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THE JOURNEY MAN 1977

 

 

 

THE JOURNEY WOMAN 1977

 

 

26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
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X
Y
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-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
9
-
-
-
-
5
6
-
-
-
1
-
-
-
-
6
-
8
+
=
43
4+3
=
7
-
7
-
7
-
-
-
-
-
-
-
-
8
9
-
-
-
-
14
15
-
-
-
19
-
-
-
-
24
-
26
+
=
115
1+1+5
=
7
-
7
-
7
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
-
-
1
2
3
4
-
-
7
8
9
-
2
3
4
5
-
7
-
+
=
83
8+3
=
11
1+1
2
-
2
-
1
2
3
4
5
6
7
-
-
10
11
12
13
-
-
16
17
18
-
20
21
22
23
-
25
-
+
=
236
2+3+6
=
11
1+1
2
-
2
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
+
=
351
3+5+1
=
9
-
9
-
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
+
=
126
1+2+6
=
9
-
9
-
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
+
=
1
occurs
x
3
=
3
-
3
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
+
=
2
occurs
x
3
=
6
-
6
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
+
=
3
occurs
x
3
=
9
-
9
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
+
=
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
+
=
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
+
=
6
occurs
x
3
=
18
1+8
9
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
+
=
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
+
=
8
occurs
x
3
=
24
2+4
6
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
+
=
9
occurs
x
2
=
18
1+8
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
45
-
-
26
-
126
-
54
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
4+5
-
-
2+6
-
1+2+6
-
5+4
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
-
-
-
-
-
-
-
-
-
-
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9

 

 

1
I
9
9
9
3
SAY
45
9
9
4
HAVE
36
18
9
1
I
9
9
9
9
MENTIONED
99
45
9
4
GODS
45
18
9
6
DIVINE
63
36
9
8
CREATORS
99
36
9
-
-
-
-
-
-
-
-
-
-
4
GODS
45
18
9
6
DIVINE
63
36
9
7
THOUGHT
99
36
9
-
-
-
-
-
-
-
-
-
-
4
GODS
45
18
9
6
DIVINE
63
36
9
4
LOVE
54
18
9
-
-
-
-
-
-
-
-
-
-
4
HAVE
36
18
9
1
I
9
9
9
9
MENTIONED
99
45
9
8
INSTINCT
108
36
9
19
CONSCIENCE
90
45
9
5
DEITY
63
27
9
-
-
-
-
-
-
-
-
-
-
4
HAVE
36
18
9
1
I
9
9
9
9
MENTIONED
99
45
9
8
QUO-VADIS
108
36
9
4
HAVE
36
18
9
1
I
9
9
9
9
MENTIONED
99
45
9
4
THAT
49
13
4

 

 

 

 

11
THE ADVENT
-
-
-
3
THE
33
15
6
6
ADVENT
66
21
3
9
THE ADVENT
99
36
9
-
-
9+9
3+6
-
2
THE ADVENT
9
9
9

 

WISE WISDOM LOST AT SEA DROWNED IN A SEE OF KNOWLEDGE

 

 

 

 

...

 

 

I

SAY

HAVE I MENTIONED GODS DIVINE CREATORS

GODS DIVINE THOUGHT

GODS DIVINE LOVE

HAVE I MENTIONED INSTINCT, CONSCIENCE, DEITY

HAVE I MENTIONED QUO-VADIS HAVE I MENTIONED

THAT

 

THOSE PATENT PATENTED PATIENT PATTERN MAKERS

 

 

Nature's Numbers
Ian Stewart 1995

Numerology is the easiest-and consequently the most dangerous-method for finding patterns. It is easy because anybody can do it and dangerous for the same reason. The difficulty lies in distinguishing significant numerical patterns from accidental ones. Here's a case in point. Kepler was fascinated with patterns in nature, and he devoted much of his life to looking for them in the behaviour of the planets. He devised a simple and tidy theory for the existence of precisely six planets (in his time only Mercury, Venus, Earth, Mars, Jupiter, and Saturn were known). He also discovered a very strange pattern relating the orbital period of a / planet- the time it takes to go once around the Sun-to its distance from the Sun. Recall that the square of a number is what you get when you multiply it by itself: for example, the square of 4 is 4 x 4 = 16. Similarly, the cube is what you get when you multiply it by itself twice: for example, the cube of 4 is 4 x 4 x 4 = 64. Kepler found that if you take the cube of the distance of any planet from the Sun and divide it by the square of its orbital period, you always get the same number. It was not an especially elegant number, but it was the same for all six planets.

Which of these numerological observations is the more significant? The verdict of posterity is that it is the second one, the complicated and rather arbitrary calculation with squares and cubes. This numerical pattern was one of the key steps towards Isaac Newton's theory of gravity, which has explained all sorts of puzzles about the motion of stars and planets. In contrast, Kepler's neat, tidy theory for the number of planets has been buried without trace. For a start it must have been wrong, because we now know of nine planets, not six. There could be even more, farther out from the Sun, and small enough to be undetectable But more important, we no longer expect to find a neat, tidy theory for the number of planets. We think that the Solar System condensed from a cloud of gas surrounding the Sun, and the number of planets presumably depended on the amount of matter in the gas cloud, how it was distributed, and how fast and in what directions it was moving. An equally plausible gas cloud could have given us eight planets, or eleven; the number is accidental, depending on the initial conditions of the gas cloud, rather than universal, reflecting a general law of nature"

Page 6

" The big problem with numerological pattern-seeking is that it generates millions of accidentals for each universal. Nor is it always obvious which is which. For example, there are three stars, roughly equally spaced and in a straight line, in the belt of the constellation Orion. Is that a clue to a significant law of nature?
Here's a similar question. Io, Europa, and Ganymede are three of Jupiter's larger satellites. They orbit the planet in , respectively, 1.77, 3.55, and 7.16 days. Each of these numbers is almost exactly twice the previous one. Is that a significant pattern? Three stars in a row, in terms of orbital period. Which pattern if either, is an important clue..."
    "… In addition to numerical patterns there are geometric ones…"
    "… Until recently the main shapes that appealed to mathematicians were very simple ones: triangles, squares, pen / Page 7 /tagons, hexagons, circles, ellipses, spirals, cubes, spheres, cones, and so on. All of these shapes can be found in nature, although some are far more common, or more evident, than others. The rainbow, for example, is a collection of circles, one for each colour. We don't normally see the entire circle just an arc; but rainbows seen from the air can be complete circles. You also see circles in the ripples on a pond, in the human eye, and on butterflies wings.
         Talking of ripples, the flow of fluids provides an inexhaustible supply of nature's patterns. There are waves of many different kinds-surging toward a beach in parallel ranks, spreading in a V-shape behind a moving boat, radiating outward from an underwater earthquake…"
"…There are swirling spiral whirlpools and tiny vortices. And there is the apparently structureless, random frothing of turbulent flow, one of the great enigmas of mathematics and physics. There are similar patterns in the atmosphere, too, the most dramatic being the vast spiral of a hurricane…"
    "…There are also wave patterns on land. The most strikingly mathematical landscapes on Earth are to be found in the great ergs, or sand oceans, of the Arabian and Sahara deserts. Even when the wind blows steadily in a fixed direction, sand dunes form. The simplest pattern is that of transverse dunes, which-just like ocean waves-line up in parallel straight rows at right angles to the prevailing wind direction. Sometimes the rows themselves become wavy in which case they are called barchanoid ridges; sometimes they break up into / Page 8 / innumerable shield-shaped barchan dunes. If the sand is slightly moist, and there is a little vegetation to bind it together, then you may find parabolic dunes-shaped like a U, with the rounded end pointing in the direction of the wind. These sometimes occur in clusters, and they resemble the teeth of a rake. If the wind direction is variable, other forms become possible. For example, clusters of sand shaped dunes can form, each having several irregular arms radiating from a central peak. They arrange themselves in a random pattern of spots.

