Cont: Deeper than primes - Continuation 2

[jsfisher]

This is not an helpful reply.

It wasn't a reply. It was an observation. It was specifically commenting on the naive concept you have for what Mathematics is. You do not know what Mathematics is, and you continually mischaracterize it. You vilify what you do not understand.

Mathematics is not, as you say, a quantitative-only framework.

 

[doronshadmi]

It wasn't a reply. It was an observation. It was specifically commenting on the naive concept you have for what Mathematics is. You do not know what Mathematics is, and you continually mischaracterize it. You vilify what you do not understand.

More propaganda without any support.

Mathematics is not, as you say, a quantitative-only framework.

I definitely do not claim that, exactly the opposite, I use mathematics also as a qualitative framework, demonstrated by *\+ among nested natural numbers.

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

You chose not to reply to what comes after the first sentence in http://www.internationalskeptics.com/forums/showpost.php?p=12516414&postcount=3260.

This is not a fruitful discussion, so please this time try to reply to the rest of the post.

Thank you.

 

[jsfisher]

I definitely do not claim that, exactly the opposite

Ummm, you sure about that?

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

 

[doronshadmi]

Ummm, you sure about that?

1) Traditional Mathematics is not the only possibility to do Mathematics.

2) As usual you stopped reading the entire www.internationalskeptics.com/forums/showpost.php?p=12512487&postcount=3235 in order to actually understand my notions, which are not limited to verbal_symbolic-only reasoning, as done over and over again in your case.

3) Please show that in Traditional Mathematics 3=1*3=1+1+1 not because of a quantitative-only consideration.

 

[jsfisher]

Traditional Mathematics is not the only possibility to do Mathematics.

As has been well-established in this thread and all those that have gone before it, the term, traditional Mathematics, has referred to the entirety of Mathematics. Your so-called doronetics is something else, something that is not traditional Mathematics. At least that is how you have presented it.

As I have maintained, more than once, Mathematics is vast enough, and open enough, to embrace all sorts of bizarre concepts and approaches. One just needs to come with definitions and consistency. You have consistently failed on both counts in all aspects of doronetics.

I would ask you, now, to define what you mean by "traditional Mathematics" since you have implied your meaning is at odds with mine, but based on long-standing experience, that would be a fool's errand to request you define anything.

Be all that is it may, no matter how narrowly you may interpret "traditional", you will be hard-pressed to exclude from "traditional Mathematics" logic, meta-logic, predicate calculus, set theory, and many more, none of which are quantitative-only in nature.

 

[Apathia]

I'm afraid I may be the only one here who gets what you intend."

I want to walk this back. I think Jfisher and others do see your intention with the nesting of numbers is to provide a place for qualitative and value judgements, and a context in which persons are not mere quantitative numbers. But to the detail of it, they don't see what, for example, the cybernetic kernels stand for and the meaning you give the nested numbers. By default they take numbers and operations with numbers mathematical literally.

I confess when I first saw your cybernetic kernals, I didn't have some direct perception of what the were supposed to mean. I had to read you carefully and ask questions to find out what you meant to be saying with them.

There are many people here, and people you know personally, who don't get the presentation but who see and act in quality of being above mere quantities.

 

[doronshadmi]

As has been well-established in this thread and all those that have gone before it, the term, traditional Mathematics, has referred to the entirety of Mathematics.

One just needs to come with definitions and consistency.

What you call the entirety of Mathematics, is a framework that rigorously proves things by verbal_symbolic-only reasoning.

Also definitions are accepted only in terms of verbal_symbolic-only reasoning, so your "Mathematics is vast enough, and open enough, to embrace all sorts of bizarre concepts and approaches" is closed under verbal_symbolic-only reasoning, and since you are aware of this limitation you actually avoid http://www.internationalskeptics.com/forums/showpost.php?p=12516414&postcount=3260.

 

[doronshadmi]

Moreover, the verbal_symbolic-only definitions of Traditional Mathematics are based on philosophical notions, as demonstrated, for example, in www.internationalskeptics.com/forums/showpost.php?p=12444040&postcount=3229.

The problem is that it is not Mathematics. It may be a philosophy of some sort, and it may provide a basis for mathematical development, but it is not Mathematics.

Still, I am enjoying dialogue the between you and Apathia. It has provided new insight into why Philosophy has little relevance beyond questions of human values and ethics.

And as I have said many times before: Mathematics doesn't care what you want to believe or disbelieve. It will continue to be useful and consistent (as far as we know) independent of any protest you offer. If you ever produce something even vaguely like that, then you will capture my full attention. For now, though, it is amusing but little else.

