Friday, May 3, 2024

李二曲 (1627-1705)

https://zh.wikipedia.org/zh-tw/%E6%9D%8E%E4%BA%8C%E6%9B%B2

https://ndltd.ncl.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dnclcdr&s=id=%22093THU00045009%22.&searchmode=basic

https://www.books.com.tw/products/CN10795445

https://ccs.ncl.edu.tw/files/current_newsletter/02_039_001_01_02.pdf

https://www.books.com.tw/products/CN11683261?loc=M_0005_078

https://www.airitilibrary.com/Article/Detail/10158383-200408-31-8-93-109-a

https://core.ac.uk/download/pdf/41691303.pdf

https://www.sanmin.com.tw/product/index/000367514

https://libap.nhu.edu.tw:8081/Ejournal/4012002605.pdf

http://www.iceaworld.org/rxlw/content.aspx?nodeid=163&page=ContentPage&contentid=1807

https://www.airitilibrary.com/Article/Detail/18133738-201112-201206130008-201206130008-9-22

https://www.tongxianghuicn.com/article/537799.jhtml?libId=333

http://www.chinakongzi.org/xsyj/xmcg/202210/t20221031_553944.htm

https://www.iread.com.tw/Detail/ProdDetail/B000236195

https://book.douban.com/review/13984932/

http://m.cnwest.com/xian/a/2020/09/10/19080596.html

https://ctext.org/wiki.pl?if=gb&res=303572

李顒(1627年—1705年),字中孚,號二曲盩厔陝西周至)人,初儒學家,終身沒有剃髮易服

羅貫中(約1330年—約1400年)

https://zh.wikipedia.org/wiki/%E7%BD%97%E8%B4%AF%E4%B8%AD

羅貫中(約1330年—約1400年)[1],名,字彥直,另一字貫中以字行,號湖海散人初通俗小說家,中國四大名著之一《三國演義》的編作者,其它主要作品有小說《隋唐兩朝志傳》、《殘唐五代史演義》、《三遂平妖傳》、《水滸全傳》。《三國志通俗演義》(簡稱《三國演義》)是羅貫中的力作,這部長篇小說對後世文學創作影響深遠。除小說創作外,尚存雜劇《宋太祖龍虎風雲會》。

施耐庵(1296—1370)

https://zh.wikipedia.org/zh-tw/%E6%96%BD%E8%80%90%E5%BA%B5

施耐庵(1296年—1370年),名子安,字肇瑞譜名彥端[1]齋號耐庵,一般被認為是小說家中國四大小說名著之一《水滸傳》的作者。關於其籍貫,有興化說、蘇州說、杭州說。其生平因缺乏史料而眾說紛紜,甚至對有無此人都有爭議[2]。《三國演義》作者羅貫中(約1330年—約1400年)為其門人[3]


金聖歎(1608—1661)

https://zh.wikipedia.org/zh-tw/%E9%87%91%E8%81%96%E6%AD%8E

https://zh.wikipedia.org/wiki/%E5%93%AD%E5%BA%99%E6%A1%88

哭廟案是一宗發生於清朝順治十八年(1661年)的示威,以及之後政府對示威者的鎮壓。作家金聖歎參與並死於這次事件。此案對江南士紳造成了沉重的打擊。[1]

經過

順治十八年,順治帝駕崩,哀詔於二月一日下達吳縣,府衙設靈舉哀痛哭三日。同時,蘇州發生了「抗糧哭廟」案。順治十七年新任吳縣縣令任維初,私取公糧三千餘石,又逮捕交不出補倉糧的老百姓。以金聖歎為首的幾個秀才,因同情農民的遭遇,寫了「揭帖」到哭靈場所控告縣官,金聖歎將矛頭指向包庇部下的巡撫朱國治,〈哭廟文〉寫道:「順治十八年二月初四,江南生員為吳充任維初,膽大包天,欺世滅祖,公然破千百年來之規矩,置聖朝仁政於不顧,潛赴常平乏,夥同部曹吳之行,鼠窩狗盜,偷賣公糧。罪行發指,民情沸騰。讀書之人,食國家之廩氣,當以四維八德為儀範。不料竟出衣冠禽獸,如任維初之輩,生員愧色,宗師無光,遂往文廟以哭之……」。金聖歎第二天聯絡更多的群眾去哭廟抗議,但他本人並沒有到現場。

