Cont: Deeper than primes - Continuation 2

[zooterkin]

Thank you Apathia for your open participating that do not fall into the trivial solution of classes of objects, which are treated as closed wholes (exactly because the partial paradigm that subjective aspects must be omitted in order to, so called, rigorously define the "purity" of being objects, instead of wisely find the subjective as a key that actually open objects into wider state of being in real space\time realm).

Some concrete example:

By Traditional Mathematics 3=1*3=1+1+1, because it is a quantitative-only framework.

By Organic Mathematics 3=1*3=1+1+1 if we choose to deal with quantitative-only framework, but we also can choose to use a qualitative framework, such that 3=1*3 (we ignore the quality of each 1, which enables to gather them by one operation of multiplication) ≠ 3=1+1+1 (we do not ignore the quality of each 1, by adding their qualities to each other, which defines 3 as a qualitative integrator).

What qualities do you mean?

Do you understand that 3*1 is exactly the same as adding three 1s together?

for example:


[qimg]https://farm5.staticflickr.com/4904/45975460572_34d1bcf338.jpg[/qimg]


As observed by verbal_symbolic AND visual_spatial reasoning 3=1*3 ≠ 3=1+1+1 if quality is not ignored.

Where do you explain what those pictures mean? What qualities do the 1s have?

 

[Apathia]

What qualities do you mean?

Do you understand that 3*1 is exactly the same as adding three 1s together?

Where do you explain what those pictures mean? What qualities do the 1s have?

Zooterkin,

I apologize for a bit of bad form by commenting on questions you addressed to Doron. I'm grabbing an opportunity here to state the problem I so long windily tried to yesterday. Also chances that Doron's reply will answer your questions are marginal at best.

Doron does understand that 3*1 is the same as adding three 1s together.
His 3*1 ≠ 3=1+1+1 is not the same as the quantitative addition of 1+1+1. The quantitative addition is of three items, objects, or things. As such it doesn't acknowledge their Subjective being. (Or Uniqueness" as I called it.). For example three cats 1+1+1 = 3*1. They add up together as a class of three of the same sort, or as three animals, or as three things. However for Lindy they aren't merely three things, or just three cats. They're her precious companions Cleo, Shorts, and Brandenburg. Even when she sets out their three eating bowls, they aren't three objects to her. Each is practically a person.

Now Doron's gripe with Mathematics as is (apart from the infinity critique) is that it makes whoever, whatever it speaks of objects in categories, completely ignoring their Subjective being. This is the quality he is concerned with. Now if there were just some way to rework Mathematics so it could show this quality in the process, wouldn't we have a more respectful world? So he offers a "Qualitative Addition" by means of diagrams and brackets.

I suppose that one could use those brackets to remind oneself that the cats spoken of are uniquely themselves beyond any categorization. However, the moment I say "Lindy has three cat companions," even if I write it "Lindy has (three) (cat) companions," I've already made an objective statement in which the cats are a matter of objective discourse. Yes, Shorts is a being beyond objective reference, and Shorts, Brandenburg, and Cleo, as such do not sum to three cats. But in using the operation of addition they do, for objective purposes. They become the addition of three items. Their category is three items.

If I want to be in a subjective discourse with them, I can as any old cat lady talk to them. However in such an exchange (to what extent they respond) I'm not engaged in doing addition.

The point is that the moment I do addition, multiplication, subtraction, division I'm mentally manipulating objects of some general class. Even if I use brackets, italics, bolds, capitals, diagrams, for purpose of the mathematical operations, my discourse is about objects in classes. The gimmicks might remind me that outside of the operations, Brandenburg, Shorts, and Cleo are beings in their own light. But the doing of the addition is inescapably an objective activity and manipulation.

So, you ask the obvious question, isn't 3*1 exactly the same as adding three 1s together? Yes, it is, even if it's called a "Qualitative Addition."

Doron's Not Equal is to say that the aren't qualitatively equal. Each one of those 1s is supposed to be, not a mere quantity one, but a Unique being beyond quantification, or only secondarily countable. Each is one as a whole of itself.

