Ing added by one transducer are often or usually within the
Decoding powers of another transducer of similar size.
TR ANS M I S S I ON F ROM S YS TE M TO S YS T EM
Transmitting” variety. It may be as well at this point to
Clarify a matter on which there has been some confusion. Though
It is tempting to think of variety (or information) as passing
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A N I N T R O D UC T I O N T O C Y B E R NE T I C S
T RA N SMISSI O N O F VA R IE TY
Through a transducer, or variety passing from one transducer to
Another, yet the phrase is dangerously misleading. Though an
Envelope can contain a message, the single message, being
Unique, cannot show variety; so an envelope, though it can con-
Tain a message, cannot contain variety: only a set of envelopes can
Do that. Similarly, variety cannot exist in a transducer (at any
Given moment), for a particular transducer at a particular moment
Is in one, and only one, state. A transducer therefore cannot “con-
Tain” variety. What can happen is that a number of transducers
(possibly of identical construction), at some given moment, can
Show variety in the states occupied; and similarly one transducer,
On a number of occasions, can show variety in the states it occu-
Pied on the various occasions.
What is said here repeats something of what was said in S.7/5,
But the matter can hardly be over-emphasised.)
It must be remembered always that the concepts of “variety”, as
Used in this book, and that of “information”, as used in communi-
Cation theory, imply reference to some set, not to an individual.
Any attempt to treat variety or information as a thing that can exist
In another thing is likely to lead to difficult “problems” that
Should never have arisen.
Transmission at. one step. Having considered how variety
Changes in a single transducer, we can now consider how it passes
From one system to another, from T to U say, where T is an abso-
Lute system and U is a transducer.
T → U
As has just been said, we assume that many replicates exist, iden-
Tical in construction (i.e. in transformation) but able to be in vari-
Ous states independently of each other. If, at a given moment, the
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T’s have a certain variety, we want to find how soon that variety
Spreads to the U’s. Suppose that, at the given moment, the T’s are
Occupying nT distinct states and the U’s are occupying nut (The
Following argument will be followed more easily if the reader will
Compose a simple and manageable example for T and U on which
The argument can be traced.)
T is acting as parameter to U, and to each state of Twill corre-
Spond a graph of U. The set of U’s will therefore have as many
Graphs as the T’s have values, i.e. nT graphs. This means that from
Each U-state there may occur up to nT different transitions (pro-
Vided by the nT different graphs), i.e. from the U-state a represent-
Ative point may pass to any one of not more than nT U-states. A
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Set of U’s that has all its representative points at the same state can
Thus, under the effect of T’s variety, change to a set with its points
Scattered over not more than nT states. There are nu such sets of
U’s, each capable of being scattered over not more than nT states,
So the total scattering cannot, after one step, be greater than over
NTnU states. If variety is measured logarithmically, then the vari-
Ety in U after one step cannot exceed the sum of those initially in
U and T. In other words, the U’s cannot gain in variety at one step
By more than the variety present in the T’s.
This is the fundamental law of the transmission of variety from
System to system. It will be used frequently in the rest of the book.
Ex. 1: A system has states (t,u) and transformation t' = 2', u' = u + t, so t dominates
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