[MD] Idealistic static value patterns

[mail at tuukkavirtaperko.net]

Sorry, I meant Mark, not Matt. :) (Matt is welcome too!)
Also, the symbols didn't come out quite right in the e-mail. Guess I  
should have sent it in Unicode UTF-8. As a test, I will send this mail  
in UTF-8 and attach the following formulae:

     Modp(q) = q – p⌊q⁄p⌋

     ∀k(k ∈ {1,2,3} ⇒ ∀m(m ∈ ℕ ∩ [1,n[ ⇒ ℘(kIm) ⊆ kIm + 1))
     ∀k(k ∈ {1,2,3} ⇒ ℘(kIn) ⊆ 1 + Mod3(k)I1))

If you can see the symbols right, ℘ is the power set function, and  
⌊q⁄p⌋ applies the floor function to q/p. If not, you'll just have to  
resort to the original link...

-Tuukka



Quoting mail at tuukkavirtaperko.net:

> 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
>>
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