He allows for an operation of the addition of objects in perspective of "Verbal-symbolic AND Visual-spatial." He wants a approach in Mathematics where the Subjective is integral to the operation. I don't see that he has achieved this. And naturally as soon as he uses the language of Mathematics, readers take it as matters of objective quantities and can't see where Subjectivity fits in. The brackets and diagrams signify a dimension of subjective being, but unless told that they signify such the reader hasn't a clue beyond ordinary mathematical operations. The use of them does not naturally engage a Visual-spatial perspective, an awareness of Being, or Unity Awareness. By default the mathematician takes them as merely quantitative extensions.

Again, my bad for answering questions directed to Doron. I welcome him answering you himself (since this is his thread) and correcting me if I've misunderstood.

His brackets, diagrams, and charts do serve the purpose of calling his readers attention to a dimension of being that is beyond objective quantification (provided they see that) Maybe they could serve as a reminder that we are beyond categories. But I've yet to see a mathematical operation that engages Subjective relation.

 

[Hevneren]

What qualities do you mean?

Do you understand that 3*1 is exactly the same as adding three 1s together?

Where do you explain what those pictures mean? What qualities do the 1s have?

I think the qualities are color and size.

Sum=1
(+1) is one big red thing

Sum=2
(1*2) means two red things of equal size and shape
((+1)+1) means one big yellow thing and one smaller red thing

Sum=3
(1*2) means three red things of equal size and shape
((+1)+1) means one big green thing, one small yellow thing, and two red things of equal size and shape (this one I actually don't get, as this sum is 4, not 3)
(((+1)+1)+1) means one big green thing, one small yellow thing, and one small red thing.

Apparently, multiplication applies to identical things while addition can apply to things of different size and color.

Please don't ask me what significance this has, or how it can be put to use.

 

[doronshadmi]

I think the qualities are color and size.

Sum=1
(+1) is one big red thing

Sum=2
(1*2) means two red things of equal size and shape
((+1)+1) means one big yellow thing and one smaller red thing

Sum=3
(1*2) means three red things of equal size and shape
((+1)+1) means one big green thing, one small yellow thing, and two red things of equal size and shape (this one I actually don't get, as this sum is 4, not 3)
(((+1)+1)+1) means one big green thing, one small yellow thing, and one small red thing.

Apparently, multiplication applies to identical things while addition can apply to things of different size and color.

Please don't ask me what significance this has, or how it can be put to use.

Here is the visual_spatial AND verbal_symbolic example:


[qimg]https://farm5.staticflickr.com/4904/45975460572_34d1bcf338.jpg[/qimg]


By using quantitative-only framework 3 things are gathered by one operation, since we ignore the unique quality of each thing (3 identical red forms along the perimeter).

By using qualitative-only framework 3 things are gathered by 3 operations (please take the gathering in terms of a circle) since we do not ignore the uniqueness of each thing (3 unique forms along the perimeter).

Organic Mathematics is a mathematical framework that enables to define the spectrum among quantitative-only and qualitative-only frameworks, and in ordered to do that visual_spatial AND verbal_symbolic skills are used.

(this one I actually don't get, as this sum is 4, not 3)

Only the forms that can be along the perimeter are considered, in this visual_spatial AND verbal_symbolic example.

But here is where the snake strikes: numbers are in use and quantity quickly buries its fangs into your leg. For you see, we have three ones, three uniques. The mind quickly gives them they classifier of "uniques," or "1s" so that there can be a number of them.

The snake is one's ignorance of different levels of uniqueness of the gathered things. In this case one can't distinguish between a given result that is based on one operation among multiple things, and a given result that is based on multiple operations among multiple things.

 

[doronshadmi]

What qualities do you mean?

The uniqueness of each gathered thing.

Do you understand that 3*1 is exactly the same as adding three 1s together?

Do you understand that this result is based on quantitative-only framework?

Where do you explain what those pictures mean? What qualities do the 1s have?

Please use also your visual_spatial skills (in addition to your verbal_symbolic skills) to find the answer by yourself.

 

[doronshadmi]

Apparently, multiplication applies to identical things while addition can apply to things of different size and color.

