四维空间：科学与想象的碰撞
The 4th Dimension: Where Science and Imagination Collide
1. Introduction
我们大多数人都习惯于观看 2D 电影，尽管屏幕上的人物看起来有深度和质感，但实际上画面是平面的。但是，当我们戴上 3D 眼镜时，我们看到的是一个可以行走其中的世界。我们可以想象在这样一个三维世界中生活，因为我们实际上就生活在这样一个世界中。对于只知道二维生活的人来说，三维世界是无法理解的。许多研究人员认为，这就是我们看不到四维空间或四维空间之外的其他维度的原因。物理学家假设至少有 10 个维度，但我们中的大多数人永远不会 "看到 "它们。因为我们只知道三维空间的生活，我们的大脑不知道如何寻找更多的东西。
Most of us are accustomed to watching movies in 2D; even though characters on the screen appear to have depth and texture, the image is actually flat. But when we put on 3D glasses, we see a world that we could walk in. We can imagine existing in such a three-dimensional world because we actually live in one. For someone who's only known life in two dimensions, the third dimension would be impossible to comprehend. According to many researchers, this is the reason we can't see the fourth dimension or any other dimension beyond that. Physicists work under the assumption that there are at least 10 dimensions, but the majority of us will never "see" them. Because we only know life in 3D, our brains don't understand how to look for anything more.
2. What Is a Dimensional Space?
数学和物理学中的维空间描述了物体存在或移动的不同方向或坐标。它是一个数学概念，用于理解和形象化我们世界中事物的定位和运动。
A dimensional space in mathematics and physics describes the different directions or coordinates in which objects can exist or move. It's a
mathematical concept used to understand and visualize the positioning and movement of things in our world.
在日常生活中，我们经常使用三个维度：高度（上下）、宽度（左右）和深度（前后）来描述物体的位置。这三个维度构成了所谓的三维空间。然而，在更高级的数学和物理学中，维度空间可以不止三个维度，它们可以帮助科学家和数学家理解复杂的现象，如量子力学、弦理论或更高维度的数据分析。
In our everyday world, we often use three dimensions: height (up and down), width (left and right), and depth (forward and backward) to describe the location of objects. These three dimensions create what's called 3D space. However, in more advanced mathematics and physics, dimensional spaces can have more than three dimensions and they help scientists and mathematicians understand complex phenomena like quantum mechanics, string theory, or data analysis in higher dimensions.
这些高维空间更难可视化，因为它们超出了我们的日常经验，但它们对于解决各种问题和研究复杂系统至关重要。
These higher-dimensional spaces are harder to visualize because they go beyond our everyday experience, but they are essential for solving
various problems and studying intricate systems.
3. Looking Beyond This Dimensional Space
1884 年，埃德温-艾博特（Edwin A. Abbot）出版了一部长篇小说，描绘了如何看到超越自身维度的问题。在《平地》（Flatland： 在《平地：多维的浪漫》中，艾博特描述了一个生活在二维世界中的正方形的生活。生活在二维世界中意味着正方形周围有圆形、三角形和长方形，但正方形看到的只是其他线条。有一天，一个球体拜访了这个正方形。
In 1884, Edwin A. Abbot published a novella that depicts the problem of seeing dimensions beyond your own. In Flatland: A Romance of Many Dimensions, Abbot describes the life of a square living in a two-dimensional world. Living in 2D means that the square is surrounded by circles, triangles, and rectangles, but all the square sees are other lines. One day, the square is visited by a sphere.
第一眼看上去，球体对正方形来说只是一个圆，正方形无法理解球体在解释三维物体时的意思。最后，球体把正方形带到了三维世界，正方形明白了。他看到的不仅仅是线条，而是有深度的整体形状。
On first glance, the sphere just looks like a circle to the square and the square can't comprehend what the sphere means when he explains 3D objects. Eventually, the sphere takes the square to the 3D world and the square understands. He sees not just lines but entire shapes that have depth.
正方体有恃无恐地问球体，三维世界之外还有什么；球体大吃一惊。球体无法理解三维世界之外的世界，因此它代表了读者。我们的大脑没有受过训练，无法看到我们的世界之外的任何东西，因此很可能需要来自另一个维度的东西才能让我们理解。
Emboldened, the square asks the sphere what exists beyond the 3D world; the sphere is appalled. The sphere can't comprehend a world beyond this and in this way stands in for the reader. Our brains aren't trained to see anything other than our world and it will likely take something from another dimension to make us understand.