Chapter 6

Page 81

"Nature's symmetries can be found on every scale, from the structure of subatomic particles to that of the entire universe. Many chemical molecules are symmetric. The methane molecule is a tetrahedron - a triangular-sided pyramid - with one carbon atom at its center and four hydrogen atoms at its corners Benzene has the sixfold symmetry of a regular hexagon. The fashionable molecule buckminsterfullerene is a truncated icosahedral cage of sixty carbon atoms. (An icosahedron is a regular solid with twenty triangular faces;
"truncated" means that the corners are cut off.) Its symmetry lends it a remarkable stability, which has opened up new possibilities for organic chemistry.
    On a slightly larger scale than molecules, we find symmetries in cellular structure; at the heart of cellular replication lies a tiny piece of mechanical engineering. Deep within each / Page 82  / living cell, there is a rather shapeless structure known as the centrosome, which sprouts long thin microtubules, basic components of the cell's internal "skeleton", like a diminutive sea urchin. Centrsomes were first discovered in 1887 and play an important role in organizing cell division. How-ever in one respect the structure of the centresome is astonishingly symmetric. Inside it has two structures, known as centrioles, positioned at right angles to each other. Each centriole is cylindrical, made from twenty-seven microtubules fused together along their lengths in threes, and arranged with perfect ninefold symmetry. The microtubules themselves also have an astonishingley regular symmetric form. They are hollow tubes, made from a perfect regular checkerboard pattern of units that contain two distinct proteins, alpha- and betatubulin. One day, perhaps, we will understand why nature chose these symmetric forms. But it is amazing to see symmetric structures at the core of a living cell. "

 

CELL = 3533 = CELL

3533 = CELL = 3533

CELL = 3533 = CELL

CELL = 5 = CELL

SEE EL EL SEE

C ELL ELL C

CIRCLE = 5 5 = CIRCLE

 

 

THE GALACTIC CLUB

Intelligent life in outer space?

Ronald N. Bracewell 1974

Page 1

Chapter 1

ARE WE ALONE?


"Growing in size and complexity
Living things, masses of atoms, DNA, protein
Dancing a pattern ever more intricate.
Out of the cradle onto the dry land
Here it is standing
Atoms with consciousness
Matter with curiosity.
Stands at the sea
Wonders at wondering
I
A universe of atoms
An atom in the universe."

Richard P. Feynman

 

 

ADVENT 733 ADVENT

 

THIS IS THE SCENE OF THE SCENE UNSEEN

THE UNSEEN SEEN OF THE SCENE UNSEEN THIS IS THE SCENE

 

 

MATHEMATICS AND THE IMAGINATION

Edward Kasner and James Newman

1940

Assorted Geometries-Plane and Fancy 

Page 124

"Analytical four-dimensional Eu-clidean geometry is the system formed by theorems derived from these definitions.
Note that nothing has been said in either of these defini-tions about space; neither the space of our sense percep-tions, nor the space of the physicist, nor that of the philos-opher. All that we have done is to define two systems of mathematics which are logical and self-consistent, which may be played like checkers, or charades, according to stated rules. Anyone who finds a resemblance between his game of checkers or charades and the physical reality of his experience is privileged to point morals and to make capital of his suggestion.
But having established that we are in the realm of pure conception, beyond the most elastic bounds of imagina-tion, who is satisfied? Even the mathematician would like / Page 125 / to nibble the forbidden fruit, to glimpse what it would be like if he could slip for a moment into a fourth dimension. It's hard to grub along like moles down here below, to hear someone tell of a fourth dimension, to make careful note of it, and then to plow along, giving it no further thought. To make matters worse, books on popular sci-ence have made everything so ridiculously simple-rela-tivity, quanta, and what not-that we are shamed by our inability to picture a fourth dimension as something more concrete than time.
Graphic representations of four-dimensional figures have been attempted: it cannot be said these efforts have been crowned with any great success. Fig. 31(diagram omitted) illustrates" the four-dimensional analogue of the three-dimensional cube, a hypercube or tesseract: Our difficulties in drawing this figure are in no way diminished by the fact that a three-dimensional figure can only be drawn in perspective on a two-dimensional surface-such as this page-, while the four-dimensional object on a two dimensional page is only a perspective of a "perspective."
Yet since a2 equals the area of a square, a3 the volume / Page 126 / of a cube, we feel certain that a4 describes something, whatever that something may be. Only by analogy can we reason that that "something" is the hypervolume (or content) of a tesseract. Reasoning further, we infer that the tesseract is bounded by 8 cubes (or cells), has 16 vertices, 24 faces and 32 edges. But visualization of the tesseract is another story.
Fortunately, without having to rely on distorted dia-grams, we may use other means, using familiar objects to help our limping imagination to depict a fourth dimen-sion.
The two triangles A and B in Fig. 32 are exactly alike. Fig 32 ( triangles diagram omitted).
Geometrically, it is said they are congruent, * meaning that by a suitable motion, one may be perfectly super-posed on the other. Evidently, that motion can be carried out in a plane, i.e., in two dimensions, simply by sliding triangle A on top of triangle B.** But what about the two triangles C and D in Fig. 33?
One is the mirror image of the other. There seems to be no reason why by sliding or turning in the plane, C / Page Page 127 / cannot be superimposed on D. Strangely enough, this cannot be done. C or D must be lifted out of the plane, from two dimensions into a third, to effect superposition. Lift C up, turn it over, put it back in the plane, and then it can be slid over D.
Now, if a third dimension is essential for the solution of certain two-dimensional problems, a fourth dimension would make possible the solution of otherwise unsolvable problems of three dimensions. To be sure, we are in the Fig.33.(triangles diagram omitted) realm of fancy, and it need hardly be pointed out that a fourth dimension is not at hand to make Houdinis of us all. Yet, in theoretical inquiries, a fourth dimension / Page  128 / is of signal importance, and part of the warp and woof of modern theoretical physics and mathematics. Ex-amples chosen from these subjects are quite difficult and would be out of place, but some simpler ones in the lower dimensions may prove amusing.
If we lived in a two-dimensional world, so graphically described by Abbott in his famous romance, Flatland, our house would be a plane figure, as in Fig. 34.(Figure omitted) Entering through the door at A, we would be safe from our friends and enemies once the door was closed, even though there were no roof over our head, and the walls and windows were merely lines. To climb over these lines would mean getting out of the plane into a third dimension, and of course, no one in the two-dimensional world would have
any better idea of how to do that than we know how to escape from a locked safe..deposit vault by means of a fourth dimension. A three-dimensional cat might peek at a two-dimensional king, but he would never be the wiser.
When winter comes to Flatland, its inhabitants wear gloves. Three-dimensional hands look like this: ( Page 129 diagrams omitted )

Page 130

Modern science has as yet devised no relief for the man who finds himself with two right gloves instead of a right and a left. In Flatland, the same problem would exist. But there, Gulliver, looking down at its inhabitants from the eminence of a third dimensionl would see at once that, just as in the case of the two triangles on page 127, all that is necessary to turn a right glove into a left
one is to lift it up and turn it over. Of course, no one in Flatland would or could lift a finger to do that, since it involves an extra dimension.
If then, we could be transported into a fourth dimen-sion, there is no end to the miracles we could perform-starting with the rehabilitation of all ill-assorted pairs of gloves. Lift the right glove from three-dimensional space into a fourth dimension, turn it around, bring it back and it becomes a left glove. No prison cell could hold the four-dimensional Gulliver-far more of a men-ace than a mere invisible man. Gulliver could take a knot and untie it without touching the ends or breaking it, merely by transporting it into a fourth dimension and slipping the solid cord through the extra loophole.
Or he might take two links of a chain apart without breaking them. All, this and much' more would seem absurdly simple to him, and he would regard our help lessness with the same amusement and pity as we look upon the miserable creatures of Flatland.
                                    