Please don't ask me what significance this has, or how it can be put to use.

By defining the difference and the spectrum between quantity and quality of gathered things, one is educated to be opened to moral aspects among multiple things, for example:

It is easy to commit genocide if people can be gathered by one operation (the uniqueness of each person is ignored).

It is hard to commit genocide if people can't be gathered by one operation (the uniqueness of each person is not ignored).

 

[zooterkin]

The uniqueness of each gathered thing.

Why are the three 1s in 3*1 not as unique as the three in 1+1+1?

Please use also your visual_spatial skills (in addition to your verbal_symbolic skills) to find the answer by yourself.

Please explain how you decide to colour the pictures differently in the two cases.

 

[doronshadmi]

Why are the three 1s in 3*1 not as unique as the three in 1+1+1?

Because they are identical, which is not the case of (((+1)+1)+1)

Please explain how you decide to colour the pictures differently in the two cases.

Arbitrarily, all we care about is the ability to gather things by one operation, or not, according to their uniqueness.

zooterkin, please be opened to www.internationalskeptics.com/forums/showpost.php?p=12514135&postcount=3246, if you really wish to follow after my insights about the considered case.

An example of the elastic property of the considered framework:

 

[doronshadmi]

Here are the transitions from multiplication-only to addition-only, within numbers 1 to 6, such that the smaller numbers are nested within the larger numbers:

 

[Hevneren]

Only the forms that can be along the perimeter are considered, in this visual_spatial AND verbal_symbolic example.

Now you're advocating genocide. The poor, yellow shape. Just because it didn't get a part of the perimeter, we are supposed to just disregard it. Why not just throw it in the oven while we're at it?

 

[Apathia]

Here is the visual_spatial AND verbal_symbolic example:


[qimg]https://farm5.staticflickr.com/4904/45975460572_34d1bcf338.jpg[/qimg]


By using quantitative-only framework 3 things are gathered by one operation, since we ignore the unique quality of each thing (3 identical red forms along the perimeter).

By using qualitative-only framework 3 things are gathered by 3 operations (please take the gathering in terms of a circle) since we do not ignore the uniqueness of each thing (3 unique forms along the perimeter).

Organic Mathematics is a mathematical framework that enables to define the spectrum among quantitative-only and qualitative-only frameworks, and in ordered to do that visual_spatial AND verbal_symbolic skills are used.




Only the forms that can be along the perimeter are considered, in this visual_spatial AND verbal_symbolic example.



The snake is one's ignorance of different levels of uniqueness of the gathered things. In this case one can't distinguish between a given result that is based on one operation among multiple things, and a given result that is based on multiple operations among multiple things.

"Levels of uniqueness" I don't think you mean some are more unique than others but that there's a different parsing of different uniques, so that they aren't counted or sum up in the same way.

You are, as can be plainly seen, quantifying the uniques. They are assigned a number (1) and subject to the operation of addition, though with brackets to show they are special. The brackets are to say, "Wait! You can't just add these together as if they were ordinary things or just things of a sort. They're special, unique. You can't count them the same way." In one way you can go mere quantity. In another you parse out the specials.

I wasn't very clear about the snake of ignorance, but the other participants demonstrated my point. It's not just that they don't get what this "uniqueness" means, but that if they did, they still wouldn't know without being told what the unique, special, quality objects were that are being bracketed. 1 what? By default they're going to see objects among objects that are numbered and have the + operation applied to them.
Objects, number, + even if you have brackets, they still don't know what those bracketed 1s are, and with a given of Objects, number, +, they naturally go mere quantity.

My second point is that Objects, number, + immediately entails that the uniques are being objectified and quantified. Of course that is allowed by Verbal-symbolic AND Visual-spatial. Your intent is to use quantity but give a nod to quality. However when I use my calculator, it only deals with what can be quantified. It does the mathematical operation without any awareness of subjective quality. I suppose someone could design a program where the different sums, solutions or outcomes were presented. Again the user would have to tell the calculator what were the specials.
What I'm trying to say is that you are nevertheless objectifying and quantifying the Uniques. At best you are attempting to give them some respect, so the VIPs aren't lumped in with the hoi polloi. This doesn't quite get beyond objectification, and certainly not classifying (for uniques or specials, or quality goods get their own class, aka "level").

