差不多先生傳‧胡適

你知道中國最有名的人是誰？提起此人，人人皆曉，處處聞名，他姓差，名不多，是各省各縣各村人氏。你一定見過他，一定聽過別人談起他，差不多先生的名字，天天掛在大家的口頭，因為他是中國全國人的代表。

差不多先生的相貌，和你和我都差不多。他有一雙眼睛，但看的不很清楚；有兩隻耳朵，但聽的不很分明；有鼻子和嘴，但他對於氣味和口味都不很講究；他的腦子也不小，但他的記性卻不很精明，他的思想也不細密。

他常常說：「凡事只要差不多，就好了。何必太精明呢？」

他小時候，他媽叫他去買紅糖，他買了白糖回來，他媽罵他，他搖搖頭道：「紅糖，白糖，不是差不多嗎？」

他在學堂的時候，先生問他：「直隸省的西邊是哪一省？」他說是陝西。先生說：「錯了，是山西，不是陝西。」他說：「陝西同山西，不是差不多嗎？」

後來他在一個錢鋪裏做夥計；他也會寫，也會算，只是總不會精細 ；十字常常寫成千字，千字常常寫成十字。掌櫃的生氣了，常常罵他，他只笑嘻嘻地賠小心道：「千字比十字多一小撇，不是差不多嗎？」

有一天，他為了一件要緊的事，要搭火車到上海去，他從從容容地走到火車站，遲了兩分鐘，火車已開走了。他白瞪著眼，望著遠遠的火車上的煤煙，搖搖頭道：「只好明天再走了，今天走同明天走 ，也還差不多；可是火車公司未免太認真了。八點三十分開，同八點三十二分開，不是差不多嗎？」他一面說，一面慢慢地走回家，心裏總不很明白為甚麼火車不肯等他兩分鐘。

有一天，他忽然得一急病，趕快叫家人去請東街的汪先生。那家人急急忙忙跑去，一時尋不著東街的汪大夫，卻把西街的牛醫王大夫請來了。差不多先生病在脇上，知道尋錯了人；但病急了，身上痛苦，心裏焦急，等不得了，心裏想道：「好在王大夫同汪大夫也差不多，讓他試試看罷。」於是這位牛醫王大夫走近脇前，用醫牛的法子給差不多先生治病。不上一點鐘，差不多先生就一命嗚呼了。

差不多先生差不多要死的時候，一口氣斷斷續續地說道：「活人同死人也差……差……差……不多，……凡事只要……差……差……不多……就……好了，何……必……太……太認真呢？」他說完了這句格言，就絕了氣。

他死後，大家都很稱讚差不多先生樣樣事情看得破，想得通；大家都說他一生不肯認真，不肯算帳，不肯計較，真是一位有德行的人 。於是大家給他取個死後的法號，叫他做圓通大師。

他的名譽愈傳愈遠，愈久愈大，無數無數的人，都學他的榜樣，於是人人都成了一個差不多先生。──然而中國從此就成了一個懶人國了。

 

幾何光學的主要目的之一是研究光線『成像原理』。雖然我們之前談過『點光源』。若問為什麼人眼能見『不發光』之物的呢？假使解釋因為物會『反射光』！難到只有特定『反射角』易賭物乎？！分明天上明月朗朗可隨人行各方能見，豈非無理耶！！所以在偶讀科學月刊上的《幾何光學三條線？》文章後大感驚訝，猛然想起了『差不多』先生，特寫在這裡，以免『反射』與『漫反射』混淆，要是『無量光』變成『三條線』總是不妙也！！？？

Diffuse reflection

Diffuse reflection is the reflection of light from a surface such that an incident ray is reflected at many angles rather than at just one angle as in the case of specular reflection. An illuminated ideal diffuse reflecting surface will have equal luminance from all directions which lie in the half-space adjacent to the surface (Lambertian reflectance).

A surface built from a non-absorbing powder such as plaster, or from fibers such as paper, or from a polycrystalline material such as white marble, reflects light diffusely with great efficiency. Many common materials exhibit a mixture of specular and diffuse reflection.

The visibility of objects, excluding light-emitting ones, is primarily caused by diffuse reflection of light: it is diffusely-scattered light that forms the image of the object in the observer’s eye.

