What is the difference between "dichotomous", "binary", "boolean", etc.?

To classify species we use a method called: dichotomous biological key. It works base on true and false cycles. In computer sciences true and fulse working is called boolean and binary is a 0 and 1 system (which is like true and false).

What is the difference between them? Can I use term "Binary biological key"? Are these really different?

• I'm no programmer, but I thought what you are referring to was a boolean, not binary. Binary's a number system, boolean's true/false. Commented Jan 15, 2013 at 19:55
• yes you are right Commented Jan 15, 2013 at 20:01
• It's not quite correct that "true and false working is called Binary". The number system is called binary (meaning base-2, as opposed to decimal, or base-10). However, binary as an adjective just means "appearing in pairs" - e.g. "binary star" or "binary explosive". If you want to specify that something can have one of two states - not more, not less - then "dichotomous" is an excellent word. If you're talking about philosophy, try Manichaean. Commented Jan 15, 2013 at 20:06
• The number system, the logical system, the mathematics, and the cladistic system are all mixed up here. Not to mention their terminology, which is all over the map. Anyone who's unclear on the concepts and their distinctions and limitations shouldn't be writing about them, or attempting to refer to them terminologically. Commented Jan 15, 2013 at 21:00
• I am not native. I supposed maybe "Binary biological key" is Correct just like "dichotomous biological key" Commented Jan 15, 2013 at 21:53

Boolean refers to Boolean algebra, named after George Boole.

While Boolean true/false values have other uses in computer science - a heavy use of it today - the thing that makes it Boolean isn't just that it can such values can only be true or false, but that one can also do Boolean algebra on it (e.g. in the expression `x ∧ (y ∨ ¬z)` expressed in computer code as e.g. `x && (y || !z)` (C-style), `x AND (y OR NOT z)` (Basic-style) and others). If we had a programming language that allowed of branching on a two-way value, but didn't allow for such Boolean algebra, then such values wouldn't truly be Boolean.

You don't do Boolean algebra with a dichotomous key, so it would would be incorrect to call it Boolean.

Binary means anything involving two things. A dichotomous key is hence a binary approach, but this meaning is different to some more specific meanings of binary (it has nothing to do with the binary number system, for example).

A dichotomy refers to splitting something into two parts. Hence everything that is dichotomous is binary, but not everything that is binary is dichotomous.

So, Boolean is wrong, binary is valid, but not as precise as dichotomous which is completely correct.

In most programming languages, boolean variables are either `true` or `false`; in Ruby, however, a boolean variable is `true` only if it is neither `false` nor `nil`. Moreover, Boolean operations can operate on objects other than boolean variables, and allow don't-care values as valid inputs.

A binary operation involves a choice between two, and only two, mutually exclusive alternatives, and thus does accomplish a dichotomy. However, binary as an adjective simply describes something that consists of two parts.

In biology, dichotomous key is a standard term to the extent that you will find it in most dictionaries:

dichotomous key, n. : biology : a key to classification based on a choice between two alternative characters [MW Unabridged]

There isn't a compelling reason to call it anything else.

• +1 for using the standard term for the domain. Using 'boolean' in a biology paper would probably be as jarring as using 'dichotomous key' in a Ruby program, even though English-wise they mean almost the same thing.
– Lynn
Commented Jan 16, 2013 at 3:36
• @Lynn it wouldn't just be jarring, it would be wrong. If you can't do Boolean algebra with it, it isn't Boolean. Commented Jan 16, 2013 at 12:08

The words mean somewhat similar things in this context (a boolean value is either true or false and never both, so it could be considered a common example of a dichotomy). Boolean, however, contains a concept of "right", where dichotomous only contains the concept of being different.

Very often in biology there isn't a clear mapping to "true" and "false", so calling it boolean could misleadingly imply that there is. Indeed, from a brief googling of this method, it seems to not include the concept that one member of these "couplets" is right and the other is wrong, merely that they're distinct, so dichotomous is more right than boolean.

In some other case, where all else were equal, the convention would win out, so I'd (for example) still recommend to call it a dichotomous biological key and not a boolean biological key.

• A biological example: 1.If it have 8 legs, go to 2, else go to 3. Commented Jan 15, 2013 at 22:22

If you have a dichotomous key represented as a branching diagram in a text book that you wanted to automate into a piece of software, then you would almost certainly use boolean variables to track each decision point.

So the logic is the same in each case, but the language conventions adopted by each discipline involve different labels.

Are you referring to the documented definition of the term Dichotomous key (a key for the identification of organisms based on a series of choices between alternative characters MW); A written tool for identification of plants and animals. It is written as a sequence of paired questions, the choice of which determines the next pair of questions until a name or identification is reached. Wikipedia)?

If not, you would probably better chose another term instead.

The different meanings of dichotomous, binary and boolean are already explained well.