Name: Anonymous 2011-04-21 9:26
Next, a few words that will have to be used repeatedly. Consider
the simple example in which, under the influence of sunshine,
pale skin changes to dark skin. Something, the pale skin, is
acted on by a factor, the sunshine, and is changed to dark skin.
That which is acted on, the pale skin, will be called the operand,
the factor will be called the operator, and what the operand is
changed to will be called the transform. The change that occurs,
which we can represent unambiguously by
pale skin -> dark skin
is the transition.
The transition is specified by the two states and the indication
of which changed to which.
TRANSFORMATION
The single transition is, however, too simple. Experience has
shown that if the concept of “change” is to be useful it must be
enlarged to the case in which the operator can act on more than
one operand, inducing a characteristic transition in each. Thus the
operator “exposure to sunshine” will induce a number of transitions,
among which are:
cold soil->warm soil
unexposed photographic plate->exposed plate
coloured pigment->bleached pigment
Such a set of transitions, on a set of operands, is a transformation.
CHANGE
Another example of a transformation is given by the simple
coding that turns each letter of a message to the one that follows
it in the alphabet, Z being turned to A; so CAT would become
DBU. The transformation is defined by the table:
A->B
B->C
…
Y->Z
Z->A
Notice that the transformation is defined, not by any reference to
what it “really” is, nor by reference to any physical cause of the
change, but by the giving of a set of operands and a statement of
what each is changed to. The transformation is concerned with
what happens, not with why it happens. Similarly, though we may
sometimes know something of the operator as a thing in itself (as we know something of sunlight), this knowledge is often not
essential; what we must know is how it acts on the operands; that
is, we must know the transformation that it effects.
the simple example in which, under the influence of sunshine,
pale skin changes to dark skin. Something, the pale skin, is
acted on by a factor, the sunshine, and is changed to dark skin.
That which is acted on, the pale skin, will be called the operand,
the factor will be called the operator, and what the operand is
changed to will be called the transform. The change that occurs,
which we can represent unambiguously by
pale skin -> dark skin
is the transition.
The transition is specified by the two states and the indication
of which changed to which.
TRANSFORMATION
The single transition is, however, too simple. Experience has
shown that if the concept of “change” is to be useful it must be
enlarged to the case in which the operator can act on more than
one operand, inducing a characteristic transition in each. Thus the
operator “exposure to sunshine” will induce a number of transitions,
among which are:
cold soil->warm soil
unexposed photographic plate->exposed plate
coloured pigment->bleached pigment
Such a set of transitions, on a set of operands, is a transformation.
CHANGE
Another example of a transformation is given by the simple
coding that turns each letter of a message to the one that follows
it in the alphabet, Z being turned to A; so CAT would become
DBU. The transformation is defined by the table:
A->B
B->C
…
Y->Z
Z->A
Notice that the transformation is defined, not by any reference to
what it “really” is, nor by reference to any physical cause of the
change, but by the giving of a set of operands and a statement of
what each is changed to. The transformation is concerned with
what happens, not with why it happens. Similarly, though we may
sometimes know something of the operator as a thing in itself (as we know something of sunlight), this knowledge is often not
essential; what we must know is how it acts on the operands; that
is, we must know the transformation that it effects.