Cont: Deeper than primes - Continuation 2

[doronshadmi]

Dear Apathia,


First of all thank you for your open heart AND reasoning, which enables you to know that the non-composed hugging hands is not a collection of the hugged

Collapsing the baskets into one creates the paradox

The attempt to define the non-composed in terms of its finitely or infinitely many expressions (in terms of the composed) creates the paradox.


The paradox is solved by being aware of the following hierarchy of existence:

1. Actual infinity existence (the non-composed).

2. The finitely weaker exitance w.r.t (1) (the finitely composed expression of (1), which is not the non-composed).

3. The infinitely weaker exitance w.r.t (1) (the infinitely composed expression of (1), which is not the non-composed).

"The Barber shaves" goes into one basket, and the "only those men in town who don't shave themselves" into another basket.

So dear Apathia, we do not use two baskets in order to solve the paradox, because by doing so, we are still closed under the exitance of being composed.

Actual infinity existence (the non-composed) is not one-of-many existence (its existence is defined in terms of quality).

Its qualitative existence is defined, whether it weakens itself in order to expresses itself in terms of the composed (each expression is defined in terms of one-of-many finitely or infinitely many things (its existence is defined in terms of quantity), or not.

Please observe the following diagram by using visual_spatial AND verbal symbolic reasoning:

What we observe is ______ (non-composed object) that its bent forms (where being bent does not change the fact that each bent form is actually non-composed) are reflected as marks along it, such that the non-finite series 2(a+b+c+d+...) (which is a composed form) is infinitely weaker than the non-composed property of ______

As a result 2(a+b+c+d+...) < some fixed (or accurate) quantitative value that was given to the non-composed quality of _______ (where infinitely many reflected non-composed bent forms with the same fixed (or accurate) quantitative value, actually define the series 2(a+b+c+d+...) such that it is < the given fixed (or accurate) quantitative value, exactly because of the inability to define the quality of ______ by quantitative values).

As a result, there is an endlessly smaller ___ as the complement of 2(a+b+c+d+...) to the quantitative accurate value that was given to ______ (where this complement quantitative value is endlessly changing (its fixed (or accurate) quantitative value, can't be defined)).

 

[doronshadmi]

I wrote:

Let's return to the ground in order to demonstrate visual_spatial AND verbal_symbolic reasoning in terms of finite objects, as follows:

[qimg]https://c1.staticflickr.com/7/6146/6017791855_8ac80e49f9_o_d.jpg[/qimg]

This diagram demonstrates uncertainty and redundancy as the fundamental terms for information, where (A,B) is the particular case of distinct information under quantities (1,1).

It must be stressed that distinct information is a fundamental term in case of mathematical objects like distinct members of a given non-empty set.

So, by using visual_spatial AND verbal_symbolic reasoning, one realizes that distinct information is not fundamental.

You write:

Now you might think you are in the clear by counting how many things are in the basket. But sorry, according to Doron you are missing a subtlety. Take just pennies and chuck 'em in a basket. You pick up a penny and then another one. Two pennies, right? Well what was the second penny you picked up? One could say it was another instance of the same thing. Penny, Penny there it is again. You don't have two. This is "Redundancy." But is the second penny you picked up really just an instance of the first. It looks the same, but there's reason to count it as a different thing of itself. This is "Uncertainty."

This is a beautiful explanation, which actually adds another dimension to the framework, which is Distinction.

In the visual_spatial AND verbal_symbolic diagram, as appears above, it is easily seen that the foundation of each diagram is defined by non-composed _

On the top of this foundation, there are two vertical | , where each one of their edges is marked by . or *

. indicates that a given information is not available, where * indicates that a given information is available.

Uncertainty is the case where lower AND upper edges of a given vertical | are marked by *

Redundancy is the case where lower OR upper edges of a given vertical | are marked by *

By following these simple visual_spatial AND verbal_symbolic rules, one easily aware that, for example, (A,B), (B), (A), () information forms, stand at the basis of the sets {A,B}, and its power set {{A,B},{B},{A},{}} (where both of them are some particular examples of distinct information).

