scalar

Etymology

It is borrowed from Latin scālāris (“of a ladder or flight of steps”),^{[2][3][4][5][6][7]} from scāla (“ladder, steps”), mostly used in the plural scālae,^[2][3][4][8] the source of scale in the sense of a graded series.^[2][3][8] Wiktionary derives the Latin noun from scandō (“to climb”).^[1] The mathematical noun was coined in 1846 by the Irish mathematician William Rowan Hamilton,^[3][2][1] and Merriam-Webster Unabridged takes the sense "able to be represented by a point on a scale" as probably formed anew from scale and -ar.^[6]

Earliest recorded meaning

Resembling a ladder: 1656, in Thomas Blount's Glossographia,^[2][4][3] later used in botany for scalariform.^[2][7]

Semantic evolution

For two centuries the word kept the Latin sense "ladder-like".^[2][4] In 1846 Hamilton used it in his work on quaternions for a real number, a quantity with magnitude but no direction, as opposed to the vector;^[2][3][6] the noun and the matching adjective date from his paper.^[2][9] The mathematical sense then spread to physics, for quantities such as mass, time or temperature.^[6][10] In the 20th century the adjective was connected with other senses of scale: with the musical scale from 1928^[2][6] and with a graded scale from 1959.^[2] Wiktionary also records a computing sense, a single value as opposed to an array.^[1]

Timeline

• 1656 – resembling a ladder.^[2][4][6]
• 1846 – in mathematics, a real number in quaternions; a quantity with magnitude but no direction; also as an adjective.^[2][4][6]
• 1928 – of or relating to a musical scale.^[2]
• 1959 – of or relating to a graded scale.^[2]

Meanings

Adjective

1. (mathematics) Having magnitude but no direction; of or relating to a scalar: scalar multiplication.^[10][6][2]
2. Able to be represented by a point on a scale; graded.^[6][2]
3. Of or relating to a musical scale: scalar runs on the piano.^[6][2]
4. Arranged like a ladder, in a series of steps, and in botany scalariform.^[6][2][7]

Noun

1. (mathematics) A quantity, such as mass, time or temperature, that has magnitude but no direction and can be described by a single number, as opposed to a vector.^[10][6][2]
2. (mathematics) An element of the field over which a vector space is defined.^[10]

Word family

• pseudoscalar
• scalar field
• scalar product
• scalar triple product

Related words

• scale
• escalate
• scalariform
• ascend
• descend

References

1. ^ a b c d e Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ a b c d e f g h i j k l m n o p q r s t Oxford English Dictionary Online (accessed March 2026), Oxford: Oxford University Press
3. ^ a b c d e f Harper, Douglas. Online Etymology Dictionary, https://www.etymonline.com
4. ^ a b c d e f Barnhart, Robert K. (1988), The Barnhart Dictionary of Etymology
5. ^ The American Heritage Dictionary of the English Language (online 2024), 5th ed., Boston: Houghton Mifflin Harcourt
6. ^ a b c d e f g h i j k l Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
7. ^ a b c Shorter Oxford English Dictionary on Historical Principles (2002), 5th ed., ed. William R. Trumble and Angus Stevenson, Oxford: Oxford University Press
8. ^ a b Klein, Ernest. A Comprehensive Etymological Dictionary of the English Language. 2 vols. Amsterdam: Elsevier, 1966–1967.
9. ^ Barnhart, Robert K., ed. (1995), The Barnhart Concise Dictionary of Etymology, New York: HarperCollins
10. ^ a b c d Collins English Dictionary (2023), Glasgow: HarperCollins