Numbering Peano Seems Like the Simplest Thing

miser> astraendo> A040601g> 2004-06-05 -17:31 -0700

Second Example: After Dennis proposes an initial example, Bill surprises Dennis with some code and Dennis exclaims on how much this provides in demonstration of the tacit understandings that we introduce.  (All times in these notes are Pacific Daylight Time (PDT), gmt-0700.)

The Initial Example:

interface com.orcmid.cs.pa.Num
{
/* That is, defined in package com.orcmid.cs.pa
*/

com.orcmid.cs.pa.Num next();

com.orcmid.cs.pa.Num pred();

Boolean is0();
} // Num

2004-05-22-18:46 E-mail follow-up from Bill Anderson:

Subject: Re: FW: [Orcmid's Lair] 5/22/2004 11:46:39 AM

Dennis, I decided to do what seemed like the simplest thing and wrote the attached interface that does compile.

Of course, it doesn't really help with understanding what a Num is; it just says they are ints. This is really shallow, quick, hacking.  I will read your notes more carefully and think about it.

package com.orcmid.cs.pa;

public interface Num
{

    public int next();

    public int pred();

    public boolean is0();
}

2004-05-23-10:03 Dennis Responds by E-mail

1. We have moved from comments to e-mail. That is interesting.
2. Although my note was intentionally crude, I see that our automatic induction of meaning has already led to something interesting. I had not omitted the result type of pred() and next(), although I can see how that could be seen as a mistake by me.
3. Here is an update based on your version.
   • It is interesting to wonder whether there is some advantage in changing the names of pred() and next() to something else, although that has only a temporary advantage.
   • Likewise, I am not happy about isOrigin versus is0, although changing the name is useful. I am not certain about "origin" is all.
4. There is more, but I wanted to turn that much around.

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

public interface Num
{

    public Num next();

    public Num pred();

    public boolean isOrigin();
}

/* 0.01 (band) sent by band on 2004-05-22-1846 -0700
        This version reflects an interesting and very instructive
        misunderstanding of what I had in mind.
   0.02 (orcmid)I have changed the package identification for placement in 
        a tree that I will also place on the web.  I have also changed the
        methods to produce (other) Num interfaces to make clear what I had
        in mind.  I also don't want to use "0" for the origin, so I have
        renamed that method.  The idea is to capture the essence of natural
        numbers for counting and have this be a way of accessing their
        computational manifestations in Java.  There is more to say here,
        but it needs to be in separate notes, with the Java part kept as
        Spartan as possible.  The package declaration is buried in a comment
        because of problems of developing a package before there is one, and
        my own ignorance around getting classpath working properly.
   $Ηeader: /Java2/com/orcmid/llc/pa/pn/Num.java 2     04-05-23 9:50 Orcmid $
   */

2004-05-23-10:58 Bill Responds by E-mail . . .

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created 2004-06-03-22:23 -0700 (pdt) by orcmid $$Author: Orcmid $ $$Date: 04-06-05 17:32 $ $$Revision: 6 $