Gregory Benford - The Fourth Dimension

VIP免费

2024-11-19 1 0 56.42KB 9 页 5.9玖币

侵权投诉

GREGORY BENFORD

THE FOURTH DIMENSION

Suppose that next to you, right now, a pale gray sphere appeared. It grew from

baseball-sized to a diameter as big as you -- grainy, gray, cool to the touch

-- then shrank to a point . . . and disappeared.

You would probably interpret it as a balloon blown up, then deflated. But

where did the flat balloon go?

Or you could realize that you had been visited by a denizen of a higher

dimension -- a four dimensional sphere, or hypersphere. In three dimensions,

it looks like a sphere, the most perfect of figures, just as a sphere

projected in two dimensions makes a circle. The fact that this isn't an

everyday occurrence implies that travel between dimensions is uncommon, but

not that it is illogical.

Probably you would not have thought of such ideas before 1884. That is due to

the Reverend Edwin Abbott Abbott, M.A., D.D., headmaster of the City of London

School.

Respected, well liked, he led a strictly regular life, as proper as a

parallelogram. He had published quite a few conventional books with titles

like Through Nature to Christ, Parables for Children and How to Tell the Parts

of Speech. These did not prepare the world for his sudden excursion into the

fantastic, in 1884. Beneath his exterior he was a bit odd, and his short novel

Hatland has proved his only hedge against oblivion, an astonishingly prescient

fantasy of mathematics.

Abbott's oddity began with his repeated name, which a mathematical wit might

see as A times A or A Squared, A[sup 2]. Abbott's protagonist is A Square, a

much troubled spirit. Liberated into another character, Abbott seems to have

broken out of his cover as a prim reverend, and poured out his feelings.

The book has a curiously obsessive quality, which perhaps accounts for its

uneasy reception. Reviewers termed it "soporific," "prolix,"" mortally

tedious," "desperately facetious, "while others found it "clever,"

"fascinating," "never been equaled for clarity of thought," and "mind

broadening," and they even likened it to Gulliver's Travels. This last

comparison is just, because beneath the math drolleries lurks a penetrating

satire of Victorian society.

A Square's society is as constrained as were the prim Victorians. Women are

not full figures but mere lines. Soldiers are triangles with sharp points,

adept at stabbing. The more sides, the higher the status, so hexagons outrank

squares, and the high priests are perfect circles.

In a delicious irony, the upper classes are polygons with equal sides --but

their views certainly do not embrace equality. Mathematicians term equal-sided

figures "regular," and in nineteenth century terms, proper upper class

polygons are of the regular sort.

A Square learns that his view of the world is too narrow. There is a third

dimension, grander and exciting. but his hidebound fellows cannot see it. This

opening-out is the central imaginative event of the novel, Abbott echoing an

emergent idea.

In the late nineteenth century higher dimensions were fashionable.

Mathematicians had laid the foundations for rigorous work in higher-

dimensional space, and physicists were about to begin using four-dimensional

spacetime. Twenty centuries after Euclid, the mathematician Bernhard Riemann

took a great leap in 1854, liberating the idea of dimensions from our spatial

senses. He argued that ever since Rene Descartes had described spaces with

algebra, the path to discussing higher dimensions had been dear, but unwalked.

Descartes' analytic geometry defined lines as things described by one set of

coordinates, distances along one axis. A plane needed two independent

coordinate sets, a solid took three. With coordinates one could map an object,

defining it quantitatively: not "Chicago is over that hill." but "Chicago is

fifteen miles that way." This appealed more to our logical capacity, and less

to our sensory experience.

Riemann described worlds of equal logical possibility, with dimensions ranging

from one to infinity. They were not spatial in the ordinary sense. Instead,

Riemann took dimension to refer to conceptual spaces, which he named

manifolds.

This wasn't merely a semantic change. Weather, for example, depends on several

variables -- say, n -- like temperature, pressure, wind velocity, time of day,

etc. One could represent the weather as a moving point in an n-dimensional

space. A plausible model of everyday weather needs about a dozen variables, so

to visualize it means seeing curves and surfaces in a twelve-dimensional

world. No wonder we understand the motions of planets (which even Einstein

only needed four dimensions to describe), but not the weather.