Our romance must end. If it has aided some readers in making a fourth dimension more real and has satisfied a common anthropomorphic thirst, it has served its pur-pose. For our own part, we confess that the fables have never made the facts any clearer.
An idea originally associated with ghosts and spirits / Page 131 / needs, if it is to serve science, to be as far removed as possible from fuzzy thinking. It must be clearly and courageously faced if its true essence is to be discovered. But it is even more stupid to reject and deride than to glorify and enshrine it. No concept that has come out of our heads or pens marked a greater forward step in our thinking, no idea of religion, philosophy, or science broke. more sharply with tradition and commonly accepted knowledge, than the idea of a fourth dimension.
Eddington has put it very well: 6
However successful the theory of a four-dimensional world may be, it is difficult to ignore a voice inside us which whispers: "At the back of your mind, you know that a fourth dimension is all nonsense." I fancy that voice must often have had a busy time in the past history of physics. What nonsense to say that this solid table on which I am writing is a collection of electrons moving with prodigious speed in empty spaces, which relatively to electronic dimensions are as wide as the spaces between the planets in the solar system! What nonsense to say that the thin air is trying to crush my body with a load of 14lbs. to the square inch! What nonsense that the star cluster which I see through the telescope, obviously there now, is a glimpse into a past age 50,000 years ago! Let us not be beguiled by this voice. It is discredited. . . .
We have found a strange footprint on the shores of the un- known. We have devised profound theories, one after another to account for its origin. At last, we have succeeded in recon-structing the creature that made the footprint. And lo! It is our own.

Page 127

( Fig 34.- This is no blueprint but an actual house in Flatland.diagram omitted) 

Notes page 126 *See the chapter on paradoxes for an exact definition.
**Actually, "sliding on top or' would be impossible in a physical two-dimensional world.

 

 

THE MAGIC MOUNTAIN

Thomas Mann

1875 1955

Page 10

"Number 34"

 

 

 

 

 

T
=
2
-
3
THE
33
15
6
F
=
6
-
9
FLATLANDS
89
35
8
-
-
8
-
12
Add to Reduce
122
50
14
-
-
-
-
1+2
Reduce to Deduce
1+2+2
5+0
1+4
-
-
8
-
3
Essence of Number
5
5
5

 

 

A RANDOM WALK IN SCIENCE

An Anthology compiled by RL Weber 1973

Flatland: a romance of many dimensions

"From Nature [An anonymous letter entitled 'Euclid, Newton, and Einstein,' published in Nature on February12, 1920, called attention to a little book by Edwin Abbott Abbott (1838-1926), best known for his scholarly Shakespearian Grammar, his life of Francis Bacon and a number of theological discussions.]
Some thirty or more years ago, a little jeu d'esprit was written by Dr Edwin Abbott, entitled 'Flatland.' At the time of its pulication it did not attract as much attention as it deserved. Dr Abbott pictures intelligent beings whose whole experience is confined to a plane, or other space of two dimensions, who have no faculties by which they can become conscious of anything outside that space and no means of moving off the surface on which they live. He then asks the reader, who has the consciousness of the third dimension, to imagine a sphere descending upon the plane of Flatland and passing through it. How will the inhabitants regard this phenomenon? They will not see the approaching sphere and will have no conception of its solidity. They will only be conscious of the circle in which it cuts their plane. This circle, at first a point, will gradually increase in diameter, driving the inhabitants of Flatland outwards from its circumference, and this will go on until half the sphere has passed through the plane, when the circle will gradually contract to a point and then vanish, leaving the Flatlanders in undisturbed possession of their country.
Their experience will be that of a circular obstacle gradually expanding or growing, and then contracting, and they will attribute to growth in time what the external observer in three dimensions assigns to motion in the third dimension, through three-dimensional space. Assume the past and future of the universe to be all depicted in four-dimensional space and visible to any being who has consci-ousness of the fourth dimension. If there is motion of our three- dimensional space relative to the fourth dimension, all the changes we experience and assign to the flow of time will be due simply to this movement, the whole of the future as well as the past always existing in the fourth dimension.

From Edwin A Abbott Flatland A Romance of Many Dimensions (New York: Barnes and Noble) 1963 

 

[In a vision the narrator, a native of Flatland, has been indoctrinated by Abbott, Flatland. Sphere to carry the Gospel of Three Dimensions to his blind benighted countrymen in Flatland.]
I. 'Pardon me, 0 Thou Whom I must no longer address as the Perfection of all Beauty; but let me beg thee to vouchsafe thy
servant a sight of thine interior.'
Sphere. 'My what?' Page 94

I. 'Thine interior: thy stomach, thy intestines.'
Sphere. 'Whence this ill-timed impertinent request? . . .'
 I. 'But my Lord has shewn me the intestines of all my countrymen in the Land of Two Dimensions by taking me with him into the Land of Three. What therefore more easy than now to take his servant on a second journey into the blessed region of the Fourth Dimension, where I shall look down with him once more upon this land of Three Dimensions, and see the inside of every three- dimensional house, the secrets of the solid earth, the treasures of the mines in Spaceland, and the intestines of every solid living creature, even of the noble and adorable Spheres'.
Sphere. 'But where is this land of Four Dimensions?'

I. 'I know not: but doubtless my Teacher knows'.
Sphere. 'Not I. There is no such land. The very idea of it is utterly inconceivable. . . . Men are divided in opinion as to the facts. And even granting the facts, they explain them in different ways. And in any case, however great may be the number of different explanations, no one has adopted or suggested the theory of a Fourth Dimension. Therefore, pray have done with this trifling, and let us return to business.' "

 

THE FLATLANDS

 

T
=
2
-
3
THE
33
15
6
F
=
6
-
9
FLATLANDS
89
35
8
-
-
8
-
12
Add to Reduce
122
50
14
-
-
-
-
1+2
Reduce to Deduce
1+2+2
5+0
1+4
-
-
8
-
3
Essence of Number
5
5
5

 

THE MAGIC MOUNTAIN

Thomas Mann 1875 - 1955

Page 711

"These were the moments when the "Seven-Sleeper," not knowing what had happened, was slowly stirring himself in the grass, before he sat up, rubbed his eyes - yes, let us carry the figure to the end, in order to do justice to the movement of our hero's mind: he drew up his legs, stood up, looked about him. He saw himself released, freed from enchantment-not of his own motion; he was fain to confess, but by the operation of exterior powers, of whose activities his own liberation was a minor incident Indeed! Yet though his tiny destiny fainted to nothing in the face of the general, was there not some hint of a personal mercy and grace for him, a manifestation of divine goodness and justice? Would Life receive again her erring and " delicate " child-not by a cheap and easy slipping back to her arms, but sternly, solemnly, peni-entially - perhaps not even among the living, but only with three salvoes fired over the grave of him a sinner? Thus might he return. He sank on his knees, raising face and hands to a heaven that howsoever dark and sulphurous was no longer the gloomy grotto of his state of sin."

