This is the first time I’ve been invited to write and submit a book review, and in the spirit of this year’s Guangdong College Entrance Examination essay topic, I took on the task~
Writing an article for submission is painful. That piece “A Brief Talk on the Popularization of Philosophy,” though it was published too, had been written rather casually at the time; writing specifically for submission really was a first for me, and it seems I’m still not quite suited to it.
Ideally I could have written it better, but on the one hand I was rushing to finish it before my graduation trip, and on the other hand this book in fact did not particularly attract me, so I might as well keep it simple.
After a quick comparison, I found that the published version and my original version had not really been altered much at all, mainly just some punctuation adjustments. I wonder whether the editors were not careful enough, or whether they were simply respecting the author~ (As long as the meaning isn’t changed, I’d actually quite welcome a bit of polishing~)
There is one error in the electronic version: in my original text I said that Lulu Bang was “a toy shaped like a ‘J’ with two horns,” but in the electronic version the “J” became a “?”, which changes the meaning completely. The “J” is the symbol Word automatically substitutes; when you type “:-)” it automatically turns into this smiling face. I probably should have simply said “smiley-face-shaped” toy, which would have been safer, but after all the image of “J” is the most intuitive, so I left it unchanged. I wonder how it actually appeared in the printed newspaper……
I didn’t come up with the title. I found that I really couldn’t think of a suitable one; when putting something on the blog, I usually just use the book title directly. When Senior Brother Butian “interrogated” me about the title, I seem to have said something like “A Guidebook to the Mathematical World,” and Senior Brother asked back whether it was only the mathematical world. At the time I seem to have gone to the seaside or somewhere else to play, and never bothered with it; anyway, whatever. In the end it became “The Mathematical World,” which is fine too.
In fact, following the logic of the original book—“A Fantastic Journey Through the Number Realm”—“The Number World” would be the most apt. However, this can easily lead to misunderstanding, because in fact the mathematics section of this book is mainly geometry. And not every reader can easily regard geometry as part of the “number world.” In truth, whether physics or mathematics, both are constructing a “mathematical world,” or rather a “number world,” and the main text of this book often uses “number” to refer to the entire world through which the protagonists travel. Therefore, according to the logic and distinctive features of this book, “The Guide to the Number World” is indeed the most apt.
http://www.sciencenet.cn/sbhtmlnews/2008/6/207938.html
A Guide to the Mathematical World
This is a peculiar book.
Speaking of the method of this popular science book, rather than calling it novel and distinctive, it would be more accurate to say it is old-hat through and through—the typical “XX Wanders Through the Kingdom of Science” formula: the usual pattern is an all-knowing “old man of knowledge” leading a curiosity-struck “little brat” around on tours and giving explanations. This formula is especially well suited to being arranged into comic strips or cartoons “not suitable for adults,” and it has long been a familiar sight in popular science for children.
But the distinctive feature of *Two-Dimensional In and Out* lies in this: it is not popular science for children, but unquestionably belongs to “high-end popular science”—higher-dimensional geometry, fractals, projective planes, topology, group theory, Schrödinger’s cat, the twin paradox, time travel, black holes, the Big Bang, elementary particles, string theory…… So many of the deepest and most cutting-edge fields in mathematics and physics are “traveled through” in *Two-Dimensional In and Out*.
Since *A Brief History of Time*, similar “high-end popular science” works have long appeared one after another; although excellent new works do appear from time to time, it is hard to avoid a kind of “aesthetic fatigue,” not to mention the many copycat works that are merely riding the wave.
Yet *Two-Dimensional In and Out* can still stand apart.
The protagonist of *Two-Dimensional In and Out* is Vicky, the great-granddaughter of Mr. A. Fangfang, the protagonist of *The Wonderful World of Two Dimensions* (her form is a line segment). *The Wonderful World of Two Dimensions* is a strange book written in 1884 by the British clergyman Abbot. The original intention of that book may have been mainly to use a science-fiction story to criticize social ills, but because of its fascinating imagination concerning a non-three-dimensional world, it became an immortal classic in the history of popular science. More than a hundred years have passed with endless reprintings, and it has also inspired countless imitators and continuations; *Two-Dimensional In and Out* is one of them.
Even so, *Two-Dimensional In and Out* does not actually spend much ink on the “two-dimensional country.” Two-Dimensional Country is merely the starting point of the journey; for most of the book, Vicky travels everywhere in the number world together with Lulu Bang (who plays the role of the all-knowing guide, and appears as a toy in the shape of a “?” with two horns).
In this typical children’s popular science model of “tourist—guide,” the identity of the tourist or the image of the guide has no substantive significance; whether the erudite guide is called an “old man of knowledge,” a “know-it-all,” or “Lulu Bang,” the role they play is basically the same. Still, the image of this sage undoubtedly reflects the author’s tastes and style—obviously, Lulu Bang’s image is completely different from the traditional scientist image of a “bald, bespectacled, white-bearded old man in a lab coat”; this mischievous and quirky image also foreshadows the writing style of this book.