Conventional math parses in it's own way.
Animal control sends Rodney out to round up (capture) the stray cats in Glen Hall Park. He's to keep a tally of the cats he gathers into the truck.
It's Noon and Rodney has already gathered eight cats. As cats go he has a tally of 8. However he's gathered three cats with collars into the truck. The names on the collars are Brandenburg, Shorts, and Cleo. These are not stray cats. They are special in that they have homes. They are unique as their owners think of them as family.

So how many cats does Rodney have? Of course it's not the mere number 8. What we conventionally do is identify what we are talking about. Rodney has 3 stray cats. This is what he must tally. Shorts, Cleo, and Brandenburg are just along for the ride.

This is how we conventionally deal with the special cases. We sort by verbal-symbolic sorts or classes. Calling Cleo, Shorts, and Brandenburg "uniques," and bracketing them off as the uniques nevertheless places them in a class. The sort they are in this case is "uniques" (if not landed cat gentry). How does Rodney escape regarding them as a sort when he tallies that there are 5 cats instead of 8? He doesn't. At best he recognizes they are special when doing the tally. If someone were to ask him how many cats, without qualification, he'd say 8. So look we conventionally qualify in doing calculations by identifying what as opposed to what.

But Rodney isn't relating to the subjectivity of Cleo, Brandenburg, and Shorts when he's doing the simple math. If he spends some time playing with the them, then in that context they are Unique beyond uniques. It's in doing such that he relates in being.

You and I are playing now. I'm not seeing you as of some sort or in some numerical state. If I started doing that, I'd be suspending the being and doing counting. English does have a qualitative use of the word "count." You count means you are without peer.

 

[Apathia]

By defining the difference and the spectrum between quantity and quality of gathered things, one is educated to be opened to moral aspects among multiple things, for example:

It is easy to commit genocide if people can be gathered by one operation (the uniqueness of each person is ignored).

It is hard to commit genocide if people can't be gathered by one operation (the uniqueness of each person is not ignored).

It is easier to exclude, marginalize, segregate, and vilify people, if your only relation to them is category and number.

 

[doronshadmi]

"Levels of uniqueness" I don't think you mean some are more unique than others but that there's a different parsing of different uniques, so that they aren't counted or sum up in the same way.

Apathia, the principle is very simple, the result is complex.

Given a whole number > 1 , it has at least two extreme states:

1) Summation by one operation.

2) Summation by multiple operations that are at most equal to the number of the summarized objects.

The notion of number and summation is used, but under a given number one enables to define internal structures, which are the spectrum between one operation of summation, and multiple operations of summation.

a) By summarize multiple objects with one operation, one actually ignores the their unique qualities.

b) By summarize multiple objects with multiple operations that are at most equal to the number of the summarized objects, one actually cares about the unique quality of each object.

I chose multiplication in order to demonstrate (a) and addition in order to demonstrate (b), where the framework is the transitions between (a) and (b) in both directions.

Such framework can be represented by many visual_spatial AND verbal_symbolic ways, but the insights that are derived form (a)(b) spectrum can help us to understand better the complex associations among single objects, and the need to expose\develop their non-trivial values, which go beyond their quantitative-only aspects (mathematical insights that can be used in order to develop moral frameworks).

It is easier to exclude, marginalize, segregate, and vilify people, if your only relation to them is category and number.

It is easier to exclude, marginalize, segregate, and vilify people, if your only relation to them is done quantitatively by a single operation.

If you carefully observe www.internationalskeptics.com/forums/showpost.php?p=12514319&postcount=3249 by using visual_spatial AND verbal_symbolic reasoning, you may realize that the natural numbers have another dimension in addition of being quantifiers and ordinals, which is distinction, which enables to discover\develop the quality of quantified\ordered single objects.

Actually given some quantity of whole numbers > 1, the ability to order them is based on the ability to distinguish between them.