 

PLATO

THE REPUBLIC

Translated with an introduction by

Desmond Lee

1953

Page 316

PART SEVEN [BOOK SIX] .
§ 7. THE SIMILE OF THE CAVE

"This is a more graphic presentation of the truths presented in the analogy of the Line,' in particular, it tells us more about the two states of mind called in the Line analogy Belief and Illusion. We are shown the ascent of the mind from illusion to pure philosophy, and the difficulties which accompany its progress. And the philosopher, when he has achieved the supreme vision, is required to return to the cave and serve his fellowls, his very unwillingness to do so being his chief qualification.

As Cornford pointed out, the best llIay to understand the simile is to replace' the clumsier apparatus' of the cave by the cinema, though today television is an even better comparison. It is the moral and intellectual condition of the average man from llIhich Plato starts; and though clearlY the ordinary man knollls the difference between substance and ShadO1ll in the physical llIorld, the simile suggests that his moral and intellectual opinions often bear as little relation to the tntth as the average film or television programme does to real life.

1 The words used for 'belief' and 'illusion' do not (with the possible exception of a use of pistis in Book X; see p. 430) occur elsewhere in Plato in the sense in which they are used here. Pistis, 'belief', conveys overtones of assurance and trustworthiness: 'commonsense assurance' (Cross and WoozIey,p. 226). Eikasia, 'illusion', is a rare word whose few occurrences elsewhere in Greek literature give us little guidance. It can mean 'conjecture', 'guesswork', and some prefer so to translate it here.
But 'illusion' is perhaps more appropriate for a 'state of mind '.

Page 317

THE PHILOSOPHER RULER

'I want you to go on to picture the enlightenment or ignorance of our human condition somewhat as follows.

Imagine an underground chamber like a cave, with a long entrance open to the daylight and as wide as the cave. In this chamber are men who have been prisoners there since they were children, their legs and necks being so fastened that they can only look straight ahead of them and cannot turn their heads. Some way off, behind and higher up, a fire is burn-ing, and between the fire and the prisoners and above them runs a road, in front of which a curtain-wall has been built, like the screen at puppet shows between the operators and their audience, above which they show their puppets.'
'I see.'
'Imagine further that there are men carrying all sorts of gear along behind the curtain-wall, projecting above it and including figures of men and animals made of wood and, stone and all sorts of other materials, and that some of these  men, as you would expect, are talking and some not.'
An odd picture and an odd sort of prisoner.'
'They are drawn from life,'1 I replied.' For, tell me, do you think our prisoners could see anything of themselves or their fellows except the shadows thrown by the fire on the wall of the cave opposite them?'
'How could they see anything else if they were prevented from moving their heads all their lives?' 
'And would they see anything more of the objects carried along the road?'
'Of course not.'
'Then if they were able to talk to each other, would they not assume that the shadows they saw were the real things?' 'Inevitably.'
And if the wall of their prison opposite them reflected / Page 318 /  sound, don't you think that they would suppose, whenever one of the passers-by on the road spoke, that the voice be- longed to the shadow passing before them?'
'They would be bound to think so.'
' And so in every way they would believe that the shadows of the objects we mentioned were the whole truth.'1
'Yes, inevitably.'
'Then think what would naturally happen to them if they were released from their bonds and cured of their delusions. Suppose one of them were let loose, and suddenly compelled to stand up and turn his head and look and walk towards the fire; all these actions would be painful and he would be too dazzled to see properly the objects of which he used to see the shadows. What do you think he would say if he was told that what he used to see was so much empty nonsense and that he was now nearer reality and seeing more correctly, because he was turned towards objects that were more real, and if on top of that he were compelled to say what each of the passing objects was when it was pointed out to him? Don't you think he would be at a loss, and think that what he used to see was far truer2 than the objects now being pointed out to him?'
'Yes, far truer.'
I ' And if he were made to look directly at the light of the fire, it would hurt his eyes and he would turn back and retreat to the things which he could see properly, which he would think really clearer than the things being shown him.
'Yes.'
'And if,' I went on, 'he were forcibly dragged up the steep and rugged ascent and not let go till he had been dragged out into the sunlight, the process would be a painful one, to which he would much object, and when he emerged into the light his eyes would be so dazzled by the glare of it that he wouldn't be able to see a single one of the things he was now told were real.'3
Page 319

