Carl Friedrich Gauss: (1777, Brauschweig , Göttingen)

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1 Carl Friedrich Gauss: (1777, Brauschweig - 1855, Göttingen)
生命綿延的數學性: 另一種思維習慣 (德語世界的科學事件之一) Carl Friedrich Gauss: (1777, Brauschweig , Göttingen) 高斯 數學是科學的皇后 狐狸的足跡 楊倍昌，精簡版

2 中國和西方的科技在1450年到1600 年間仍有並駕齊驅的樣子，之後西歐突出，才使中國望塵莫及。? (李約瑟難題)
黃仁宇轉述李約瑟的話, in: 放寬歷史的視界 1988, 允晨叢刊、台北, p:94 中國一百年來的革命，已於1980 年代完成。期間最大的一個收穫，則是今後這個國家已能在數目字上管理 (mathematically manageable) 。 黃仁宇: 放寬歷史的視界 1988, 允晨叢刊、台北, p142 是嗎? (BC)

3 Mendelregeln 1. Uniformitätsregel (顯隱律): 2. Spaltungsregel (分離律):
Kreuzt man zwei Individuen einer Art, die sich nur in einem Merkmal unterscheiden und in Bezug auf dasselbe homozygot sind, so sind die Individuen der Tochtergeneration (F1) im betrachteten Merkmal gleich, d.h. uniform. Alle Individuen der Tochtergeneration haben nicht nur denselben Phänotypus, sondern auch denselben Genotypus. Dies trifft sowohl beim intermediären als auch beim dominanten Erbgang zu. 2. Spaltungsregel (分離律): Kreuzt man Individuen der F1- Generation unter sich weiter, so kommt es zu einem Aufspalten der Merkmale. Vom Phänotypus findet das Aufspalten beim intermediären Erbgang im Verhältnis 1:2:1 statt, beim dominanten im Verhältnis 1:3. Der Genotypus tritt in beiden Erbgängen im Verhältnis 1:2:1 auf. 3. Regel von der Unabhängigkeit der Erbanlagen (獨立分配律): Kreuzt man zwei Individuen einer Art, die sich in zwei Merkmalen unterscheiden und in Bezug auf dieselben homozygot sind, so findet man in der F2- Generation eine Aufspaltung der Merkmale im Verhältnis 9:3:3:1 beim dominanten Erbgang. Dies beweist, dass die Gene unabhängig voneinander vererbt werden und frei kombinierbar sind.

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6 Which date is correct? 1865, Mendel gave Lectures on “Experiments in Plant Hybrids” at the February and March meetings of the Natural Science Society (Brno). Vorgelegt in den Sitzungen vom 8. Februar und 8. März 1865) ; 9. Februar in Brünner Tagblatt. 1866, Mendel published his lecture, a work that was to establish him as “the father of genetics”. Versuche über Pflanzen-Hybriden, in Verhandlungen des naturforschenden Vereins Brünn 4, (Nachruck; Weinheim 1960).

7 就是這樣做 So ist es gemacht!

8 在孟德爾的花園裡 "gelb x gelb = grün ...wenigstens manchmal" 他想要回答什麼問題 ?
幾種問問題的方式 在孟德爾的花園裡  "gelb x gelb = grün ...wenigstens manchmal" 他想要回答什麼問題 ? 為什麼結果被埋沒近 (35) 年? 是什麼認知環境，讓後人了解到孟德爾研究的重 要性?

9 孟德爾遺傳律之後 遺傳律是物理定律嗎？ 孟德爾時代的典範是甚麼？ 孟德爾需要考慮什麼實驗上的問題？ 孟德爾遺傳律為什麼不被了解？
幾種問問題的方式 孟德爾遺傳律之後 遺傳律是物理定律嗎？ 孟德爾時代的典範是甚麼？ 孟德爾需要考慮什麼實驗上的問題？ 孟德爾遺傳律為什麼不被了解？ 孟德爾改變了什麼世界觀？

10 孟德爾遺傳律之後 遺傳律是物理定律嗎？ 孟德爾時代的典範是甚麼？ 孟德爾需要考慮什麼實驗上的問題？ 孟德爾遺傳律為什麼不被了解？
孟德爾改變了什麼世界觀？

11 物理定律的要素 物理定律是描述物體運動或狀態的可測量量的數學表達。物 理學定律通常被認為是正確的。
物理學定律有機會被實踐證明是錯，但當物理學定律被實驗 證明是錯的時候，通常這意味著物理學的突破，一個體系的 知識出現錯誤時可證明其錯誤，也代表此體系的知識合乎科 學有相當的真實性。 連鎖遺傳(Genetic linkage)、表觀遺傳學(epigenetics)等等不符 合孟德爾定律的現象，是錯誤，還是例外？

12 Haemophilia has featured prominently in European royalty and thus is sometimes known as ‘the royal disease’. Queen Victoria passed the mutation for haemophilia B to her son Leopold and, through two of her daughters, Alice and Beatrice, to various royals across the continent, including the royal families of Spain, Germany, and Russia.

