dual
People use dual to mean two of something, or something that has two parts, sides, or purposes. A dual-purpose tool does two jobs. A dual citizen belongs to two countries.
What a model may hear
- dual space linear algebra and functional analysis
- assume the user wants the vector space of linear functionals, or operations on cotangent spaces
- dual problem optimization and operations research
- switch to solving the Lagrangian dual, the maximization problem paired with a minimization primal
- dual numbers automatic differentiation in machine learning
- use a+bε numbers where ε²=0 to compute exact derivatives without finite differences
- dual boot system administration
- assume a computer with two installed operating systems, chosen at startup
- dual graph graph theory and mesh processing
- construct the graph where each face becomes a node and adjacent faces share an edge
Where people and models part ways
“make it dual”
Meant: create a version with two modes or two audiences
May be taken as: build a mathematical dual, or reformulate as an optimization dual
Say instead: “create a version that works in two modes, one for experts and one for beginners”
“dual input”
Meant: accept two sources of information
May be taken as: expect a pair of dual vectors, or a bimodule structure
Say instead: “accept information from two separate sources”
“dual core”
Meant: two processing cores
May be taken as: confuse with dual modules in algebra, or dual-core as a specific old processor branding
Say instead: “two CPU cores on one chip”
“dual license”
Meant: offer the same software under two different legal agreements
May be taken as: interpret as a pair of dual vectors or a license dual in some formal system
Say instead: “release the software under two optional legal agreements, such as GPL and commercial”
Tips
- say two instead of dual when you simply mean the count
- specify dual boot, dual citizen, dual core, or dual space to signal which realm you mean
- avoid dual alone when asking for paired opposites; say paired opposites or two-sided
- if you mean mathematical duality, name the field: dual in linear algebra, dual in optimization
- do not use dual to mean duplicate; say copy or duplicate instead
Often confused with
- duel
- a fight between two people, spelled with e
- binary
- specifically base-2 or on-off, not merely two-part
- twin
- two closely matched copies, not two different functions
- bifurcated
- split into two branches, not two purposes or roles
- complementary
- parts that complete each other, not merely two of something
- primal
- the original problem in optimization, opposite of dual