#zhenqing
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Chapters: 1/1
Fandom: 陈情令 | The Untamed (TV), 魔道祖师 - 墨香铜臭 | Módào Zǔshī - Mòxiāng Tóngxiù
Rating: Teen And Up Audiences
Warnings: No Archive Warnings Apply
Relationships: Ā-Qìng/Ōuyáng Zǐzhēn
Characters: Ā-Qìng (Módào Zǔshī), Ōuyáng Zǐzhēn, Jīn Líng | Jīn Rúlán, Lán Yuàn | Lán Sīzhuī, Lán Jǐngyí
Additional Tags: Fluff, Fluff and Humor, Misunderstandings, I Love the Junior Ensemble (Módào Zǔshī), Alternate Universe - Canon Divergence, Silly, Junior Quartet Dynamics (Módào Zǔshī)
Summary:
A-Qing pickpockets Ouyang Zizhen, and he falls in love at first sight. The Juniors TRY to help him win her over. It does not start out well…
Or 4 times A-Qing pickpockets Ouyang Zizhen, and 1 time Ouyang Zizhen receives something in return.
Based on the prompt to write something silly or fun involving A-Qing.
#ouyang zizhen#mo dao zu shi#the untamed#a-qing#fic rec#i can't beLIEVE i never recommended this before but here it is og#zhenqing
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#Chinese artist Li Zhenqing 's carving works：Jade elegant ribbon pen holder.Great Wall Treasure Code K2350131356#carving works#Chinese art#Jade carving#Title:Jade elegant ribbon pen holder. Work introduction: Chinese artist Li Zhenqing 's carving works#which made of Myanmar jade with exquisite design and supertechnical skills.
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hello! it's always nice to meet new turtles in the fandom (even if you are an older one)! i'm just wondering how you got into this abyss and what made you believe szd??? hope you have a nice day!
Hello to you to anon! It's nice to finally be online and meet you as well as others 😊
As for how I got myself here... A long story ahead (and apologies for the length)!
Disclaimer: CPN
I was looking for a drama to watch. It really started out that simple. My friend was nagging me to start watching The Untamed and she was convinced that by the end of it, she'll also get me into shipping the two main actors. I thought it was bold of her to assume that I'll start shipping the actors because I really don't get into RP ships at all. It never felt right to me because celebrities are people and their careers get affected by this stuff. It was just very icky to me, but she was dead-set on convincing me, saying, "You'll see" and "Just trust me".
It went like this: I got into The Untamed, was amazed by the chemistry between the two leads, started adoring The Untamed as an adaptation but was curious about the novel, went on to read MDZS and realized that the adaptation really did an amazing job.
I went on to read thousands of metas and analyses about CQL (because I really dig analyses) and just kept loving it more and more.
Around the time I was done with the novel, my friend sent me the BTS she saved at the time (even the ones which disappeared after five minutes or so) and I just fell in love with both of them. The bickering, the 'did you eat', the fighting... they were so cute!
These two were friends, I was sure of that, but I had no answers to 'are they a thing' question. At first, I thought it was simply fan-service (because bl dramas tend to do that) but the way these two smiled at each other and what they said at times... it really didn't sound fake to me at all. So, reluctantly, I got hooked. I got to know gg more, then got to know dd and found myself falling deep into an unclimbable hole. I became their fan.
As I was researching more, I never really doubted that their bond was fake. I didn't spend my time looking at all the 'bad bad rumors' about them but rather just focused on the positive stuff.
Now, as for my journey to bjyxszd: A lot of factors led to it but here are some contenders.
BTS clips - I don't think coworkers get mad about who the other is texting. Also, I firmly believe they are bickering like an old married couple and that dd stares WAY TOO MUCH at gg. He's the definition of 'giggling, feet in the air, teenager with a crush'. gg isn't spared either, because at times, the way he so lovingly stares at dd... I guess something really helped them get into their characters more. Also, the way dd cares whether gg ate or not... It's safe to conclude that just by watching the BTS, you'll know they care a lot about each other.