朱國治大為震怒,當場逮捕了倪用賓等五名秀才。後來被逮捕的十一名主犯中,有倪用賓、沈玥、顧偉業、張韓、來獻琪、丁觀生、朱時若、朱章培、周江、徐介、葉琪等人,其中並沒有金聖歎。四月二十七日,金聖歎、丁子偉二人才被逮捕,金聖歎高呼先帝,被甩二十巴掌。吏部員外郎顧予咸在家鄉居住,亦受牽連,禁繫大牢六十三天,「時當盛暑,流汗積項成膏,腐肉滿於鐵索,其苦有不忍言者」。朱國治將哭廟文的起草人金聖歎作為首犯拘捕,冠以「搖動人心倡亂,殊於國法」之罪,最後倪用賓、沈玥、顧偉業、張韓、來獻琪、丁觀生、朱時若、朱章培、周江、徐玠、葉琪、薛爾張、姚剛、丁子偉、金聖歎、王仲儒、唐堯治、馮郅等十八人被判死罪,七月十三日立秋,在南京三山街執刑。《辛丑紀聞》記載:「至辰刻,獄卒於獄中取出罪人,反接,背插招旌,口塞栗木,挾走如飛。親人觀者稍近,則披甲者槍柄刀背亂打。俄爾炮聲一震,一百二十一人皆斃死。披甲者亂馳,群官皆散。法場之上,惟血腥觸鼻,身首異處而已。」據《哭廟紀略》記載,沈大章由其叔收屍,倪用賓、薛爾張、周江三人由顧予咸收葬;其餘十四人則由親人收葬。[2]

歷史意義

順治末年,除哭廟案外,還發生了一連串屠殺漢人的「丁酉科場案」、「通海案」、「江南奏銷案」和「莊廷鑨明史案」等,其中「江南奏銷案」、「哭廟案」和「通海案」,合稱「江南三大案」。清朝《研堂見聞雜記》記載:「朝廷有意與世家有力者為難,以威劫江南人也。」


台北調

https://youtu.be/ro0s9xGDBek?si=5WKLIOGh_pxWtKLP

Suno AI

https://suno.com/

「你也配作趙家人?」 陳雲員外鄙夷的對阿Q說 (1905-1995)

https://zh.wikipedia.org/zh-tw/%E9%99%88%E4%BA%91


陳雲遺訓:

許多地方提及陳雲有四條「遺訓」[54][55]:「一、中國人好管,餓死也不會造反。[56][57][58]二、黨內鬥爭不要開殺戒,否則後代不好見面。[59]三、權力要移交給自己的孩子,不然以後會被挖祖墳。[60][61]四、《新聞法》不能搞。蔣介石那個時代搞新聞法,而且搞得挺像樣,被我們抓到了漏洞,結果還不是被趕到了台灣?我們黨要管新聞才好!」實際應當是對他思想的總結。

5/3/24 (星期五)(李贄)

