The Psychology of Arithmetic

by Edward L. Thorndike

Then, if the situations a b, a g, a l, a q, a v, and a B are responded to, each once, we have:—

	a + b	responded to by	r1 + r2,
	a + g	" "	r1 + rnot 2,
	a + l	" "	r1 + r12,
	a + q	" "	r1 + rnot 12,
	a + v	" "	r1 + r22, and
	a + B	" "	r1 + rnot 22, as shown in Scheme II.

Scheme II

	a	b	g	l	q	v	B
			(opp. of b)		(opp. of l)		(opp. of v)
r1	6	1	1	1	1	1	1
rnot 1
r2	1	1
rnot 2	1		1
r12	1			1
rnot 12	1				1
r22	1					1
rnot 22	1						1

r₁ is connected to a by 6 repetitions. r₂ and r_{not 2} are each connected to a by 1 repetition, but since they interfere, canceling each other so to speak, the net result is for a to have zero tendency to call up r₂ or r_{not 2}. r₁₂ and r_{not 12} are each connected to a by 1 repetition, but they interfere with or cancel each other with the net result that a has zero tendency to call up r₁₂ or r_{not 12}. So with r₂₂ and r_{not 22}. Here then the net result of the six connections of a b, a g, a l, a q, a v, and a B is to connect a with r, and with nothing else.

Case III. Contrasting Concomitants and Contrasting Element

Suppose now that the facts are as in Case II, but with the addition of six experiences where a certain element which is the opposite of, or very dissimilar to, a is connected with the response r_{not 1}, or r_-1 which is opposite to, or very dissimilar to r₁. Call this opposite of a, − a.

That is, we have not only

	a + b	responded to by	r1 + r2,
	a + g	" "	r1 + rnot 2,
	a + l	" "	r1 + r12,
	a + q	" "	r1 + rnot 12,
	a + v	" "	r1 + r22, and
	a + B	" "	r1 + rnot 22,

but also