在原文書中碰到 orthogonal 時，總是會讓我停下來，想想作者要表達的意思到底是什麼。我在 Collins COBUILD Advanced Leaner's Dictionary 2006 和 Longman Dictionary of Contemporary English 4th Edition 都查不到這個單字，但是分別在以下網路資源中找到這個單字的中文翻譯：

另外，從 Google 也可以查到一堆採用 "正交" 作為對應中文的例子。

試將這些查到的中文詞彙套用到以下例句：

Alternately, we can cut across the system in an entirely orthogonal way.
譯：我們還可以用另一種完全正交（矩形、直角）的方式切割系統。

However, the fact remains that we cannot construct a complex system in both ways simultaneously, for they are completely orthogonal views.
譯：然而，事實上我們無法同時用兩種方式建構系統，因為它們是完全正交（矩形、直角）的觀點。

上述例句摘自 Grady Booch 的 Object-Oriented Analysis and Design with Applications 3rd Edition，前後文主要是在討論演算法分解（功能分解）與物件導向分解這兩種分割系統的方式。即使有完整的上下文，看了這種直接對號入座的譯法恐怕也 是讓人摸不著頭腦。

中文的資源不夠用，最好的辦法就是找原文的解釋了。以下解釋摘自英文維基百科（在該字的 Derived Meanings 小節）：

Orthogonality is a system design property facilitating feasibility and compactness of complex designs. Orthogonality guarantees that modifying the technical effect produced by a component of a system neither creates nor propagates side effects to other components of the system. The emergent behavior of a system consisting of components should be controlled strictly by formal definitions of its logic and not by side effects resulting from poor integration, i.e. non-orthogonal design of modules and interfaces.

以下則是 SearchStorage.com  的解釋：

In geometry, orthogonal means "involving right angles" (from Greek ortho, meaning right, and gon meaning angled). The term has been extended to general use, meaning the characteristic of being independent (relative to something else). It also can mean: non-redundant, non-overlapping, or irrelevant. In computer terminology, something - such as a programming language or a data object - is orthogonal if it can be used without consideration as to how its use will affect something else.

從以上的解釋可以發現，orthogonal 有許多衍生意義，而用在前面舉的兩個例句時，比較適合的翻譯應為「無關」、「互不影響」（「正交」一詞反而讓人覺得涉及的事物彼此有關、有交集）。根據這些線索，試將前二例句重譯如下：

Alternately, we can cut across the system in an entirely orthogonal way.
譯：我們還可以用另一種截然不同的方式切割系統。

However, the fact remains that we cannot construct a complex system in both ways simultaneously, for they are completely orthogonal views.
譯：然而，事實上我們無法同時用兩種方式建構系統，因為它們是完全不同的觀點。

這裡我將 orthogonal 均譯為「不同的」，主要是希望在不離原意太遠的前提下，讓句子讀起來更順。也許您有更好的譯法？