 

[Apathia]

Dear Apathia,


First of all thank you for your open heart AND reasoning, which enables you to know that the non-composed hugging hands is not a collection of the hugged

I can't but agree 100% with that sentiment. Also that the hugged are non-composed.

The attempt to define the non-composed in terms of its finitely or infinitely many expressions (in terms of the composed) creates the paradox.

Thank you for pulling that back into its context. It's tempting to treat so-called finite elements as merely finite. However the important point is that as you have described all things are of the Infinite as well.

So dear Apathia, we do not use two baskets in order to solve the paradox, because by doing so, we are still closed under the exitance of being composed.

This is an excellent corrective. I oversimplified. Of course it's not two baskets but the non-composed tree of baskets where in the end there aren't separate and separable objects in baskets, but the Eternal and Infinite (non-composed) Tree.

Actual infinity existence (the non-composed) is not one-of-many existence (its existence is defined in terms of quality).

Its qualitative existence is defined, whether it weakens itself in order to expresses itself in terms of the composed (each expression is defined in terms of one-of-many finitely or infinitely many things (its existence is defined in terms of quantity), or not.

Please observe the following diagram by using visual_spatial AND verbal symbolic reasoning:

[qimg]https://farm5.staticflickr.com/4015/4430320710_daf5b36c0f_o.jpg[/qimg]

What we observe is ______ (non-composed object) that its bent forms (where being bent does not change the fact that each bent form is actually non-composed) are reflected as marks along it, such that the non-finite series 2(a+b+c+d+...) (which is a composed form) is infinitely weaker than the non-composed property of ______

As a result 2(a+b+c+d+...) < some fixed (or accurate) quantitative value that was given to the non-composed quality of _______ (where infinitely many reflected non-composed bent forms with the same fixed (or accurate) quantitative value, actually define the series 2(a+b+c+d+...) such that it is < the given fixed (or accurate) quantitative value, exactly because of the inability to define the quality of ______ by quantitative values).

As a result, there is an endlessly smaller ___ as the complement of 2(a+b+c+d+...) to the quantitative accurate value that was given to ______ (where this complement quantitative value is endlessly changing (its fixed (or accurate) quantitative value, can't be defined)).

The thing to take home from this this morning is that even a whole number is non-composed. 2, for example is not composed of finite elements that can sum up to it. But doesn't 1 + 1 = 2? Only in a very narrow way. By the tree of Redundancy/Uncertainty there's much more to 2. 2 is actually an unbounded Redundancy/Uncertainty Tree.

You can do a finite tree for it, but this is a special case. The point is that 2 is not merely a quantity, but a quality.

Also in Doron's framework there are not fixed quantities except as narrow. special cases.

This doesn't do much for applied math. And that's an understatement.

The pithy statement of it all is that this is the way Doron asserts the principle that a whole is not a sum of its parts.

My inner Taoist likes it. My inner Hindu can see Krishna taking Arjuna aside and saying, "Take a look at this." My inner Buddhist wants to make some classic corrections to it. And I have some philosophical concerns. But I smile at the audacity of taking what we objectify the most and letting it shine in its own transcendence. It's the Quality of it that I like.

 

[Apathia]

This is a beautiful explanation, which actually adds another dimension to the framework, which is Distinction.

In the visual_spatial AND verbal_symbolic diagram, as appears above, it is easily seen that the foundation of each diagram is defined by non-composed _

On the top of this foundation, there are two vertical | , where each one of their edges is marked by . or *

. indicates that a given information is not available, where * indicates that a given information is available.

Uncertainty is the case where lower AND upper edges of a given vertical | are marked by *

Redundancy is the case where lower OR upper edges of a given vertical | are marked by *

By following these simple visual_spatial AND verbal_symbolic rules, one easily aware that, for example, (A,B), (B), (A), () information forms, stand at the basis of the sets {A,B}, and its power set {{A,B},{B},{A},{}} (where both of them are some particular examples of distinct information).

Yes. A reminder that distinct information is available in the tree. No one's bank account is going be in a quantity flux.

