blocks|key|1437482|text|Orthogonality是表示“更改A不会更改B”的属性。正交系统的一个例子是无线电，其中改变电台不会改变音量，反之亦然。|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|1437483|非正交系统就像直升机，改变速度可以改变方向。|1437484|在编程语言中，这意味着当您执行一条指令时，除了该指令之外什么也不会发生(对于调试非常重要)。|1437485|当提到instruction+sets时，还有一个特定的含义。|1437486|entityMap|0|LINK|mutability|MUTABLE|url|http://en.wikipedia.org/wiki/Orthogonal|1|http://en.wikipedia.org/wiki/Orthogonal_instruction_set^0|0|D|0|0|0|0|3|G|1|0^^$0|@$1|2|3|4|5|6|7|T|8|@]|9|@$A|U|B|V|1|W]]|C|$]]|$1|D|3|E|5|6|7|X|8|@]|9|@]|C|$]]|$1|F|3|G|5|6|7|Y|8|@]|9|@]|C|$]]|$1|H|3|I|5|6|7|Z|8|@]|9|@$A|10|B|11|1|12]]|C|$]]|$1|J|3|-4|5|6|7|13|8|@]|9|@]|C|$]]]|K|$L|$5|M|N|O|C|$P|Q]]|R|$5|M|N|O|C|$P|S]]]]

<a href="http://en.wikipedia.org/wiki/Orthogonal" rel="noreferrer">Orthogonality</a> is the property that means "Changing A does not change B". An example of an orthogonal system would be a radio, where changing the station does not change the volume and vice-versa. 

A non-orthogonal system would be like a helicopter where changing the speed can change the direction.

In programming languages this means that when you execute an instruction, nothing but that instruction happens (very important for debugging).

There is also a specific meaning when referring to <a href="http://en.wikipedia.org/wiki/Orthogonal_instruction_set" rel="noreferrer">instruction sets</a>.

blocks|key|1222624|text|想象一下，它能够改变一件事，而不会对另一件事产生看不见的影响。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1222625|entityMap^0|0^^$0|@$1|2|3|4|5|6|7|D|8|@]|9|@]|A|$]]|$1|B|3|-4|5|6|7|E|8|@]|9|@]|A|$]]]|C|$]]

Think of it has being able to change one thing without having an unseen affect on another part.

blocks|key|1437634|text|广义上，正交性是两个事物之间的一种关系，它们彼此之间的影响最小。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1437635|这个术语来自数学，其中两个向量是正交的，如果它们以直角相交。|1437636|考虑一个典型的二维笛卡尔空间(具有X/Y轴的典型网格)。绘制两条直线:+x=1和y=1。这两条直线是正交的。您可以通过更改x来更改x=1，这对另一行没有任何影响，反之亦然。|1437637|在软件中，这个术语可以适当地用在你谈论的系统的两个相互独立的部分的情况下。|1437638|entityMap^0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|J|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|K|8|@]|9|@]|A|$]]|$1|D|3|E|5|6|7|L|8|@]|9|@]|A|$]]|$1|F|3|G|5|6|7|M|8|@]|9|@]|A|$]]|$1|H|3|-4|5|6|7|N|8|@]|9|@]|A|$]]]|I|$]]

Broadly, orthogonality is a relationship between two things such that they have minimal effect on each other.
The term comes from mathematics, where two vectors are orthogonal if they intersect at right angles.
Think about a typical 2 dimensional cartesian space (your typical grid with X/Y axes). Plot two lines: x=1 and y=1. The two lines are orthogonal. You can change x=1 by changing x, and this will have no effect on the other line, and vice versa.
In software, the term can be appropriately used in situations where you're talking about two parts of a system which behave independently of each other.

blocks|key|1222842|text|大多数答案都非常冗长，甚至晦涩难懂。重点是:如果工具是正交的，可以添加、替换或删除它，以支持更好的工具，而不会搞砸其他一切。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1222843|这是木匠有锤子和锯子的区别，可以用来锤子或锯子，或者有一些新的锤子/锯子组合，它的设计是锯木，然后把它锤击在一起。这两种工具都适用于锯切和锤击，但如果您的任务需要锯切，而不是锤击，那么只有正交工具才能工作。同样，如果你需要用螺丝而不是锤子，你不需要扔掉你的锯子，如果它是正交的(不与你的锤子混在一起)。|1222844|典型的例子是unix命令行工具:您有一个工具用于获取磁盘内容(dd)，另一个工具用于从文件中过滤行(grep)，另一个工具用于将这些行写入文件(cat)，等等。这些工具都可以随意混合和匹配。|1222845|entityMap^0|0|0|0^^$0|@$1|2|3|4|5|6|7|H|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|I|8|@]|9|@]|A|$]]|$1|D|3|E|5|6|7|J|8|@]|9|@]|A|$]]|$1|F|3|-4|5|6|7|K|8|@]|9|@]|A|$]]]|G|$]]

Most of the answers are very long-winded, and even obscure. The point is: if a tool is orthogonal, it can be added, replaced, or removed, in favor of better tools, without screwing everything else up.