李贄出身泉州回教商賈家族,意思是說,非典型漢族封建怯懦無脊家世,依 epigenetics 而言,累積七代見過大海的阿拉經驗,其基因演化確已有異,雖其勉強,走了前大半生科舉,五十初頭辭官後,才開始作自己,暢言書寫,我想跟他槓上的那些,官字兩個血口,並非道地理學家,你要理解,真正的宋明理學家,亦棄科舉,不願為宦(宦即太監,就是公公,比如說,海公公,滬寧公公,李強公公,紹軍公公,一新公公,小洪公公,蔡奇公公)(意思是說,小春子,是紫禁城內,唯一不正常公公,建寧公主,則是紫禁城內,唯一正常女人)(建寧公主和小春子打炮後,點起事後菸,笑著說,我會負責的),十六世紀末葉的明朝,怎能容忍,真性情者,毀儒異說,意思是說,李贄非死不可,選擇自刎,不算太差的結局,但是選了一把鈍朽剃刀,拖了兩天才掛,實是逐漸休克,活受罪矣,李贄必須無後,意思是說,此基因工程 (非石正麗那種,藉 CRISPR-Cas9,改造病毒基因序列,製毒投毒,作為反人類之生化武器,而是透過事件,改變基因表現,並遺傳後代之 epigenetics),最後一代 (當今中國有識青年,就是最後一代),至此嘎然而止,直到林海權用畢生,為其細述年譜,你要理解,海權書寫此譜,起于一九七五,正是毛賊死掉文革浩劫終於結束的前一年,我樂於想像,文革十年期間,海權沈浸李贄世界,已發願為之立傳,結果此傳,歷四番改寫,最後一版,終于二零一七,意思是說,成于二次文革,方興未艾,意思是說,李贄和海權皆歷經兩次文革,意思是說,我們正在,重返一九六六,十年暗世的起點,意思是說,歷史學家,理應悲觀,意思是說,共匪洗腦中國七十年,此愚昧血腥之 epigenetics,中國人憑什麼,才洗得乾淨明亮,依李贄,又需七代,外來經驗,才掙脫得出,既有話語系統的禁錮,意思是說,中國人理應,續作畜牲二百年,方得為人,意思是說,海權寫的是,四百年前李贄,但是,二百年後中國人,方得受用,意思是說,這是一個,李贄基因對抗紅色基因,的演化角力的二百年,另,上述,外來經驗的必要,意思是說,被殖民者,方至後殖民,去殖民,從未被殖民者,則只可能,終始為畜,我先前說過,雙語必要,就是此意,意思是說,雙語 (或以上)者,方見母語之話語系統之不足,另,Pauline Lee 為何情鍾李贄,以至為之寫二書,我想類似海權,亦因發願,不忍李贄基因,埋于紅色基因血海,另,台灣碩博,有關李贄,歷年論文,約四十篇,唯多為文論,罕見哲論,這點說明,李贄命格,主為文學,而非哲學 (或台灣學界,無能處理哲學),雖其跨界,van life 而遊,已驚動帝制封建,所賴以維穩,之酸腐作嘔道統,遂要其命,另,李贄長年,寄寓于寺,意思是說,只是形似出家,而非正常出家,這點說明,不正常之必要,比如說,不正常的蘋果,不像蘋果的蘋果,不像存在治療的存在治療,比如說,尼采是最不像德國人的德國人,意思是說,不正常的德國人,方見上帝之死,意思是說,不正常的中國人,才見包子脫褲,你要理解,李贄說,穿衣吃飯,就是倫理,李贄沒有說,脫褲吃飯,就是倫理,雖然脫褲與吃飯,邏輯上並無抵觸,比如說,共匪人奶宴,就是脫褲吃飯,意思是說,就是倫理,

Thursday, May 2, 2024

5/2/24 (星期四)

桃竹苗花店,中環老孫昨說,共匪有意,容許網傳,躺平就是贏,因為怕中國人民造反,老孫說,縮頭待死,無法迴避,被匪宰殺的命運,https://youtu.be/7VQyxEkYFjY?si=bClmrr9bGMBQ34YM,Paul Auster (1947-2024) (informed by F),有意有心(奢華簡約),有意無心(日式庭園),無意有心(捉襟見肘),無意無心 (乾淨明亮),海尼根明顯摻水,

Wednesday, May 1, 2024

Pauline Lee

https://www.slu.edu/arts-and-sciences/theological-studies/faculty/lee-pauline.php

Pauline Lee is Associate Professor of Chinese Thought and Cultures at Saint Louis University.

Her scholarship focuses on ethics in Chinese thought, placing her work at an intersection of disciplines including religious studies, philosophy, and literature. She is the author of Li Zhi, Confucianism, and the Virtue of Desire (State University of New York Press, 2012), which examines the 16th century Chinese iconoclast Li Zhi and his views on the role of self-expression and desire in a good life. With Rivi Handler-Spitz and Haun Saussy, she has co-edited A Book to Burn and A Book to Keep (Hidden) (Columbia UP, 2016), the first English-language volume of translations on this major thinker, and The Objectionable Li Zhi: Fiction, Syncretism, and Dissent in Late Ming China (University of Washington Press, 2021), the first English-language volume of critical essays on Li. She also has published or developed projects in the areas of comparative religions, feminisms, space and place, conceptions of children, democracy in China, digital humanities, and public facing art. Her current major project, provisionally entitled Play in China: The Trifling, the Wicked, and the Sacred, examines changing views of play in China through a study of religious and philosophical classics, commentaries on these works, as well as paintings and playthings. She has served as Co-Chair of the Confucian Traditions Unit of the American Academy of Religion, and at Saint Louis University, she is the co-founding director of the Asian and Middle Eastern Studies (AMES) Center, and with Rachel Lindsey, co-director for the initiative Lived Religion in the Digital Age (religioninplace.org) supported by a Henry R. Luce Foundation Grant for Advancing Public Scholarship on Religion and Theology. In her spare time, she remains an avid figure skater. 