Diffuse and specular reflection from a glossy surface.^[1] The rays represent luminous intensity, which varies according to Lambert’s cosine law for an ideal diffuse reflector.

Mechanism

Diffuse reflection from solids is generally not due to surface roughness. A flat surface is indeed required to give specular reflection, but it does not prevent diffuse reflection. A piece of highly polished white marble remains white; no amount of polishing will turn it into a mirror. Polishing produces some specular reflection, but the remaining light continues to be diffusely reflected.

The most general mechanism by which a surface gives diffuse reflection does not involve exactly the surface: most of the light is contributed by scattering centers beneath the surface,^[2][3] as illustrated in Figure 1. If one were to imagine that the figure represents snow, and that the polygons are its (transparent) ice crystallites, an impinging ray is partially reflected (a few percent) by the first particle, enters in it, is again reflected by the interface with the second particle, enters in it, impinges on the third, and so on, generating a series of “primary” scattered rays in random directions, which, in turn, through the same mechanism, generate a large number of “secondary” scattered rays, which generate “tertiary” rays, and so forth.^[4] All these rays walk through the snow crystallytes, which do not absorb light, until they arrive at the surface and exit in random directions.^[5] The result is that the light that was sent out is returned in all directions, so that snow is white despite being made of transparent material (ice crystals).

For simplicity, “reflections” are spoken of here, but more generally the interface between the small particles that constitute many materials is irregular on a scale comparable with light wavelength, so diffuse light is generated at each interface, rather than a single reflected ray, but the story can be told the same way.

This mechanism is very general, because almost all common materials are made of “small things” held together. Mineral materials are generally polycrystalline: one can describe them as made of a 3D mosaic of small, irregularly shaped defective crystals. Organic materials are usually composed of fibers or cells, with their membranes and their complex internal structure. And each interface, inhomogeneity or imperfection can deviate, reflect or scatter light, reproducing the above mechanism.

Few materials do not cause diffuse reflection: among these are metals, which do not allow light to enter; gases, liquids, glass, and transparent plastics (which have a liquid-like amorphous microscopic structure); single crystals, such as some gems or a salt crystal; and some very special materials, such as the tissues which make the cornea and the lens of an eye. These materials can reflect diffusely, however, if their surface is microscopically rough, like in a frost glass (Figure 2), or, of course, if their homogeneous structure deteriorates, as in cataracts of the eye lens.

A surface may also exhibit both specular and diffuse reflection, as is the case, for example, of glossy paints as used in home painting, which give also a fraction of specular reflection, while matte paints give almost exclusively diffuse reflection.

Figure 1 – General mechanism of diffuse reflection by a solid surface (refraction phenomena not represented)

Specular vs. diffuse reflection

Virtually all materials can give specular reflection, provided that their surface can be polished to eliminate irregularities comparable with light wavelength (a fraction of a micrometer). A few materials, like liquids and glasses, lack the internal subdivisions which give the subsurface scattering mechanism described above, so they can be clear and give only specular reflection (not great, however), while, among common materials, only polished metals can reflect light specularly with great efficiency (the reflecting material of mirrors usually is aluminum or silver). All other common materials, even when perfectly polished, usually give not more than a few percent specular reflection, except in particular cases, such as grazing angle reflection by a lake, or the total reflection of a glass prism, or when structured in certain complex configurations such as the silvery skin of many fish species or the reflective surface of a dielectric mirror.

Diffuse reflection from white materials, instead, can be highly efficient in giving back all the light they receive, due to the summing up of the many subsurface reflections.

Figure 2 – Diffuse reflection from an irregular surface

Colored objects

Up to this point white objects have been discussed, which do not absorb light. But the above scheme continues to be valid in the case that the material is absorbent. In this case, diffused rays will lose some wavelengths during their walk in the material, and will emerge colored.

Diffusion affects the color of objects in a substantial manner because it determines the average path of light in the material, and hence to which extent the various wavelengths are absorbed.^[6] Red ink looks black when it stays in its bottle. Its vivid color is only perceived when it is placed on a scattering material (e.g. paper). This is so because light’s path through the paper fibers (and through the ink) is only a fraction of millimeter long. However, light from the bottle has crossed several centimeters of ink and has been heavily absorbed, even in its red wavelengths.