Interviews/Show appearances - Lots of 'slips of tongue' and even one time dd didn't get a signal from gg that they (hadn't) visited the waterfall. dd's 'true feelings' (zhenqing shigan; 真情实感) and both me and gg having similar reactions (except I was stunned for about twenty minutes first), gg getting distracted by dd biting his lips, old cow who eats young grass (how the hell did this go by), dd wanting to say their team name was bjyx yet gg (thank God) arguing against it, them working as a team on Happy Camp even if they were on different teams and this is just from the top of my head. I'm sure I missed a lot. Also, web ai zz and that smile, holy shit. gg repeating "Ai?" afterwards got me staring at my screen for half an hour in silence.
No fan-service - They hadn't appeared together supporting the same brand as most CPs usually do. You're telling me that gg is dd's "good friend" yet he hadn't ever hugged him? Which brings me to:
Body language - Along with the endless videos of differences between dd and someone else and gg and someone else compared to them with each other. Some bxg even posted videos of 'other couples vs yizhan' and they do say a lot.
Clothes sharing/Wearing the 'couple sets'
Sneakers + Ice cream - I still don't know how I can explain the emotions this had awakened in me. Really sad it had to go due to that incident but it is what it is.
Songs - because I adore music and think that it can say a lot of stuff which remains unsaid. "The Boy"; "If I Were Young"; "If I Were A Song"... I had "Once A Couple" by Liang Bo on repeat for several days after I took a closer look at their DDU playlists. Both of them have amazing taste in music (even if bitter).
And, like I said, much, much more. I think what really made me believe bjyxszd was not only these moments of candy which prove this and that but the way the supertopics are still standing long, long after the promotion for the show had ended. I realized what this implies and I understood that they might've needed support.
So, yes... I believe in them, I support them wholeheartedly and I still pray that they are always happy. If something were to happen, I'll still be here no matter what. I just adore them both equally and am excited to see how their careers will develop.
And there you go anon! I hope you have an amazing day 😊
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Yan Zhenqing Kai Shu Writing S ... Price 17.99$ CLICK TO BUY
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颜真卿祭侄文稿特展-东京国立博物馆
16/02/2019
如果借用米其林的标准，东京国立的这次颜真卿特展肯定属于“值得为之专门计划一次行程”的三星级别的。
If we were to use Michelin standards, the recent special exhibition of Yan Zhenqing at the Tokyo National Museum would certainly be classified as a three-star attraction, worthy of planning a special trip for.
来排大队的大概除了鸡国人就是霓虹人，比例大约五五；
除了从台北借来的两大主角（颜鲁公的天下第二和褚遂良版的天下第一）还很有诚意的调集了全日本的珍品来为其烘托气氛呢：有若干如雷贯耳的名碑的唐拓宋拓孤本，王羲之的乐毅论…
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Framed Chinese Calligraphy: Art, History, and the Enduring Use of Brushstroke
Tracing the Rich History and Contemporary Relevance of Framed Chinese Calligraphy
Framed Chinese calligraphy is a tangible witness to an ancient art style that has smoothly crossed decades. These painstakingly created figures continue to serve as compelling windows into China's history, culture, and aesthetic expression as they find their place within elegant frames. In this post, we will travel back in time to investigate the multifarious use and historical significance of framed Chinese calligraphy in the past, as well as its continuous relevance now.
The Ancient Roots of Chinese Calligraphy
Chinese calligraphy may be traced back to the dawn of Chinese civilization. Its history is intertwined with the evolution of the Chinese writing system and ink and brush techniques. Calligraphy was more than just a medium of communication; it was a type of art that encapsulated the spirit of Chinese culture.
Chinese philosophers, poets, and painters developed their calligraphy talents for millennia, attempting to portray the rhythm and vitality of life in their brushstrokes. Famous calligraphers such as Wang Xizhi and Yan Zhenqing's work became legendary, and their works were regarded as masterpieces.