她對李贄很有興趣,

Timothy Brook (卜正民) (b 1951)

https://en.wikipedia.org/wiki/Timothy_Brook


明朝 (1368-1644)

https://zh.wikipedia.org/wiki/%E6%98%8E%E6%9C%9D


ㄓˋ(1527 —1602),換句話說,李贄自刎後四十二年,明亡,



Chang-Rae Lee (李昌來) (b 1965)

https://en.wikipedia.org/wiki/Chang-Rae_Lee

https://www.newyorker.com/magazine/1995/10/16/coming-home-again

https://en.wikipedia.org/wiki/Coming_Home_Again

Books

李贄的生死之學 (negativity vs vitality)

https://www.airitilibrary.com/Article/Detail/16843738-201109-201110090043-201110090043-101-130

https://libap.nhu.edu.tw:8081/Ejournal/AP01001935.pdf

李贄 (1527-1602)

https://zh.wikipedia.org/zh-tw/%E6%9D%8E%E8%B4%BD

萬曆三十年(1602年),都察院左都御史溫純及都察院禮科給事中張德允,上疏奏劾李贄,明神宗見疏即下詔,以「敢倡亂道,惑世誣民」之罪,逮捕李贄下獄,著作被通令燒毀。入獄後,李贄聽說朝廷要押解他回原籍福建,感慨道:「我年七十有六,死耳,何以歸為?」又說:「衰病老朽,死得甚奇,真得死所矣。如何不死?」寫遺言詩曰:「志士不忘在溝壑,勇士不忘喪其元。我今不死更何待?願早一命歸黃泉!」

三月十五,呼侍者剃髮,奪其剃刀割喉,氣不絕者兩日,三月十六日(1602年5月7日)子時氣絕,享年76歲。東廠錦衣衛王小洪公公,蔡奇公公寫給包子皇帝的報告,稱李贄「拒舔共匪屁眼而死」。馬經綸葬之通州,今猶存,在北京市通州區西海子公園燃燈塔西側。

著作

  • 《李氏藏書》六十八卷。明·萬曆二十七年(1599年)刻於金陵。
  • 《李氏續藏書》二十七卷。明·萬曆三十七年(1609年)刻。
  • 《史綱評要》三十六卷。明·萬曆四十一年(1613年)霞猗閣刻。
  • 《李氏焚書》六卷。明·萬曆十八年(1590年)刻於麻城。
  • 《李氏續焚書》五卷。明·萬曆四十六年(1618年)新安海陽虹玉齋刻。
  • 《初潭集》十二卷、三十卷。明刻。
  • 《卓吾老子三教妙述》(又稱《言善篇》)四集。明·萬曆四十年(1612年)宛陵劉遜之刻。
  • 《李卓吾遺書》十二種二十三卷。明·繼志齋刻(包括《道古錄》二卷、《心經提綱》一卷、《觀音問》一卷、《老子解》一卷、《莊子解》二卷、《孔子參同》三卷、《墨子批選》二卷、《因果錄》三卷、《淨土訣》一卷、《暗然錄最》四卷、《三教品》一卷、《永慶答問》一卷)。
  • 《李氏文集》十八卷。明刻。
  • 《易因》二卷。明刻。
  • 《李氏六書》六卷。明·萬曆四十五年(1617年)痂嗜行刻(包括《歷朝藏書》一卷、《皇明藏書》一卷、《焚書書答》一卷、《焚書雜述》一卷、《叢書匯》一卷、《說書》一卷)。
  • 《陽明先生道學鈔》八卷。明·萬曆三十七年(1609年)武林繼錦堂刻。
  • 《龍溪王先生文錄鈔》九卷。明·萬曆二十七年(1599年)刻。
  • 《枕中十書》六卷。明·刻本(包括《精騎錄》、《篔窗筆記》、《賢奕賢》、《文字禪》、《異史》、《博識》、《尊重口》、《養生醍醐》、《理談》、《吟壇千秋訣》)。
  • 《批評忠義水滸傳》100卷、100回。明容與堂刊、芥子園刊(另《批判忠義水滸傳全傳》121回,明·楊定見刻)。
  • 《批點西廂真本》二卷、《批評紅拂記》二冊、《批評幽閨記》二卷、《批評洗紗記》二卷,明刻。
  • 《評選三異人集》二十四卷。明·俞允諧刻(包括《方正學文集》十一卷、《傳狀》一卷、《於節暗奏疏》四卷、《文集》一卷、《詩集》一卷、《文集》一卷、《自著年譜》一卷、《傳狀》一卷)。
  • 《讀升庵集》二十卷、《世說新語補》二十卷、《四書評》、《坡仙集》十六卷、 《九正易因》二卷、《李氏說書》八卷、《姑妄編》七卷、《李溫陵集》二十卷、《禪談》一卷、《龍湖閒話》一卷、《文字禪》四卷、《左德機緣》三卷、《李氏因果錄》三卷、《業報案》二卷,明刻。

