Latest / Classic Science Fiction Books / 03 - Flatland- A Romance of Many Dimensions - Edwin Abbott Abbott

Transcript

03 - Flatland- A Romance of Many Dimensions - Edwin Abbott Abbott · Classic Science Fiction Books

0:00
Speaker 1: Part one, Section six of Recognition by sight, I am
0:06
Speaker 1: about to appear very inconsistent. In previous sections. I have
0:11
Speaker 1: said that all figures in flatland present the appearance of
0:14
Speaker 1: a straight line, and it was added or implied that
0:18
Speaker 1: it is consequently impossible to distinguish by the visual organ
0:23
Speaker 1: between individuals of different classes. Yet now I am about
0:28
Speaker 1: to explain to my Spaceland critics how we are able
0:32
Speaker 1: to recognize one another by the sense of sight. If, however,
0:37
Speaker 1: the reader will take the trouble to refer to the
0:39
Speaker 1: passage in which recognition by feeling is stated to be universal,
0:43
Speaker 1: he will find this qualification among the lower classes. It
0:49
Speaker 1: is only among the higher classes, and in our more
0:52
Speaker 1: temperate climates, that sight recognition is practiced. That this power
0:58
Speaker 1: exists in any regions and for any classes, is the
1:02
Speaker 1: result of fog which prevails during the greater part of
1:06
Speaker 1: the year in all parts save the torrid zones. That
1:11
Speaker 1: which is with you in Spaceland, and unmixed evil, blotting
1:15
Speaker 1: out the landscape, depressing the spirits and enfeebling the health,
1:20
Speaker 1: is by us recognized as a blessing scarcely inferior to
1:24
Speaker 1: air itself, and as the nurse of arts and parent
1:28
Speaker 1: of sciences. But let me explain my meaning without further
1:33
Speaker 1: eulogies on this beneficent element. If fog were non existent,
1:39
Speaker 1: all lines would appear equally and indistinguishably clear. And this
1:45
Speaker 1: is actually the case in those unhappy countries in which
1:49
Speaker 1: the atmosphere is perfectly dry and transparent. But wherever there
1:54
Speaker 1: is a rich supply of fog, objects that are at
1:58
Speaker 1: a distant, say, of three feet, are appreciably dimmer than
2:02
Speaker 1: those at a distance of two feet eleven inches. And
2:06
Speaker 1: the result is that, by careful and constant experimental observation
2:11
Speaker 1: of comparative dimness and clearness, we are enabled to infer
2:15
Speaker 1: with great exactness the configuration of the object observed. An
2:21
Speaker 1: instance will do more than a volume of generalities to
2:25
Speaker 1: make my meaning clear. Suppose I see two individuals approaching
2:30
Speaker 1: whose rank I wish to ascertain they are. We will
2:34
Speaker 1: suppose a merchant and a physician, or in other words,
2:38
Speaker 1: an equilateral triangle and a pentagon. How am I to
2:43
Speaker 1: distinguish them? Reader's note. The following paragraph makes reference to
2:49
Speaker 1: an accompanying diagram. Diagram one is a rightward pointing equilateral triangle.
2:55
Speaker 1: The vertical left hand side of which is marked B C,
2:59
Speaker 1: the other two sides being marked B A and C A.
3:04
Speaker 1: Dotted lines are drawn from B and C to a
3:06
Speaker 1: point further to the right to form an Isosceles triangle.
3:11
Speaker 1: The far right hand point of this triangle represents the
3:15
Speaker 1: eye of the observer, and a horizontal dotted arrow pointing
3:19
Speaker 1: left from it indicates his eye glance. A broad vertical
3:25
Speaker 1: line DAE is drawn to indicate what the observer sees.