It's the difference between a carpenter having a hammer and a saw, which can be used for hammering or sawing, or having some new-fangled hammer/saw combo, which is designed to saw wood, then hammer it together. Either will work for sawing and then hammering together, but if you get some task that requires sawing, but not hammering, then only the orthogonal tools will work. Likewise, if you need to screw instead of hammering, you won't need to throw away your saw, if it's orthogonal (not mixed up with) your hammer.

The classic example is unix command line tools: you have one tool for getting the contents of a disk (dd), another for filtering lines from the file (grep), another for writing those lines to a file (cat), etc. These can all be mixed and matched at will.

blocks|key|1222504|text|来自wikipedia|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|1222505|计算机科学|1222506|正交性是一种系统设计属性，有助于复杂设计的可行性和紧凑性。正交性保证修改系统组件产生的技术效果既不会产生副作用，也不会传播到系统的其他组件。由组件组成的系统的紧急行为应该严格由其逻辑的形式化定义来控制，而不是受到由于集成不良而产生的副作用，即模块和接口的非正交设计。正交性减少了测试和开发时间，因为它更容易验证既不会导致副作用也不依赖它们的设计。|1222507|例如，一辆汽车具有正交的组件和控制(例如，加速车辆不会影响任何其他组件，但仅涉及加速功能的组件)。另一方面，非正交设计可能会影响转向、制动(例如电子稳定控制)或速度调整悬架。1因此，这种用法可以从数学中正交的使用中得到:当且仅当基础向量相互正交时，可以通过将向量分别投影到一组基本向量的每个成员上，将其投影到子空间。|1222508|如果任何指令可以在任何寻址模式下使用任何寄存器，则称指令集是正交的。此术语源于将指令视为其组成部分是指令字段的向量。一个字段标识要操作的寄存器，另一个字段指定寻址模式。正交指令集对寄存器和寻址模式的所有组合进行唯一编码。|1222509|entityMap|0|LINK|mutability|MUTABLE|url|http://en.wikipedia.org/wiki/Orthogonal|1^0|2|9|0|0|0|0|2F|1|1|0|0^^$0|@$1|2|3|4|5|6|7|U|8|@]|9|@$A|V|B|W|1|X]]|C|$]]|$1|D|3|E|5|6|7|Y|8|@]|9|@]|C|$]]|$1|F|3|G|5|6|7|Z|8|@]|9|@]|C|$]]|$1|H|3|I|5|6|7|10|8|@]|9|@$A|11|B|12|1|13]]|C|$]]|$1|J|3|K|5|6|7|14|8|@]|9|@]|C|$]]|$1|L|3|-4|5|6|7|15|8|@]|9|@]|C|$]]]|M|$N|$5|O|P|Q|C|$R|S]]|T|$5|O|P|Q|C|$R|S]]]]

from <a href="http://en.wikipedia.org/wiki/Orthogonal" rel="nofollow noreferrer">wikipedia</a>:

Computer science

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. Orthogonality reduces testing and development time because it is easier to verify designs that neither cause side effects nor depend on them.

For example, a car has orthogonal components and controls (e.g. accelerating the vehicle does not influence anything else but the components involved exclusively with the acceleration function). On the other hand, a non-orthogonal design might have its steering influence its braking (e.g. electronic stability control), or its speed tweak its suspension.<a href="http://en.wikipedia.org/wiki/Orthogonal" rel="nofollow noreferrer">1</a> Consequently, this usage is seen to be derived from the use of orthogonal in mathematics: One may project a vector onto a subspace by projecting it onto each member of a set of basis vectors separately and adding the projections if and only if the basis vectors are mutually orthogonal.

An instruction set is said to be orthogonal if any instruction can use any register in any addressing mode. This terminology results from considering an instruction as a vector whose components are the instruction fields. One field identifies the registers to be operated upon, and another specifies the addressing mode. An orthogonal instruction set uniquely encodes all combinations of registers and addressing modes.

blocks|key|1223105|text|正交性是指语言由一组独立的原语构造组成的程度，这些原语构造可以根据需要进行组合以表达程序。如果对要素的组合方式没有限制，则要素是正交的|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1223106|Example+:+non-orthogonality|code-block|syntax|javascript|1223107|PASCAL:函数不能返回结构化类型。函数式语言是高度正交的。|1223108|entityMap^0|0|0|0^^$0|@$1|2|3|4|5|6|7|K|8|@]|9|@]|A|$]]|$1|B|3|C|5|D|7|L|8|@]|9|@]|A|$E|F]]|$1|G|3|H|5|6|7|M|8|@]|9|@]|A|$]]|$1|I|3|-4|5|6|7|N|8|@]|9|@]|A|$]]]|J|$]]