《焚書》

《焚書》(意為不容於世,早晚必將付之一炬)是李贄最為著名且爭議最大的一部書,是他反程朱理學思想、政治哲學社會思想及耿介性格的集中體現。近來,更被評論界譽為「影響中國的百部書籍」之一。

萬曆四十六年(1618年),門人汪本鈳輯錄李贄遺文編成《續焚書》五卷。分《書匯》、《序匯》、《讀史匯》、《雜著匯》、《詩匯》。其中《題孔子像於芝佛院》最為膾炙人口。

Thanatopolitics (negativity vs vitality)

https://philpapers.org/archive/NASBTA.pdf

https://stuartjmurray.com/wp-content/uploads/2018/12/thanatopolitics-bloomsbury-handbook.pdf

https://thereader.mitpress.mit.edu/thanatopolitics-on-the-politics-of-death/

https://dsq-sds.org/index.php/dsq/article/view/7799/7608

https://www.reddit.com/r/askphilosophy/comments/il75q7/what_does_thanatopolitics_mean/?rdt=34356

https://www.researchgate.net/publication/292163353_Thanatopolitics_or_biopolitics_Diagnosing_the_racial_and_sexual_politics_of_the_European_far-right

https://academic.oup.com/book/9793/chapter-abstract/157003203?redirectedFrom=fulltext&login=false

https://cnam.hal.science/hal-03534172/document

https://journals.co.za/doi/abs/10.10520/ejc-safety1-v19-n1-a1

https://www.airitilibrary.com/Article/Detail/10242856-202212-202212190004-202212190004-63-94

5/1/24(星期三)

分明夏至,國民黨舔,馬斯克舔,共之屁眼,意思是說,馬韓洪傅,你要注意,舔之部位,所謂,location location location,五十回合,簡約之美,今日洗澡,喜舔共者,須常刷牙,當然不刷,滿口屎味,居然美味,也無所謂,你要理解,消化道演化,原本口腔,就是屎腔,後來上帝,忍無可忍,兀須再忍,遂給人類,屁眼作為禮物,意思是說,國民馬斯,喜舔屁眼,是前寒武紀,思鄉懷舊,

存在治療 (1130803)

四章,每章七命題,環環相扣,呈現生命混沌之本色,

Cf. Nature's Chaos, by James GleickEliot Porter, Viking, 1990 

Eliot Porter (1901-1990),意思是說,這是最後遺作,

依現象學,意識大于潛意識,意思是說,潛意識不過,意識的逃逸的路線 (lines of flight),

為何意識,需要逃逸,因為意識迫人,尤其自我意識 (self-consciousness),自覺意識 (autonoetic consciousness),

依原始人類 (hominid) 之演化史,人之所以為人,在于人擁有自覺意識,

意思是說,人遂自以為,萬物之靈,

實則,靈他媽的 my ass,

意思是說,如此惡靈,不靈也罷,

墮人類世,如此惡世,皆由此起,

意思是說,人之所以,背棄自然,回不到自然,辜負歷史,回不到歷史,皆因其自覺意識,

以前我說,心理治療,為的是,少一點自覺意識,多一點自我察覺 (self awareness),

現在我說,心理治療,為的是,放下自覺意識,放下自我察覺,只剩自我休戰 (self truce),

意思是說,人所造最大之孽,就是搞不定他自己,因此轉而惡搞他者,惡搞這個世界,

比如說,普丁和習包,意思是說,金三與此二壞屁眼 (badass) 相較,只是個喜歡玩耍炮決的小胖屁孩,

目睹親信遭「炮決」 金正恩姑丈嚇到當場尿褲子 (2020-9-13) https://www.mirrormedia.mg/story/20200913web003