3:31
Speaker 1: DAE is bright at the center and darkens sharply towards
3:35
Speaker 1: its ends. End of reader's note. It will be obvious
3:41
Speaker 1: to every child in spaceland who has touched the threshold
3:44
Speaker 1: of geometrical studies, that if I can bring my eye
3:48
Speaker 1: so that its glance may bisect an angle A of
3:52
Speaker 1: the approaching stranger, my view will lie, as it were,
3:56
Speaker 1: evenly between his two sides that are next to me
4:00
Speaker 1: is C A and A B, so that I shall
4:03
Speaker 1: contemplate the two impartially, and both will appear of the
4:07
Speaker 1: same size. Now, in the case of one the merchant,
4:13
Speaker 1: what shall I see? I shall see a straight line DAE,
4:18
Speaker 1: in which the middle point A will be very bright,
4:22
Speaker 1: because it is nearest to me, but on either side
4:25
Speaker 1: the line will shade away rapidly into dimness, because the
4:29
Speaker 1: sides AC and A B recede rapidly into the fog,
4:34
Speaker 1: and what appear to me as the merchant's extremities viz.
4:38
Speaker 1: D and E will be very dim Indeed, Reader's note
4:43
Speaker 1: The following paragraph makes reference to an accompanying diagram. Diagram
4:48
Speaker 1: two is a regular pentagon sitting on a horizontal base,
4:52
Speaker 1: with C one at the apex, A one at middle right,
4:57
Speaker 1: and B one at lower right. Longer dotted lines are
5:01
Speaker 1: drawn out towards the right, upwards from B one and
5:05
Speaker 1: downwards from C one to form an irregular pentagon. The
5:10
Speaker 1: far right hand point of the extended pentagon represents the
5:14
Speaker 1: eye of the observer, and a dotted arrow pointing from
5:18
Speaker 1: it towards the center of the lower left edge of
5:21
Speaker 1: the pentagon indicates his eye glance. Again, a broad line
5:27
Speaker 1: D one A one e one parallel to the lower
5:30
Speaker 1: left edge of the pentagon is drawn to indicate what
5:34
Speaker 1: the observer sees. D one A one e one is
5:38
Speaker 1: bright at the center and darkens very gradually towards its ends.
5:44
Speaker 1: End of Reader's note. On the other hand, in the
5:48
Speaker 1: case of two the physician, though I shall here also
5:52
Speaker 1: see a line D one, A one, E one with
5:55
Speaker 1: a bright center A one, Yet it will shade away
5:59
Speaker 1: less rapidly into dimness, because the sides A one, C one,
6:03
Speaker 1: A one, B one recede less rapidly into the fog.
6:07
Speaker 1: And what appear to me the physician's extremities is D
6:12
Speaker 1: one and E one will be not so dim as
6:15
Speaker 1: the extremities of the merchant. The reader will probably understand
6:21
Speaker 1: from these two instances, how after a very long training
6:25
Speaker 1: supplemented by constant experience, it is possible for the well
6:29
Speaker 1: educated classes among us to discriminate with fair accuracy between
6:34
Speaker 1: the middle and lowest orders by the sense of sight.
6:39
Speaker 1: If my spaceland patrons have grasped this general conception so
6:43
Speaker 1: far as to conceive the possibility of it, and not
6:47
Speaker 1: to reject my account as altogether incredible, I shall have
6:51
Speaker 1: attained all I can reasonably expect. Were I to attempt
6:55
Speaker 1: further details, I should only perplex Yet, for the sake
7:00
Speaker 1: of the young and inexperienced, who may perchance infer from
7:04
Speaker 1: the two simple instances I have given above of the
7:07
Speaker 1: manner in which I should recognize my father and my sons.
7:11
Speaker 1: That recognition by sight is an easy affair, it may
7:15
Speaker 1: be needful to point out that, in actual life, most
7:18
Speaker 1: of the problems of sight recognition are far more subtle
7:22
Speaker 1: and complex. If, for example, when my father the triangle
7:28
Speaker 1: approaches me, he happens to present his side to me
7:32
Speaker 1: instead of his angle, then until I have asked him
7:35
Speaker 1: to rotate, or until I have edged my eye round him,
7:39
Speaker 1: I am for the moment doubtful whether he may not
7:42
Speaker 1: be a straight line or in other words, a woman
7:46
Speaker 1: reader's note. The following paragraph makes reference to an accompanying diagram.
7:52
Speaker 1: The diagram shows a hexagon with points at top and bottom.
