# Re: Whoopie ! The natural INTEGERS are indeed monads

```OOps#2: I would have to be a super-Gauss to explain the 12/17ary system.
The last time I really *studied* math-rules was in 1948, preparing for my
Ph.D. exam, - since then I only forget.```
```
12/17 is surely a value, hopefully applicable in erecting a math-system,
like with "2" the binary, or with "10" the decimal. The rest is application
(ha ha). Ask the super-duper universal computer of yours.

Sorry for erring into such un-serious and un-scientific corners.

Have a good Christmas time

John
--------------------------

On Sun, Dec 9, 2012 at 8:44 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:

> Hi John,
>
>
> On 08 Dec 2012, at 21:32, John Mikes wrote:
>
> Bruno:
>
> how about expanding our closed (mathematical) minds into not only decimal,
> binary, etc., but also a (hold on fast!) 12/17ary number systems?
> in that case 17 would be non-primary, divisible by 2,3,4,6 besides the 1.
>
>
> I am not sure I understand what a 12/17 ary system. Thanks for using the
> base 10 for 12 and 17, at least.
>
> Just playing my mind on math. (You may have an even wider mind).
>
>
> Not sure.
>
>
> Also zero can be "thought of" in non-human logic as participant in
> calculations.
>
>
> The chinese makes them so, and basically all numbers, except 3, 4, 5, 6,
> .... were first seen as useful participants until we develop the axiomatic
> method where we can work on any system on numbers as long as we find some
> axioms making it possible to share the discoveries with others.
>
>
>
> John M
> PS: no response required indeed. My agnosticism at work.
>
>
> Oops! Too late :)
>
> Best,
>
> Bruno
>
>
>
>
> On Sat, Dec 8, 2012 at 5:06 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:
>
>>
>> On 07 Dec 2012, at 14:33, Roger Clough wrote:
>>
>>
>>> Obviously, I meant the natural integers, not the natural numbers,
>>> whatever they be.
>>>
>>
>> Natural numbers = the non negatiove integers: 0, 1, 2, 3, ....
>> or 0, s(0), s(s(0)), ...
>>
>> Bruno
>>
>>
>>
>>
>>>
>>> ----- Have received the following content -----
>>> Sender: Roger Clough
>>> Time: 2012-12-07, 08:18:36
>>> Subject: Whoopie ! The natural numbers are indeed monads
>>>
>>>
>>> Hi Bruno Marchal
>>>
>>>
>>> 1) We in fact agree about what 1p is, except IMHO it is the
>>> Supreme Monad viewing the world THROUGH an individual's
>>> 1p that I would call the inner God. Or any God.
>>>
>>> 2) Previously I dismissed numbers as being monads because I
>>>
>>> But natural numbers are different because
>>> even though they are only mental substances, they're still
>>> substances, by virtue of the fact that they can't be subdivided.
>>> So they are of one part each.
>>>
>>> Thus the natural numbers are monads, even though they have no
>>> physical correlates. Sorry I've be so slow to see that.
>>>
>>> That reallyiopens doors Then numbers can see each other with 1p.
>>>
>>> WHOOPEE !
>>>
>>> [Roger Clough], [rclo...@verizon.net]
>>> 12/7/2012
>>> "Forever is a long time, especially near the end." -Woody Allen
>>>
>>> ----- Receiving the following content -----
>>> From: Bruno Marchal
>>> Time: 2012-12-06, 12:44:46
>>> Subject: Re: On the need for perspective and relations in modelling the
>>> mind
>>>
>>>
>>>
>>>
>>> On 05 Dec 2012, at 11:05, Roger Clough wrote:
>>>
>>>
>>> Hi Bruno Marchal
>>>
>>> Indeed, we can not code for [1p].  But we need not abandon
>>> itr entirely, as you seem to have done, and as cognitive
>>> theory has done.
>>>
>>>
>>> On the contrary, I define it is a simple way (the owner of the diary)
>>> the the self-multiplication thought experiment (UDA). It is enough to
>>> understand that physics emerge from the way the "numbers see themselves".
>>>
>>>
>>> But in the math part, I define it by using the fact that the
>>> incompleteness phenomenon redeemed the Theatetus definition. The Bp & p
>>> definition. It is a bit technical.
>>>
>>>
>>> Don't worry. The 1p is the inner god, the first person, the knower, and
>>> it plays the key role for consciousness and matter.
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>  We can replace [1p] by its actions -
>>> those of perception,  in which terms are relational (subject: object).
>>> You seem to deal with everything from the 3p perspective.
>>>
>>>
>>> That's science. But don't confuse the level. My object of study is the
>>> 1p, that we can attribute to machine, or person emulated by machines. I
