[MD] Idealistic static value patterns

Fri Jan 13 03:06:26 PST 2012

Mark,

providing more intuitive explanations is something I could at least do  
in the book. The web stuff is better as a reference and good because  
of my insatiable urge to publish at least something all the time, even  
if it made little sense to non-mathematicians. But first! I gotta make  
sure I understand the stuff myself, as all of it is not written by me.  
Your questions, actually, are great practice for this.

T = {Tm | 1 ? m ? n}

This splits each set T into n patterns. n = 4 is the traditional  
Pirsig solution.

     Nm ? Sm
     Nm ? Om

Here normative patterns are included in the descriptive patterns. They  
are supposed to explain the structure of the descriptive patterns.

?(Rm) = Sn ? (m ? 1) ? Om

This means that subjective and objective quality emerge from romantic  
quality in addition to emerging from each other. And like the picture  
(http://moq.fi/CM-2.png) shows, subsets of subjective quality S emerge  
from romantic quality R in inverse order compared to subsets of  
objective quality O. This explains why n = 1 would comprise a dull  
theory. The inversion of order could not be noticed if both S and O  
had only one pattern!

The power set function ? means emergence. The power set of any set T  
includes all subsets of that set, but not necessarily the elements of  
the subsets. Say you have a set T with elements:

a,b,c

The power set of that set T would contain the following sets:

T0 = {} (empty set)
T1 = {c}
T2 = {b}
T3 = {b,c}
T4 = {a}
T5 = {a,c}
T6 = {a,b}
T7 = {a,b,c}

Power sets do not necessarily contain the elements of the subsets,  
only the subsets. This explains why normative quality does not contain  
sensory perceptions despite emerging from intellectual quality, which  
does.

Let's examine the following snippet:

BEGIN PASTE

     1I :=def O
     2I :=def N
     3I :=def S

Let ?(T) denote the powerset of an arbitrary set T in our set theory.  
Let us define a number-theoretic function Modn:? ? ? ? [0,n[ of one  
free variable such that for every p ? ?+ and q ? ?:

     Modp(q) = q ? p?q?p?

Thus, Modp(q) is the remainder that results when a natural number q is  
divided by a positive integer p. Let the following two formulas of our  
set theory hold:

     ?k(k ? {1,2,3} ? ?m(m ? ? ? [1,n[ ? ?(kIm) ? kIm + 1))
     ?k(k ? {1,2,3} ? ?(kIn) ? 1 + Mod3(k)I1))

END PASTE

This basically formalizes the notion that each pattern emerges from  
the pattern preceding it. The 1I, 2I and 3I simply give index names to  
objective quality, normative quality and subjective quality. The cycle  
uses these index names to refer to them.

This line:

?k(k ? {1,2,3} ? ?m(m ? ? ? [1,n[ ? ?(kIm) ? kIm + 1))

makes the cycle run within one pattern system, such as objective  
quality. But it does not make the cycle shift from one pattern system  
to another. That is done by this line:

?k(k ? {1,2,3} ? ?(kIn) ? 1 + Mod3(k)I1))

Mod3kI divides the index number of I with 3, gets the remainder and  
adds one. In effect:

1I => remainder of 1/3, which is 1 => add 1 to that => 2
2I => remainder of 2/3, which is 2 => add 1 to that => 3
3I => remainder of 3/3, which is 0 => add 1 to that => 1

By the way, I uncovered two mistakes in the formulas while explaining  
this to you, so this is certainly a very useful activity! They weren't  
due to Timo but due to my own mistakes.

What does this do then?

     Modp(q) = q ? p?q?p?

It defines a function. This function performs the calculation q/p and  
applies the floor function to the result. The floor function is  
denoted by ? and ? and it practically just rounds down the input it  
receives.

1/3 = 0,3333... => apply floor function => 0
2/3 = 0,6666... => apply floor function => 0
3/3 = 1 => apply floor function => 1

This sort of works as a trigger. Whenever the floor function outputs  
0, p is not "activated" because p * 0 = 0. But if we are at the last  
indexed pattern 3I, the floor function outputs 1. As we all know, p *  
1 = p.

p could stand for "payload", if you will. (BOOM!!)

Whenever payload is not activated, Modp is an innocuous function. You  
input a number, and it outputs the same number. But when payload is  
activated at the end of the cycle, it outputs 0.