 

[doronshadmi]

The thing to take home from this this morning is that even a whole number is non-composed. 2, for example is not composed of finite elements that can sum up to it. But doesn't 1 + 1 = 2? Only in a very narrow way. By the tree of Redundancy/Uncertainty there's much more to 2. 2 is actually an unbounded Redundancy/Uncertainty Tree.

You can do a finite tree for it, but this is a special case. The point is that 2 is not merely a quantity, but a quality.

Also in Doron's framework there are not fixed quantities except as narrow. special cases.

This doesn't do much for applied math. And that's an understatement.

The pithy statement of it all is that this is the way Doron asserts the principle that a whole is not a sum of its parts.

My inner Taoist likes it. My inner Hindu can see Krishna taking Arjuna aside and saying, "Take a look at this." My inner Buddhist wants to make some classic corrections to it. And I have some philosophical concerns. But I smile at the audacity of taking what we objectify the most and letting it shine in its own transcendence. It's the Quality of it that I like.

Now I am your student, so I'll ask you some questions about what you wrote because they are your original insights.

1) Do you mean that the non-composed 0_1 + the non-composed 0_1 is not the non-composed 0__2 in terms of quality (It has to be stressed that in terms of quantity 0_1+0_1=0__2)?

2) By "2 is actually an unbounded Redundancy/Uncertainty Tree." do you speak about the 2-valued unbounded logical tree, as a particular case of an unbounded Redundancy/Uncertainty Tree?

3) What do you mean by "The point is that 2 is not merely a quantity, but a quality."?

4) How do you came to the conclusion that "... in Doron's framework there are not fixed quantities except as narrow. special cases."?

5) By "This doesn't do much for applied math. And that's an understatement." are you talking about what is considered as the current applied math, or your statement is time independent?

-------

Also I wish to correct something that I wrote in www.internationalskeptics.com/forums/showpost.php?p=12422107&postcount=3122 :


Instead of: Redundancy is the case where lower OR upper edges of a given vertical | are marked by *

It has to be: Redundancy is the case where lower OR upper edges of more than one given vertical | are marked by *

 

[Apathia]

Now I am your student, so I'll ask you some questions about what you wrote because they are your original insights.

I might by my ignorance say something that seems original.

1) Do you mean that the non-composed 0_1 + the non-composed 0_1 is not the non-composed 0__2 in terms of quality (It has to be stressed that in terms of quantity 0_1+0_1=0__2)?

I don't mean to negate anything that comes on the tree. I think my use of the word "quality" was imprecise or not as you intended in your usage. While I'm getting the big picture, some details of my word usage don't mesh.
As the notation on the tree goes, 0_1+0_1 certainly = 0_2.
I was saying something like: Suppose we have 2 mangoes. (Or that's how it appears to counting closed under verbal-symbolic reckoning.) But the second mango we pick up may be reckoned as a Redundancy. Without the Uncertainty, you just have one. It's the same mango again.

2) By "2 is actually an unbounded Redundancy/Uncertainty Tree." do you speak about the 2-valued unbounded logical tree, as a particular case of an unbounded Redundancy/Uncertainty Tree?

I'm probably confusing trees here. My point is that the whole number 2 is a whole that is more than the sum of its parts. There is the context in which it is, the context that math as it is currently done exploits. There is where 0_1+0_1=0_2. But 2 is not just that. Nothing that we call a "whole" is merely the sum of its parts. 2 comes to be in a more complex way involving a tree I can't delineate yet but is inspired by your number and logic trees.

Perhaps you say 2 is not a whole but a part the sum of other finite parts. But I see your same critique if speaking of infinities as composed wholes carried over to (in some sense) the so-called finite numerals themselves. So that there is a sense in which 2 is not a composed whole, but its meaning is in a tree generated from the binary principles of Whole and Part, or maybe Empty and Full. 2 has meaning beyond just distinct information.

I may be wrong about your presentation of 2, be here's where I saw for myself something very interesting. Say we talk about organs in the body. The Stomach is both a whole and a part. It consists of groups of specialized cells. However what it individually is, is not a mere sum of those groups or cells. There is an important sense in which it is not a reductionist mere sum of its constituent parts, even though it is a part of a larger organism. You and I may be members of say a family or tribe. As individuals we are not merely composed things. And what the tribe is is not a mere addition of things like you and me. I meet you as you, not as a mere sum of pieces or as a mere piece of some conceptual whole or a mere instance of a concept. While you and I are not the non-composed INFINITE, we are still its expressions where non-composition informs everything.