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The Historical Use of Framed Calligraphy
The practice of framing calligraphy is also ancient. Framed calligraphy was a representation of knowledge, refinement, and cultural sophistication in traditional Chinese residences. These artworks were publicly displayed, frequently in the study or major living areas, and served as a source of inspiration as well as a reminder of timeless knowledge.
Emperors and intellectuals alike understood the value of framed calligraphy in conveying sentiments, goals, and ideals. Imperial decrees and important documents were frequently published in calligraphic style, with intricate designs framing them to indicate their importance.
Framed Calligraphy Today: A Blend of Tradition and Modernity
Framed Chinese calligraphy is still a treasured practice in the modern world. However, its application has expanded beyond scholarly investigations. Framed calligraphy is now in high demand for a variety of reasons.
Artistic Expression: Many contemporary artists continue to explore the beauty of calligraphy while challenging traditional techniques. Framed calligraphy pieces are collected as works of art that strike a profound aesthetic and emotional chord with viewers.
Interior Decor: Framed calligraphy has found a home in contemporary interior design. These works of art bring a touch of cultural refinement to homes and businesses by mixing traditional charm with modern aesthetics.
Personalization & Gifts: Framed calligraphy is a popular option for personalized gifts and special occasions. People hire calligraphers to create personalized pieces that express their feelings, blessings, or goals.
Conclusion: A Timeless Tradition in Modernity
Framed Chinese calligraphy, with its rich history and diverse contemporary applications, exemplifies the continuing power of artistic expression. These brushstrokes, which continue to adorn our homes, offices, and cultural spaces, connect us to the knowledge of the past and inspire us for the future. Framed calligraphy is a live art form that bridges the gap between tradition and contemporary, reminding us of the eternal beauty of ink and brush on paper.
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Wenling, China
A woman repairs fishing nets at a port during the annual summer fishing ban, which covers the Bohai Sea, the Yellow Sea, the East China Sea, and parts of the South China Sea.
Photography by Liu Zhenqing
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Fated Meeting
Ouyang Zizhen x A'Qing fanfic
Genre: Fluff, Dates, Aged-Up Characters, Canon Divergence, Happy Ending
Pairing: Ouyang Zizhen/A'Qing
Summary: AQing bumps into Ouyang Zizhen and steals from him, only to be asked out for a meal. What do they learn about each other, and what happens when AQing holds onto Ouyang Zizhen's money pouch until he starts searching for it?
Author: Tinyjiyang (AO3/Twt)
Commissioned by @briee-elle
Read it here
#the untamed#mdzs#ouyang zizhen#a'qing#aqing#mdzsficrecs#mdzs fic#the untamed fic#mylastbraincql#fytheuntamed#oyzzxaq#zhenqing
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Figure 1. Zheng Xiaoxu’s Portrait (from The Mad Monarchist)
Graduate Research: Chinese Scroll and Fan Work, Part 9
This week we turn our eye to two undated couplets (Figures 2 and 3) by Chinese statesman, diplomat, and calligrapher Zheng Xiaoxu (1860-1938, Figure 1) from our Zhou Cezong Collection of Chinese scroll and fan work.
According to celebrated Chinese writer Lin Yutang (1895-1976, twice nominated for Nobel Prize in Literature), in appreciating Chinese calligraphy, “the meaning is entirely forgotten, and the lines and forms are appreciated in and for themselves.” Thus, let’s skip the literal meaning of these two couplets and just focus on their lines and structures. And hopefully, this focus will help us to date them.