The claim of jsfisher that Mathematics is independent of its Philosophy, is actually the philosophical view of Platonists, which claim about the independent existence of mathematical objects from those who define them, which has direct influence on their formal mathematical definitions.

 

[doronshadmi]

I want to walk this back. I think Jfisher and others do see your intention with the nesting of numbers is to provide a place for qualitative and value judgements, and a context in which persons are not mere quantitative numbers. But to the detail of it, they don't see what, for example, the cybernetic kernels stand for and the meaning you give the nested numbers. By default they take numbers and operations with numbers mathematical literally.

I confess when I first saw your cybernetic kernals, I didn't have some direct perception of what the were supposed to mean. I had to read you carefully and ask questions to find out what you meant to be saying with them.

There are many people here, and people you know personally, who don't get the presentation but who see and act in quality of being above mere quantities.

As given in www.internationalskeptics.com/forums/showpost.php?p=12514227&postcount=3248 cybernetic kernels are degrees of awareness' self-interference.

There is an inverse proportionality between the number of self interferences and the degree of self awareness and diversity.

In order to easily understand it one simply uses visual_spatial AND verba_symbolic reasoning, which is something that most of the posters here simply refuse to do.

 

[doronshadmi]

Be all that is it may, no matter how narrowly you may interpret "traditional", you will be hard-pressed to exclude from "traditional Mathematics" logic, meta-logic, predicate calculus, set theory, and many more, none of which are quantitative-only in nature.

Please use logic, meta-logic, predicate calculus, set theory, and many more (as defined by Traditional Mathematics) in order to define the quality of natural numbers (please be aware that the order among natural numbers can't be defined unless the quantity of each natural number is defined).

 

[Apathia]

As given in www.internationalskeptics.com/forums/showpost.php?p=12514227&postcount=3248 cybernetic kernels are degrees of awareness' self-interference.

There is an inverse proportionality between the number of self interferences and the degree of self awareness and diversity.

In order to easily understand it one simply uses visual_spatial AND verba_symbolic reasoning, which is something that most of the posters here simply refuse to do.

I'm more adept at words and language then Mathematics. Of course I'm "verbal-symbolic" a lot, but I compensate by maintaining my childhood eye. I will stop and notice things, for example a tree, as not just another example of abstract tree on my path, but as its own individual self. I just let it present itself to me as its concrete self. When I pay full attention, it seems as if the tree is a person in response to me. I know objectively that it's not a person in the sense I am. That it's not a sentient being. So I don't make a dyad (a tree fairy) out of the encounter. Instead I deepen my focus to the reality that isn't (but is) the Tree and me to the single Awareness.

I do not tire of gazing at the Moon with fresh eyes and being in the moment as it presents itself in the light of its own being. I really enjoy the wonder. This is the kind of experience I took your "visual-spatial" to mean.


A little more accessible to me than the cybernetic kernel illustration is the wave analogy. We have used it as a metaphor of individual things in a seamless reality. There is Unity and Diversity. This is a verbal-symbolic metaphor. You go on to make a diagram of harmonics that expands the metaphor. In communication with you, I know what you mean to say by that diagram, and I relate to it as meaning a precious truth.

If I stop at the beach to really see the waves, I don't necessarily treat them as a metaphysical metaphor. I just suspend my concepts and enjoy. Afterwards I might begin commenting, this is just like the concept of ...

When I just let the wave diagram and the cybernetic kernel illustrations just be themselves they leap off the page as beauty. I have to then apply some verbal-symbolic conceptualizing to see their intended meaning. Then I see the purposes and the connections with other expressions, such as the cyclical, Yin-Yang, the foundations of Taoist Philosophy, the Heat/Cold paradigm of Traditional Chinese Medicine, and the inner workings of the I-Ching. But while I'm just being present with the concrete before me, I'm not getting metaphysical and conceptual.

So this is why I say the purpose and meaning you give these diagrams doesn't jump out on its own. It doesn't occur to the viewers unless they are told what these expressions are intended to mean. For some this will take just a few words. People who practice Awareness will sooner get your drift. But even some who are quite concrete as opposed to abstract may not get the meaning. (I child for example who though s/he's very visual-spatial, would not get the concepts. You may remember that poem by Walt Whitman "The Learned Astronomer." Whitman may likely be confused if you tried to present Organic Mathematics to him and just not get it. Yet he would "Sing the Body Electric."

