The pages：245 ~ 248
(3) Transformations of Form and Function
Closely related to Huxley’s method of studying allometric growth is D’Arcy Thompson’s (1917) famous method of transformations in which he compares related forms such as shown in Fig. 6.6 by the superimposition of Cartesian coordinates. A rectangular system is drawn over a two-dimensional representation of one form so that the distortions of the coordinates may be studied that result from drawing lines through the homologous points on the second form. This method is purely descriptive and difficult to quantify. But it illustrates the topological relationships between certain forms and how certain differences in structure may be accounted for by a single principle, usually changes in growth gradients during ontogeny. In cases where specific dimensions can be compared allometrically, we would find different values for the parameters a and b (compare
However, there mat be intracellular genetic alterations such that ontogenetic histories are altered resulting in two different mature forms. The situation is diagrammed in Fig. 6.7. There are two molecular structures, Σ1 and Σ2, that are at the basis of two developmental histories H1 and H2. Σ1 and Σ2 are related to one another by the specification of a molecular transformation called Tm. The developmental histories H1 and H2, result in mature structures S1 and S2. In the case described by D’Arcy Thompson, an apparent transformation relation, Tα, persists that is characterized through the distorted coordinate systems. Notice, however, that the biological connection rests entirely in the molecular and “invisible” transformation Tm and that the apparent transformation Tα is more or less incidental—certainly not essential—for it is obvious that some or even most molecular transformations will alter the developmental histories in such a way that the corresponding two mature structure either lose their isomorphism (as in the isolated case of two-headed monsters or other deformities) or remain the same to the eyes of the unaided observer as in the case of certain inherited diseases such as hemophilia. Thus, D’Arcy Thompson transformations are probably special cases of a much more universal phenomenon.
FIG. 6.6 Morphological relations between selected species shown here as geometric transformations. (a) Argyropelecus olfersi and Sternoptyx diaphana; middle: Scarus sp. and Pomacanthus; (b) Diodon and Orthagoriscus. (From Thompson, 1917.)
A discussion of these transformations has some unsuspected relevance to the biological study of language, particularly the comparison of human language with animal forms of communication. We have said before that what is true of ontogeny and transformations of molecular structures is also relevant to the biological foundations of behavior because of the dependence of the latter upon the former. Thus, the emergence of a species-specific form of behavior has, essentially, a molecular transformational history. Just as in the case of mature structure, mature forms of behavior are the result of species-specific developmental histories H1 and H2, and the biological connections between any two forms of behavior must be sought for on the level of the molecular transformations Tm. What we have said of the apparent transformation Tα, holds a fortiori for the comparison of behavior.
Correspondences on this surface level will be special cases: in many more instances, all isomorphism will be lost to our eyes. We would expect mature behavior forms (that is, the homologues to S1 and S2) to vary with much greater freedom and into many more directions than gross structure, because the selection biases upon skeletal form are likely to be much more restraining than on behavioral modality, and it is also possible that epigenetic canalization (Waddington, 1956 and 1957) allows of fewer directional alternatives in the case of structural alterations than behavioral ones. Although these are speculations, it is a fact that there is greater variety in behavior among animals than in their types of Bauplan or structural pattern. In the light of this, the present thesis on the biological origins of language becomes very clear.
FIG. 6.7. Species are related to each other by transformations in molecular structure of genic material. These transformations affect the developmental histories of the animals in the course of which the original relationship may become obscured: the resulting mature structure may or may not bear resemblance to one another.
We assume that our potential for language has a biological history that is written in terms and on the level of molecular transformations Tm; but this belief commits us in no way to expect the occurrence of apparent transformations Tα. If human language be S2, we cannot even be sure, in fact, what may be token of S1. Similarly, if a superficial resemblance is pointed out to us between language and some behavioral aspect of another species, we cannot be certain how close or distant the underlying relationship Tm actually is, or for that matter, if there is any such relationship whatever. Because modifications of behavior may be freer and go into many more directions than modifications of structures, molecular transformations Tm may leave in many fewer cases apparent transformations Tα than is the case for skeletal structure and thus there is the danger of being misled by similarities that are in fact not objective but that are entirely due to anthropomorphic interpretation of animal’s activities. (Examples of this are not restricted to animal “language” but may be found in statements about animal “play”, or animal “families”, or animal “pleasures.”)
The transformational picture leads us to expect that molecular alterations indirectly caused changes in the temporal and spatial dimensions of the species’ developmental history and that the resulting alterations in structure and function brought with them prolonged and changed periods during which one function could be influenced by others, thus creating critical periods of special sensitivities and opening up new potentials and capacities. This is just the framework within which we would like to see our thoughts move; it is too vague to be a theory. Let us look at it as the direction for possible explanations that are yet to come.