Figure 2. UWM Special Collections (cs 000004)
Figure 3. UWM Special Collections (cs 000054)
In 1889, Zheng became the protégé of Weng Tonghe (1830-1904), who was Guanxu Emperor’s teacher and one of the most supportive figures of the Hundred Days’ Reform. Influenced by Weng’s artistic taste, Zheng regarded the calligraphy of Tang Dynasty calligrapher Yan Zhenqing (709-785) as a model. In one Zheng’s early calligraphic examples (Figure 4), he exhibited a distinctive, plump, and powerful stroke with a well-knit, balanced structure, which is similar to Yan’s Record of Duobao Pagoda (Figure 5, the forefather of brushwork in standard writing) written in 752. In addition, Zheng imitated Yan’s round brush by adopting “hiding” and “protecting” movement of the brush tip (according to ancient calligraphic theorist Cai Yong, calligraphers should “hide the head” and “protect the tail” of the brushstroke). However, because the turn and thrust is limited, the image is static and frontal, confined to a flat linear schema, and showing rigidity and lassitude.
Figure 4. Zheng’s Early Calligraphy (from this source)
Figure 5. Yan Zhenqing’s Record of Duobao Pagoda (from this source)
Immediately after Xinhai Revolution in 1911, Zheng spent some time in Shanghai with his boon companions such as Chen Sanli, whom I discussed in a previous post, and Shen Zengzhi, whose cursive hanging scroll is also preserved in our Zhou Cezong Collection. During this period, he maintained an eclectic interest in ancient calligraphic rubbings, such as those from stone inscriptions, epitaphs, Buddhist votive stelae, and cliff engravings created in the Han (202 BC-220 AD) and Northern Dynasties (386-581). Our first couplet in Figure 2 is the epitome of his inclusive studies of the stelae. For instance, the longest horizontal stroke of 寺 (Figure 6) presents a dramatic thinning-and-thickening brush movement, which is akin to brush style of the horizontal line in下（Figure 7) from the Stele on Ritual Implements in the Confucian Temple (Liqi Stele, dated 156 CE). According to Yang Shoujing (1839-1915), whose work is also preserved in our collection, this stele has an eccentric instability concealed in the level-headed stability; and a strict denseness hidden in the elegant sparseness. Zheng’s 寺 is the symbol of this contradictory yet complementary comment. Another example of Zheng’s cross-fertilization could be detected in the character “分” and “明” in Figure 8. The rigid 丿 in “分”, and the rugged 𠃌 in “明” can find similar genealogical traits from their counterparts in Figure 9, which is from Yang Dayan Zao Xiang Ji created around 506 AD. Here, Zheng’s previous flat schema has been transformed to some contrasting variations in a sense of two-dimensionality, bringing vitality to the works. Nevertheless, the rigidity still permeates; and ruggedness is also his Achilles’s heel, indicating a smidgen of strenuousness, which is at variance with Chinese artistic standard of naturalness.
Figure 6: Detail from Figure 2. Figure 7: From Liqi Stele (Palace Museum Collection)
Figure 8: Detail from Figure 2. Figure 9: From Yang Dayan (Harvard Collection).
From 1906 to 1907, during the excavation in the deserts of Northern China, Sir Marc Aurel Stein found a group of wooden slips with calligraphic inscriptions written around 98 BC. In 1912, his friend Édouard Émmannuel Chavannes sent the copy of these slips to Luo Zhenyu (1866-1940), whose couplet scroll in Oracle Bone script is also preserved in our Zhou Cezong Collection. Luo invited Wang Guowei (1877-1927, Liang Qichao’s friend), a great sinologist, to collate, edit, and interpret those slips, which became the famous monograph entitled Liu Sha Zhui Jian (The Lost Wooden Slips Excavated in the Flowing Sands) published in 1914.
When Zheng saw this publication, he was enchanted by the calligraphic values of these slips, as he contended that with the finding of these slips, the secrecy of calligraphy would be thoroughly revealed. Generally speaking, compared with the standardized clerical writing in Figure 7, the running or cursive characters on these slips were rendered with undulation and flexibility (see Figure 10 and 11), devoid of axial balance and austere sublimity. By turning and flicking the brush in a silent pirouette on the paper, the slip writer constantly changed in speed and direction, suggesting a strong foreshortening and movement in space. This untrammeled style significantly enlivens Zheng’s artistic idioms. In Figure 12, the slanting angle and the flaring, wavelike motion of the second horizontal stroke bears uncanny resemblance to those of the first horizontal stroke in Figure 10. The brush is fully articulated in a vivacious spontaneity, carrying a natural three-dimensionality.
