain I cannot mean
that what I see is a mile off, or that it is the image or likeness of
anything which is a mile off, since that every step I take towards it the
appearance alters, and from being obscure, small, and faint, grows clear,
large, and vigorous. And when I come to the mile's end, that which I saw
first is quite lost, neither do I find anything in the likeness of it.
45. In these and the like instances the truth of the matter stands thus:
having of a long time experienced certain ideas, perceivable by touch, as
distance, tangible figure, and solidity, to have been connected with
certain ideas of sight, I do upon perceiving these ideas of sight
forthwith conclude what tangible ideas are, by the wonted ordinary course
of Nature like to follow. Looking at an object I perceive a certain
visible figure and colour, with some degree of faintness and other
circumstances, which from what I have formerly observed, determine me to
think that if I advance forward so many paces or miles, I shall be
affected with such and such ideas of touch: so that in truth and
strictness of speech I neither see distance itself, nor anything that I
take to be at a distance. I say, neither distance nor things placed at a
distance are themselves, or their ideas, truly perceived by sight. This I
am persuaded of, as to what concerns myself: and I believe whoever will
look narrowly into his own thoughts and examine what he means by saying
he sees this or that thing at a distance, will agree with me that what he
sees only suggests to his understanding that after having passed a
certain distance, to be measured by the motion of his body, which is
perceivable by touch, he shall come to perceive such and such tangible
ideas which have been usually connected with such and such visible ideas.
But that one might be deceived by these suggestions of sense, and that
there is no necessary connexion between visible and tangible ideas
suggested by them, we need go no farther than the next looking-glass or
pictures to be convinced. Note that when I speak of tangible ideas, I
take the word idea for any the immediate object of sense or
understanding, in which large signification it is commonly used by the
moderns.
46. From what we have shown it is a manifest consequence that the ideas
of space, outness, and things placed at a distance are not, strictly
speaking, the object of sight; they are not otherwise perceived by the
eye than by the ear. Sitting in my study I hear a coach drive along the
street; I look through the casement and see it; I walk out and enter into
it; thus, common speech would incline one to think I heard, saw, and
touched the same thing, to wit, the coach. It is nevertheless certain,
the ideas intromitted by each sense are widely different and distinct
from each other; but having been observed constantly to go together, they
are spoken of as one and the same thing. By the variation of the noise I
perceive the different distances of the coach, and know that it
approaches before I look out. Thus by the ear I perceive distance, just
after the same manner as I do by the eye.
47. I do not nevertheless say I hear distance in like manner as I say
that I see it, the ideas perceived by hearing not being so apt to be
confounded with the ideas of touch as those of sight are. So likewise a
man is easily convinced that bodies and external things are not properly
the object of hearing; but only sounds, by the mediation whereof the idea
of this or that body or distance is suggested to his thoughts. But then
one is with more difficulty brought to discern the difference there is
betwixt the ideas of sight and touch: though it be certain a man no more
sees and feels the same thing than he hears and feels the same thing.
48. One reason of which seems to be this. It is thought a great absurdity
to imagine that one and the same thing should have any more than one
extension, and one figure. But the extension and figure of a body, being
let into the mind two ways, and that indifferently either by sight or
touch, it seems to follow that we see the same extension and the same
figure which we feel.