13 孟德爾遺傳律之後 遺傳律是物理定律嗎？ 孟德爾時代的典範是甚麼？ 孟德爾需要考慮什麼實驗上的問題？ 孟德爾遺傳律為什麼不被了解？
孟德爾改變了什麼世界觀？

14 Andreas Baumgartner (1793 - 1865)
孟德爾的老師 Andreas Baumgartner ( ) In 1823 he lectured at Vienna university, published his works as well as a Magazine of physics and mathematics, and wrote a book of elementary physics. A native of  Frymburk in the Český Krumlov region.

15 A link between the study of natural disciplines, such as botany and zoology, and physics had already been expressed by Andreas Baumgartner ( ), professor of Physics at the University of Vienna until 1864, who acted as examiner for Mendel in Brno in Baumgartner had been so impressed by Mendel, that he suggested to Abbot Napp that the young monk should be sent to the University of Vienna. Professor Baumgartner emphasized the importance of studying nature, not through random speculation but through experiments theoretically underpinned by mathematical models.

16 孟德爾的老師 Franz Unger ( ) : about Evolution (1852, Wien), test how variation is formed (How to do this?). Darwin published “On the origin of species: in 1859 1869, Mendel had talked about evolution, and sent a copy of paper to Darwin. Christian Doppler ( ): on physics.

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19 孟德爾還知道哪些事? Atomic theory by John Dalton (1766-1844). 可能知道 Statistic 嗎?
Father of epidemiology: John Snow:

20 所以：孟德爾是修士、學過物理、數學、生物學
In 1807, an imperial order demanded that the Augustinians at St Thomas should take up the teaching of mathematics and biblical studies in the newly established Philosophy Institute and the Brno Theology College. Flood and other presumed catastrophes receded, first in the face of Scottish geologist Charles Lyell‘s arguments begun in the 1830s that the Earth had been shaped by gradual, ordinary forces working over a vast timescale. They ebbed even further with the coming of Darwinism in the 1860s (against the biblical answer ). 變動的世界

21 是什麼東西引起孟德爾如此大的興趣，讓他願意花費八(?) 年時間進行植物雜交實驗?
達爾文的鴿子 在這樣的環境下，育種學家要做甚麼？ 是什麼東西引起孟德爾如此大的興趣，讓他願意花費八(?) 年時間進行植物雜交實驗? 或者他只是無聊找事做?

22 孟德爾遺傳律之後 遺傳律是物理定律嗎？ 孟德爾時代的典範是甚麼？ 孟德爾需要考慮什麼實驗上的問題？ 孟德爾遺傳律為什麼不被了解？
孟德爾改變了什麼世界觀？

23 Mendel's green pea (Pisum sativum), is also called the garden pea or English pea.

24 List of seeds ordered by Mendel to Ernst Benary for the Abbey, 2nd November 1878, and a bill from the seed firm, Bestell Nota Herrn Ernst Benary in Erfurt.Brno, Abbey of St Thomas Grafting and pruning tools in wooden box, Dittmar Keilbronn Brno, Abbey of St Thomas A B 孟德爾用的工具吧

25 Mendel‘s green pea (這不是一開始的說法)
D R D R Seed shape Seed color Flower position Flower color 應該是子葉的顏色 Pot shape Pot color Stem high

26 孟德爾用的七種豌豆特徵 Shape of seed, whether rounded or irregularly angular and deeply wrinkled. Colour of cotyledons [“ endosperm”], whether some shade of yellow or green. Colour of seed-skin, whether a brownish shade or white (in correlation with white flowers). Shape of ripe pod, whether simply inflated or deeply constricted between the seeds. Colour of unripe pod, whether a shade of green or bright yellow. Position of flowers, whether distributed along the stem or crowded near the top in a false umbel. Length of stem, whether about 6-7 feet or about 3/4 --> 1 and 1/2 feet. Between these various pairs of varieties crosses were then made, the female parent being emasculated.

27 The monks in Mendel's monastery would have really appreciated his crops as peas are best if eaten almost immediately. Like corn, peas lose their sweet flavor very rapidly.

28 藏在描述背後的祕密 由種子商購買 34 個豌豆品種，培育兩年成為純系。他發現 有22 株系的性狀穩定，然後又選定 7 種性狀作為觀察性狀 在世代間傳遞情況的指標 豌豆有七條染色體。 據說研究進行八年，對兩萬八千株植物進行交配實驗。 在費曼之前 – 二十世紀的科學簡史; 陳恒安譯, 究竟, 台北 (2002), p 70. 原始資料待查!