4. The Fourth Dimension
但另一个空间是什么呢？神秘主义者曾将其视为灵魂居住的地方，因为他们不受我们尘世规则的约束。爱因斯坦在他的狭义相对论中将时间称为第四维度，但同时指出时间与空间密不可分。
But what is this other dimension? Mystics used to see it as a place where spirits lived since they weren't bound by our earthly rules. In his theory of special relativity, Einstein referred to time as the fourth dimension but noted that time is inseparable from space.
科幻小说迷们可能会把这个结合体认作时空，事实上，时空连续体的概念已经被科幻小说家普及了几个世纪（例如雷-布拉德伯里的《火星编年史》或乔-霍尔德曼的《永远的战争》）。如今，一些物理学家将四维空间描述为垂直于立方体的任何空间--问题是我们大多数人无法想象垂直于立方体的东西。
Science-fiction aficionados may recognize that union as space-time and indeed the idea of a space-time continuum has been popularized by science-fiction writers for centuries (e.g. Ray Bradbury's The Martian Chronicles or Joe Haldeman's The Forever War). Today, some physicists describe the fourth dimension as any space that's perpendicular to a cube — the problem being that most of us can't visualize something that is perpendicular to a cube.
研究人员利用爱因斯坦的观点来确定我们能否穿越时空。虽然我们可以在三维世界中向任何方向移动，但我们只能在时间上向前移动。因此，穿越时空到过去几乎是不可能的，尽管一些研究人员仍对找到连接不同时空段的虫洞抱有希望。
Researchers have used Einstein's ideas to determine whether we can travel through time. While we can move in any direction in our 3D world, we can only move forward in time. Thus, traveling to the past has been deemed near-impossible though some researchers still hold out hope for finding wormholes that connect to different sections of space-time.
5. Beginnings of the Concept
19 世纪初，数学家和思想家们开始探索我们熟悉的三维空间（深度、宽度和高度）之外的第四空间维度。奥古斯特-费迪南德-莫比乌斯（August Ferdinand Möbius）就是思考这一额外维度可能性的人之一。四维空间的一个引人入胜之处在于，在四维空间中，三维物体可以旋转，看起来就像它自己的镜像，这一概念挑战了我们对空间的直观理解。
In the early 19th century, mathematicians and thinkers began to explore the idea of a fourth spatial dimension beyond our familiar three dimensions (depth, width, and height). August Ferdinand Möbius was among those who pondered the possibilities of this additional dimension. One of the intriguing aspects of the fourth dimension is that in it, a three-dimensional object could be rotated in such a way that it would appear as its own mirror image, a concept that challenges our intuitive understanding of space.
魔方，又称超立方体，是四维空间的一种常见视觉表现形式。它是立方体（三维物体）概念向四维空间的延伸。虽然在我们的三维世界中将其形象化具有挑战性，但数学家们使用图表和模型来帮助传达魔方的概念。
The tesseract, also known as a hypercube, is a common visual representation of 4D space. It is an extension of the concept of a cube (a 3D object) into the fourth dimension. While it's challenging to visualize in our three-dimensional world, mathematicians use diagrams and models to help convey the idea of a tesseract.
19 世纪晚期，数学家伯恩哈德-黎曼为真正的四维几何学奠定了基础，为理解和处理高维空间提供了数学框架。这项工作成为后来数学和物理学发展的基础，特别是在研究弯曲空间和相对论方面。
Later in the 19th century, mathematician Bernhard Riemann laid the foundations for true four-dimensional geometry, providing a mathematical framework for understanding and working with higher-dimensional spaces. This work became fundamental to later developments in mathematics and physics, particularly in the study of curved spaces and the theory of relativity.
6. Types of Dimensional Spaces
在数学和物理学中，我们会遇到我们熟悉的三维空间之外的各种维度空间。
In mathematics and physics, we encounter various types of dimensional spaces beyond our familiar three-dimensional world.
零维空间（0D）： 这种空间通常被称为单点或单子，代表一个没有空间范围或自由度的单一位置或值。它是所有维度空间中最简单、最抽象的空间，是数学，尤其是集合论和抽象代数的基础概念。
Zero-Dimensional Space (0D): Often referred to as a single point or a singleton, this space represents a single location or value with no spatial extent or degrees of freedom. It is the simplest and most abstract of all dimensional spaces, serving as a foundational concept in mathematics, especially in set theory and abstract algebra.