But distinction goes beyond order development, because unique properties of each singleton under a given summation, are not necessarily ordered by a common principle, end this is exactly the gateway for moral development by new insights of the concept of natural number.

For example, lets take this 5 things:




By summarize them with 1 operation we do not care about there unique qualities.

By summarize them with 5 operations we do care about their unique qualities.


Please be aware that 1 and 5 are still used as quantitative properties of the number of operations, yet by 1 operation among the things, we do not care about their unique qualities, where by 5 operations among the things we do care about their unique qualities (even if we don't order them according to a common property).

 

[Apathia]

Apathia, the principle is very simple, the result is complex.

Given a whole number > 1 , it has at least two extreme states:

1) Summation by one operation.

2) Summation by multiple operations that are at most equal to the number of summarized objects.

The notion of number and summation is used, but under a given number one enables to define internal structures, which are the spectrum between one operation of summation, and multiple operations of summation.

a) By summarize multiple objects with one operation, one actually ignores the their unique qualities.

b) By summarize multiple objects with multiple operations that are at most equal to the number of the summarized objects, one actually cares about the unique quality of each object.

I chose multiplication in order to demonstrate (a) and addition in order to demonstrate (b), where the framework is the transitions between (a) and (b) in both directions.

Such framework can be represented by many visual_spatial AND verbal_symbolic ways, but the insights that are derived form (a)(b) spectrum can help us to understand better the complex associations among single objects, and the need to expose\develop their non-trivial values, which go beyond their quantitative-only aspects (mathematical insights that can be used in order to develop moral frameworks).



It is easier to exclude, marginalize, segregate, and vilify people, if your only relation to them is done quantitatively by a single operation.

If you carefully observe

To use the cat story I did in my previous post:
Rodney has captured 8 cats. This is summation by one operation.

However among these cats are Cleo, Brandenburg, and Shorts who are not stray cats but beloved "family members" and deserve some respect. So sort out the cat situation into two operations: the count of the stray cats that comes to five and the count of the landed gentry cats that comes to three.
This is Summation by Multiple Operations. Shorts, Cleo, and Brandenburg are then given the special treatment they deserve by not being lumped in with the hoi polio. They are the aristocats!

Or in another example of Summation by Multiple Operations the cats are individually unique by separate operations for each one. Cleo stand alone. Shorts stand alone. Brandenburg stand alone. Stray cats = 3. (Our aristocats simply in effect aren't counted.) (Or you can in effect not count the strays but give each one of them a unique name.)

It's interesting that except in the multiple operation instance where each is a stand alone, there is an accompanying criteria of selecting and sorting which, for example, assigns a special quality to Brandenburg, Shorts, and Cleo that the other gathered cats don't have. Lindy's cats get a special respect and are sorted by it. They are of a quality sort the others are not. Those other wretched cats are excluded form the kitty landed gentry Lindy's three pets enjoy. Lindy's are in a class of their own.

Now of course it's possible to remove this limiting division into excluding classes. That's when each cat is a stand alone that is not gathered by an operation, not counted. In that circumstance each is a unique being and I'm not thinking 1, 2, 3.

The counting entails having some general quality that makes them of the same sort or class and therefore objects of that sort. The most general sort they share with others is that they are items, things, objects. So without exclusions we can just begin gathering and counting 1 object, 2, objects, 3 objects and here's a soda can, 4 objects, and so on.

Now one can say, "3 beings." That's nice. It does respect a quality. It does remind us that they are more than objects, though in counting three beings we have approached them objectively. Subjectivity is outside the operations of addition be they one or multiple.

The President of the USA has ordered that a new question be asked on the census forms. The census held every ten year in America counts the population of US residents. It counts that number. It also asks of the race, sex, and religions of US residents. So in separate operations it gives the count of how many male, female, White, Black, Hispanic, Catholics, Non-religious, and others reside in America. Now President Trump wants to add an additional question about citizenship. He wants to know how many non-citizens are living in America. He wants that count, that segment of a multiple operation count, so he can give them special treatment, that is to say marginalize, exclude, and if possible deport. As he has said, they aren't of the quality that he wants in our country. So here's something very unfortunate. Even though we can do a multiple operation that gives a separate sum for non-citizen residents, that doesn't of itself treat them morally and humanely. It's what we do with that information that has moral significance. And if we're really going to treat then with Equality, we will regard them as beings rather than numbers of a vilified category that we arrived at with a multiple summation.