And, when a colored object has both diffuse and specular reflection, usually only the diffuse component is colored. A cherry reflects diffusely red light, absorbs all other colors and has a specular reflection which is essentially white. This is quite general, because, except for metals, the reflectivity of most materials depends on their refraction index, which varies little with the wavelength (though it is this variation that causes the chromatic dispersion in a prism), so that all colors are reflected nearly with the same intensity. Reflections from different origin, instead, may be colored: metallic reflections, such as in gold or copper, or interferential reflections: iridescences, peacock feathers, butterfly wings, beetle elytra, or the antireflection coating of a lens.

Importance for vision

Looking at one’s surrounding environment, the vast majority of visible objects are seen primarily by diffuse reflection from their surface. This holds with few exceptions, such as glass, reflective liquids, polished or smooth metals, glossy objects, and objects that themselves emit light: the Sun, lamps, and computer screens (which, however, emit diffuse light). Outdoors it is the same, with perhaps the exception of a transparent water stream or of the iridescent colors of a beetle. Additionally, Rayleigh scattering is responsible for the blue color of the sky, and Mie scattering for the white color of the water droplets of clouds.

Light scattered from the surfaces of objects is by far the primary light which humans visually observe.^[7][8]

 

當知『矩陣光學』並非是另類『幾何光學』，祇不過『光線追跡』在『近軸近似』下『幾何光學』之『數學』方便『表達工具』而已矣？？！！不免還得用著『針孔相機模型』

Pinhole camera model

The pinhole camera model describes the mathematical relationship between the coordinates of a 3D point and its projection onto the image plane of an ideal pinhole camera, where the camera aperture is described as a point and no lenses are used to focus light. The model does not include, for example, geometric distortions or blurring of unfocused objects caused by lenses and finite sized apertures. It also does not take into account that most practical cameras have only discrete image coordinates. This means that the pinhole camera model can only be used as a first order approximation of the mapping from a 3D scene to a 2D image. Its validity depends on the quality of the camera and, in general, decreases from the center of the image to the edges as lens distortion effects increase.

Some of the effects that the pinhole camera model does not take into account can be compensated, for example by applying suitable coordinate transformations on the image coordinates, and other effects are sufficiently small to be neglected if a high quality camera is used. This means that the pinhole camera model often can be used as a reasonable description of how a camera depicts a 3D scene, for example in computer vision and computer graphics.

A diagram of a pinhole camera.

The geometry and mathematics of the pinhole camera

NOTE: The x₁x₂x₃ coordinate system in the figure is left-handed, that is the direction of the OZ axis is in reverse to the system the reader may be used to.

The geometry related to the mapping of a pinhole camera is illustrated in the figure. The figure contains the following basic objects:

• A 3D orthogonal coordinate system with its origin at O. This is also where the camera aperture is located. The three axes of the coordinate system are referred to as X1, X2, X3. Axis X3 is pointing in the viewing direction of the camera and is referred to as the optical axis, principal axis, or principal ray. The 3D plane which intersects with axes X1 and X2 is the front side of the camera, or principal plane.
• An image plane where the 3D world is projected through the aperture of the camera. The image plane is parallel to axes X1 and X2 and is located at distance  from the origin O in the negative direction of the X3 axis. A practical implementation of a pinhole camera implies that the image plane is located such that it intersects the X3 axis at coordinate -f where f > 0. f is also referred to as the focal length^{[citation needed]} of the pinhole camera.
• A point R at the intersection of the optical axis and the image plane. This point is referred to as the principal point or image center.
• A point P somewhere in the world at coordinate relative to the axes X1,X2,X3.
• The projection line of point P into the camera. This is the green line which passes through point P and the point O.
• The projection of point P onto the image plane, denoted Q. This point is given by the intersection of the projection line (green) and the image plane. In any practical situation we can assume that  > 0 which means that the intersection point is well defined.
• There is also a 2D coordinate system in the image plane, with origin at R and with axes Y1 and Y2 which are parallel to X1 and X2, respectively. The coordinates of point Q relative to this coordinate system is .

The geometry of a pinhole camera

 

The pinhole aperture of the camera, through which all projection lines must pass, is assumed to be infinitely small, a point. In the literature this point in 3D space is referred to as the optical (or lens or camera) center.^[1]

Next we want to understand how the coordinates  of point Q depend on the coordinates  of point P. This can be done with the help of the following figure which shows the same scene as the previous figure but now from above, looking down in the negative direction of the X2 axis.