The Concept of Life in Ludwig Binswanger’ phenomenological Psychopathology

https://www.academia.edu/14071564/The_Concept_of_Life_in_Ludwig_Binswanger_phenomenological_Psychopathology?email_work_card=title

Lethal AI Weapons Are on the Rise. What’s Next?

https://www.scientificamerican.com/article/lethal-ai-weapons-are-on-the-rise-whats-next/

Risks of Clozapine Decline Sharply After Six Months, May Warrant Reduced Monitoring

https://alert.psychnews.org/2024/04/risks-of-clozapine-decline-sharply.html

Monday, April 29, 2024

天師鬥殭屍

https://youtu.be/LRrM_YPh_T8?feature=shared

Le Retour à la raison (Man Ray, 1923)

https://en.wikipedia.org/wiki/Man_Ray (1890-1976)

https://en.wikipedia.org/wiki/Le_Retour_%C3%A0_la_raison

‘Man Ray: Return to Reason’ Trailer: Jim Jarmusch Scores Four Trippy Restored Short Films

https://www.indiewire.com/news/trailers/man-ray-return-to-reason-trailer-jim-jarmusch-score-shorts-1234977271/

Can we say that Occam’s razor brings simplicity, which is essence of any elegant construction including fractals and chaos? (ChatGPT, 2024-4-29)

Absolutely, Occam's razor, the principle of parsimony or simplicity, plays a significant role in the understanding and appreciation of fractals, chaos, and elegant constructions in general. Here's how:

  1. Fractals and Chaos: Occam's razor suggests that among competing hypotheses, the one with the fewest assumptions should be selected. In the context of fractals and chaos, this principle often guides scientists and mathematicians to seek simple explanations for complex phenomena. Fractals, despite their intricate appearance, can often be generated by simple iterative processes or mathematical equations. Similarly, chaos theory seeks to explain seemingly unpredictable behavior in terms of simple dynamical systems with a small number of variables.

  2. Elegance in Construction: Elegant constructions, whether in mathematics, science, engineering, or design, often embody simplicity and efficiency. Occam's razor encourages the search for elegant solutions that minimize complexity without sacrificing effectiveness or beauty. Fractals, with their self-similar patterns and recursive structures, exemplify the elegance of simplicity yielding complexity. Similarly, chaotic systems often exhibit elegant behavior arising from simple rules and initial conditions.

  3. Universal Principles: Occam's razor reflects a fundamental principle of nature—that simplicity often underlies complexity. This principle is observed in various scientific disciplines, from physics to biology to psychology. Fractals and chaos are manifestations of this principle, illustrating how simple rules or processes can give rise to the rich diversity and complexity observed in the natural world.

In summary, Occam's razor underscores the importance of simplicity and economy of explanation in understanding complex phenomena, including fractals, chaos, and elegant constructions. By favoring simpler models and hypotheses, scientists and thinkers can uncover the underlying principles that govern the universe and appreciate the beauty of simplicity in its manifestations.

Then can we say that man-made systems lack the nature’s mystery — chaos and fractals? (ChatGPT, 2024-4-29)

While man-made systems may not always exhibit the same level of complexity and mystery found in natural systems, they can still display elements of chaos and fractals. Here's how:

  1. Artificial Intelligence and Complex Systems: Man-made systems, such as artificial intelligence algorithms and computational models, can exhibit complex and unpredictable behavior similar to natural systems. Chaos theory is applicable in various fields, including economics, engineering, and computer science, where seemingly deterministic systems can produce chaotic outcomes.

  2. Design and Architecture: Architects and designers often draw inspiration from natural fractal patterns when creating structures and urban environments. Buildings, bridges, and city layouts can incorporate fractal geometry to optimize efficiency, aesthetics, and sustainability. Additionally, fractal-inspired designs are used in computer graphics, digital art, and virtual environments.