Ⅲ. EVIDENCE FOR INHERITANCE OF LANGUAGE POTENTIAL
The inheritance of behavioral traits in man can never be definitively demonstrated because of our inability to do breeding experiments. Also, absolute control of the environment is difficult to achieve. If we are staunch believers in the sole determination of behavior by the social environment was held constant. It is always possible to argue that there might have been subtle differences in human relations so that even two individuals who are raised in the same home might have experienced different treatment, invisible to the observer, and that all differences in behavior might be due to these variations. Similar but converse arguments are also possible in the case of identical behavior in apparently different environments.
與赫克斯利的學習方法異速生長發展有關的是D'Arcy湯普森的 ( 1917 )著名的轉換方法，他比較相關的形式在圖片6.6中。藉由扭曲的座標能被研究出結果從化線通過同種的指向在第二種型態。這種方法純粹描寫並且難定量。但是它說明拓撲學的關係在某些形式之間和藉由單一的原則某些在結構上不同能計算出來，通常在個體發生期間成長的坡度會改變，在這個事件中，特定的尺寸被異速生長來比較，我們可以發現不同的參數值a和b(比較尼德姆，1964。在異速生長的公式上)。在一個D'Arcy湯普森的轉變的重要討論裡，Woodger ( 1945 )指出此現象證明這個必須被了解在基因的觀點和胚胎學上，因為沒有成熟的外型可以改變，藉由一個轉換的過程成為其他外型。
圖6-6形態聯繫在選擇的種類之間被顯示這裡作為幾何學變革。(a) Argyropelecus olfersi 和Sternoptyx diaphana; 中部: Scarus sp. 和Pomacanthus; (b) Diodon 和Orthagoriscus 。(從湯普森1917 年。)
然而，可能有細胞內的遺傳學的改變，因此個體發生的歷程被改變成兩種不同的成熟的形式。此位置在圖6.7中表示出。有兩種分子的構造Σ1 和 Σ2，是建立在兩種發展歷程基礎上H1 和H2。Σ1 和 Σ2是藉由分子轉換的說明，稱為Tm，來和另一個相關。H1 和H2的發展歷程，起因於成熟的架構S1 和S2。在D'Arcy湯普森的描述中，一個明顯的轉變關係，Ta，堅持那是被透過扭曲的坐標系統表現特性。注意，然而，生物學的連結完全地基於分子和無形的轉換Tm和表面的轉換Ta式或多或少附帶的─無疑地不是必要的─對於這個是明確的，一些或甚至更多的分子轉換將改變此發展歷程，在相同的兩種成熟構造中任一個失去他們的異種同形(當在兩隻手的怪物或其他畸形的分離事件中) 或者例如像血友症那樣特定的遺傳病對未受幫助的觀察者保持相同的眼睛。關於這些變革的討論有與語言的生物研究的一些未預料到的相關性，特別是比較在溝通上人的語言以動物形式呈現。我們以前說什麼是真實的分子結構的個體發生學和變革與行為的生物基礎是還相關的這是由於後者依賴在前。因此，行為有一個特定種類的形式，根本上，分子變革歷史。正在成熟結構情況下，行為的成熟形式是特定種類的發展歷史H1和H2的結果，並且生物連接在任何行為之間的二個形式必須被尋找為在分子變革上Tm的水平。我們說明顯變革Tα的控制更不必說為行為比較。
書信在這個表面水平上將是特殊情況：在許多事例，所有同構(同種異形)將丟失對我們的眼睛。我們比總結構會盼望成熟行為形式(那是同源染色體對S1 和S2) 變化隨更加偉大的自由和入許多方向，因為選擇偏向於骨骼形式可能是克制在關於行為的形式，並且它還可能的外成疏導(Waddington, 1956 年和1957) 比關於行為那些允許少的定向選擇在結構改變情況下。雖然這些是猜想，這是事實有更加巨大的品種在行為在動物之中比在他們的類型Bauplan 或結構樣式。根據此，當前論文在語言的生物起源變得非常清楚。
我們假設，我們的在語言的潛力有被寫用術語和在分子變革上Tm的水平的生物歷史；但這信仰使我們絕不期待明顯的變革Tα發生。如果人的語言是S2，我們無法甚而是肯定的，實際上，什麼可以是S1 象徵。同樣，如果表面相似被指出對我們在語言和某一其它種類之間的關於行為的方面，我們無法肯定多麼接近或潛在的關係Tm的距離，實際上是或就此而言。由於行為的修改和進入許多方向比結構的修改也許是更加自由的，分子變革Tm可以離開在許多少量案件明顯的變革Tα比骨骼結構和那裡因而由不是實際上客觀的而是整個地歸結於動物的活動的似人解釋的相似性危險(這種例子不被限於動物〝語言〞 而是也許被發現在聲明關於動物〝戲劇〞，或動物〝家庭〞，或動物〝樂趣〞)。