7:56
Speaker 1: The vertical right hand side is marked A B. Dotted
8:01
Speaker 1: lines are drawn downward from the topmost and upward from
8:04
Speaker 1: the bottomost points of the hexagon, and extended to the
8:08
Speaker 1: right until they meet, forming an irregular pentagon. The far
8:13
Speaker 1: right hand point of the pentagon represents the eye of
8:16
Speaker 1: the observer. The line A B is extended to where
8:20
Speaker 1: it meets the dotted lines to form a broad vertical
8:23
Speaker 1: line at C A B D. The middle portion of
8:27
Speaker 1: this line A B is bright and the outer portions darken.
8:32
Speaker 1: Towards C and D end of reader's note. Again, when
8:38
Speaker 1: I am in the company of one of my two
8:40
Speaker 1: hexagonal grandsons, contemplating one of his sides A B full front,
8:46
Speaker 1: it will be evident from the accompanying diagram that I
8:50
Speaker 1: shall see one whole line A B in comparative brightness,
8:55
Speaker 1: shading off hardly at all at the ends, and two
8:58
Speaker 1: smaller lines C, A and B D dim throughout and
9:03
Speaker 1: shading away into greater dimness toward the extremities C and D.
9:09
Speaker 1: But I must not give way to the temptation of
9:12
Speaker 1: enlarging on these topics. The meanest mathematician in Spaceland will
9:17
Speaker 1: readily believe me when I assert that the problems of
9:20
Speaker 1: life which present themselves to the well educated when they
9:24
Speaker 1: are themselves in motion, rotating, advancing or retreating, and at
9:29
Speaker 1: the same time attempting to discriminate by the sense of
9:32
Speaker 1: sight between a number of polygons of high rank moving
9:35
Speaker 1: in different directions, as for example, in a ball room
9:39
Speaker 1: or conversazione, must be of a nature to task the
9:42
Speaker 1: angularity of the most intellectual and amply justify the rich
9:47
Speaker 1: endowments of the learned. Professors of geometry, both static and
9:51
Speaker 1: kinetic in the illustrious University of Wentbridge, where the science
9:56
Speaker 1: and art of sight recognition are regularly taught to lo
10:00
Speaker 1: large classes of the elite of the States. It is
10:04
Speaker 1: only a few of the sciens of our noblest and
10:06
Speaker 1: wealthiest houses who are able to give the time and
10:09
Speaker 1: money necessary for the thorough prosecution of this noble and
10:13
Speaker 1: valuable art. Even to me, a mathematician of no means
10:17
Speaker 1: standing and the grandfather of two most hopeful and perfectly
10:21
Speaker 1: regular hexagons, defined myself in the midst of a crowd
10:25
Speaker 1: of rotating polygons of the higher classes is occasionally very perplexing,
10:30
Speaker 1: and of course to a common tradesman or surf such
10:33
Speaker 1: a site is almost as unintelligible as it would be
10:36
Speaker 1: to you, my reader, were you suddenly transported into our country,
10:42
Speaker 1: in such a crowd, you could see on all sides
10:44
Speaker 1: of you nothing but a line, apparently straight, but of
10:48
Speaker 1: which the parts would vary irregularly and perpetually in brightness
10:52
Speaker 1: or dimness. Even if you had completed your third year
10:56
Speaker 1: in the pentagonal and hexagonal classes in the university, and
11:00
Speaker 1: were perfect in the theory of the subject, you would
11:03
Speaker 1: still find that there was need of many years of
11:06
Speaker 1: experience before you could move in a fashionable crowd without
11:10
Speaker 1: jostling against your betters, whom it is against etiquette to
11:14
Speaker 1: ask to feel, and who, by their superior culture and breeding,
11:20
Speaker 1: know all about your movements, while you know very little
11:23
Speaker 1: or nothing about theirs. In a word, to comport oneself
11:28
Speaker 1: with perfect propriety. In polygonal society, one ought to be
11:33
Speaker 1: a polygon oneself. Such, at least is the painful teaching
11:37
Speaker 1: of my experience. It is astonishing how much the art,
11:42
Speaker 1: or i may almost call it instinct of sight recognition
11:46
Speaker 1: is developed by the habitual practice of it and by
11:50
Speaker 1: the avoidance of the custom of feeling. Just as with you,
11:55
Speaker 1: the deaf and dumb, if once allowed to gesticulate and
11:59
Speaker 1: to use the and alphabet, will never acquire the more
12:02
Speaker 1: difficult but far more valuable art of lip speech and
12:06
Speaker 1: lip reading. So it is with us as regards seeing
12:10
