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Groups > sci.math > #641449

Re: A new category of thought

From "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups comp.theory, sci.logic, sci.math, sci.lang
Subject Re: A new category of thought
Date 2025-11-29 15:53 -0800
Organization A noiseless patient Spider
Message-ID <10gg10v$3r0gs$1@dont-email.me> (permalink)
References (1 earlier) <20251129094642.874@kylheku.com> <10gfcpa$3ji8m$1@dont-email.me> <20251129121613.116@kylheku.com> <10gfmc1$3nf97$1@dont-email.me> <jzJWQ.9555$fEH6.6841@fx41.iad>

Cross-posted to 4 groups.

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On 11/29/2025 1:27 PM, Richard Damon wrote:
[...]
> Godel proved that such a system can't exist if it can represent the 
> properties of the Natural Number.

I hope this can exist. Sorry for any typos with the n-ary tree, n=2 
here. Can you notice any errors I missed?  natural number in the tree 
has two unique children. I can derive these children from any natural 
number. I can get at a child's parent just from its mapped natural. It's 
100% full circle.

       0
      / \
     /   \
    1     2
   / \   / \
  3   4 5   6
...........

The children of 1 are:

c[0] = 1 * 2 + 1 = 3
c[1] = c[0] + 1  = 4


Nice! Now, to map back

The parent of 3 is:

p = ceil(3 / 2) - 1 = 1


The parent of 4 is:

p = 4 / 2 - 1 = 1


The parent of 5 is:

p = ceil(5 / 2) - 1 = 2

The parent of 6 is:

p = 6 / 2 - 1 = 2


Notice I do not have to use ceil in the case of 2-ary when the natural 
number in question is even? Premature optimization? ;^)

It works even with using ceil all the time:


Take the parent of 3 and 4:

p = ceil(3 / 2) - 1 = 1
p = ceil(4 / 2) - 1 = 1


Lets try a parent at zero with its 2-ary children of 1 and 2:

p = ceil(1 / 2) - 1 = 0
p = ceil(2 / 2) - 1 = 0


;^D


I need to adapt it for negative numbers. Think of the following 2-ary tree:


-1   -2
   \ /
    0
   / \
+1   +2


So, lets try it out... The children on the negative side of zero. Flip 
things wrt +1 becomes -1:

c[0] = 0 * 2 - 1 = -1
c[1] = c[0] - 1  = -2

Well, that works! Let's get the parent of -2, and flip the sign on the 
-1 to +1, should be zero: Also, lets flip ceil to floor:

p = floor(-2 / 2) + 1 = 0

Nice, lets try -1:

p = floor(-1 / 2) + 1 = 0


It works... Interesting to me.

Lets try -3, its parent should be -1:

p = floor(-3 / 2) + 1 = -1

Also, -4's parent should be -1:

p = floor(-4 / 2) + 1 = -1

Nice!

-5 and -6 should both have a parent of -2:


p = floor(-5 / 2) + 1 = -2
p = floor(-6 / 2) + 1 = -2

perfect.