(From left to right) Figure 10: From Luo Zhenyu, Liu Sha Zhui Jian, p. 65. Figure 11: From Liu Sha Zhui Jian, p. 64. Figure 12: Detail from Figure 3.
From these three works, Zheng shows his audience the evolution of his mimetic representation. For the first phrase (Figure 4), his imitation of Yan was restricted by insipid flatness and slight flexure. After 1911, his exploration to ancient stele rubbings (Figure 2) gave his works a contrasting vitality, though the rigidity still lingers. For the final phrase (Figure 3), the pristine style of the wooden slips provided him a fresh impetus to awaken his vivacity, creating organic relationship in the image.
Figure 13. Three Greek Statues (from ca. 560 BC to 480 BC)
From Wen C. Fong, Art as History: Calligraphy and Painting as One (New Jersey: Princeton University Press, 2014), p. 113.
The art historian E. H. Gombrich once made a similar-style comparisons for a group of ancient Greek statues (Figure 13). Naming them as the representation of the “Greek miracle” which illustrated the advancement of Western European civilization, he indicated in pictorial representation, archaic art began from restricted frontal schema, and then moved to the gradual adjustment to the natural appearances. This phenomenon can be equally applied to analyze Zheng’s work, which could be seen as his gradual accumulation of corrections due to the observation of ancient artworks.
Chinese art historian Wen C. Fong proposed the possible reason for this phenomenon. He noted that the disillusionment of the ancient literati with Chinese politics made them “turn away from the world of human affairs” and sought spiritual solace in the pursuit of artistic and literary expression. The impulse to express themselves in art led to the enlivening of Chinese art and civilization. Zheng is the exemplar of this explanation. He was once a most celebrated constitutionalist in the late Qing. After 1911, he lived in Shanghai as a loyalist to the defunct Qing Dynasty until February 1924, when he went to the Forbidden City to serve as a trusted advisor to Puyi (the last Chinese emperor, 1906-1967). Within these thirteen years, he became disillusioned with politics, and began to regard art as his safety valve, thereby pushing the boundaries of his artistic practices.
From these analyses, we can hypothesize that these two couplets in Special Collections were created during the same period of time (1911-1924). Figure 2 was created first, foretelling the coming of the more mature style in Figure 3. Most importantly, these analyses give us a good example to see how the student and scholar of Chinese calligraphy may use brushstroke and structure as evidence to evaluate, authenticate, and date artworks.
After Puyi and Zheng were evicted from the palace in November 1924, they settled in the Japanese concession of Tianjin. In 1931, under Zheng’s arrangement, Puyi went to Manchuria and became the leader of the Manchurian state, Manchukuo. Zheng became the regime’s Prime Minister with Japanese support. This collaboration with the Japanese tarnished the reputation of Zheng’s previous political and artistic achievements.
– Jingwei Zeng, Special Collections graduate researcher.
#graduate research#Jingwei#Chinese scrolls#Chinese calligraphy#Chinese art#Zheng Xiaoxu#Yan Zhenqing#Chinese politics#calligraphy#art history#couplet#Zhou Cezong Collection#Tse-Tsung Chow Collection
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Li Bi, from Alchemists, Mediums, and Magicians: Stories of Taoist Mystics
Alchemists, Mediums, and Magicians: Stories of Taoist Mystics is a collection of biographies of 144 historical figures associated with Daoism, compiled under the title Xuanping lu 玄品錄 by daoist Zhang Tianyu 張天雨 (1279-1350) and translated by Thomas Cleary.