'Certainly not at first,' he agreed.
'Because, of course, he wo'uld need to grow accustomed to the light before he could see things in the upper world outside the cave. First he would find it easiest to look at shadows, next at the reflections of men and other objects in water, and later on at the objects themselves. After that he would find it easier to observe the heavenly bodies and the
sky itself at night, and to look at the light of the moon and b stars rather than at the sun and its light by day.'
'Of course.'
'The thing he would be able to do last would be to look directly at the sun itself, and gaze at it without using reflec- tions in water or any other medium, but as it is in itself.'
'That must come last.'
'Later on he would come to the conclusion that it is the sun that produces the changing seasons and years and con-trols everything in the visible world, and is in a sense, responsible for everything that he and his fellow-prisoners used to see.'
'That is the conclusion which he would obviously reach.' , And when he thought of his first home and what passed for wisdom there, and of his fellow-prisoners, don't you think he would congratulate himself on his good fortune and be sorry for them?'
'Very much so.'
'There was probably a certain amount of. honour and glory to be won among the prisoners, and prizes for keen- sightedness for those best able to remember the order of sequence among the passing shadows and so be best able to divine their future appearances. Will our released prisoner hanker after these prizes or envy this power or honour? Won't he be more likely to feel, as Homer says, that he would far rather be "a serf in the house of some landless man ",l or indeed anything else in the world, than hold the opinions and live the life that they do? '
'Yes,' he replied, 'he would prefer anything to a life like, theirs.'
'Then what do you think would happen,' I asked, 'if he / Page 320 / went back to sit in his old seat in the cave? Wouldn't his eyes be blinded by the darkness, because he had come in suddenly out of the sunlight?'
'Certainly.'
'And if he had to discriminate between the shadows, in competition with the other prisoners, while he was still blinded and before his eyes got used to the darkness - a process that would take some time - wouldn't he be likely to make a fool of himself? And they would say that his visit to the upper world had ruined his sight, and that the ascent was not worth even attempting. And if anyone tried to release them and lead them up, they would kill him if they could lay hands on him.'
'They certainly would.'
'Now, my dear Glaucon,' I went on, 'this simile must be connected throughout with what preceded it.l The realm revealed by sight corresponds to the prison, and the light of the fire in the prison to the power of the sun. And you won't go wrong if you connect the ascent into the upper world / Page 321 / and the sight of the objects there with the upward progress of the mind into the intelligible region. That at any rate is my interpretation, which is what you are anxious to hear; the truth of the matter is, after all, known only to god.1 But in my opinion, for what it is worth, the final thing to be perceived in the intelligible region, and perceived only with difficulty, is the form of the good; once seen, it is inferred to be responsible for whatever is right and valuable in anything, producing in the visible region light and the source of light, and being in the intelligible region itself controlling source of truth and intelligence. And anyone who is going to act rationally either in public or private life must have sight of it.'
'I agree,' he said, 'so far as I am able to understand you.' 'Then you will perhaps also agree with me that it won't be surprising if those who get so far are unwilling to involve themselves in human affairs, and if their minds long to remain in the realm above. That's what we should expect if our simile holds good again.'
'Yes, that's to be expected.'
'Nor will you think it strange that anyone who descends from contemplation of the divine to human life and its ills should blunder and make a fool of himself, if, while still blinded and unaccustomed to the surrounding darkness, he's forcibly put on trial in the law-courts or elsewhere about the shadows of justice or the figures2 of which they are shadows and made to dispute about the notions of them held by men, who have never seen justice itself.'
'There's nothing strange in that.' 'But anyone with any sense,' I said, 'will remember that the eyes may be unsighted in two ways, by a transition either from light to darkness or from darkness to light, and will recognize that the same thing applies to the mind. So when he sees a mind confused and unable to see clearly he will not laugh without thinking, but will ask himself whether it has come from a clearer world and is confused by the unaccus-tomed darkness, or whether it is dazzled by the stronger light of the clearer world to which it has escaped from its / Page 322 / previous ignorance, The first condition of life is a reason for congratulation, the second for sympathy, though if one wants to laugh at it one can do so with less absurdity than at the mind that has descended from the daylight of the upper world,'
'You put it very reasonably,'
'If this is true,' I continued, 'we must reject the concep-tion of education professed by those who say that they can put into the mind knowledge that was not there before - rather as if they could put sight into blind eyes..
'It is a claim that is certainly made,' he said,
'But our argument indicates that the capacity for know-ledge is innate in each man's mind, and that the organ by which he learns is like an eye which cannot be turned from darkness to light unless the whole body is turned; in the same way the mind as a whole must be turned away from the world of change until its eye can bear to look straight at reality, and at the brightest of all realities which is what we call the good. Isn't that so?'
'Yes,'
'Then this turning around of the mind itself might be made a subject of professional skill,' which would effect the conversion as easily and effectively as possible, It would not be concerned to implant sight, but to ensure that someone who had it already was not either turned in the wrong direction or looking the wrong way.'
'That may well be so,'
'The rest, therefore, of what are commonly called excel-lences2 of the mind perhaps resemble those of the body, in that they are not in fact innate, but are implanted by sub-sequent training and practice; but knowledge, it seems, must surely have a diviner quality, something which never loses its power, but whose effects are useful and salutary or again useless and harmful according to the direction in which it is turned, Have you never noticed how shrewd is the glance of the type of men commonly called bad but clever? They have small minds. but their sight is sharp and piercing enough in / Page 323 / matters that concern them; it's not that their sight is weak, but that they are forced to serve evil, so that the keener their sight the more effective that evil is,'
'That's true.'
'But suppose,' I said, 'that such natures were cut loose, when they were still children, from all the dead weights natural to this world of change and fastened on them by sensual indulgences like gluttony, which twist their minds' vision to lower things, and suppose that when so freed they were turned towards the truth, then this same part of these same individuals would have as keen a vision of truth as it has of the objects on which it is at present turned,'
'Very likely,'
'And is it not also likely, and indeed a necessary conse- quence of what we have said, that society will never be properly governed either by the uneducated, who have no knowledge of the truth, or by those who are allowed to t spend all their lives in purely intellectual pursuits? The un-educated have no single aim in life to which all their actions, public and private, are to be directed; the intellectuals will take no practical action of their own accord, fancying them-selves to be out of this world in some kind of 'eartWy paradise,'
'True.'
'Then our job as lawgivers is to compel the best minds to attain what we have called the highest form of knowledge, and to ascend to the vision of the good as we have described, and when they have achieved this and see well enough, a' prevent them behaving as they are now allowed to,'
'What do you mean by that?'
'Remaining in the upper world, and refusing to return again to the prisoners in the cave below and share their labours and rewards, whether trivial or serious.'
'But surely,' he protested, 'that will not be fair, We shall be compelling them to live a poorer life than they might live,'
'The object of our legislation,' I reminded him again, 'is, not the special welfare of any particular class in our society, / Page 324 / but of the society as a whole;I and it uses persuasion or compulsion to unite all citizens and make them share together the benefits which each individually can confer on the community; and its purpose in fostering this attitude is not to leave everyone to please himself, but to make each man a link in the unity of the whole.'
'You are right; I had forgotten,' he said.
'You see, then, Glaucon,' I went on, 'we shan't be unfair to our philosophers, but shall be quite fair in what we say when we compel them to have some care and responsibility for others. We shall tell them that philosophers born in other states can reasonably refuse to take part in the hard work of politics; for society produces them quite involun-tarily and unintentionally, and it is only just that anything that grows up on its own should feel it has nothing to repay for an upbringing which it owes to no one. "But," we shall say, "we have bred you both for your own sake and that of the whole community to act as leaders and king-bees in a hive; you are better and more fully educated than the rest and better qualified to combine the practice of philosophy and politics. You must therefore each descend in turn and live with your fellows in the cave and get used to seeing in the dark; once you get used to it you will see a thousand times better than they do and will distinguish the various shadows, and know what they are shadows of, because you have seen the truth about things admirable and just and good. And so our state and yours will be really awake, and not merely dreaming like most societies today, with their shadow battles and their struggles for political power, which they treat as some great prize. The truth is quite different: the state whose prospective rulers come to their duties with least enthusiasm is bound to have the best and most tranquil government, and the state whose rulers are eager to rule the worst." '2
'I quite agree.'

Page325 (number omitted)

'Then will our pupils, when they hear what we say, dissent and refuse to take their share of the hard work of government, even though spending the greater part of their time together in the pure air above?'
They cannot refuse, for we are making a just demand of  just men. But of course, unlike present rulers, they will approach the business of government as an unavoidable necessity.'
'Yes, of course,' I agreed. 'The truth is that if you want a well-governed state to be possible, you must find for your future rulers some way of life they like better than govern-ment; for only then will you have government by the truly rich, those, that is, whose riches consist not of gold, but of the true happiness of a good and rational life. If you get, in public affairs, men whose life is impoverished and desti-tute of personal satisfactions, but who hope to snatch some compensation for their own inadequacy from a political career, there can never be good government. They start fighting for power, and the consequent internal and domestic conflicts ruin both them and society.'
'True indeed.'
'Is there any life except that of true philosophy which looks down on positions of political power?'
'None whatever.'
'But what we need is that the only men to get power should be men who do not love it, otherwise we shall have rivals' quarrels.'
'That is certain.'
Who else, then, will you compel to undertake the responsibilities of Guardians of our state, if it is not to be those who know most about the principles of good govern- ment and who have other rewards and a better life than the politician's ?'
'There is no one else.'..."

Note 1 page 317

I. Lit: 'like us'. How 'like' has been a matter of controversy. Plato can hardly have meant that the ordinary man cannot distinguish between shadows and real things. But he does seem to be saying, with a touch of caricature (we must not take him too solemnly), that the ordinary man is often very uncritical in his beliefs, which are little more than a 'careless acceptance of appearances , (Crombie).

Notes page 318

1. Lit: 'regard nothing else as true but the shadows'. The Greek word alethes (true) carries an implication of genuinenes, and some
translators render it here as 'real'.
2. Or 'more real'. 3. Or 'true', 'genuine'.