Basically, the Modp function doesn't do more than that. But see this  
formula again:

?k(k ? {1,2,3} ? ?(kIn) ? 1 + Mod3(k)I1))

In this formula, 1 is added to anything Modp outputs. So if Modp  
outputs the same number, this function nevertheless adds one to it.  
But if Modp outputs 0, this function again adds 1, which is necessary,  
because 0I does not correspond to any defined form of quality.

Enough of the formalisms.

Matt:
> What we have, however, is a problem with results from Quality
> comprising itself in a set.  This would be similar to the "set of all
> sets" which in formally invalid.  However, it is true in my opinion
> that the set of Quality also contains Quality, so this may be
> abstracted by you using a recursive technique (a challenge for you
> since I can't present it formally).  So the question is, if Quality is
> everything, can it also include itself?

It is very important to stress that it doesn't make any sense to ask  
where Quality is contained in this process. This process is about  
static quality.

Matt:
> I did note that you are using a combinatorial approach, where the set
> would equal n! (or the product of the whole intergers making up n)
> minus the intergers themselves.  You would create a kind of table
> which would depict that set.  It should be possible to make this table
> multi-dimensional to account for all your sub-qualities.

I'm not sure what set = n! means. If j is the number of the elements  
in the set,  2 ^ j is the number of subsets in the power set, not j!.  
Did I get this right?

Matt:
> I especially like your linkistic quality.  Perhaps you can tell me
> something about that!

Tuukka:
Me too. :D They are definitely the least defined part of this theory.  
I'll get back to this later...

-Tuukka

All

Quoting 118 <ununoctiums at gmail.com>:

> Hi Tuukka,
>
> On 1/12/12, mail at tuukkavirtaperko.net <mail at tuukkavirtaperko.net> wrote:
>> Hi Matt! =)
>>
>> To be sure, the math stuff I'm doing right now... well... it sure
>> doesn't work out like that! :D I have to reduce the formulae to tree
>> structures to understand what they are about in the first place, and I
>> don't, at least not yet, do that completely intuitively.
>>
>> If you're a math geek, you'll like this:
>>
>> http://www.moq.fi/?p=242
>>
>> =)
>>
> Mark:
> I took a look at this and did not understand most of it.  It may be
> useful for some of us if you provide a common English conclusion of
> what the various results mean in terms of MoQ.  Perhaps you could also
> define your operators so that we can see what you are doing.  It is
> hard to look up those symbols on google :-).
>
> It looks like set theory to me.  The use of set theory to interogate
> Quality is interesting since we may be dealing with infinite sets.  I
> presented some on this in previous posts, but then lost interest (or
> did not get any response) and moved on.  I did get to read several
> books on the subject which made it fulfilling for me.  There are
> interesting correspondences in infinte sets.  For example, in a right
> (pythagorean) triangle the number of points on the hypotenuse is
> exactly the same as the number of points on the base.  It is possible
> that in the "real world" there are exactly the same amount of points
> in each of your quality sets (except maybe your linkistic quality (if
> you spelled that as it is supposed to mean).
>
> What we have, however, is a problem with results from Quality
> comprising itself in a set.  This would be similar to the "set of all
> sets" which in formally invalid.  However, it is true in my opinion
> that the set of Quality also contains Quality, so this may be
> abstracted by you using a recursive technique (a challenge for you
> since I can't present it formally).  So the question is, if Quality is
> everything, can it also include itself?
>
> I did note that you are using a combinatorial approach, where the set
> would equal n! (or the product of the whole intergers making up n)
> minus the intergers themselves.  You would create a kind of table
> which would depict that set.  It should be possible to make this table
> multi-dimensional to account for all your sub-qualities.
>
> I especially like your linkistic quality.  Perhaps you can tell me
> something about that!
>
> Cheers,
> Mark
>
>> Moq_Discuss mailing list
>> Listinfo, Unsubscribing etc.
>> http://lists.moqtalk.org/listinfo.cgi/moq_discuss-moqtalk.org
>> Archives:
>> http://lists.moqtalk.org/pipermail/moq_discuss-moqtalk.org/
>> http://moq.org/md/archives.html
>>
> Moq_Discuss mailing list
> Listinfo, Unsubscribing etc.
> http://lists.moqtalk.org/listinfo.cgi/moq_discuss-moqtalk.org
> Archives:
> http://lists.moqtalk.org/pipermail/moq_discuss-moqtalk.org/
> http://moq.org/md/archives.html
>