Li Bi was styled Changyuan. He originally lived in Demon Valley. At the age of seven he knew how to write compositions, and in 728 he was summoned to meet the emperor as an extraordinary child. He was most favored by Zhang Jiuling,(67) who called him his little friend.
When he grew up, he studied widely and became expert in the I Ching. He used to travel around to Mount Song, Mount Hua, and Mount Zhongnan, seeking the spiritual immortals’ art of not dying.
During the Tianbao era [742–755], he went to the imperial establishment and presented Proposal for Restoring the Yellow Emperor’s Nine Cauldrons. The emperor, considering him quick-witted, had him lecture on Lao-tzu. He had a command of the principles and obtained the position of attendant scholar.
When Xiaozong [should be "Suzong": it seems the translator confused 肃 with 萧] assumed the throne at Lingwu in 756, he was making inquiries searching for him when Bi showed up on his own. Once he had interviewed him, the emperor was pleased, having had the successes and failures of the empire set forth to him. He was going to give Bi an official post, but Bi stoutly refused. Instead he asked to be allowed to attend discussions of national affairs as a guest and join the imperial entourage on excursions. Everyone pointed and said, “The priest is the ruler, while the layman is the hermit.” [I think it's a mistranslation of the phrase 衣黃者圣人也 衣白者山人也 - "In the yellow dress - the ruler, in the white dress (i.e. in commoner's clothes) - the hermit."]
Thus the emperor bestowed the gold seal and purple cord of court rank upon him and appointed him minister of war for the Infantry of the Chief Commander, king of Guangping.
The emperor once said, “You wait on the deities above, you are our teacher in the center, and now you judge the infantry of Guangping below. Thus are we, father and son [emperor and king] sustained by the principles of your Way.” Cui Yuan(68) and Li Fuguo(69) were jealous of the closeness and confidence Bi enjoyed. Bi feared there would be trouble and requested retirement on Mount Heng. An imperial decree provided him with a salary of a third-ranked official, presented him with the outfit of a retired gentleman, and prepared a dwelling for him on Mount Lu.
Bi once took a curved pine branch to use as a backrest, calling it “fostering balance.” Later he found one shaped like a dragon, which he presented to the emperor. All around vied to imitate this.
When Daizong became emperor [in 763], he summoned Bi and housed him in the library of Penglai Hall. At first he didn’t eat meat, but since rank was bestowed on him he was forced to eat meat by imperial decree.
When Dezong [r. 780–805] was at the Sanctuary in Service of Heaven, he summoned Bi to his temporary headquarters and appointed him policy adviser. Bi first had a road cut through the mountains to the Triple Gate [sluices of the Yellow River] to facilitate shipping. Because of this effort, he was promoted to minister of rites, then in three years to associate manager of affairs.
The emperor once casually remarked, “Lu Qi(70) was puritanical and outspoken, but he had little learning and could not broaden us with the ancient Way. Everyone pointed out his treachery, but we never noticed.”
Bi replied, “Had Your Majesty been able to sense Qi’s evil, how could the troubles of the Jianzhong era(71) have occurred? Li Kui(72) combined the foreign commanders of Chinese armies, while Yan Zhen-qing(73) used Xilie. The damage done to longstanding benevolence and goodwill was great indeed.
“Also, Yang Yan(74) was condemned, though not executed; Lu Qi brought about his downfall and made Guan Bo(75) minister. When Li Huaiguang(76) became successful, Lu Qi goaded him into revolt. This is deceiving heaven.”
The emperor said, “What you say happened, true enough, but you must know what Sang Damo(77) said about the chaos of the Jianzhong era, that it was destined to be so?”
Bi replied, “So-called destiny is something said after the fact. Leaders make destiny; they shouldn’t plead destiny. If you plead destiny, then there’s no rewarding good and no punishing evil!”
The emperor said, “I’ll try not to say ‘destiny’ anymore.”