Note page 319 Odyssey, XI, 489.

Note Page 320

1. I.e. the similes of the Sun and the Line (though pp. 267-76 must surely also be referred to). The detailed relations between the three similes have been much disputed, as has the meaning of the word here translated 'connected'. Some interpret it to mean a detailed corre-spondence ('every feature. . . is meant to fit' - Cornford), others to mean, more loosely, 'attached' or 'linked to'. That Plato intended some degree of 'connection' between the three similes cannot be in doubt in view of the sentences which follow. But we should remember that they are similes, not scientific descriptions, and it would be a mistake to try to find too much detailed precision. Plato has just spoken of the prisoners 'getting their hands' on their returned fellow and killing him. How could they do that if fettered as described at the opening Of the simile (p. 317)? But Socrates was executed, so of course they must.
This translation assumes the following main correspondences:
Tied prisoner in the cave' illusion
Freed prisoner in the cave Belief
Looking at shadows and reflections in the world outside the cave and the ascent thereto Reason
Looking at real things in the world outside the cave Intelligence
Looking at the sun Vision of the form of the good.

Note 1 page 321 1. a. footnote 4, p.133 

Note 1 page 322 1. Techne., Arete,

Note 1 page 324 1. cr. 420b and 4660 above, pp. 18fand 252.
2. Socrates takes up here a point made to Thrasymachus at 347b, p.89.

 

 

 

ZERO ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE

 

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5
5
-
-
-
-
-
5
-
-
-
-
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
-
-
20
-
5
SEVEN
65
29
20
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
EIGHT
-
-
-
-
-
-
-
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
-
-
31
-
5
EIGHT
49
31
31
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
NINE
-
-
-
-
-
-
-
-
-
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
24
-
4
NINE
42
24
24
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
45
-
40
First Total
522
243
225
-
2
6
3
8
70
42
7
24
63
-
-
4+5
-
4+0
Add to Reduce
5+2+2
2+4+3
2+2+5
-
-
-
-
-
7+0
4+2
-
2+4
6+3
-
-
9
-
4
Second Total
9
9
9
-
2
6
3
8
7
6
7
6
9
-
-
-
-
-
Reduce to Deduce
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
4
Essence of Number
9
9
9
-
2
6
3
8
7
6
7
6
9

 

ZERO ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
=
8
-
1
Z
8
8
8
-
-
-
-
-
-
-
-
8
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
W
=
5
-
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
F
=
6
-
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
F
=
6
-
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
X
=
6
-
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
45
-
40
First Total
522
243
225
-
2
6
3
8
70
42
7
24
63
-
-
4+5
-
4+0
Add to Reduce
5+2+2
2+4+3
2+2+5
-
-
-
-
-
7+0
4+2
-
2+4
6+3
-
-
9
-
4
Second Total
9
9
9
-
2
6
3
8
7
6
7
6
9
-
-
-
-
-
Reduce to Deduce
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
4
Essence of Number
9
9
9
-
2
6
3
8
7
6
7
6
9

 

ZERO ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
S
=
1
-
1
S
19
10
1
-
1
-
-
-
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
T
=
2
-
1
T
20
2
2
-
-
2
-
-
-
-
-
-
-
U
=
3
-
1
U
21
3
3
-
-
-
3
-
-
-
-
-
-
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
V
=
4
-
1
V
22
4
4
-
-
-
-
4
-
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
W
=
5
-
1
W
23
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
N
=
5
-
1
N
14
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
E
=
5
-
1
E
5
5
5
-
-
-
-
-
5
-
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
-
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
O
=
6
-
1
O
15
6
6
-
-
-
-
-
-
6
-
-
-
F
=
6
-
1
F
6
6
6
-
-
-
-
-
-
6
-
-
-
X
=
6
-
1
X
24
6
6
-
-
-
-
-
-
6
-
-
-
G
=
7
-
1
G
7
7
7
-
-
-
-
-
-
-
7
-
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
H
=
8
-
1
H
8
8
8
-
-
-
-
-
-
-
-
8
-
H
=
8
-
1
Z
8
8
8
-
-
-
-
-
-
-
-
8
-
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
R
=
9
-
1
R
18
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
-
1
I
9
9
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
45
-
40
First Total
522
243
225
-
2
6
3
8
70
42
7
24
63
-
-
4+5
-
4+0
Add to Reduce
5+2+2
2+4+3
2+2+5
-
-
-
-
-
7+0
4+2
-
2+4
6+3
-
-
9
-
4
Second Total
9
9
9
-
2
6
3
8
7
6
7
6
9
-
-
-
-
-
Reduce to Deduce
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
4
Essence of Number
9
9
9
-
2
6
3
8
7
6
7
6
9

 

 

1
occurs
x
2
=
2
=
2
2
occurs
x
3
=
6
=
6
3
occurs
x
1
=
3
=
3
4
occurs
x
2
=
8
=
8
5
occurs
x
14
=
70
7+0
7
6
occurs
x
7
=
42
4+2
6
7
occurs
x
1
=
7
=
7
8
occurs
x
3
=
24
2+4
6
9
occurs
x
7
=
63
6+3
9
45
-
-
40
-
225
-
54
4+5
-
-
4+0
-
2+2+5
-
5+4
9
-
-
4
-
9
-
9

 

 

Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
8
-
-
6
-
6
5
-
-
-
-
6
-
-
8
-
-
-
-
-
6
-
-
-
-
9
-
-
-
1
9
6
-
1
-
-
-
5
-
-
9
-
8
-
-
5
9
5
-
112
26
-
-
15
-
15
14
-
-
-
-
15
-
-
8
-
-
-
-
-
15
-
-
-
-
9
-
-
-
19
9
24
-
19
-
-
-
14
-
-
9
-
8
-
-
14
9
14
-
256
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
5
9
-
-
-
-
5
-
2
5
-
-
2
-
9
5
5
-
6
-
3
9
-
6
-
4
5
-
-
-
-
-
-
5
4
5
-
-
5
-
7
-
2
-
-
-
-
5
113
-
5
18
-
-
-
-
5
-
20
23
-
-
20
-
18
5
5
-
6
-
21
18
-
6
-
22
5
-
-
-
-
-
-
5
22
5
-
-
5
-
7
-
20
-
-
-
-
5
266
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
26
5
18
15
-
15
14
5
-
20
23
15
-
20
8
18
5
5
-
6
15
21
18
-
6
9
22
5
-
19
9
24
-
19
5
22
5
14
-
5
9
7
8
20
-
14
9
14
5
522
8
5
9
6
-
6
5
5
-
2
5
6
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
-
1
9
6
-
1
5
4
5
5
-
5
9
7
8
2
-
5
9
5
5
225
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
2
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
5
-
-
-
--
5
5
-
-
5
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
5
5
-
5
-
-
-
-
-
5
-
5
5
5
-
-
-
6
-
6
-
-
-
-
--
6
-
-
-
-
-
-
-
6
6
-
-
-
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
8
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
9
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
45
-
5
-
-
-
--
5
5
-
-
5
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
5
5
-
5
-
-
5
5
-
-
-
-
5
4+5
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
9
8
5
9
6
-
6
5
5
-
2
5
6
-
2
8
9
5
5
-
6
6
3
9
-
6
9
4
5
-
1
9
6
-
1
5
4
5
5
-
5
9
7
8
2
-
5
9
5
5
-
Z
E
R
O
-
O
N
E
-
T
W
O
-
T
H
R
E
E
-
F
O
U
R
-
F
I
V
E
-
S
I
X
-
S
E
V
E
N
-
E
I
G
H
T
-
N
I
N
E
9