The geometry of a pinhole camera as seen from the X2 axis

 

In this figure we see two similar triangles, both having parts of the projection line (green) as their hypotenuses. The catheti of the left triangle are  and f and the catheti of the right triangle are  and  . Since the two triangles are similar it follows that

or 

A similar investigation, looking in the negative direction of the X1 axis gives

or 

This can be summarized as

 

which is an expression that describes the relation between the 3D coordinates of point P and its image coordinates  given by point Q in the image plane.

 

，談那『理想化』的『成像系統』，說這目不可見之『一條光線』 ，惟願能聚焦吧！！若講懸疑，光線直行，遇物『剪影成像』，此『像』為『像』乎？是『虛』還是『實』？？西方學者柏拉圖曾經借此演說『洞穴寓言』，論述『教育』之本質！！東方方士李少翁過去用來『招魂』漢武帝嬪妃李夫人，設帳弄影上演了一齣

皮影戲

皮影戲，又稱影子戲或燈影戲， 是一種民間藝術，顧名思義其演出是利用燈光把獸皮或紙板做成的人物剪影照射在白色的影幕上，以表演故事的戲劇，是世界許多國家皆有的一種戲劇形式，如土耳其的皮影戲稱為 Karagöz。藝人在幕後操縱著皮影人物，再伴以音樂和歌唱方式演出，有「電影始祖」之美譽。

在過去電影、電視等等媒體尚未發達的年代，皮影戲曾是十分受歡迎的民間娛樂活動之一。在陝西、甘肅天水等地農村，這種拙樸的漢族民間藝術形式很受人們的歡迎。

中國傳統皮影戲

歷史

皮影戲又叫燈影戲，它是用燈光照射到刮薄的牛羊皮上，通過人物剪影的活動來表演故事情節的一種民間戲劇藝術。皮影是起源於中華民族的藝術，結合了民間工藝與戲曲。

皮影戲歷史悠久，不少文獻記載漢武帝時，方士李少翁進言說他有招魂之術，並設帳弄影以招嬪妃李夫人之亡靈^[1]。正如陝西皮影的流傳：「皮影戲始於漢，興於唐，盛於宋」。另一說亦與亡靈有關 ，唐代俗講僧在佛寺利用燈影說理和超渡亡靈。所以，皮影與宗教有密切的關係。

無論如何，皮影戲至宋朝時已有相當的規模與水平，而且相當盛行 。南宋時，杭州更有「繪革社」的影戲組織出現。至元代，軍隊更帶同皮影班子隨軍遠征，將皮影傳到中亞的國家；在13-15世紀，由西亞再傳到歐洲各國。皮影盛行於關中一帶，傳統劇目就有計數百本，唱腔則多達幾十種。

皮影戲於明朝萬曆(1573年-1619年)年間已十分盛行。明末清初，皮影藝術與道教結合，產生了環縣道情皮影。至清朝，皮影藝術已發展到了鼎盛時期。當時很多大戶人家，都以請名師刻制影人、安置精工影箱和私養影班為榮。清光緒以前，皮影戲的影人是用牛皮鏤空製作的，花紋粗糙，也無色彩，後來經過藝人的努力，改用7層皮紙做的襯殼來製作，並雕刻出各種花紋，著上色彩，同時根據故事中的影人形象，配有人物臉譜。影人一般7寸左右。而在民間，亦有很多大大小小的皮影戲班。

但在清朝後期，有些地方官府害怕皮影戲場聚眾起事，曾出現禁演影戲和拘捕皮影人之事。第二次世界大戰時民不聊生，皮影更一蹶不振。不過在抗日戰爭中，福建漳州就以皮影戲來宣傳抗日的鬥爭 。自中國解放後，殘存皮影戲班和藝人，在當時政府的扶持下，得以復甦。但到文化大革命時期，皮影藝術因破四舊而再遭打擊。改革開放後，傳統文化逐漸受到重視。雖然皮影戲得以復甦和發展，但仍受電子影視和流行文化所衝擊。中國的皮影藝術經過長期的流變，已形成不同的地方流派，諸如山西皮影、隴東皮影、陝西皮影 、北京皮影、山東皮影、青海皮影、寧夏皮影等，各自反映出獨有的風格特色。

 

？？不知是『差』的『多』『不多』耶！！？？