 

[Apathia]

For example, lets take this 5 things:




By summarize them with 1 operation we do not care about there unique qualities.

By summarize them with 5 operations we do care about their unique qualities.


Please be aware that 1 and 5 are still used as quantitative properties of the number of operations, yet by 1 operation among the things, we do not care about their unique qualities, where by 5 operations among the things we do care about their unique qualities (even if we don't order them according to a common property).

Actually in the summation of 5 operations we are ignoring their unique qualities for a generalization of items collected and counted. 1 thing, then add thing = 2 things. 2 things then add thing = 3 things. 3 things then add thing = 4 things. 4 things then add thing = 5 things. We ignore their individual differences for the bland quantifier of things, or items, or objects.

By not summing we would better represent their individuality. 1 stand alone crazy crow. 1 stand alone thumbsup. 1 stand alone house. And so on.

But even this isn't respecting their Being which transcends even individuality.
So the best we can do is say, "5 beings" meaning there is a state of being five. This doesn't exclude that there is a state of being one just as present. And it points beyond that to the state of Unity.

Using "being" as the quantifier and qualifier is an objective statement but points to subjectivity. "person, persons" is also used in this way.

It's a matter of dispute whether cats are persons. I say they are if you speak to them as such.

 

[doronshadmi]

By not summing we would better represent their individuality. 1 stand alone crazy crow. 1 stand alone thumbsup. 1 stand alone house. And so on.

You can't know one-of-many thing, without comparing it to the other many things.

In my example the comparison is done under "Being 5" which is the unified root of *\+ spectrum of 1,1,1,1,1 individuals.

But even this isn't respecting their Being which transcends even individuality.
So the best we can do is say, "5 beings" meaning there is a state of being five.

Being 5 transcends *\+ operations, where 5 beings (1,1,1,1,1) are manipulated by *\+ operations.

-------------------

By using visual_spatial AND verbal_symbolic reasoning as done, for example, in www.internationalskeptics.com/forums/showpost.php?p=12514319&postcount=3249
the bottom horizontal line represents the state of being, which manifests itself as *\+ operations among n>1 beings.


A named bottom horizontal line, means that the unique quality of each 1 is known right from the unified state of being of the manifested number.

By this model, natural numbers are actually forms of developed awareness, as already demonstrated in www.internationalskeptics.com/forums/showpost.php?p=12514227&postcount=3248 (in this example the word "memory" is used instead of the word "being").

 

[Apathia]

You can't know one-of-many thing, without comparing it to the other many things.

Yes without comparison and contrast you don't have existing things that can be gathered into a quantity. Existence means that something is a thing that stands out from other things or is one of a group of things. An existing thing can be stand alone or it can be of a sum of other things of the same sort.
However it is not stand alone as it's own existence and existing as one of a sort or class on the same level, gear, or place of consideration. The different qualities of existence are not to flattened onto one level of existence where mere quantity of just one sorting applies. We must address each quality of existence on its own level. Each collecting, each gathering is a level of its own. By treating the considered thing as existing only in one level of sorting (or classing) we miss the other qualities of its existence. If we just clump by race, we miss individual personhood. Your diagrams and brackets are a way of saying, "Stop! Look! There are other layers of existence here that you must not ignore. You have to sum according to each to get the full picture."

To some extent we do separate levels of summation already. In the census example there is a sum of residents and then there are other sums of races. Multiple summations are done. What we hope is that there is also a summation of persons. So that we don't ignore the quality of personhood and think that one summation of race contains lives that don't matter as much as another.