Shortly he was made a scholar of the Library Honoring Literature, working on national history. Bi requested that the first day of the cycle of the second lunar month be made the Day of Harmony in the Center(78) instead of the last day of the lunar cycle of the first month and that on that occasion the great ministers be given royal relative residence rulers, signifying the sizing up of bureaucrats. He presented a book on agriculture to teach basic production. The emperor was very pleased and issued an order making the second day of the second month, the third day of the third month, and the ninth day of the ninth month three official holidays, when everyone was to be given a bonus of a string of a thousand cash and invited to a banquet.
In the eighth month of 788, the sun eclipsed the two stars associated with literature and culture. Bi said, “Those stars govern maps and books; among the great ministers there will be someone aggrieved. Since I’m both a managing minister and a scholar, it must be me.” The next year, as it turned out, he died.
Bi had free access to the imperial palace, and he worked for four emperors, so he was the object of the jealousy of crafty sycophants numerous times, yet he always escaped by his wits. Moreover, time and again there were factional plots, of which he was able to alert the emperor, and he also improved and enlightened government himself. The restoration of the two capitals praised by historian Liu Bi was due in large part to the planning of Li Bi; his contribution was even greater than Lu Lian’s(79) and Fan Li’s.
Footnotes:
67. Zhang Jiuling (678–740) was a scholar and poet who held a number of high positions under the Tang dynasty, including director of the Secretariat and grand councillor.
68. Cui Yuan was a regional inspector and officer of the Secretariat under Emperor Suzong (r. 756–762).
69. Li Fuguo (704–762) was a eunuch who held high offices in the department of the military under Emperor Suzong.
70. Lu Qi was prime minister under Emperor Dezong, who is faulted for judging people on appearances.
71. This refers to a rebellion of regional authorities. The Jianzhong era lasted from 780 to 784.
72. Li Kui (711–784) held numerous offices under the Tang dynasty, including commissioner for entry into alliance with Tufan. Tufan was a Tibetan state considered a major threat to Tang dynasty China.
73. Yan Zhenqing (709–785) commanded several successful battles against the rebel An Lushan and served in a number of posts under the Tang dynasty, including minister of works and minister of justice. When Li Xilie rebelled, Lu Qi sent Yan to negotiate a surrender, intending to encompass Yan’s death. Yan stood up to Li’s threats and won the latter’s respect. Yan was later assassinated.
74. Yang Yan (727–781) was briefly a minister of state for Emperor Dezong. He is noted for reforming the tax system.
75. Guan Bo held many posts under the Tang dynasty. He is said to have been promoted for prime minister by Lu Qi because the latter considered him easy to control.
76. A regional inspector.
77. A famous prognosticator.
78. On this occasion the emperor customarily gave a banquet for the ministers of state.
79. That is, Lu Zhonglian.
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JueYing is very excited to be an auntie to a-Qing's kids? she makes them presents and looks forward to cuddling them. She makes xiao xingchen round 2 a little bug plushie.
Jueying, Xingchen, and caterpillar-shidi like to gather for cuddles in A-Qing's lap! She's melting with love. Meanwhile, husband OYZZ is sketching a portrait of his tiny new family + his little sister-in-law.
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Yan Zhenqing Kai Shu Writing S ... Price 17.99$ CLICK TO BUY
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Mathematics of scale: Big, small and everything in between
by Mitchell Newberry
How many lakes are in Alaska? Thermokarst lakes on Alaska’s North Slope are self-similar and fractal. Painting by Cherissa Dukelow, CC BY-SA
Breathe. As your lungs expand, air fills 500 million tiny alveoli, each a fraction of a millimeter across. As you exhale, these millions of tiny breaths merge effortlessly through larger and larger airways into one ultimate breath.
These airways are fractal.
The branches within lungs are an example of self-similarity. Brockhaus and Efron Encyclopedic Dictionary/Wikimedia
Fractals are a mathematical tool for describing objects with detail at every scale. Mathematicians and physicists like me use fractals and related concepts to understand how things change going from small to big.
