Fwd: "octonion" - Word of the Day from the OED

[Dave Monroe]

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Subject: "octonion" - Word of the Day from the OED
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OED Online Word of the Day
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octonion, n.

DRAFT ENTRY Dec. 2008
Math.

Brit. /ktnn/, U.S. /ktonin/  Forms: 18- octonion, 19- octonian. [<
classical Latin octn eight each, eight at a time (see OCTONAL adj.) +
-ION suffix1, after QUATERNION n. Compare earlier BIQUATERNION n.
  In the form octonian after -IAN suffix.]

    1. A. McAulay's name for: a type of complex number in which the
coefficients are quaternions, i.e. a number having the form x = p + q,
where p and q are real quaternions, and is a scalar with 2 being equal
to either 1 or 0; = BIQUATERNION n. 2. Now rare.

1895-6 A. MCAULAY in Proc. Royal Soc. 59 169 Octonions is a name
adopted for various reasons in place of Clifford's Bi-quaternions.
1898 A. MCAULAY Octonions 19 An octonion is a quantity which requires
for its specification and is completely specified by a motor and two
scalars. 1910 Encycl. Brit. XXII. 722/2 Clifford makes use of a
quasi-scalar , commutative with quaternions... He considers two cases,
viz. 2 = 1 suitable for non-Euclidean space, and 2 = 0 suitable for
Euclidean space; we confine ourself to the second, and will call the
indicated bi-quaternion p + q an octonion... Clifford considers an
octonion p + q as the quotient of two motors + , ´ + ´.

    2. A type of hypercomplex number with eight coefficients, having
the form x = x0 + x1e1 + x2e2 + x3e3 + x4e4 + x5e5 + x6e6 + x7e7,
where the xn are real numbers and the en are imaginary units which, in
conjunction with 1 and -1, form a closed, non-commutative,
non-associative system under multiplication. Cf. OCTAD n. 2a, OCTAVE
n.2 2d.

1908 Amer. Jrnl. Math. 30 60 The factoring of a complex system of
eight units into a two-unit system and a four-unit system presents no
new difficulties... The octonian system is easily seen to be the
compound of the ordinary complex system and the quaternion system.
1969 Bull. Amer. Math. Soc. 75 980 (title) Octonion planes in
characteristic two. 1991 Jrnl. Math. Physics 32 1383 (title) The Dirac
equation in a non-Riemannian manifold... An analysis using the algebra
of quaternions and octonions. 2002 New Scientist 9 Nov. 32/4 Octonions
have revealed themselves as the most important system of all. That's
because they are crucial to string theory.

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