一维空间（1D）： 这是用直线表示的最简单的维度空间。在一维世界中，物体和实体只能沿单一轴线（如时间轴）移动，空间自由度仅限于一维。
One-Dimensional Space (1D): This is the simplest dimensional space represented as a straight line. In a one-dimensional world, objects and entities can only move along a single axis (like a timeline), limiting their spatial freedom to one dimension.
二维空间（2D）： 这种空间包括像纸张一样覆盖一个平面的坐标。它用于绘制和分析物体在两个方向上的位置。
Two-Dimensional Space (2D): This space includes coordinates that cover a plane like a sheet of paper. It's used for mapping and analyzing objects' positions in two directions.
三维空间（3D）： 我们的日常空间包括三个维度：高度、宽度和深度。通过这些维度的相互作用，我们可以描述物理世界以及物体如何在其中移动。
Three-Dimensional Space (3D): Our everyday space involves three dimensions: height, width, and depth. The interaction of these dimensions allows us to describe the physical world and how objects move within it.
四维空间（4D）： 在物理学中，时间通常被认为是第四维，对于理解爱因斯坦广义相对论中的时空至关重要。
Four-Dimensional Space (4D): In physics, time is often considered the fourth dimension, essential in understanding space-time in Einstein's theory of general relativity.
欧氏 n 维空间（nD）： 这是一种超越常规三维空间的空间思维方式。这个空间可以有任意数量的维数（n），其中点与点之间的距离和角度是以一致的、熟悉的方式测量的。
Euclidean n-Dimensional Space (nD): It's a way of thinking about space that goes beyond our usual three dimensions. This space can have any number of dimensions (n) where distances and angles between points are measured in a consistent, familiar way.
向量空间： 这些空间可以有任意有限的维数，是线性代数的基础，在物理学、计算机制图和工程学中发挥着重要作用。
Vector Spaces: These spaces can have any finite number of dimensions and are fundamental in linear algebra, which plays a vital role in physics,computer graphics, and engineering.
希尔伯特空间： 量子力学中用于描述量子系统状态的无穷维空间。
Hilbert Spaces: Infinite-dimensional spaces used in quantum mechanics to describe the state of quantum systems.
函数空间： 这些空间以函数为元素，用于各种数学和科学学科。
Function Spaces: These spaces involve functions as their elements and are used in various mathematical and scientific disciplines.
流形： 这些空间在每个点附近看起来都像欧几里得空间，但整体形状可能不同。
Manifolds: These spaces look like Euclidean space near every point but may have a different overall shape.
相空间： 物理学中用于描述预测动态系统未来行为所需的整套变量。
Phase Spaces: Used in physics to describe the complete set of variables needed to predict the future behavior of a dynamic system.
7. Why Is It Important to Understand the Fourth Dimension?
如果我们不能利用四维空间进行时间旅行，如果我们甚至看不到四维空间，那么了解它又有什么意义呢？了解这些更高的空间维度对数学家和物理学家来说非常重要，因为这有助于他们理解世界。高维度在理论物理学中起着至关重要的作用，它让人们深入了解现实的基本性质，并解决量子力学和广义相对论中的复杂问题。通过探索这些维度，科学家们可以发展出统一自然基本力量的理论，并对宇宙在最大和最小尺度上的行为做出预测。
If we can't use the fourth dimension to time travel and if we can't even see the fourth dimension, then what's the point of knowing about it? Understanding these higher spatial dimensions is important to mathematicians and physicists because it helps them understand the world. Higher dimensions play a crucial role in theoretical physics, providing insights into the fundamental nature of reality and solving complex problems in quantum mechanics and general relativity. By exploring these dimensions, scientists can develop theories that unify the fundamental forces of nature and make predictions about the universe's behavior at both the largest and smallest scales.
Reference:
Molly,E.&Desiree,B.,(2023). The 4th Dimension: Where Science and ImaginationCollid,[online]Available at:
<https://science.howstuffworks.com/science-vs-myth/everyday-myths/see-the-fourth-dimension.htm?s1sid=vqcloqrp43du46hn8ifbszr7&srch_tag=rkfjyysqgobaw2kfrjxk7t4mp2jnr2uo>[Accessed 16 July 2024].