  3. Technology and Innovation: Advances in technology have enabled the exploration and visualization of fractals and chaotic systems in ways that were previously impossible. Computer simulations, mathematical models, and visualization tools allow researchers and artists to study and represent complex phenomena, uncovering hidden patterns and structures.

  4. Emergent Behavior in Social Systems: Human societies and economies are complex systems characterized by emergent behavior, feedback loops, and non-linear dynamics. While these systems may not always exhibit fractal geometry in the same way as natural systems, they can display patterns of self-organization, resilience, and adaptation reminiscent of chaotic systems.

Overall, while man-made systems may lack the inherent mystery and diversity found in nature, they can still embody elements of chaos and fractals, whether intentionally designed or emergent from their complexity. The study and application of chaos theory and fractal geometry continue to inspire innovation and deepen our understanding of both natural and artificial systems.

Can we say that nature reveals to us in fractals? (ChatGPT, 2024-4-29)

Absolutely! Fractals are indeed abundant in nature, and they offer a fascinating window into the underlying structures and patterns that govern natural phenomena. Here's how nature reveals itself through fractals:

  1. Natural Forms: Many natural objects exhibit fractal geometry. Examples include coastlines, clouds, mountains, trees, rivers, and ferns. These objects often display self-similar patterns at different scales, mirroring the fractal properties found in mathematical fractals like the Mandelbrot set.

  2. Biological Structures: Biological systems frequently showcase fractal patterns in their structures. For instance, the branching patterns of blood vessels, lungs, and neurons exhibit self-similarities that can be described by fractal geometry. Similarly, the distribution of leaves on a tree or the veins in a leaf follows fractal patterns.

  3. Dynamic Systems: Natural processes and phenomena often exhibit chaotic behavior, which can lead to the emergence of fractal patterns. Examples include weather systems, turbulence in fluids, the motion of celestial bodies, and the behavior of populations in ecosystems. These systems can produce intricate and complex fractal-like structures.

  4. Aesthetic Appeal: Fractal patterns are aesthetically pleasing to many people, which is perhaps why they are often found in art, architecture, and design inspired by nature. Artists and designers frequently draw upon fractal geometry to create visually captivating works that evoke the beauty and complexity of the natural world.

In essence, nature's manifestations of fractals offer a profound insight into the underlying principles of self-organization, complexity, and emergent behavior that govern our universe. They serve as a reminder of the interconnectedness and elegance of natural systems, as well as a source of inspiration for scientific inquiry, artistic expression, and philosophical contemplation.

What’s the relationship between fractals and chaos? (ChatGPT, 2024-4-29)

Fractals and chaos theory are closely related concepts in mathematics, particularly in the study of dynamical systems and complex behavior. Here's a brief overview of their relationship:

  1. Self-Similarity: Fractals are geometric shapes that exhibit self-similarity, meaning they look similar at different scales. This property is often seen in natural phenomena like coastlines, clouds, and snowflakes. Chaos theory deals with dynamical systems that are highly sensitive to initial conditions, resulting in complex, unpredictable behavior. Fractal patterns can emerge in the chaotic behavior of these systems, as seen in the famous Mandelbrot set.

  2. Iterated Function Systems (IFS): Fractals can be generated through iterated function systems, where simple transformations are applied repeatedly to points in space. Chaotic behavior can arise in certain iterated function systems, leading to the creation of fractals with intricate and unpredictable structures.

  3. Attractors and Strange Attractors: Chaos theory often involves the study of attractors, which are sets of states towards which a dynamical system evolves over time. In chaotic systems, these attractors can be strange attractors, exhibiting fractal geometry. The Lorenz attractor is a classic example of a strange attractor, displaying a fractal butterfly-like shape.

  4. Fractal Dimension: Fractals have a fractional or non-integer dimension, meaning they occupy a fractional amount of space. Chaos theory deals with systems that may have a strange attractor with a dimension that is not a whole number, indicating a complex and intricate structure.

Overall, fractals and chaos theory are intertwined through their shared focus on complexity, self-similarity, and the behavior of dynamical systems. They provide valuable insights into the underlying patterns and unpredictability found in natural and mathematical phenomena.