vector

The story surprised me to hear that the world’s most common mental model is something like “a vector is an arrow” or “a vector is a quantity with direction and magnitude”.

A New and Complete Dictionary of Arts and Sciences of 1764

• vector explains it as “an astronomical term, a line connecting a planet and its center (or elliptical focus).
• It also says that the origin of the name is because the planets look like they are being CARRIED by the lines.
• By the way, vector means “carry” in Latin.

Encyclopaedia Perthensis of 1816

• The idiom Radius Vector appears, but there is no occurrence of vector by itself.

A book written in 1855 explaining Newtonian mechanics

• The word vector appears, but only in the idiomatic form “radius vector.

• As far as the equation goes, it’s not what we would call a vector today.

  • r is, in today’s terms, “the length of the line segment connecting the focal point of the ellipse to a point on the ellipse.”

• 1687 Newton’s Principia Mathematica

• 1835 Hamilton, Definition of complex numbers without square roots of negative numbers

• 1843 Hamilton generalizes complex numbers and defines quaternions, calling the imaginary part by the term vector

• 1878 Clifford invents the concept of inner and outer products, showing that the equivalent of the product of quaternions can be defined for three pairs of numbers

• 1881 Gibbs, in writing a textbook on electromagnetism, uses only the three pairs of numbers in the imaginary part (vector part) of the quaternions in isolation.

  • It was much later that the non-3D “arrows” that we now read as vectors came to be called vectors.

• 1636 Affine transformations studied as a branch of geometry

• 1857 Linear transformations including Cayley and affine transformations are represented by matrices

  • In the same year, Glassman, in the course of his research, creates the concepts of linear independence, scalar times dimension, and

• 1888 Peano gives a modern definition of vector space

  • In this area, the vector is finally formulated, as we now call it.

Elements of Vector Analysis by Gibbs (1881)

• 
• The beginning is similar to the current definition of a vector space
• But when you start saying there are three unit vectors, you’re implicitly assuming a three-dimensional space.
  • 
• Define two types of multiplication for vectors on p. 5
  • 
• And this result
  • 
  • and attributed to [quaternion

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