Doubling

Doubling refers to an increase by a factor of two, meaning a quantity becomes twice its original value. The term is used across disciplines to describe both the act of increasing and the resulting value.

In mathematics and the sciences, doubling is represented by the function f(x) = 2x. Many growth processes are described in terms of doubling time—the period required for a quantity to double. In exponential growth with constant relative rate r, the doubling time is t_d = ln(2)/r, yielding a fixed interval for successive doublings.

In finance and economics, doubling is central to discussions of investment growth and interest. The Rule of 72 provides a rough estimate of the years needed to double a sum at a fixed annual rate: years ≈ 72 ÷ rate. For example, at 6% annual return, money doubles in about 12 years.

In biology, doubling occurs in genetics and cell biology through events such as whole-genome duplication or polyploidy, where the chromosome set is doubled. Such duplications can influence evolution and development, as seen in some plants and other organisms. Errors in cell division can also produce higher ploidy levels, with biological consequences.

In computing and computer science, doubling is a design principle used in data structures, notably dynamic arrays that double their capacity when full to maintain efficient insertions. The concept of doubling also appears in other fields as a general description of twofold increase, though the specifics vary by context.