 

 

1
occurs
x
2
=
2
=
2
2
occurs
x
3
=
6
=
6
3
occurs
x
1
=
3
=
3
4
occurs
x
2
=
8
=
8
5
occurs
x
14
=
70
7+0
7
6
occurs
x
7
=
42
4+2
6
7
occurs
x
1
=
7
=
7
8
occurs
x
3
=
24
2+4
6
9
occurs
x
7
=
63
6+3
9
45
-
-
40
-
225
-
54
4+5
-
-
4+0
-
2+2+5
-
5+4
9
-
-
4
-
9
-
9

 

 

Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
-
8
-
-
6
6
5
-
-
-
6
-
8
-
-
-
-
6
-
-
-
9
-
-
1
9
6
1
-
-
-
5
-
9
-
8
-
5
9
5
-
112
26
-
-
15
15
14
-
-
-
15
-
8
-
-
-
-
15
-
-
-
9
-
-
19
9
24
19
-
-
-
14
-
9
-
8
-
14
9
14
-
256
Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
-
-
5
9
-
-
-
5
2
5
-
2
-
9
5
5
6
-
3
9
6
-
4
5
-
-
-
-
5
4
5
-
5
-
7
-
2
-
-
-
5
113
-
5
18
-
-
-
5
20
23
-
20
-
18
5
5
6
-
21
18
6
-
22
5
-
-
-
-
5
22
5
-
5
-
7
-
20
-
-
-
5
266
Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
-
26
5
18
15
15
14
5
20
23
15
20
8
18
5
5
6
15
21
18
6
9
22
5
19
9
24
19
5
22
5
14
5
9
7
8
20
14
9
14
5
522
8
5
9
6
6
5
5
2
5
6
2
8
9
5
5
6
6
3
9
6
9
4
5
1
9
6
1
5
4
5
5
5
9
7
8
2
5
9
5
5
225
Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
2
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
-
5
-
-
--
5
5
-
5
-
-
-
-
5
5
-
-
-
-
-
-
-
5
-
-
-
-
5
-
5
5
5
-
-
-
-
5
-
5
5
5
-
-
-
6
6
-
-
-
--
6
-
-
-
-
-
6
6
-
-
6
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
7
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
8
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
9
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
9
Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
45
-
5
-
-
--
5
5
-
5
-
-
-
-
5
5
-
-
-
-
-
-
-
5
-
-
-
-
5
-
5
5
5
-
-
5
5
-
-
-
5
4+5
Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
9
8
5
9
6
6
5
5
2
5
6
2
8
9
5
5
6
6
3
9
6
9
4
5
1
9
6
1
5
4
5
5
5
9
7
8
2
5
9
5
5
-
Z
E
R
O
O
N
E
T
W
O
T
H
R
E
E
F
O
U
R
F
I
V
E
S
I
X
S
E
V
E
N
E
I
G
H
T
N
I
N
E
9

 

ZERO ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
0
-
Z
=
8
-
4
ZERO
64
28
1
-
1
-
-
-
-
-
-
-
-
1
-
O
=
6
-
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
2
-
T
=
2
-
3
TWO
58
13
4
-
-
-
-
4
-
-
-
-
-
3
-
T
=
2
-
5
THREE
56
29
2
-
-
2
-
-
-
-
-
-
-
4
-
F
=
6
-
4
FOUR
60
24
6
-
-
-
-
-
-
6
-
-
-
5
-
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
-
6
-
-
-
6
-
S
=
1
-
3
SIX
52
16
7
-
-
-
-
-
-
-
7
-
-
7
-
S
=
1
-
5
SEVEN
65
20
2
-
-
2
-
-
-
-
-
-
-
8
-
E
=
5
-
5
EIGHT
49
31
4
-
-
-
-
4
-
-
-
-
-
9
-
N
=
5
-
4
NINE
42
24
6
-
-
-
-
-
-
6
-
-
-
45
-
-
-
42
-
40
Add
522
225
45
-
1
4
3
8
5
18
14
8
9
4+5
-
-
-
4+2
-
4+0
Reduce
5+2+2
2+2+5
4+5
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
6
-
4
Deduce
9
9
9
-
1
4
3
8
5
9
5
8
9

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
0
-
Z
=
8
1
4
ZERO
64
28
1
-
1
-
-
-
-
-
-
-
-
1
-
F
=
6
2
5
FIRST
72
27
9
-
-
-
-
-
-
-
-
-
9
2
-
S
=
1
3
6
SECOND
60
24
6
-
-
-
-
-
-
6
-
-
-
3
-
T
=
2
4
5
THIRD
59
32
5
-
-
-
-
-
5
-
-
-
-
4
-
F
=
6
5
6
FOURTH
88
34
7
-
-
-
-
-
-
-
7
-
-
5
-
F
=
6
6
5
FIFTH
49
31
4
-
-
-
-
4
-
-
-
-
-
6
-
S
=
1
7
5
SIXTH
80
26
8
-
-
-
-
-
-
-
-
8
-
7
-
S
=
1
8
7
SEVENTH
93
30
3
-
-
-
3
-
-
-
-
-
-
8
-
E
=
5
9
6
EIGHTH
57
39
3
-
-
-
3
-
-
-
-
-
-
9
-
N
=
5
10
5
NINTH
65
29
2
-
-
2
-
-
-
-
-
-
-
45
-
-
-
41
-
54
Add
687
300
48
-
1
2
6
4
5
6
7
8
9
4+5
-
-
-
4+1
-
5+4
Reduce
6+8+7
3+0+0
4+8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
5
-
9
Deduce
21
3
12
-
1
2
6
4
5
6
7
8
9
-
-
-
-
-
-
-
Reduce
2+1
-
1+2
-
-
-
-
-
-
-
-
-
-
9
-
-
-
5
-
9
Essence
3
3
3
-
1
2
6
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
0
-
Z
=
8
1
4
ZERO
64
28
1
-
1
-
-
-
-
-
-
-
-
9
-
N
=
5
10
5
NINTH
65
29
2
-
-
2
-
-
-
-
-
-
-
7
-
S
=
1
8
7
SEVENTH
93
30
3
-
-
-
3
-
-
-
-
-
-
8
-
E
=
5
9
6
EIGHTH
57
39
3
-
-
-
3
-
-
-
-
-
-
5
-
F
=
6
6
5
FIFTH
49
31
4
-
-
-
-
4
-
-
-
-
-
3
-
T
=
2
4
5
THIRD
59
32
5
-
-
-
-
-
5
-
-
-
-
2
-
S
=
1
3
6
SECOND
60
24
6
-
-
-
-
-
-
6
-
-
-
4
-
F
=
6
5
6
FOURTH
88
34
7
-
-
-
-
-
-
-
7
-
-
6
-
S
=
1
7
5
SIXTH
80
26
8
-
-
-
-
-
-
-
-
8
-
1
-
F
=
6
2
5
FIRST
72
27
9
-
-
-
-
-
-
-
-
-
9
45
-
-
-
41
-
54
Add
687
300
48
-
1
2
6
4
5
6
7
8
9
4+5
-
-
-
4+1
-
5+4
Reduce
6+8+7
3+0+0
4+8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
5
-
9
Deduce
21
3
12
-
1
2
6
4
5
6
7
8
9
-
-
-
-
-
-
-
Reduce
2+1
-
1+2
-
-
-
-
-
-
-
-
-
-
9
-
-
-
5
-
9
Essence
3
3
3
-
1
2
6
4
5
6
7
8
9