Speaker 1: and feeling. None who in early life resort to feeling
12:15
Speaker 1: will ever learn seeing in perfection. For this reason, among
12:21
Speaker 1: our higher classes, feeling is discouraged or absolutely forbidden from
12:27
Speaker 1: the cradle their children, instead of going to the public
12:30
Speaker 1: elementary schools, where the art of feeling is taught, are
12:34
Speaker 1: sent to higher seminaries of an exclusive character, and at
12:39
Speaker 1: our illustrious university, to feel is regarded as a most
12:43
Speaker 1: serious fault, involving rustication for the first offense and expulsion
12:49
Speaker 1: for the second. But among the lower classes, the art
12:54
Speaker 1: of sight recognition is regarded as an unattainable luxury. A
12:59
Speaker 1: common trade cannot afford to let his son spend a
13:02
Speaker 1: third of his life in abstract studies. The children of
13:06
Speaker 1: the poor are therefore allowed to feel from their earliest years,
13:11
Speaker 1: and they gain thereby a precocity and an early vivacity,
13:15
Speaker 1: which contrast, at first most favorably with the inert, undeveloped,
13:20
Speaker 1: and listless behavior of the half instructed youths of the
13:24
Speaker 1: polygonal class. But when the latter have at last completed
13:28
Speaker 1: their university course and are prepared to put their theory
13:32
Speaker 1: into practice, the change that comes over them may almost
13:36
Speaker 1: be described as a new birth. And in every art, science,
13:41
Speaker 1: and social pursuit they rapidly overtake and distance their triangular competitors.
13:49
Speaker 1: Only a few of the polygonal class fail to pass
13:52
Speaker 1: the final test or leaving examination at the university. The
13:57
Speaker 1: condition of the unsuccessful minority is truly pitiable. Rejected from
14:03
Speaker 1: the higher class, they are also despised by the lower.
14:07
Speaker 1: They have neither the matured and systematically trained powers of
14:12
Speaker 1: the polygonal bachelors and masters of arts, nor yet the
14:16
Speaker 1: native precocity and mercurial versatility of the useful tradesmen. The
14:22
Speaker 1: professions the public services are closed against them, and though
14:27
Speaker 1: in most states they are not actually debarred from marriage,
14:32
Speaker 1: yet they have the greatest difficulty in forming suitable alliances,
14:36
Speaker 1: as experience shows that the offspring of such unfortunate and
14:41
Speaker 1: ill endowed parents is generally itself unfortunate, if not positively irregular.
14:49
Speaker 1: It is from these specimens of the refuse of our
14:51
Speaker 1: nobility that the great tumults and seditions of past ages
14:55
Speaker 1: have generally derived their leaders. And so great is the
14:59
Speaker 1: miss mischief, thence arising that an increasing minority of our
15:03
Speaker 1: more progressive statesmen are of opinion that true mercy would
15:08
Speaker 1: dictate their entire suppression by enacting that all who failed
15:12
Speaker 1: to pass the final examination of the university should be
15:15
Speaker 1: either imprisoned for life or extinguished by a painless death.
15:21
Speaker 1: But I find myself digressing into the subject of irregularities
15:25
Speaker 1: a matter of such vital interest that it demands a
15:29
Speaker 1: separate section, Section seven of irregular figures. Throughout the previous pages,
15:39
Speaker 1: I have been assuming what perhaps should have been laid
15:42
Speaker 1: down at the beginning as a distinct and fundamental proposition,
15:46
Speaker 1: that every human being in flatland is a regular figure,
15:50
Speaker 1: that is to say, of regular construction. By this I
15:54
Speaker 1: mean that a woman must not only be a line,
15:57
Speaker 1: but a straight line. That an artisan or soldier must
16:02
Speaker 1: have two of his sides equal, that tradesmen must have
16:06
Speaker 1: three sides equal, lawyers, of which class I am a
16:10
Speaker 1: humble member, four sides equal, and generally, that in every
16:15
Speaker 1: polygon all the sides must be equal. The size of
16:20
Speaker 1: the sides would, of course, depend upon the age of
16:23
Speaker 1: the individual. A female at birth would be about an
16:27
Speaker 1: inch long, while a tall adult woman might extend to
16:31
Speaker 1: a foot. As to the males of every class, it
16:35
Speaker 1: may be roughly said that the lengths of an adult sides,
16:38
Speaker 1: when added together, is three feet or a little more.