Are we not non-composed in a sense? Our being is not contained by concepts. It's open ended. Who we are can't be reduced to the mechanical iterations of our constituent parts. A whole at any level is not a whole yet emerges as a whole greater than the sum of its parts.
Anyway, I thought I saw an expression of that in your creation of trees from binary principles, and an extension of that to numbers.

3) What do you mean by "The point is that 2 is not merely a quantity, but a quality."?

I see now that I misunderstood and misapplied what you illustrated in Thread 3121.

4) How do you came to the conclusion that "... in Doron's framework there are not fixed quantities except as narrow. special cases."?

Again my bad. However Distinctive Information is not always given. It's not all there is to the tree of Redundancy/Uncertainty.

5) By "This doesn't do much for applied math. And that's an understatement." are you talking about what is considered as the current applied math, or your statement is time independent?

Your approach hits the house of mathematics like a bulldozer, and then rips up most of Mathematical assumptions since Euclid. You offer some new corner stones, but as yet there is not the structure that would provide a new way to do the many calculations the current mathematics is used for. Your examples show a kind of arithmetic tree but not a way to do higher math calculations and arrive at solutions. I suppose your employment requires or required you to do various calculations. Did you find a way to do those with your Organic Mathematics? I suppose it's possible that you have a mind that just sees the numerical solution. I congratulate you if you do. But he rest of our world of math-impaired people (such as myself) need algorithms.
-------

Also I wish to correct something that I wrote in www.internationalskeptics.com/forums/showpost.php?p=12422107&postcount=3122 :


Instead of: Redundancy is the case where lower OR upper edges of a given vertical | are marked by *

It has to be: Redundancy is the case where lower OR upper edges of more than one given vertical | are marked by *

Thanks for providing that correction in your subsequent post.

What I thought I saw in your "Organic Mathematics" was an expression of the open endedness of all things in our world. We are of both the Finite and the Infinite giving us a "non-composed" quality as well. Our meaning comes from the Infinite, not finite bits that add up to merely objects that function in such and such a way. I strive to remember to look at others in their own light, a light that transcends whatever class or utility my ego wants to box them in. I refuse to hold myself and you under verbal-symbolic classes and labels of friend, foe, frenemy. We are each the presence of the
non-composed INFINITY. Rational thinking without Heart leaves us mere bips on a chart of classifications or even a tree of binary values if we aren't awake. My ethic is to let people blossom as who they are rather than instances and representatives of some intellectual classification. Not letting people be present in their own becoming is bigotry. This is very visual-spatial, you see for I encounter the concrete person. And beyond my concepts I relish the Unity of our becoming.

Some years ago I found a way to open my heart to people and make a non-verbal connection. Alas I found that most people were disturbed to feel that. It messed with their ego boundaries. So now I'm careful not to assault their fortresses, but I still find ways to speak to them as more than what they stuff behind their walls.

Oops, I've carried on too much. But anyway, that's what I thought I saw your finger pointing to: that sense in which we are transcendent and non-composed. I think that's where you want to go.

 

[doronshadmi]

I might by my ignorance say something that seems original.

Please think about the meaning of a real dialog, at least, as I get it.

Real dialog, in my view, is done among, at least, two persons, such that each one of them is both student and teacher of the other. By doing so we get an open learning environment, which is in my opinion, the optimal framework for, probably, the next original (and maybe useful) results for, at least, the dialog's participators.

Moreover, by being both student AND teacher, each participator is actually an organic unit learning, which can't be reduced into teacher-only, student-only parts.

From this organic approach, an open learning environment is more than the sum of its participators, since each participator is a student AND teacher, which actually reflects the essence of such learning environment.

Furthermore, by being both student AND teacher, each person becomes a concrete factor for the dialog's fretful blooming.