Orthogonality means the degree to which language consists of a set of independent primitive constructs that can be combined as necessary to express a program. 
 Features are orthogonal if there are no restrictions on how they may be combined

<pre><code>Example : non-orthogonality
</code></pre>

PASCAL: functions can't return structured types. 
Functional Languages are highly orthogonal.

blocks|key|1222920|text|在编程语言中，如果编程语言特性没有限制(或异常)，则称其为正交特性。例如，在Pascal中，函数不能返回结构化类型。这是对从函数返回值的限制。因此，我们认为它是一个非正交特征。;)|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1222921|entityMap^0|0^^$0|@$1|2|3|4|5|6|7|D|8|@]|9|@]|A|$]]|$1|B|3|-4|5|6|7|E|8|@]|9|@]|A|$]]]|C|$]]

In programming languages a programming language feature is said to be orthogonal if it is bounded with no restrictions (or exceptions).
 For example, in Pascal functions can't return structured types. This is a restriction on returning values from a function. Therefore we it is considered as a non-orthogonal feature. ;)

blocks|key|1223034|text|编程语言中的正交性意味着可以以相对较少的方式组合一组相对较小的原语构造，以构建该语言的控制和数据结构。此外，任何可能的原语组合都是合法且有意义的。例如，考虑数据类型。假设一种语言有四种基本数据类型(整型、浮点型、双精度型和字符型)和两种类型运算符(数组和指针)。如果两个类型运算符可以应用于它们自身和四个原始数据类型，则可以定义大量的数据结构。正交语言特征的含义与其在程序中出现的上下文无关。(“正交”一词来自于正交向量的数学概念，它们彼此独立。)正交性源于基元之间关系的对称性。缺乏正交性会导致语言规则的例外。例如，在支持指针的编程语言中，应该可以定义一个指针来指向该语言中定义的任何特定类型。但是，如果不允许指针指向数组，则无法定义许多潜在有用的用户定义数据结构。我们可以通过比较IBM大型机和VAX系列小型机汇编语言的一个方面来说明正交性作为一种设计概念的用途。我们考虑一种简单的情况:将两个驻留在内存或寄存器中的32位整数值相加，并用总和替换其中一个值。IBM大型机有两条用于此目的的指令，它们的形式如下|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1223035|A+Reg1,+memory_cell
AR+Reg1,+Reg2|code-block|syntax|javascript|1223036|其中Reg1和Reg2表示寄存器。它们的语义是|1223037|Reg1+←+contents(Reg1)+%2B+contents(memory_cell)
Reg1+←+contents(Reg1)+%2B+contents(Reg2)|1223038|32位整数值的VAX加法指令为|1223039|ADDL+operand_1,+operand_2|1223040|它的语义是|1223041|operand_2+←+contents(operand_1)+%2B+contents(operand_2)|1223042|在这种情况下，任一操作数可以是寄存器或存储器单元。VAX指令设计是正交的，因为单个指令可以使用寄存器或存储器单元作为操作数。有两种方法可以指定操作数，它们可以以所有可能的方式组合在一起。IBM的设计不是正交的。四个操作数组合中只有两个是合法的，并且这两个操作数组合需要不同的指令A和AR。IBM的设计受到更多的限制，因此可写性较差。例如，您不能将两个值相加并将和存储在内存位置中。此外，由于限制和额外的说明，IBM的设计更加难以学习。正交性与简单性密切相关:语言的设计越正交，语言规则要求的例外就越少。更少的例外意味着设计中更高程度的规则性，这使得语言更容易学习、阅读和理解。任何学过英语重要部分的人都可以证明，学习它的许多规则例外是困难的(例如，i在e之前，c之后除外)。|1223043|entityMap^0|0|0|0|0|0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|W|8|@]|9|@]|A|$]]|$1|B|3|C|5|D|7|X|8|@]|9|@]|A|$E|F]]|$1|G|3|H|5|6|7|Y|8|@]|9|@]|A|$]]|$1|I|3|J|5|D|7|Z|8|@]|9|@]|A|$E|F]]|$1|K|3|L|5|6|7|10|8|@]|9|@]|A|$]]|$1|M|3|N|5|D|7|11|8|@]|9|@]|A|$E|F]]|$1|O|3|P|5|6|7|12|8|@]|9|@]|A|$]]|$1|Q|3|R|5|D|7|13|8|@]|9|@]|A|$E|F]]|$1|S|3|T|5|6|7|14|8|@]|9|@]|A|$]]|$1|U|3|-4|5|6|7|15|8|@]|9|@]|A|$]]]|V|$]]