Riemann revolutionized mathematics and his general ideas diffused into our

culture. By 1880, C.H. Hinton had pressed the issue by building elaborate

models to further his extra-dimensional intuition, he tried to explain ghosts

as higher-dimensional apparitions. Pursuing the analogy, he wrote of a fourth-

dimensional God from whom nothing could be hidden. The afterlife, then,

allowed spirits to move along the time dimension, reliving and reassessing

moments of life. Spirits from hyper-space were the subject of J.K.F. Zollner's

1878 Transcendental Physics, which envisioned them moving everywhere by short-

cut loops through the fourth dimension.

Mystics responded to the fashion by imagining that God, souls, angels and any

other theological beings resided as literal beings of mass ("hypermatter") in

four-space. This neatly explains why they can appear anywhere they like, and

God can be everywhere simultaneously, the way we can look down on a Flatland

and perceive it as a whole. Some found such transports of the imagination

inspiring, while others thought them crass and far too literal. I am unaware

of Abbott himself ever subscribing to such beliefs.

Still, Abbott and his adventure-some Square longed for the strange. More than

any other writer, Abbott coined the literary currency of dimensional metaphor.

By having a point of view which is literally above it all, surveying the

follies of a two-dimensional plane, Abbott can adroitly satirize the staid

rigidities of his Victorian world. (Perhaps this is why he first published

Flatland under a pseudonym.)

"Irregulars" are cruelly executed, for example. Do they stand for foreigners?

Gypsies? Cripples? We are left to fill in some blanks, but the overall shape

of the plot is clear -- flights of fancy are punished, and A Square does not

finish happily.

At a deeper level, the book harks toward deep scientific issues, and the

difficulty of comprehending a physical reality beyond our immediate senses.

This is the great theme of modem physics. The worlds of relativity and the

quantum are beyond the rough-and-ready ideas we chimpanzees have built into

us, from our distant ancestors' experience at throwing stones and poking

sticks on African plains.

Still deeper, in this fanciful narrative the good Reverend tries to speak

indirectly of intense spiritual experience. The trip into the higher realm of

three dimensions is a fine metaphor for a mystical encounter.

The thrust of the deceptively simple narrative is to make us examine our basic

assumptions. After all, our visual perceptions of the world are two-

dimensional patterns, yet we somehow know how to see three-dimensionality. One

knows instantly the difference between a ball and a fiat disk by their shading

in available light. Objects move in front of each other, like a woman walking

by a wall. We automatically discount a possible interpretation -- that the

woman has somehow dissolved the wall for an instant as she passes. Instead, we

see her in her three-dimensionality. The eye has learned the world's geometry

and discards any other scheme.

A Square learns this lesson early as he first visits Lineland in a dream. The

only distinction the natives can have is in their length. They see each other

as points, since they move along the same universal straight line. They

estimate how far away others are by their acute sense of hearing picking up

the difference between a bass left voice and a tenor right; the time lag in

arrival tells the distance. The king is longest, men next, then boys are

stubby lines. Women are mere points, of lower status. Their views of each

other are partial and instinctive. They never dream of how narrowly they see

their world.

This sets the stage for A Square's conceptual blowout when a Sphere visits him

and yanks him up into the hallucinogenic universe of three dimensions. Its

realities are surrealistic. A Square straggles to fathom what for us is

instinctive.

The reality of three dimensions we take for granted, but for us, what is the

reality of two dimensions? Would flatlanders have physical presence in our

world -- that is, could we perceive a two-dimensional universe embedded in our

own? Could we yank them up into our world?

Flatlanders could be as immaterial as shadows, mere patterns in our view. If

an isosceles triangle soldier cut your throat it would not hurt. Abbott did

not consider this in his first edition, but in the second he says that A

Square eventually believes that flatlanders have a small but real height in

our universe. A Square discusses this with the ruler of Flatland:

* I tried to prove to him that he was "high," as well as long and broad,

although he did not know it. But what was his reply? "You say I am 'high';

measure my 'highness' and I will believe you." What could I do? I met his

challenge!

If flatlanders were even quite thick, they would not be able to tell, if in

that direction they had no ability to move or did not vary. Height as a

concept would lie beyond their knowable range. Or if they did vary in height,

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

5.9 玖币 0人已下载

立即下载 VIP免费下载

摘要：

GREGORYBENFORDTHEFOURTHDIMENSIONSupposethatnexttoyou,rightnow,apalegraysphereappeared.Itgrewfrombase...

展开>> 收起<<

Gregory Benford - The Fourth Dimension.pdf

共9页,预览3页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Gregory Benford - The Fourth Dimension

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: