『箱子』 boxes 是一個『奧秘』的觀點，有如《打開黑箱！！》之所言︰

科學追求真理，為的是打開大自然的黑箱；然而真理明白若昭，就是透明的白箱。我們總在求真的旅途上一知半解，努力化灰箱為白箱。如果偵錯就是科學，除錯即求真理，那這一段話用在『偵錯』與『除錯』上來講依然合適。這也說明為什麼人們喜歡用不同的灰度，來表達對『箱內之物』的認識與了解了。

………

千萬不要隨便對

Black box

In science, computing, and engineering, a black box is a device, system or object which can be viewed in terms of its inputs and outputs (or transfer characteristics), without any knowledge of its internal workings. Its implementation is “opaque” (black). Almost anything might be referred to as a black box: a transistor, algorithm, or the human brain.

The opposite of a black box is a system where the inner components or logic are available for inspection, which is most commonly referred to as a white box (sometimes also known as a “clear box” or a “glass box”).

───

□ □ 『性質』與 ○ ○『內涵』隨意假設。最好本著

知之為知之，不知為不知

的精神，『如實』的探索這些『箱子』的『功能』以及其『出入』之連接『方式』，如是或可避免某些『誤解』的吧！無須發生

……

派︰《 λ 運算︰概念導引之《補充》※真假祇是個選擇？？》文中講︰作者不知義大利羅馬的『真理之口』將會如何來決定『何謂是真？』而『什麼又是假』的呢？？

又為什麼『真』與『假』的 λ表達式是

$TRUE =_{df} (\lambda x. ( \lambda y. x))$
$FALSE =_{df} (\lambda x .( \lambda y. y))$

的呢？如果我們將『運算』看成『黑箱』，用『實驗』的方法來『研究』輸入輸出的『關係』，這一組有兩個輸入端的黑箱，對於任意的輸入『二元組』pair $(u, v)$ ，有︰

$(((\lambda x. ( \lambda y. x)) u) v) = u$
$(((\lambda x. ( \lambda y. y)) u) v) = v$

，於是將結論歸結成︰貼『真』標籤的箱子的『作用』是『選擇』輸入的『第一項』將之輸出；而貼『假』標籤的箱子的『作用』是『選擇』輸入的『第二項』將之輸出。

假使一位『軟體』工程師在函式『除錯』時，可能會採取在那個『函式』內『輸出』看看得到的『輸入』參數值是否正確？

於是將結論歸結成︰『真』標識符的函式『作用』是『選擇』輸入參數的『第一項』；『假』標識符的函式『作用』是『選擇』輸入參數的『第二項』。

那麼對一個已經打開的『白箱』，又知道作用的『函式』，怎麼會概念上『一頭霧水』的呢？？如果細思一個邱奇自然數『 0 』， $0 =_{df} (\lambda f. ( \lambda x. x))$ ，這跟『假』的 λ表達式有什麼不一樣的呢？那難道我們能說『0』就是『假』的嗎？在《布林代數》中的『0』與『1』其實是未定義的『兩態』基元概念── 就像歐式幾何學裡的『點』、『線』和『面』是『基本』概念一樣 ──，因此不管說它是『電壓高低』或者講它是『電流有無』的『數位設計』可以應用布林代數。要是我們將『0』『1』與『假』『真』概念連繫起來看，『布林邏輯』就是『真假』是什麼的『系統化』之概念內涵開展，它的『整體內容』呈現『兩態邏輯』的『方方面面』，縱使至於『孤虛』NAND 一個邏輯概念就足夠了，對於『 0 與 1 』概念本身還是『三緘其口』。……

『孤虛者』有言︰

物有無者，非真假也。苟日新，日日新，又日新。真假者，物之論也。論也者，當或不當而已矣。故世有孤虛者，言有孤虛論。

可以『中行獨復，以從道也。』，不至『迷復，凶』矣！

試問彼此井通，『彼』之『出』為『此』之『入』；『此』之『出』為『彼』之『入』。若以『此』觀『出入』者，實乃『彼』之『入出』也。故知所謂『出入』，相對『己我』所定之『名義』，存立論之所也。因而推知『有無』者『天地』之『然或不然』；『真假』者『理則』之『當或不當』。倘將『有無』匹配『真假』，終有『正反』兩說，『正言正說』── 真有，假無 ── 以及『正言若反』── 真無，假有 ── ，各站其『立場』者耶！！

生︰《》網上說︰

Design How-To

Clive Maxfield
11/21/2006 04:00 AM EST

The terms positive logic and negative logic refer to two conventions that dictate the relationship between logical values and the physical voltages used to represent them. Unfortunately, although the core concepts are relatively simple, fully comprehending all of the implications associated with these conventions requires an exercise in lateral thinking sufficient to make even the strongest amongst us break down and weep!

Before plunging into the fray, it is important to understand that logic 0 and logic 1 are always equivalent to the Boolean logic concepts of False and True, respectively (unless you’re really taking a walk on the wild side, in which case all bets are off). The reason these terms are used interchangeably is that digital functions can be considered to represent either logical or arithmetic operations (Fig 1).

1. Logical versus arithmetic views of a digital function.Having said this, it is generally preferable to employ a single consistent format to cover both cases, and it is easier to view logical operations in terms of “0s” and “1s” than it is to view arithmetic operations in terms of “Fs” and “Ts”. The key point to remember as we go forward is that logic 0 and logic 1 are logical concepts that have no direct relationship to any physical values.

Physical-to-abstract mapping (NMOS logic)
OK, let’s gird up our loins and meander our way through the morass one step at a time. The process of relating logical values to physical voltages begins by defining the frames of reference to be used. One absolute frame of reference is provided by truth tables, which are always associated with specific functions (Fig 2).

2. Absolute relationships between truth tables and functions.Another absolute frame of reference is found in the physical world, where specific voltage levels applied to the inputs of a digital function cause corresponding voltage responses on the outputs. These relationships can also be represented in truth table form. Consider a logic gate constructed using only NMOS transistors (Fig 3).

3. The physical mapping of an NMOS logic gate.With NMOS transistors connected as shown in Fig 3, an input connected to the more negative Vss turns that transistor OFF, and an input connected to the more positive Vdd turns that transistor ON. The final step is to define the mapping between the physical and abstract worlds; either 0v is mapped to False and +ve is mapped to True, or vice versa (Fig 4).

4. The physical to abstract mapping of an NMOS logic gate.Using the positive logic convention, the more positive potential is considered to represent True and the more negative potential is considered to represent False (hence, positive logic is also known as positive-true). By comparison, using the negative logic convention, the more negative potential is considered to represent True and the more positive potential is considered to represent False (hence, negative logic is also known as negative-true). Thus, this circuit may be considered to be performing either a NAND function in positive logic or a NOR function in negative logic. (Are we having fun yet?)

─── 引自《 M♪o 之學習筆記本《卯》基件︰【䷗】正言若反》

和

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傳說在機械化的黃金時代，流傳著一則故事︰

那時每一根小『螺絲釘』和小『螺絲帽』都是獨特的，不要說從這個工廠到那個工廠，就算在同一個工廠內，它們也都各有各的不同。只有那些沒有螺絲帽可以匹配的螺絲釘或沒有螺絲釘可以匹配的螺絲帽，才會被歸類成不好的。就這樣過了很多年，直到有一天艾索 ISO 出現了，推動『標準化』運動，自此一切都改變了 …。傳聞，最後一根獨特的小螺絲釘說︰『艾索，你這個老狐狸！…』。終究這些風塵往事早已被世人遺忘。

無獨有偶 ── 發生過的事，總會再次發生 ──，其後，Douglas McIlroy 先生在寫命令列的外殼程式的時候，提出了管線 pipline 的概念，並用『 | 』符號代表。比如說『甲命令 | 乙命令』，講的是把甲命令的輸出結果當成乙命令的輸入來使用。之後於 1973 年 Ken Thompson 把它擴大為『管子』pipe 的標準，寫進了 Unix 作業系統，影響至今，於是開起了一個標準串流的時代。那什麼是標準串流呢？它就是之前在『除蟲！除錯？終端機。』一文中 IPO 模型抽象化後的相容性輸出入結構，應用於命令列的各個相容的指令的輸出入檔案 ── 當然也可以是裝置檔 ── 可串接性 chainable 的標準化。它定義了『標準輸入』stdin、『標準輸出』stdout、『標準錯誤』stderr，打開了程式間溝通的橋樑。舉例來說，假如 more 代表一頁一頁的讀，cat /boot/config.txt | more 就是一頁一頁的讀取樹莓派的開機組構檔 config.txt。