I shifted to talking about existence here because I see that those different levels or layers come about through the interactions of Being AND Existing Object. For me "Being" is much more and transcends just existing. This is why I said we don't really address an individual's subjectivity and personhood talking about them and adding them up in a sum of categories. When the other is not an object to be manipulated by operations, but is at the source from which the present is flowing, then we have the root of empathy, compassion, and ethics. In that quality of relation, you and I flow as water from a single spring. That water is not countable. Mere existence, even if it's done with lots of layers of different qualities and qualifications, still make of us separable objects rather than souls. So this is why I'm never satisfied by just the charting, bracketing, graphing of states of existence or different qualities of existence. Being is the source of our ethics. If we're only plotting out our places and levels as objects of summation, we aren't in doing that being souls.

In my example the comparison is done under "Being 5" which is the unified root of *\+ spectrum of 1,1,1,1,1 individuals.


Being 5 transcends *\+ operations, where 5 beings (1,1,1,1,1) are manipulated by *\+ operations.

Yes. Being 5 or the state of being five transcends the objective existence operations of *\+. It's a we 5 that doesn't exclude the Being 1 of each of us but is our Unity and Diversity.

I see your brackets, charts, and gears as a way to speak of how states of Being are prior to and create states of existence. It's a way of setting forth what I take as three mode of discourse: the objects of it, the persons of you and we, and the seamless Unity of I Consciousness. The intention is what counts for me. So thanks again for this discussion. I continue to enjoy it.

I'm afraid I may be the only one here who gets what you intend. I haven't been successful interpreting you for the others. (Who wants to read my long posts when what they want is a simple quickie definition. Like you I'm not good at that, especially when the words I'd use in the definitions would require definitions themselves.) As I said exhibiting the multiple layers summation to signify acknowledging the ignored qualities isn't registering in their minds as such. To them it's just "Let's blow this arithmetic up by fragmenting it into a bunch more additions."

 

[doronshadmi]

In an ideal reality, we have the privilege to be aware of the quality of each individual, and how this quality contributes to the qualitative aspects of other individuals.

Such ideal reality is achieved through the transition from quantitative aspects to qualitative aspects of its individuals, as demonstrated by the model of nested natural numbers.

But in a non-ideal reality, both quantitative and qualitative aspects are considered as basics of moral decisions.

For example, there is a burning house. The firefighters do not have the time to care about the qualitative aspects of each individual, all they care is to evacuate the largest amount of persons out of the fire in the minimal possible time.

In an ideal reality, such situations do not happen in the first place.

If we use the process of nested natural number as a general model for a given developed reality, then its development is measured by the transition from its quantitative aspects to its qualitative aspects (in an ideal reality we have all the needed time to develop the qualitative aspects of each individual, during its interactions with other individuals, where the interaction is done both by being aware of the non-composed aspect of reality, which enables the smoothest harmonious interactions among its manifested expressions).

 

[doronshadmi]

I'm afraid I may be the only one here who gets what you intend. I haven't been successful interpreting you for the others.

By interpreting notions to others, those others at least wish to understand them even if these notions are not "under their current spotlight".

It seems that in this forum most of the posters do not wish to understand things that are not already "under their current spotlight".

From my experience in other forums, this "under the current spotlight" approach, is the common one among the majority of the posters.

I do not find this approach as entirely wrong, because it helped me a lot to understand my own notions by trying to translate them such that they will be understood by different "spotlights".

jsfisher is a poster that helps me a lot to understand my own notions, exactly because he almost entirely disagree with them.

There were a lot of fruitful discussions between us, which helped me to re-examine my notions from his point of view (which is mostly the traditional point of view), and there were also a lot of non-fruitful discussions between us, which is also a good thing, because it helped me to find the way to stimulate fruitful discussions.

When I say fruitful discussions, I am aware of the fact that jsfisher does not get them as such, yet our discussions still continue since 2008 in this thread.

 

[doronshadmi]

You both have a very narrow concept of Mathematics.

This is not an helpful reply.

For example, please explain in details why my notion about multiplication and addition transitions, as used among nested natural numbers, are based on very narrow concept of Mathematics?

Also please explain why visual_spatial reasoning must be translated into verbal_symbolic reasoning in order to rigorously to do Math (as you insist, for example, in the case of www.internationalskeptics.com/forums/showpost.php?p=12404383&postcount=3030)?