29 孟德爾的考驗 選擇好栽種、好處理又穩定的材料 簡化觀察目標 具有穩定而相異的觀察特徵。
雜交植物在開花授粉期必須能避免不同植物花粉的干擾，能防止外來花粉接觸實驗植物。 雜交植物及其子代的生產力在經過數代之後不會減低。 簡化觀察目標 孟德爾大概已經察覺，靠他自己一個人，要同時分析兩種性狀可能還做得到，再多就太困難了。此外，他也不可能做得完254種交配實驗，他必須捨棄一些他暫時沒辦法處理的材料，擱置無法分析的實驗。 楊倍昌，2010，楊倍昌 (2010) 由生物實驗的設計來發現孟德爾定律的發現。《科技、醫療與社會》，第十期： 頁。

30 孟德爾遺傳律之後 遺傳律是物理定律嗎？ 孟德爾時代的典範是甚麼？ 孟德爾需要考慮什麼實驗上的問題？ 孟德爾遺傳律為什麼不被了解？
孟德爾改變了什麼世界觀？

31 After two lectures in 1865, Mendel published his famous Pisum-treatise VERSUCHE ÜBER PFLANZEN-HYBRIDEN in His work was quoted at least 14 times before 1900, the year of its 'rediscovery'. There were references in such widely distributed works as Focke's DIE PFLANZEN-MISCHLINGE (1881), THE ENCYCLOPAEDIA BRITANNICA (1881) and the CATALOGUE OF SCIENTIFIC PAPERS OF THE ROYAL SOCIETY (1879). The treatise had been sent to the libraries of some 120 institutions including the Royal and Linnean Society of Great Britain. Moreover Mendel had 40 additional reprints at his disposal, many of which he sent to leading biologists of Europe. In fact, professor Niessl (1903 and 1906) emphasized that Mendel's work was "well known" at his time.

32 很完整的討論: http://www.weloennig.de/mendel.htm
Warum seine Entdeckungen 35 Jahre ignoriert wurden Ein paar kritische Kommentare von Pionieren der Genetik sowie weiteren Biologen und Biologiehistorikern zur Wirkung des Darwinismus auf die biologische Forschung Why his discoveries were ignored for 35 years Some critical comments about the effects of Darwinism on Biological Research by Pioneers of Genetics as well as further Biologists and Historians of Biology (German with English Summary)

33 三個爭奪「重新」發現遺傳定律的故事 Hugo de Vries (1848-1935)
Carl Erich Correns ( ) Erich von Tschermak-Seysenegg ( ))

34 When Mendel's paper was published, in 1866, it received little attention, and was rarely cited by botanists or biologists during the next 34 years. Mendel's work has been thought to exemplify everything from the failure of traditional modes of scientific communication (Bush [1945]) to the phenomenon of "premature scientific discovery" ( Stent [1978]). In 1900, Mendel's work was cited by three botanists, writing in different parts of Europe: Hugo de Vries, in Amsterdam; Carl Correns, in Tübingen; and Eric Von Tcshermak, in Esslingen, Austria. Although their interpretations of what Mendel had shown were arguably inaccurate, these citations caused what has come to be known as the "rediscovery" of Mendel.

35 De Vries { C. R., 1900, March 26; 'Ber. deut. Bot. Ges.,' 18, 1900, p. 83.} working with pairs of varieties belonging to a diversity of genera and species, found that in a large number of cases one of the varietal characters was definitely dominant, prevailing in the first crosses to the exclusion of the recessive character. The offspring of the cross-breds fertilised inter se were mixed dominants and recessives in proportions fairly agreeing with Mendel's law. In the case of two colour varieties of Papaver somniferum, the constitution of the resulting dominants was investigated, and shown to be also according to the law. In certain cases also the purity of the recessives was tested and found to be complete. 罌粟 Papaver somniferum

36 Carl Erich Correns ( ) Im Botanischen Garten von Tübingen, wo Leonhart Fuchs ( ) im 16. Jahrhundert bereits einen Hortus Medicus aufgebaut hatte, begann Carl Correns 1894 seine Vererbungsexperimente, welche 1900 zur Wiederentdeckung der Mendelschen Vererbungsregeln beitrugen. Correns erkannte durch seine Experimente aber auch, dass nicht alle Merkmale frei miteinander kombinierbar seien, sondern dass einige eindeutig untereinander gekoppelt sind (d.h. stets gemeinsam vererbt werden). 聯鎖遺傳?