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

Since I have to go now, I'll continue my replies to you latter

 

[doronshadmi]

Before we continue the sentence "Furthermore, by being both student AND teacher, each person becomes a concrete factor for the dialog's fretful blooming." in my previous post has to be replaced by "Furthermore, by being both student AND teacher, each person becomes a concrete factor of a fruitful and consistent dialog.

 

[doronshadmi]

Without the Uncertainty, you just have one. It's the same mango again.

In my URDT (pages 12, 13 of https://drive.google.com/file/d/0B3hcPBRBCzClakdJZjNNOW5RSTQ/view?usp=sharing ,for example, DS (B,B) under F (1,1) is not DS (B) under F (1,0). So no, it is not the same mango again.

My point is that the whole number 2 is a whole that is more than the sum of its parts.

2 is some fixed (or accurate) verbal_symbolic quantitative expression, which can't be used in order to define the non-composed qualitative property of ___ visual_spatial expression. This inability defines a whole that can't be defined as the sum of its parts.

Your approach hits the house of mathematics like a bulldozer, and then rips up most of Mathematical assumptions since Euclid. You offer some new corner stones, but as yet there is not the structure that would provide a new way to do the many calculations the current mathematics is used for.

My approach adding Actual Infinity as a non-composed quality that can't be defined in terms of quantitative compositions (collections).

Currently it is mostly like a new land with additional fertilizer (the visual_spatial reasoning) and it is given for free for anyone who wishes to plant and grow his\her mathematical crop.

What I thought I saw in your "Organic Mathematics" was an expression of the open endedness of all things in our world. We are of both the Finite and the Infinite giving us a "non-composed" quality as well. Our meaning comes from the Infinite, not finite bits that add up to merely objects that function in such and such a way. I strive to remember to look at others in their own light, a light that transcends whatever class or utility my ego wants to box them in. I refuse to hold myself and you under verbal-symbolic classes and labels of friend, foe, frenemy. We are each the presence of the
non-composed INFINITY. Rational thinking without Heart leaves us mere bips on a chart of classifications or even a tree of binary values if we aren't awake. My ethic is to let people blossom as who they are rather than instances and representatives of some intellectual classification. Not letting people be present in their own becoming is bigotry. This is very visual-spatial, you see for I encounter the concrete person. And beyond my concepts I relish the Unity of our becoming.

Some years ago I found a way to open my heart to people and make a non-verbal connection. Alas I found that most people were disturbed to feel that. It messed with their ego boundaries. So now I'm careful not to assault their fortresses, but I still find ways to speak to them as more than what they stuff behind their walls.

Oops, I've carried on too much. But anyway, that's what I thought I saw your finger pointing to: that sense in which we are transcendent and non-composed. I think that's where you want to go.

By being aware of the non-composed during its expressions, we may enliven an harmonious realm.

 

[Apathia]

Please think about the meaning of a real dialog, at least, as I get it.

Real dialog, in my view, is done among, at least, two persons, such that each one of them is both student and teacher of the other. By doing so we get an open learning environment, which is in my opinion, the optimal framework for, probably, the next original (and maybe useful) results for, at least, the dialog's participators.

Moreover, by being both student AND teacher, each participator is actually an organic unit learning, which can't be reduced into teacher-only, student-only parts.

From this organic approach, an open learning environment is more than the sum of its participators, since each participator is a student AND teacher, which actually reflects the essence of such learning environment.

Furthermore, by being both student AND teacher, each person becomes a concrete factor for the dialog's fretful blooming.

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

Since I have to go now, I'll continue my replies to you latter

For a portion of my life I was a teacher, teaching middle school aged students. With that background, I shy away from calling anyone my "student" or playing the role of "teacher." I no longer see myself as an educator. Dialog with another adult is a sharing and mutual learning opportunity. Than you for the opportunity with you.

 

[doronshadmi]

For a portion of my life I was a teacher, teaching middle school aged students. With that background, I shy away from calling anyone my "student" or playing the role of "teacher." I no longer see myself as an educator. Dialog with another adult is a sharing and mutual learning opportunity. Than you for the opportunity with you.

Student_AND_Teacher is not the same as Student-only | Teacher-only.

So there is no reason that that you shy away from calling anyone your "student" or playing the role of "teacher.", since each one of you is Student_AND_Teacher of the other, no matter what is the difference between your ages.