16:43
Speaker 1: But the size of our sides is not under consideration.
16:47
Speaker 1: I am speaking of the equality of sides, and it
16:51
Speaker 1: does not need much reflection to see that the whole
16:54
Speaker 1: of the social life in flatland rests upon the fundamental
16:58
Speaker 1: fact that nature will all figures to have their sides equal.
17:04
Speaker 1: If our sides were unequal, our angles would be unequal.
17:09
Speaker 1: Instead of its being sufficient to feel or estimate by
17:13
Speaker 1: sight a single angle in order to determine the form
17:17
Speaker 1: of an individual, it would be necessary to ascertain each
17:20
Speaker 1: angle by the experiment of feeling. But life would be
17:24
Speaker 1: too short for such a tedious groping. The whole science
17:29
Speaker 1: and art of sight recognition would at once perish. Feeling,
17:34
Speaker 1: so far as it is an art, would not long survive.
17:38
Speaker 1: Intercourse would become perilous or impossible. There would be an
17:42
Speaker 1: end to all confidence all forethought. No one would be
17:47
Speaker 1: safe in making the most simple social arrangements. In a word,
17:51
Speaker 1: civilization would relapse into barbarism. Am I going too fast
17:57
Speaker 1: to carry my readers with me to these obvious cons inclusions.
18:01
Speaker 1: Surely a moment's reflection and a single instance from common
18:05
Speaker 1: life must convince everyone that our whole social system is
18:10
Speaker 1: based upon regularity or equality of angles. You meet, for example,
18:16
Speaker 1: two or three tradesmen in the street whom you recognize
18:20
Speaker 1: at once to be tradesmen by a glance at their angles,
18:23
Speaker 1: and rapidly bedimmed sides, and you ask them to step
18:27
Speaker 1: into your house to lunch. This you do at present
18:31
Speaker 1: with perfect confidence, because everyone knows to an inch or
18:35
Speaker 1: two the area occupied by an adult triangle. But imagine
18:40
Speaker 1: that your tradesman drags behind his regular and respectable vertex
18:45
Speaker 1: a parallelogram of twelve or thirteen inches in diagonal. What
18:50
Speaker 1: are you to do with such a monster sticking fast
18:53
Speaker 1: in your house door? But I am insulting the intelligence
18:58
Speaker 1: of my readers by accumulating details which must be patent
19:01
Speaker 1: to everyone who enjoys the advantages of a residence in spaceland. Obviously,
19:07
Speaker 1: the measurements of a single angle would no longer be sufficient.
19:11
Speaker 1: Under such portentous circumstances. One's whole life would be taken
19:17
Speaker 1: up in feeling or surveying the perimeter of one's acquaintances. Already,
19:23
Speaker 1: the difficulties of avoiding a collision in a crowd are
19:26
Speaker 1: enough to tax the sagacity of even a well educated square.
19:31
Speaker 1: But if no one could calculate the regularity of a
19:34
Speaker 1: single figure in the company, all would be chaos and confusion,
19:39
Speaker 1: and the slightest panic would cause serious injuries. Or if
19:44
Speaker 1: there happened to be any women or soldiers present, perhaps
19:47
Speaker 1: considerable loss of life. Expediency therefore concurs with nature in
19:55
Speaker 1: stamping the seal of its approval upon regularity of conformation.
20:00
Speaker 1: Nor has the law been backward in seconding their efforts.
