Where does substitution collide?

The shift in what a consumer buys when a good's price changes relative to others, so that a now more expensive good is given up in favour of a good that does the same job more cheaply: goods that trade off this way are called substitutes, and the rate at which a person will swap one for the other while staying equally well off is the marginal rate of substitution. Hicks and Allen's 1934 A Reconsideration of the Theory of Value rebuilt demand theory on this trade-off, separating the pure substitution response to a relative price from the income response. The referent is a choice a buyer makes among competing goods, measured in quantities and prices, not atoms trading places in a molecule, a variable swapped inside an integral, or a letter replaced in a coded message.[1]

Unit

The change in quantity demanded from a relative price change, holding well-being fixed

Recovery means

Not applicable

Measured by

Estimated from demand data as the compensated price response, or read off indifference curves as the marginal rate of substitution

A reaction in which one atom or group of atoms in a molecule is replaced by a different atom or group, leaving the rest of the structure intact: an incoming species attacks a carbon and a leaving group departs, and the timing of those two events defines the two classic pathways, one where they happen together and one where the leaving group departs first. Hughes and Ingold's 1935 Mechanism of substitution at a saturated carbon atom set out this kinetic picture and the labels that became SN2 and SN1. The referent is a chemical transformation of real molecules, tracked by reaction rates and products, and it has nothing to do with a shopper choosing between goods, a variable exchanged in an equation, or a cipher hiding a word.[2]

Unit

One replacement of an atom or group in a molecule, per reaction step

Recovery means

Not applicable

Measured by

Followed by reaction kinetics and product analysis, distinguishing the concerted pathway from the stepwise one by how rate depends on reagent concentrations

Replacing a variable or expression with a new one so that a problem takes a simpler form, most familiar as the substitution rule for integration, where setting a new variable equal to part of the integrand turns a hard integral into an easy one and then undoes the swap at the end. Apostol's 1967 Calculus presents this rule as the integral counterpart of the chain rule, with the careful bookkeeping that keeps the rewritten integral equal to the original. The referent is a formal manoeuvre on symbols, valid by proof rather than by measurement, and it is unrelated to a buyer swapping goods, atoms trading places in a molecule, or a letter disguised in a cipher.[3]

Unit

One change of variable that rewrites an expression into an equivalent form

Recovery means

The original variable is restored by back-substitution once the rewritten problem is solved

Measured by

Verified by proof and by differentiating the result, not by observation, since the substituted form is provably equal to the original

An encryption method that hides a message by replacing each unit of the plaintext with a ciphertext symbol according to a fixed rule, as the Caesar cipher shifts every letter by a constant amount: the letters keep their positions but change their identities, which is what separates substitution from transposition, where the letters keep their identities but change their positions. Shannon's 1949 Communication Theory of Secrecy Systems analysed such ciphers formally and showed how a simple substitution leaks structure that lets a codebreaker recover the message. The referent is a secrecy scheme operating on symbols in a message, judged by how well it resists attack, and it is not a consumer's choice among goods, a chemical replacement of atoms, or a variable exchanged in an integral.[4]

Unit

One fixed mapping from plaintext symbols to ciphertext symbols

Recovery means

The plaintext is recovered by applying the inverse mapping with the key

Measured by

Judged by resistance to cryptanalysis, since a simple substitution is broken by frequency analysis of the ciphertext symbols