Designs that could almost be called outright parody are seen throughout the book, such as the Möbius cow, the gingerbread boy, the bodybuilder-shaper, and even turning Hawking into the “Eagle King” (Hawk King), which really gave the translator a hard time. But the translator unquestionably put a great deal of thought into it; although the humor of many puns is indeed difficult to render in translation, the Chinese edition still preserves the style of the original to the greatest extent. This style of writing also has its drawbacks, namely that it is not conducive to accurately conveying knowledge. For instance, if you had never heard of Hawking, then after reading this book you would still not know who on earth he was—the Chinese translator’s footnotes did add a fair amount of background information, but there is scarcely any scaffolding of background knowledge in the main text. I myself had already acquired a certain understanding of the knowledge involved in this book through other channels, so I was able to “get it” while reading; if this had been the first “high-end popular science” book I ever read, I’m afraid I would have felt lost and baffled in many places.
But does that mean this book is positioned at the very high end of high-end popular science—that is, suitable only for those who have at least already read quite a few high-end popular science books? Not at all. The children’s-popular-science-style formula adopted by this book is also telling us that even children can give it a read.
Here we need to notice: what exactly is this kind of popular science book trying to popularize?
As the name suggests, popular science is of course meant to popularize science. However, science includes not only scientific knowledge, but more importantly the thought, methods, spirit, and style of science itself. If *Two-Dimensional In and Out* were intended only to popularize scientific knowledge, then it would be a failure, or at least inefficient. But if we focus on the latter, the situation is quite different.
Returning to a question mentioned earlier: in the “tourist—guide” model, the tourist’s identity was never all that important to begin with; moreover, not much ink is spent on “Two-Dimensional Country” in this book, and it even feels a bit redundant at times, so why did the author insist on setting the journey’s starting point in the “Wonderland of Two Dimensions” rather than on the Earth we are familiar with?
The “Wonderland of Two Dimensions” provides an analogical mode of thinking, guiding us to contemplate our own world from a different perspective. When we imagine the three-dimensional world from the point of view of a resident of Two-Dimensional Country, we experience the difficulty of this imagination—we find that the residents of Two-Dimensional Country may easily imagine the world to which they are confined as absolute, and thus find it difficult to accept the idea that “the true appearance of the world may be completely different from the way our senses are able to perceive it.”
Then what about us? Are we also similarly limited by our senses, taking our world for granted and understanding it in an unexamined way?
When asked “What use is hyperbolic geometry?”, Lulu Bang replied: “Hey, let me tell you one reason, and perhaps the biggest reason of all: it is to make you realize that things may not be what they seem.” (p. 180)
This is precisely one of the great meanings of science: enabling humanity to transcend its senses. For example, the earth seems flat and motionless, but in fact it is a rotating sphere. Science is not a negation of the senses, but an expansion and transcendence of them, allowing people not to leave the Earth and yet, as if standing in outer space, to “see” the way the whole Earth moves. From elementary particles to the origin of the universe, science has enabled human cognition to surpass the shackles of sensory capacity and break through the limits of space and time.
In *Two-Dimensional In and Out*, Vicky is given a “metaphysical sensory transmitter,” enabling her to obtain an intuitive feeling for the mathematical world. Human beings have not yet invented such a machine, but they can rely on the “six divine tools”—“imagination, mathematics, analogy, induction, extrapolation, and recursion”—to experience numbers. This is precisely the core of science, and also the true theme of this book.
The introduction of knowledge is not the focus of this book. The author intends to inspire the reader, amid the dizzying succession of sights on the tour, to think and to apprehend: what exactly is geometry? What exactly is science? Even if the reader finishes the book dazed and knowing nothing, they may still have gained something more important—that is, “ignorance” itself: “things may not be what they seem,” and the world in which we live is not necessarily the shape we once took for granted, the one to which we have grown accustomed. This is what the book tries to convey to the reader.
Latest Comments
- Gu Di
2008-06-27 11:24:11
So I had misread the subtitle of the book title—it is “A Fantastic Journey Through the Number Realm,” not “Digital.”
I did notice that the word “number realm” appears many times in the text; it’s just that I first looked at the title and formed a preconceived impression.
If it’s “number realm,” then it means the “mathematical world.” But “digital world” also makes sense, because in the author’s depiction both physics and geometry are mathematized and quantified; in the section “What Is Geometry?” geometry lies in the invariance of quantity under symmetric transformations. It can be said that the geometry toured in this book is no longer the classical geometry separate from arithmetic, but also a world of numbers, and physics of course is too.
Translated from the Chinese original with AI assistance. The original text is authoritative.
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