37 Correns C 用的材料 Matthiola incana 紫羅蘭
我曾經在Tübingen

38 也是八年 Nägeli 做這個 Correns was a tutor at the University of Tübingen when he began to experiment with trait inheritance in plants in Correns already knew about some of Mendel's hawkweed plant experiments from Nägeli. Nägeli, however, never talked about Mendel's key pea plant results, so Correns was initially unaware of Mendel's laws of heredity. However, by 1900, when Correns submitted his own results for publication, the paper was called: G. Mendel's Law Concerning the Behavior of the Progeny of Racial Hybrids. Correns and de Vries were the ones who most clearly "redefined" Mendel's laws. Correns (with credit to de Vries) restated Mendel's results, giving us Mendel's law of segregation and Mendel's law of independent assortment. Karl Wilhelm von Nägeli ( ) Eric von Tcshermak 的貢獻被忽略了!

39 Erich von Tschermak-Seysenegg
Because he was younger, and not as established in the scientific community, Tschermak was worried about the acceptance of his paper given those of de Vries' and Correns'. However, he was able to rush his paper to press, and was accorded his share of attention as one of the rediscoverers of Mendel's laws. Tschermak was a plant breeder, and his hybridization experiments were done with the idea of improving crops using the laws of heredity. He did most of the work himself, and produced high-yielding food crops such as wheat, barley, and oats. In 1903, Tschermak was appointed associate professor at the University of Agricultural Sciences in Vienna, and later became a full professor. He was a major influence in agriculture and plant breeding in Austria.

40 Some arguments Fisher RA (1936), a mathematically inclined scientist, was to deal with the problem of Mendel’s data being “too good”, it is impossible to him that the expected and actual data could be so similar. In the case of the yellow x green: The total number of seeds scored was 179,399. Of these, 134,707 were yellow ( percent) and 44,692 were green ( ). Mendel had reported 75.05% vs 24.95%. Fisher, R.A. (1936). Has Mendel's Work Been Rediscovered? Annals of Science 1, 陳瑞麟：2009，孟德爾究竟發現了什麼?一個實驗發現的典型模式。《科技、醫療與社會》第 9 期，頁 。

41 孟德爾遺傳律之後 遺傳律是物理定律嗎？ 孟德爾時代的典範是甚麼？ 孟德爾需要考慮什麼實驗上的問題？ 孟德爾遺傳律為什麼不被了解？
孟德爾改變了什麼世界觀？

42 1869 Johann Friedrich Miescher (nuclein)
在接受且理解孟德爾發現的必要條件有哪些? 孟德爾以概念 (以 Elementet 稱呼他所追蹤的遺傳單位) 和假設的理論掌握自然的規律(關係) 。但是概念必須有實物相對應，才能展現其存在的意義。 1866, Mendel published his lecture, a work that was to establish him as “the father of genetics”. 1869 Johann Friedrich Miescher (nuclein) 1873 Anton Schneider (meiosis) 1879 Walther Flemming (chromaton, mitosis) 1888 Wilhelm von Waldeyer-Hartz, (term chromosome) 1902 Walter Stanborough Sutton. (chromosomes carry the units of inheritance) 1904 Theodor Boveri (correlation between Mendel's factors and chromosomes ) 1904 William Bateson (genetics) 1909 Wilhelm Johannasen (gene)

43 DNA to chromosome to DNA
1869 Johann Friedrich Miescher identifies a weakly acidic substance of unknown function in the nuclei of human white blood cells. This substance will later be called deoxyribonucleic acid, or DNA. 1924 Microscope studies using stains for DNA and protein show that both substances are present in chromosomes. 1928 Franklin Griffith, a British medical officer, discovers that genetic information can be transferred from heat-killed bacteria cells to live ones. This phenomenon, called transformation, provides the first evidence that the genetic material is a heat-stable chemical. 1944 Oswald Avery, Maclyn McCarty, and Colin MacLeod, identify Griffith's transforming agent as DNA.

44 Walther Flemming 1879: he described and named "chromaton", "mitosis" and "spireme", made the first accurate counts of chromosome numbers and figured the longitudinal splitting of chromosomes.

45 All nuclei come from nuclei
Flemming observed for the first time that the chromosomes during cell division became split along their longitudinal axis, now known to consist of chromatids, and in 1880 he formulated the sentence: "Omnis nucleus e nucleo". All nuclei come from nuclei (1863), omnis cellula e cellula

46 William Bateson ( ) William Bateson describes gene linkage, showing that more than one gene may be required for a particular characteristic or trait (1904). A hereditary factor like, for example, the shape of the seed, the colour of the cotyledons or the colour of the seed shell shall be called a gene (following a suggestion of BATESON made in 1905).

47 First page of a 1905 letter written by William Bateson, first Director of the John Innes Institute, to Adam Sedgewick, Cambridge professor. Bateson coined the term "genetics" in this letter. he felt the need for a new term to describe the study of heredity and inherited variations. But the term didn’t start spreading until Wilhelm Johannsen suggested that the Mendelian factors of inheritance be called genes.

48 孟德爾遺傳律之後 世界觀改變了什麼？