 

[Apathia]

In my URDT (pages 12, 13 of https://drive.google.com/file/d/0B3hcPBRBCzClakdJZjNNOW5RSTQ/view?usp=sharing ,for example, DS (B,B) under F (1,1) is not DS (B) under F (1,0). So no, it is not the same mango again.

Thank you for that correction. It's simply that a Redundancy is not qualitatively the same as an Uncertainty. Also the quantity is a matter of distinct information.

2 is some fixed (or accurate) verbal_symbolic quantitative expression, which can't be used in order to define the non-composed qualitative property of ___ visual_spatial expression. This inability defines a whole that can't be defined as the sum of its parts.

Do you mean that the 2 is always merely a verbal-symbolic entity?
As such it certainly remains a composed thing. By visual-spatial thinking we see wholes can never be defined as sums of their parts, and that the quantity 2 is never a whole in any sense.

Where I failed to get it was my thinking that 2 is in its full meaning a matter of both verbal-symbolic thinking AND visual-spatial thinking. And I thought that was expressed by the trees. I mistakenly thought that 2 was verbal-symbolic AND visual-spatial in its meaning and essence.

It appears to me now that you mean 2 is merely a verbal-symbolic expression for a reality that is beyond composition. It's not open ended or fluid itself but the reality beyond words that is apprehended visual-spatially is. The various trees illustrate the visual-spatial together with the verbal-symbolic but are not any kind of matrix for calculations They inform us that the concept of numbers comes about through both verbal-symbolic AND visual-spatial thinking. The point of the illustrations is to show us the Origin so that we are mindful of the Non-Composed beyond our manipulations of finite quantities.

My approach adding Actual Infinity as a non-composed quality that can't be defined in terms of quantitative compositions (collections).

Currently it is mostly like a new land with additional fertilizer (the visual_spatial reasoning) and it is given for free for anyone who wishes to plant and grow his\her mathematical crop.

Your critique of composed mathematical infinity is not altogether new. There have been numerous mathematicians who have grown crops on a field of potential infinity. But these are not your crops. They still don't come at it from a visual-spatial apprehension or acknowledge the Non-Composed Source, the Origin of which numbers are a finite expression.

By being aware of the non-composed during its expressions, we may enliven an harmonious realm.

It seems to me you are saying there is an Ultimate Source, a Reality from which all Finite expressions springs but that cannot be contained in any of them. It alone is truly non-composed. To speak of a composed Infinity is a kind of idolatry that makes images divine. But by not committing this error, we acknowledge and reverence The Source. Since we don't try to break up the Source into composed "infinities," we maintain that behind all our verbal-symbolic manipulations there is still the untouched, unsullied, UNITY.

In meditation when I "drop off body and mind" (Soto Zen Master Dogen's expression) I see things as they are in seamless Unity. When you speak of visual-spatial this is what I relate it to. I'm not in this state of consciousness when I'm calculating the day's supply of a fluid medication (Pharmacy Technician). I suppose your goal is a mathematics that during which one remains in apprehension of the UNITY. I don't see how that works yet.

For me my meditation practice is my important ritual of reorienting my thinking. In Zen bringing this vision to daily life this is simply when you are eating, just eat. When you are doing the math, just be doing the math. Be focused on what is happening as opposed to being carried away by conceptual chatter about what is supposed to and an ego-centric way of seeing and relating.

 

[Apathia]

Student_AND_Teacher is not the same as Student-only | Teacher-only.

So there is no reason that that you shy away from calling anyone your "student" or playing the role of "teacher.", since each one of you is Student_AND_Teacher of the other, no matter what is the difference between your ages.

That's good! Just don't ask me to be a guru. Again my ethic is to trust others in their process and not force them into mine.
That means I'm happy to grow with you, and am satisfied to let you be yourself. I don't have to change you so that your views conform to mine.
Here I want to understand your positions. You might learn something from my perspectives as I struggle to get you right. But if you get nothing from me, I'll still have my desired benefit of understanding you and respecting not just the sacred that is within you, but that you are sacred.

