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| 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.
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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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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