 

NUMBERS RE-ARRANGED IN NUMERICAL ORDER

 

 

 

NET ENTERS NETERS TEN

 

THE R IN EVOLUTION REVOLUTION

 

3
THE
33
15
6
4
MIND
40
22
4
2
OF
21
12
3
9
HUMANKIND
95
41
5
18
First Total
189
90
18
1+8
Add to Reduce
1+8+9
9+0
1+8
9
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
9
Essence of Number
9
9
9

 

 

 

THE LAST SUPPER 1977

 

 

The term pareidolia (pronounced /pæraɪˈdoʊliə/), referenced in 1994 by Steven Goldstein, [1] describes a psychological phenomenon involving a vague and ... en.wikipedia.org/wiki/Pareidolia

The term pareidolia (pronounced /pæraɪˈdoʊliə/), referenced in 1994 by Steven Goldstein,[1] describes a psychological phenomenon involving a vague and random stimulus (often an image or sound) being perceived as significant. Common examples include images of animals or faces in clouds, the man in the moon, and hidden messages on records played in reverse. The word comes from the Greek para- — beside, with or alongside — and eidolon — image (the diminutive of eidos — image, form, shape). Pareidolia is a type of apophenia.

EXAMPLES

Religious

Further information: Perceptions of religious imagery in natural phenomena

There have been many instances of perceptions of religious imagery and themes, especially the faces of religious figures, in ordinary phenomena. Many involve images of Jesus, the Virgin Mary, or the word Allah.

In 1978, a New Mexican woman found that the burn marks on a tortilla she had made appeared similar to Jesus Christ's face. Thousands of people came to see the framed tortilla.[2]

The recent publicity surrounding sightings of religious figures and other surprising images in ordinary objects, combined with the growing popularity of online auctions, has spawned a market for such items on eBay. One famous instance was a grilled-cheese sandwich with the Virgin Mary's face.[3]

In September, 2007, the so-called "monkey tree phenomenon" caused a minor social mania in Singapore. A callus on a tree there resembles a monkey, and believers have flocked to the tree to pay homage to the Monkey God.[4]

[edit] Rorschach test

Main article: Rorschach inkblot test

The Rorschach inkblot test uses pareidolia to attempt to gain insight into a person's mental state.[2]

[edit] Audio In 1971, Konstantin Raudive wrote Breakthrough, detailing what he believed was the discovery of electronic voice phenomenon (EVP). EVP has been described as auditory pareidolia.[2]

The allegations of backmasking in popular music have also been described as pareidolia.[2]

[edit] Explanations

[edit] Carl Sagan Carl Sagan hypothesized that as a survival technique, human beings are "hard-wired" from birth to identify the human face. This allows people to use only minimal details to recognize faces from a distance and in poor visibility, but can also lead them to interpret random images or patterns of light and shade as being faces.[5]

[edit] Clarence Irving Lewis

In his 1929 book Mind and the World Order, epistemologist and logician Clarence Irving Lewis, a founder of the philosophical school of conceptual pragmatism, used the question of how to determine whether a perception is a mirage as a touchstone for his philosophical approach to knowledge. Lewis argued that one has no way of knowing whether or not perceptions are "true" in any absolute sense; all one can do is determine whether one's purpose is thwarted by regarding it as true and acting on that basis. According to this approach, two people with two different purposes will often have different views on whether or not to regard a perception as true. [6]

Gallery (Images omitted)

 

 

DAILY MAIL

Thursday, January 24

WATCH THIS SPACE

Michael Hanlon Science Editor

THE proper word for it is pareidolia: the phenomenon where people tend to see human faces and other familiar forms in otherwise unfamiliar objects.

We have all seen faces and creatures in the sky. When Hamlet saw a strange cloud, he explained to Polonius, 'Methinks it is like a weasel' (Polonius, for his part thought it more like a camel).

People are forever seeing Jesus or the Virgin Mary in tortillas, buns, the swirls in their coffee and reflections in windows.

But, for some reason, one of the most popular places to see these unlikely visions is in space.

This week, the Mail showed an extraordinary photograph taken by the Nasa Mars Rover, Spirit, which has been trundling across the surface of the Red Planet for four years.

In the picture, which I have no reason to suspect was doctored or altered, there appears to be a greenish-brown human figure, a woman perhaps, perched on a rock, staring rather wistfully at the crater floor below her.

The longer you stare at this picture, the more convincing the 'human becomes.

But it is an illusion; there is no woman, green or otherwise, on the surface of Mars. If there were, she would suffocate and freeze in short order.

This is simply a trick of the light, shadow and perspective, the brain seeing something familiar in an alien jumble of volcanic rocks under a strange orange-pink sky.

Yet this will not be the first or the last - time we have seen strange apparitions on Mars, on Earth and on other planets. The first and best - known example of pareidolia in space was of course the Man in the Moon. I have never found its surface to look particularly human, but many people insist the pattern of dark lava plains and brighter highland areas look for all the world like a human nose, mouth and two eyes. If I squint, I suppose I can just about see it.

Mars, for some unknown reason, is home to many strange apparitions. People have been 'seeing' things on the Red Planet that aren't there for more than a century.

 

 

-
PAREIDOLIA
-
--
-
2
PA
17
8
8
1
R
18
18
9
1
E
5
5
5
1
I
9
9
9
1
D
4
4
4
2
OL
27
9
9
1
I
9
9
9
1
A
1
1
1
10
PAREIDOLIA
90
54
45
1+0
-
9+0
5+4
4+5
1
PAREIDOLIA
9
9
9

 

 

-
PAREIDOLIA
-
--
-
2
PA
17
8
8
1
R
18
18
9
3
EID
18
18
9
2
OL
27
9
9
1
I
9
9
9
1
A
1
1
1
10
PAREIDOLIA
90
54
45
1+0
-
9+0
5+4
4+5
1
PAREIDOLIA
9
9
9

 

 

-
8
P
A
R
E
I
D
O
L
I
A
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
6
-
9
-
+
=
24
2+4
=
6
-
6
-
6
-
-
-
-
-
-
9
-
15
-
9
-
+
=
33
3+3
=
6
-
6
-
6
-
8
P
A
R
E
I
D
O
L
I
A
-
-
-
-
-
-
-
-
-
-
-
-
7
1
9
5
-
4
-
3
-
1
+
=
30
3+0
=
3
-
3
-
3
-
-
16
1
18
5
-
4
-
12
-
1
+
=
57
5+7
=
12
1+2
3
-
3
-
8
P
A
R
E
I
D
O
L
I
A
-
-
-
-
-
-
-
-
-
-
-
-
16
1
18
5
9
4
15
12
9
1
+
=
90
9+0
=
9
-
9
-
9
-
-
7
1
9
5
9
4
6
3
9
1
+
=
54
5+4
=
9
-
9
-
9
-
8
P
A
R
E
I
D
O
L
I
A
T
-
-
-
-
-
-
-
-
-
-
--
-
1
-
-
-
-
-
-
-
1
-
-
1
occurs
x
2
=
2
-
2
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-