You and I translate between vastly different scales when we think about how our choices affect the world. Is this latte contributing to climate change? Should I vote in this election?
These conceptual tools apply to the body as well as landscapes, natural disasters and society.
Fractals everywhere
In 1967, mathematician Benoit Mandelbrot asked, “How long is the coast of Britain?”
It’s a trick question. The answer depends on how you measure it. If you trace the outline on a map, you get one answer, but if you walk the coastline with a meter stick, the result is quite different. Anyone who has tried to estimate the length of a rugged hiking trail from a map knows the treachery of the large-scale picture.
Satellite image of Great Britain and Northern Ireland. NASA
That’s because lungs, the British coastline and hiking trails all have fractality: their length, number of branches or some other quantity depends on the scale or resolution you use to measure them.
The coastline is also self-similar – it’s made out of smaller copies of itself. Fern fronds, trees, snail shells, landscapes, the silhouettes of mountains and river networks all look like smaller versions of themselves.
That’s why, when you’re looking at an aerial photograph of a landscape, it’s often hard to tell whether the scale bar should be 50 km or 500 m.
Your lungs are self-similar, because the body finely calibrates each branch in exact proportions, making each branch a smaller replica of the previous. This modular design makes lungs efficient at any size. Think of a child and an adult, or a mouse, a whale. The only difference between small and large is in how many times the airways branch.
Self-similarity and fractality appear in art and architecture, in the arches within arches of Roman aqueducts and the spires of Gothic cathedrals that mirror the forest canopy. Even ancient Chinese calligraphers Huai Su and Yan Zhenqing prized the fractality of summer clouds, cracks in a wall and water stains in a leaking house in 722.
Scale invariance
Self-similar objects have a scale invariance. In other words, some property holds regardless of how big they get, such as the efficiency of lungs.
In effect, scale invariance describes what changes between scales by saying what doesn’t change.
A sketch from Leonardo da Vinci’s notes on tree branches. Fractal Foundation
Leonardo da Vinci observed that, as trees branch, the total cross-sectional area of all branches is preserved. In other words, going from trunk to twigs, the number of branches and their diameter change with each branching, but the total thickness of all branches bundled together stays the same.
Da Vinci’s observation implies a scale invariance: For every branch of a certain radius, there are four downstream branches with half that radius.
Earthquake frequency has a similar scale invariance, which was observed in the 1940s. The big ones come to mind – Lisbon 1755, San Francisco 1989 – but many small earthquakes occur in California every day. The Gutenberg-Richter law says that earthquake frequency depends on the size of the earthquake. The answer is surprisingly simple. A tenfold bigger earthquake occurs roughly one-tenth as often.
Society and the power law
A 19th-century economist Vilifredo Pareto – famous in business school for the 80/20 rule – observed that the number of families with a certain wealth is inversely proportional to their wealth, raised to some exponent. Pareto measured the exponent for different years and different countries and found that it was usually around 1.5.
Pareto’s wealth distribution came to be known as the power law, ostensibly because of the exponent or “power.”
Anything self-similar has a corresponding power law. In an April paper, my colleague and I describe the corresponding power law for lungs, blood vessels and trees. It differs from Pareto’s power law only by taking into account specific ratios between branches.
The sizes of fortunes then are akin to the sizes of tree twigs or blood vessels – a few trunks or large branches and exponentially more tiny twigs.
Patterns in an oak’s branches. Schlegelfotos/shutterstock.com
Pareto thought of his distribution of wealth as a natural law, but many different models of social organization give rise to a Pareto distribution and societies do vary in wealth inequality. The higher Pareto’s exponent, the more egalitarian the society.
From understanding how humans are made up of tiny cells to how we affect the planet, self-similarity, fractality and scale invariance often help translate from one level of organization to another.
About The Author:
Mitchell Newberry is an Assistant Professor of Complex Systems at the University of Michigan
This article is republished from our content partners at The Conversation under a Creative Commons license.
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