>>> describe the 3p and the 1ps (singular and plural), and indeed their
>>> necessary statistical relation at some level.
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>> That is my argument for using semiotics, which includes 1p (or
>>> interprant) as a necessary and natural part of its triad of relations.
>>> Your responses seem to leave out such relations.  I cannot find
>>> again the quote I should have bookmarked, but in an argument
>>> for using semiotics on the web, it was said that modern cognitive
>>> theory has abandoned the self in an effort to depersonalize
>>> cognition.  While this is a valid scientific reason, it doesn't work
>>> when living breathing humans are concerned.
>>>
>>>
>>> I use computer and mathematical logic semantic. That's the advantage of
>>> comp. You have computer science.
>>>
>>>
>>>
>>>
>>>
>>> IMHO leaving out [1p ] in such a way will forever prevent
>>> computer calculations from emulating the mind.
>>>
>>>
>>> The 1p is not left out. Eventually comp singles out eight person points
>>> of view. If you think comp left out the person, you miss the meaning of the
>>> comp hope, or the comp fear.
>>>
>>>
>>> Bruno
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>> [Roger Clough], [rclo...@verizon.net]
>>> 12/5/2012
>>> "Forever is a long time, especially near the end." -Woody Allen
>>>
>>> ----- Receiving the following content -----
>>> From: Bruno Marchal
>>> Time: 2012-12-03, 13:03:12
>>> Subject: Re: Semantic vs logical truth
>>>
>>>
>>>
>>>
>>> On 03 Dec 2012, at 00:04, meekerdb wrote:
>>>
>>>
>>> On 12/2/2012 7:27 AM, Bruno Marchal wrote:
>>> The 1p truth of the machine is not coded in the machine. Some actual
>>> machines knows already that, and can justified that If there are machine
>>> (and from outside we can know this to correct) then the 1p-truth is not
>>> codable.  The 1p truth are more related to the relation between belief and
>>> reality (not necessarily physical reality, except for observation and
>>> sensation).
>>>
>>>
>>> Even the simple, and apparently formal Bp & p is NOT codable.
>>> Most truth about machine, including some that they can know, are not
>>> codable.
>>> Many things true about us is not codable either.
>>>
>>> Let me see if I understand that.  I think you are saying that p, i.e.
>>> that "p" describes a fact about the world, a meta-level above the coding of
>>> a machine.
>>>
>>>
>>> No, p is for some statement at the base level, like 1+1 = 2.
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>> That the Mars Rover believes it is south of it's landing point is
>>> implicit in its state and might be inferred from its behavior, but there is
>>> no part of the state corresponding to "I *believe* I am south of my landing
>>> point."
>>>
>>>
>>> Then Mars Rover is not L?ian. But I am not even sure that Mars Rover is
>>> Turing universal, or that it exploits its Turing universality.
>>>
>>>
>>> But PA and ZF can represent "I believe". So we can study the logic of a
>>> new 'knowledge" operator defined (at the meta level, for each arithmetical
>>> proposition) by Bp & p. For example if p is "1+1=2", it is
>>>
>>>
>>> Believe"("1+1=2") & 1+1 = 2.
>>>
>>>
>>> We cannot define such operator in arithmetic. We would need something
>>> like Believe"("1+1=2") & True("1+1 = 2"), but True, in general cannot
>>> defined in arithmetic. Yet, we can metadefine it and study its logic, which
>>> obeys a soprt of temporal intuionistic logic (interpreting the S4Grz logic
>>> obtained).
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>> One could include such second-level states (which one might want to
>>> communicate to Pasadena) but then that state would be just another
>>> first-level state. Right?
>>>
>>>
>>>
>>> Not sure I see what you mean. The meta, available by the machine is in
>>> the "I believe". It is the 3-I. The presentation of myself to myself. The
>>> 1-I will be the non definable operator above. We connect the believer to
>>> the truth. It is easy to do for the sound correct machine.
>>>
>>>
>>> Bruno
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>> Brent
>>>
>>>
>>>
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>>>
>>> http://iridia.ulb.ac.be/~**marchal/ <http://iridia.ulb.ac.be/~marchal/>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
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```