So I'm not going to judge why others here have not gotten your intent. We all have our "self-interferences," of different sorts, the most pernicious being the ego-centric ego that puts itself right in front of reality, ever blocking the view. Since my consciousness suffers the ego delusion, I'm in no position to claim more Awareness (as if it were something we had independent of others).

I kind of hoped I could explain enough of your intent that this thread could move on to an intelligent discussion of how your Organic Mathematics is supposed to work, and if it really does service a higher quality of Awareness. I figured that at least if readers saw what you were driving at, they could ask some more telling questions and make critiques relevant to your meaning. I doubt that's going to happen now. But I'm not making a moral failure of it for any of us.

Also the dialogue is more interesting to me than a goal of changing someone's mind. Especially the wretched intent to "correct" an other. Not that I don't appreciate having my thoughts corrected. I do so because I love learning and I love truth. But Leaning and Truth are more matters of Being than knowledge. It starts with letting people Be.

 

[doronshadmi]

Whitman may likely be confused if you tried to present Organic Mathematics to him and just not get it. Yet he would "Sing the Body Electric."

Then by music will shell do it.

Please observe the nested natural numbers as an evolution of a musical instrument that eventually defines the uniqueness of each key (there is no redundancy of notes).

Now awareness (represented by a cybernetic kernel that does not interfere itself in any possible level) can express itself (can celebrate its musical talent) in the most diverse ways under some finite number of keys.

Yet there is always the silence, which is the non-composed substance of any musical instrument, which never reveals itself by any key, yet enables the harmony among notes, whether there are finitely many or endlessly ever developed musical instruments.

Silence (the non-compose) is the actual alpha (NOthing={||} ) AND omega (YESthing=|{}|) among endlessly collections of sounds ({|a,b,c|}, {|a,b,c,...|}).

Modern mathematicians like jsfisher wrongly define actual infinity at the domain of collections (limit cardinal, limit ordinal, limit of convergent series (bye bye endlessly smaller thing > 0), etc.) exactly because they are unaware of the silent substance of endlessly collection of sounds.

By using also visual_spatial reasoning in addition to verbal_symbolic reasoning, one gets the opportunity to expose the mistake of verbal_symbolic reasoning that is being trapped by collections of sounds, and therefore wrongly defines actual infinity in terms of collections.

 

[Apathia]

Then by music will shell do it.

Please observe the nested natural numbers as an evolution of a musical instrument that eventually defines the uniqueness of each key (there is no redundancy of notes).

Now awareness (represented by a cybernetic kernel that does not interfere itself in any possible level) can express itself (can celebrate its musical talent) in the most diverse ways under some finite number of keys.

Yet there is always the silence, which is the non-composed substance of any musical instrument, which never reveals itself by any key, yet enables the harmony among notes, whether there are finitely many or endlessly ever developed musical instruments.

By poetry he'll do (did) it. Walt Whitman was an American poet. His "I Sing The Body Electric" was one of his poems.

Silence is just as much essential in poetry. Ambiguity as well, and rich, layered simile and metaphor. It can do all of this while at the same time invoking an immediate experience.

An old silent pond
A frog jumps into the pond,
Splash! Silence again.

(a haiku by Matsuo Bashou)

 

[doronshadmi]

An old silent pond
A frog jumps into the pond,
Splash! Silence again.

(a haiku by Matsuo Bashou)

A silent pond

A frog jumps into A silent pond

A silent pond

 

[Apathia]

A silent pond

A frog jumps into A silent pond

A silent pond

 

[doronshadmi]

Another way to show how silence is the substance of infinitely many different sounds, is demonstrated by the given "Harp of natural numbers" diagram:

There are endlessly different sounds and their combinations, that can be produced within it, where the backbone of it is the silence (the non-composed) that enables these endlessly different sounds to interact with each other in harmoniums endlessly ways.


Modern Mathematics, wrongly defines the non-composed as the limit cardinal |N|, and by doing so it wrongly defines the non-composed in terms of an infinite collection (which is a composed thing).

As observed by this diagram, Unity awareness is the silent (non-composed) backbone which referees to itself, which is and existence that is independent of the existing collection of endlessly strings along it (its exitance is beyond collections (which are composed things)).


Actual meditation enables one (which is a one-of-many thing) to be aware of the silent backbone of endlessly many things, and by not losing silence during playing, one actually expresses itself in terms of Unity awareness.

 

[doronshadmi]

Nested integer partititon

OK, let's do some traditional mathematics (related to Combinatorics and Number Theory).