20:05
Speaker 1: Irregularity of figure means with us the same as or
20:09
Speaker 1: more than a combination of moral obliquity and criminality with you,
20:14
Speaker 1: and is treated accordingly. There are not wanting. It is
20:19
Speaker 1: true some promulgators of paradoxes who maintain that there is
20:24
Speaker 1: no necessary connection between geometrical and moral irregularity. The irregular,
20:30
Speaker 1: they say, is from his birth, scouted by his own parents,
20:35
Speaker 1: derided by his brothers and sisters, neglected by the domestics,
20:40
Speaker 1: scorned and suspected by society, and excluded from all posts
20:45
Speaker 1: of responsibility, trust, and useful activity. His every movement is
20:51
Speaker 1: jealously watched by the police till he comes of age
20:54
Speaker 1: and presents himself for inspection. Then he is either destroyed
20:59
Speaker 1: if he is found to exceed the fixed margin of deviation,
21:03
Speaker 1: or else inured in a government office as a clerk
21:06
Speaker 1: of the seventh class, prevented from marriage, forced to drudge
21:12
Speaker 1: at an uninteresting occupation for a miserable stipend, obliged to
21:17
Speaker 1: live and board at the office, and to take even
21:20
Speaker 1: his vocation under close supervision. What wonder that human nature,
21:26
Speaker 1: even in the best and purest, is embittered and perverted
21:30
Speaker 1: by such surroundings. All this very plausible reasoning does not
21:37
Speaker 1: convince me, as it has not convinced the wisest of
21:41
Speaker 1: our statesmen, that our ancestors erred in laying it down
21:44
Speaker 1: as an axiom of policy, that the toleration of irregularity
21:48
Speaker 1: is incompatible with the safety of the state. Doubtless, the
21:53
Speaker 1: life of an irregular is hard, But the interests of
21:57
Speaker 1: the greater number require that it shall be hard. If
22:01
Speaker 1: a man with a triangular front and a polygonal back
22:04
Speaker 1: were allowed to exist and to propagate a still more
22:07
Speaker 1: irregular posterity, what would become of the arts of life?
22:13
Speaker 1: Are the houses and doors and churches in flatland to
22:16
Speaker 1: be altered in order to accommodate such monsters? Are our
22:21
Speaker 1: ticket collectors to be required to measure every man's perimeter
22:25
Speaker 1: before they allow him to enter a theater or to
22:28
Speaker 1: take his place in a lecture room? Is an irregular
22:32
Speaker 1: to be exempted from the militia. And if not, how
22:36
Speaker 1: is he to be prevented from carrying desolation into the
22:39
Speaker 1: ranks of his comrades. Again, what irresistible temptations to fraudulent
22:46
Speaker 1: impostures must needs beset such a creature? How easy for
22:52
Speaker 1: him to enter a shop with his polygonal front foremost,
22:56
Speaker 1: and to order goods to any extent from a confiding tradesman.
23:02
Speaker 1: Let the advocates of a falsely called philanthropy pleaders, they
23:05
Speaker 1: may for the abrogation of the irregular penal laws. I,
23:10
Speaker 1: for my part, have never known an irregular who was
23:13
Speaker 1: not also what nature evidently intended him to be, a hypocrite,
23:18
Speaker 1: a misanthropist, and, up to the limits of his power,
23:21
Speaker 1: a perpetrator of all manner of mischief. Not that I
23:26
Speaker 1: should be disposed to recommend at present the extreme measures
23:31
Speaker 1: adopted in some states where an infant whose angle deviates
23:35
Speaker 1: by half a degree from the correct angularity is summarily
23:39
Speaker 1: destroyed at birth. Some of our highest and ablest men,
23:44
Speaker 1: men of real genius, have, during their earliest days labored
23:48
Speaker 1: under deviations as great as or even greater than forty
23:52
Speaker 1: five minutes, and the loss of their precious lives would
23:56
Speaker 1: have been an irreparable injury to the state. The art
24:01
Speaker 1: of healing also has achieved some of its most glorious
24:04
Speaker 1: triumphs in the compressions, extensions, trepannings, colligations, and other surgical
24:11
Speaker 1: or dietetic operations by which irregularity has been partly or
24:16
Speaker 1: wholly cured. Advocating therefore avera media, I would lay down
24:22
Speaker 1: no fixed or absolute line of demarcation, but at the
24:26
Speaker 1: period when the frame is just beginning to set, and
24:29
Speaker 1: when the medical board has reported that recovery is improbable,
24:33
Speaker 1: I would suggest that the irregular offspring be painlessly and
24:36
Speaker 1: mercifully consumed. End of Section seven