David Kellogg On Mathematical Equations [2]

David Kellogg wrote to sys-func on 25 April at 21:12:

Thanks, Chris--very insightful! I hadn't really parsed out voice and coding, as you can tell; I had them rather muddled, I'm afraid. The clarity of analysis is astonishing, and adds a lot of understanding.

However, the understanding I get from it only reinforces the distinction that Yaegan Doran made in his presentation. Halliday emphasises that relational clauses are never redundant. As you say, there is a difference between operative "equals" and receptive "equalled by", and there is likewise a difference between encoding"v= eE/m " and decoding ""eE/m = v". When my father writes:

(i.e. w = pressure = the Rayleigh formula, (integral of pressure term + integral of velocity term) in case the math doesn't come out in the mail....)

He is decoding and then decoding again. Not reversible.

But that's the old man doing physics, not math. When he does the math, the math itself really is redundant and reversible: "equals" and "is equalled by" really are completely equivalent, viewed as math. The encoding and the decoding, viewed as math and not as physics, are completely interchangeable. 

This to me suggests that Yaegan was right--that there is a qualitative difference between math as a semiotic system and language as a semiotic system. The former CAN be redundant, and that is the very essence of an equation. The latter is NEVER fully redundant, and that is the essence of a relational process.

Blogger Comments:

[1] This is misleading, because Halliday (1985, 1994) does not discuss relational processes in terms of redundancy. What he does say is that an identifying clause is not a tautology, and explains why this is so. Halliday (1994: 124):

In any ‘identifying’ clause, the two halves refer to the same thing; but the clause is not a tautology, so there must be some difference between them. This difference is one of form and function; or, in terms of their generalised labels in the grammar, of TOKEN and VALUE – and either can be used to identify the other.

To be clear, in the previous post, it was the introduction of the notion of asymmetry that was source of confusion, and in this post, the notion of redundancy plays that role.

[2] To be clear, it is true that the default direction of coding in a physics equation is decoding, but it is not true that this is not reversible. Such an equation becomes encoding when the Token is used to identify the Value, as when E is used to identify mc²:

Decoding

Encoding

[3] To be clear, in terms of meaning, equals and is equalled by are not completely equivalent. The operative voice of equals configures the participants as Token^Value, whereas the receptive voice of is equalled by, which is not used in mathematical formalisms, configures the participants as Value^Token. (The two also differ in choice of Subject and Theme.) What is consistent, irrespective of voice, is the identity of one participant (quantity) with another.

[4] To be clear, the direction of coding is distinct from the voice of an identifying clause. Operative and receptive clauses can be decoding or encoding. The direction of coding depends on which participant is used to identify the other: if the Value is used, then the clause is decoding; if the Token is used, then the clause is encoding.

To be clear, equations, whether used in mathematics or physics, can be decoding or encoding, though decoding is the default. However, it is not true that the two are equivalent in meaning, since they differ in which participant is used to identify the other. Again, what is consistent, irrespective of the direction of coding, is the identity of one participant (quantity) with another.

[5] See the above for evidence as to why this conclusion derives from multiple misunderstandings.