Collaborative articulation of how abstraction and language is employed in the computational manifestation of numbers -- including analysis of the role of syntax, semantics, and meaning in the specification and use of software interfaces.

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A Fine Kettle of Fish, indeed.

In A Fine Kettle of Fish orcmid provides some background into a discussion on programming interfaces, and how they come to mean something. There's a lot more to it, but here I want to add my view of what I did when orcmid created pseudo-code for an interface called Num.java and I produced a Java file using 'ints.'

A week or two before we had the exchange of pseudo-code Dennis told me about a discussion on a foundations of mathematics list where people talking about the meaning and existence of numbers. I'm not sure this is correct, but it's what I remembered. And from my view I thought it was a bit odd, since I seem to be able to use numbers fairly easily without worrying about whether they exist or have any meaning other than the operational one I use without thinking.
This kind of discussion also made me think about the kind of meaning we assign and negotiate with ordinary language (as different from mathematical language).



Anyhow, this is sitting in my mind when Dennis sends me the pseudo-code for an interface to a Peano Numeral. [You'll need to look at the blog post referenced above to follow along.] He says in his note that he'd like to have something that compiles. Well this looks simple enough and, although I haven't written Java in a while, I look at some other code, and decide that a Num needs to be some kind of thing that Java can actually operate on. I'm thinking of the conversation about the meaning of numbers, my own limited understanding of Peano Numbers and Java, and decide (without talking with Dennis) that "pred" and "succ" must refer to a predecessor and successor integer number. So, hence, these methods probably deliver "ints." Now, I do wonder if they just could return Num, but I'm really short on time, compile the interface, and send it along.

Dennis says "Wow! ... that's not what I meant." And provides this response:

// package com.orcmid.llc.pa.pn;

public interface Num
{

    public Num next();

    public Num pred();

    public boolean isOrigin();
}

A few days later I'm on the train from NYC and looking at the interface and wonder what it might be to actually write a class that implements the interface. So, I start to do that, but soon realize, that I really don't know what a Peano Numeral is and what this interface provides. I need a context here. And furthermore, without that, it seems pretty hard to write a Java class that implements the three methods.

So I'm left with some questions: (1) What is a Peano Numeral?, (2) How might I use it?, and (3) then what meanings am I agreeing to, in terms of the Java language, when I implement it? I have the feeling that I'm missing something fundamental here, but don't know what that is.

posted by Bill Anderson at 6/7/2004 02:58:03 PM