Orthogonality in a programming language means that a relatively small set of
primitive constructs can be combined in a relatively small number of ways to
build the control and data structures of the language. Furthermore, every pos-
sible combination of primitives is legal and meaningful. For example, consider data types. Suppose a language has four primitive data types (integer, float,
double, and character) and two type operators (array and pointer). If the two
type operators can be applied to themselves and the four primitive data types,
a large number of data structures can be defined.
The meaning of an orthogonal language feature is independent of the
context of its appearance in a program. (the word orthogonal comes from the
mathematical concept of orthogonal vectors, which are independent of each
other.) Orthogonality follows from a symmetry of relationships among primi-
tives. A lack of orthogonality leads to exceptions to the rules of the language.
For example, in a programming language that supports pointers, it should be
possible to define a pointer to point to any specific type defined in the language.
However, if pointers are not allowed to point to arrays, many potentially useful user-defined data structures cannot be defined.
We can illustrate the use of orthogonality as a design concept by compar-
ing one aspect of the assembly languages of the IBM mainframe computers
and the VAX series of minicomputers. We consider a single simple situation:
adding two 32-bit integer values that reside in either memory or registers and
replacing one of the two values with the sum. The IBM mainframes have two
instructions for this purpose, which have the forms 

<pre><code>A Reg1, memory_cell
AR Reg1, Reg2
</code></pre>

where Reg1 and Reg2 represent registers. The semantics of these are

<pre><code>Reg1 ← contents(Reg1) + contents(memory_cell)
Reg1 ← contents(Reg1) + contents(Reg2)
</code></pre>

The VAX addition instruction for 32-bit integer values is

<pre><code>ADDL operand_1, operand_2
</code></pre>

whose semantics is

<pre><code>operand_2 ← contents(operand_1) + contents(operand_2)
</code></pre>

In this case, either operand can be a register or a memory cell.
The VAX instruction design is orthogonal in that a single instruction can
use either registers or memory cells as the operands. There are two ways to
specify operands, which can be combined in all possible ways. The IBM design
is not orthogonal. Only two out of four operand combinations possibilities are
legal, and the two require different instructions, A and AR . The IBM design
is more restricted and therefore less writable. For example, you cannot add
two values and store the sum in a memory location. Furthermore, the IBM
design is more difficult to learn because of the restrictions and the additional instruction.
Orthogonality is closely related to simplicity: The more orthogonal the
design of a language, the fewer exceptions the language rules require. Fewer
exceptions mean a higher degree of regularity in the design, which makes the
language easier to learn, read, and understand. Anyone who has learned a sig-
nificant part of the English language can testify to the difficulty of learning its
many rule exceptions (for example, i before e except after c).

blocks|key|1223198|text|正交性的基本思想是，在概念上不相关的东西不应该在系统中相关。架构中真正与其他部分无关的部分，如数据库和UI，不应该一起更改。对其中一个的更改不应导致对另一个的更改。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1223199|entityMap^0|0^^$0|@$1|2|3|4|5|6|7|D|8|@]|9|@]|A|$]]|$1|B|3|-4|5|6|7|E|8|@]|9|@]|A|$]]]|C|$]]

The basic idea of orthogonality is that things that are not related conceptually should not be related in the system. Parts of the architecture that really have nothing to do with the other, such as the database and the UI, should not need to be changed together. A change to one should not cause a change to the other.

blocks|key|1223328|text|正交性是这样一种想法，即概念上不相关的东西不应该在系统中相关，因此架构中彼此无关的部分，比如数据库和UI，不应该一起改变。对系统一部分的更改不应导致对另一部分的更改。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1223329|例如，如果您更改了屏幕上的几行代码，并导致数据库模式发生更改，则这称为耦合。您通常希望最小化几乎不相关的事物之间的耦合，因为它可能会增长，从长远来看，系统可能会成为维护的噩梦。|1223330|entityMap^0|0|0^^$0|@$1|2|3|4|5|6|7|F|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|G|8|@]|9|@]|A|$]]|$1|D|3|-4|5|6|7|H|8|@]|9|@]|A|$]]]|E|$]]

Orthogonality is the idea that things that are not related conceptually should not be related in the system so parts of the architecture that have nothing to do with each other, like the database and UI should not be changed together. A change to one part of your system should not cause the change to the other.
If for example, you change a few lines on the screen and cause a change in the database schema, this is called coupling. You usually want to minimize coupling between things that are mostly unrelated because it can grow and the system can become a nightmare to maintain in the long run.

What does "orthogonality" mean when talking about programming languages? 

What are some examples of Orthogonality?

What is "Orthogonality"?

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