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Thread

A new category of thought olcott <polcott333@gmail.com> - 2025-11-29 10:32 -0600
  Re: A new category of thought Kaz Kylheku <046-301-5902@kylheku.com> - 2025-11-29 17:53 +0000
    Re: A new category of thought olcott <polcott333@gmail.com> - 2025-11-29 12:07 -0600
      Re: A new category of thought dbush <dbush.mobile@gmail.com> - 2025-11-29 13:19 -0500
        Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-01 16:55 +0000
          Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-01 11:04 -0600
        Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-02 11:49 +0200
          Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-02 09:26 -0600
            Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-04 08:46 -0600
              Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-05 10:52 +0200
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-05 11:21 -0600
                Re: A new category of thought André G. Isaak <agisaak@gm.invalid> - 2025-12-05 19:57 -0700
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-05 21:18 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-06 11:01 +0200
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-06 06:40 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-07 12:47 +0200
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 09:16 -0600
                Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-08 02:04 +0000
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 21:21 -0600
                Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-08 09:55 +0000
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-08 12:43 -0600
                Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-06 22:16 -0500
                Re: A new category of thought polcott <polcott333@gmail.com> - 2025-12-06 21:50 -0600
                Re: A new category of thought Python <python@cccp.invalid> - 2025-12-07 05:32 +0000
                Re: A new category of thought Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2025-12-07 15:49 +0000
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 11:38 -0600
                Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-07 07:32 -0500
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 07:37 -0600
                Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-07 17:55 -0500
                Re: A new category of thought polcott <polcott333@gmail.com> - 2025-12-07 17:15 -0600
                Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-07 21:50 -0500
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 21:26 -0600
                Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-08 07:40 -0500
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-08 12:47 -0600
                Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-08 19:18 -0500
                Re: A new category of thought polcott <polcott333@gmail.com> - 2025-12-08 19:00 -0600
                Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-08 21:24 -0500
                Key new insight into halting undecidability polcott <polcott333@gmail.com> - 2025-12-08 20:34 -0600
                Re: Key new insight into halting undecidability Richard Damon <Richard@Damon-Family.org> - 2025-12-08 21:57 -0500
                Re: Key new insight into halting undecidability polcott <polcott333@gmail.com> - 2025-12-08 21:16 -0600
                Re: Key new insight into halting undecidability Richard Damon <Richard@Damon-Family.org> - 2025-12-08 22:22 -0500
                Re: Key new insight into halting undecidability polcott <polcott333@gmail.com> - 2025-12-08 21:50 -0600
                Re: Key new insight into halting undecidability Richard Damon <Richard@Damon-Family.org> - 2025-12-08 23:20 -0500
                Re: Key new insight into halting undecidability polcott <polcott333@gmail.com> - 2025-12-08 22:30 -0600
                Re: Key new insight into halting undecidability Richard Damon <Richard@Damon-Family.org> - 2025-12-09 07:42 -0500
                Re: Key new insight into halting undecidability polcott <polcott333@gmail.com> - 2025-12-09 10:05 -0600
                Re: Key new insight into halting undecidability Richard Damon <Richard@Damon-Family.org> - 2025-12-09 23:02 -0500
                Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-08 02:14 +0000
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 21:21 -0600
                Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-08 07:07 +0000
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-08 10:41 -0600
                Re: A new category of thought Python <python@cccp.invalid> - 2025-12-08 19:39 +0000
            Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-05 10:57 +0200
              Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-05 11:30 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-06 10:53 +0200
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-06 06:33 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-07 12:42 +0200
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 09:03 -0600
                Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-08 06:12 +0000
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-08 07:59 -0600
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-08 10:18 -0600
      Re: A new category of thought Kaz Kylheku <046-301-5902@kylheku.com> - 2025-11-29 20:23 +0000
        Re: A new category of thought olcott <polcott333@gmail.com> - 2025-11-29 14:51 -0600
          Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-11-29 16:27 -0500
            Re: A new category of thought "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-29 15:53 -0800
              Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-11-29 19:17 -0500
                Re: A new category of thought "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-29 16:35 -0800
                Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-11-29 20:10 -0500
                Re: A new category of thought "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-29 19:49 -0800
                Re: A new category of thought "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-29 19:50 -0800
                Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-02 01:59 +0000
                Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-01 23:11 -0500
          Re: A new category of thought Kaz Kylheku <046-301-5902@kylheku.com> - 2025-11-29 21:39 +0000
            Re: A new category of thought olcott <polcott333@gmail.com> - 2025-11-29 15:59 -0600
              Re: A new category of thought Kaz Kylheku <046-301-5902@kylheku.com> - 2025-11-29 22:44 +0000
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-11-29 17:19 -0600
                Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-11-29 19:21 -0500
                Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-02 01:13 +0000
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-01 19:50 -0600
              Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-01 13:02 +0200
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-01 11:15 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-02 10:53 +0200
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-02 08:00 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-03 12:41 +0200
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-03 09:59 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-05 10:48 +0200
                Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-05 09:30 +0000
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-05 10:41 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-06 10:37 +0200
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-06 06:24 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-07 12:39 +0200
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 08:59 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-09 15:15 +0200
                Re: A new category of thought polcott <polcott333@gmail.com> - 2025-12-09 12:04 -0600
                Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-14 13:02 +0200
                Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-02 01:39 +0000
                Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-01 20:01 -0600
          Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-01 17:37 +0000
            Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-01 13:44 -0600
  Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-11-29 15:08 -0500

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