Semantics and measurement

by Neil Rickert

There are many different conceptions of “information.”  The most important of those is that due to Claude Shannon, and often referred to as “Shannon Information“.  Shannon was particularly concerned with communication and with the problem of avoiding or minimizing loss of information due to transmission over an imperfect channel.

As used today, we typically think of Shannon information being transmitted as a sequence of symbols, often as a stream of binary digits. It is considered to be a theory of syntactic information, since the engineering considerations that motivated Shannon’s work are concerned with delivery of the symbols and questions of what those symbols mean is secondary and outside Shannon’s theory.

Warren Weaver showed how to connect Shannon’s theory with semantic notions.  Weaver looked at an overall system where meaningful ideas (or semantics) are encoded into symbols.  The resulting symbols are Shannon information, and can be transmitted.  The receiver of that transmission can then decode the stream of symbols so as to extract the meaningful ideas intended by the initiation of the message.  Ordinary language use is an example of this, with the words as symbols.  Or, in written language, the letters can be considered the symbols.  In spoken language, phonemes can be considered to be symbols.  For a discussion of the overall picture, including a good diagram, see “Shannon Weaver model of communication“.

As you can see from that diagram, the only places where semantics (meaning) is required are at the encoder where semantic information is converted to symbols, and at the decoder where the semantic information is retrieved from the symbols.  As an example, suppose that I am calling you on the telephone.  I have something meaningful, and I encode that into language as a sequence of spoken words.  So I am the encoder and I need access to meanings of the words that I am using.  Thereafter, the sounds I make, whether you consider them words or phonemes, are transmitted over the telephone circuits.  This might include copying or regenerating them at various repeater stations.  But nothing in the telephone circuits depends on meaning.  Those circuits need only ensure reliable transmission of the sequence of symbols.  Finally, the message reaches you on the other end of the phone.  And you are the decoder, recognizing the meaning that is being carried by that sequence of symbols.

Meaning (semantics) is needed at the source where it is encoded into symbols, and at the destination where the decoding extracts the meaning from the symbols.

Now look at science.  Science is usually described in terms of using data and making inferences from that data.  The data itself is all symbolic, perhaps numeric.  The rules of inference are all rules for dealing with symbols based on their form (logic or mathematics).  But the data itself comes from a process of measurement.  It is that process of measurement that is the encoder, converting semantics (the way the world is) into symbols (the numeric data).  It is at the point of measurement, that meaning is required.

Consider a simple example of measurement.  I need window shades.  So I get out a ruler, and measure the width of my window.  That measurement process converted semantic information (the way some aspect of the world happens to be) into symbols (the width that I wrote down).  I now take that symbolic information to the hardware store, and order a window shade.  The hardware store clerk gets out his ruler, and measures and cuts a suitably sized shade to exactly the size that I need.  The encoding was my action of measuring the window.  The decoding was the hardware clerk’s action of measuring the shade and cutting to the right size.  The semantics was needed at those two points.  Everything else was just a carrying of symbolic information from one point to the other, and did not require semantics.

In all of science, the operation that depends on semantics is measurement.

The conclusion should be clear.  Meaning and semantics are closely related to measurement.  This is why I say that cognition is measurement.

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