Please observe the following diagram of the natural numbers 1 to 4:

This diagram represents the transition from multiplicity to addition under a given natural number > 0, such that multiplicity is done among 1's that do not have unique identities (therefore they can be summed by a single operation) and addition is done among 1's that have unique identities (therefore they can't be summed by a single operation (unless there is only a single 1)).


Here are the transitions from multiplicity to addition under the given natural numbers 1 to 4:

1: (+1) (its own uniqueness (therefore no multiplication))


2: (1*2), ((+1)+1)


3: (1*3), ((1*2)+1), (((+1)+1)+1)


4: (1*4), ((1*2)+1*2), (((+1)+1)+1*2), ((1*2)+(1*2)), (((+1)+1)+(1*2)), (((+1)+1)+((+1)+1)), ((1*3)+1), (((1*2)+1)+1), ((((+1)+1)+1)+1)


My question is:

How can we define an equation that returns the number of these nested forms under any given natural number > 0?


My question is about nested integer partition, which is an extension of integer partition ( https://en.wikipedia.org/wiki/Partition_(number_theory) ).

My nested integer partition is defined by the transition from symmetry (no 1's under a given n>1 have a unique "name" (order is impossible)) to asymmetry (all 1's under a given n>1 have a unique "name" (order is fully possible)).

For example: in case of n=4, the most symmetrical state is defined as (1*4) and the most asymmetrical state is defines as ((((+1)+1)+1)+1).

Diagrams of natural numbers 1 to 6 are seen here:

 

[doronshadmi]

Well, I see that no one here whishes to replay to my last post, which deals with finite mathematical objects.

In that case maybe you wish to reply to https://file.scirp.org/pdf/APM_2015012614584080.pdf content, which was published Prof. Wolfgang Mueckenheim in APM journal.

 

[sackett]

Straining for a haiku
Mizu no OTO
Smart-ass Basho

 

[doronshadmi]

The perspective on if-and-which-infinity is really a matter of philosophy, not mathematics.

jsfisher, this is a philosophical view, which tries to separate between philosophy and mathematics.

The problem is that Doronshadmi takes his (philosophic) view on infinity as a basis to (selectively) reject basic mathematics.

Basic Mathematics (the very foundation of Mathematics) can't be separated from its philosophical view.

You give Doron more credit than I. His fundamental point is that points cannot gather in sufficient quantities to every become a line segment.

Exactly, a non-composed ______ is not a collection of shorter or shortest elements.

It was a fair observation at one time in mathematics history, but we are for the most part beyond that now.

The notion that a non-composed ______ is not a collection of shorter or shortest elements, is both philosophical AND mathematical issue.

Philosophy may do with it what it will, and I have no objection there.

Again you are using a limited philosophical view that artificially separates between philosophy and mathematics.

Doron, on the other hand, wants it damn much of mathematics.

I simply expend mathematics beyond the notion of collections.

He seems to be hung on "process": add a point, still not enough; add another.... This was confirmed with his misinterpretation of the Axiom of Infinity. The axiom asserts the existence of a particular infinity set (absolute infinity, by the way), but Doron insists it asserts a process for constructing a set ever increasing in size (more at potential infinity).

Actual infinity is non-composed, so any composition is not actual infinity.

As for his "represented as", Doron's views can be perfectly explained with words, as I think you have done reasonably well. Doron, however, needs more because he has lashed out from his philosophic fixation into established math.

_______ "is non-composed", uses visual_spatial AND verbal_symbolic reasoning.

He has invented a shield he thinks protects him from all criticism via this visual-spatial vs. verbal-symbol reasoning ruse.

It is not visual-spatial vs. verbal-symbol reasoning, but it is visual_spatial AND verbal_symbolic reasoning.

The graphic of six underbars he included -- serving no purpose other than to "name" his object -- was a device to slip in an unnecessary visual element he could later exploit in his "you can't get it" mantra.

_______ "is non-composed" is a straightforward notion, that is known by any one that does not get _______ as a composed object.

By the way. I am amused that ______ when rendered using Lucinda Sans Unicode for the font, ______, it clearly shows as six separable elements. Not quite the visual-spatial reasoning conclusion Doron wanted, but nonetheless valid.

A perfect demonstration of how one gets _____ only in terms of verbal_symbolic reasoning.

Generally jsfisher, you are simply avoiding http://www.internationalskeptics.com/forums/showpost.php?p=12412827&postcount=3095 because it does not fit to *your* verbal_sybolic-only reasoning, which artificially separates between philosophy and mathematics (which is actually *your* preferred philosophical view on that issue).