 

[doronshadmi]

The point of the illustrations is to show us the Origin so that we are mindful of the Non-Composed beyond our manipulations of finite quantities.

Exactly.

Your critique of composed mathematical infinity is not altogether new. There have been numerous mathematicians who have grown crops on a field of potential infinity. But these are not your crops. They still don't come at it from a visual-spatial apprehension or acknowledge the Non-Composed Source, the Origin of which numbers are a finite expression.

More precisely, the Origin of which numbers are expressed.

It seems to me you are saying there is an Ultimate Source, a Reality from which all Finite expressions springs but that cannot be contained in any of them. It alone is truly non-composed. To speak of a composed Infinity is a kind of idolatry that makes images divine. But by not committing this error, we acknowledge and reverence The Source. Since we don't try to break up the Source into composed "infinities," we maintain that behind all our verbal-symbolic manipulations there is still the untouched, unsullied, UNITY.[//quote]
Dear Apathia, Mathematics, as I define it, is based on not less than visual_spatial AND verbal_symbolic reasoning skills.

In meditation when I "drop off body and mind" (Soto Zen Master Dogen's expression) I see things as they are in seamless Unity. When you speak of visual-spatial this is what I relate it to. I'm not in this state of consciousness when I'm calculating the day's supply of a fluid medication (Pharmacy Technician). I suppose your goal is a mathematics that during which one remains in apprehension of the UNITY. I don't see how that works yet.

By being aware of the calmness of the sea during its wavy changes, one is aware of the sea with AND without waves. That is an analogy.

Now please change "waves" to "thoughts and other expressions" and "sea" to "awareness". That is an awareness about UNITY.

By practicing a technique that actually and eventually enables one to be aware with AND without thoughts and other expressions permanently, one is at UNITY awareness.

For me my meditation practice is my important ritual of reorienting my thinking. In Zen bringing this vision to daily life this is simply when you are eating, just eat. When you are doing the math, just be doing the math. Be focused on what is happening as opposed to being carried away by conceptual chatter about what is supposed to and an ego-centric way of seeing and relating.

What you describe above is still limited to thoughts and other expressions.

 

[doronshadmi]

But if you get nothing from me

Then I get nothing from you both as student AND teacher.

 

[Apathia]

More precisely, the Origin of which numbers are expressed.

I still don't get how Organic Mathematics is to induce an altered state of consciousness into UNITY.

By being aware of the calmness of the sea during its wavy changes, one is aware of the sea with AND without waves. That is an analogy.

Now please change "waves" to "thoughts and other expressions" and "sea" to "awareness". That is an awareness about UNITY.

By practicing a technique that actually and eventually enables one to be aware with AND without thoughts and other expressions permanently, one is at UNITY awareness.

This is great analogy.

What you describe above is still limited to thoughts and other expressions.

I hope what you are talking about here is the mindful pursuit of everyday activities ("Chopping wood, carrying water) which would involve thoughts and other expressions.
As for my meditation practice. though it's not perfect when thoughts and expressions distract me, I simply acknowledge them and return to just awareness of what is present. If I'm using a mantra or a yantra (or both in a seed syllable meditation), I return my focus to the target, and then once my focus is consolidated, I can drop the mantra and or yantra prop and ben in that Seamless Awareness of Unity.

Of course in this, I'm not thinking about expressions in binary principles or any kind of mathematics. The sea is calm.
And when I am mindful of the waves of thought. I calmly let them wave.

I've not attained to the ever Steadfast Radiance of the Buddhist Dharma Protector, Acalanatha, who is unruffled throughout the stormy waves of life while fiercely roaring away the demons of attachment, anger, and delusion. But this is the practice I know and it has helped make me a more graceful person.

(Disclaimer: references to metaphysical beings are solely metaphorical.)

 

[Apathia]

Then I get nothing from you both as student AND teacher.

Very well, then, Sensei!

Class is not dismissed!

 

[Apathia]

I want to go back to the Barber Paradox, because I got that so wrong, and I want to state Doron's position on that with clarity.

I'm not going to use "YESthing" and "NOthing" For the time being. That introduces a couple of terms that don't easily present their own meanings to the reader.

Again: the Barber shaves only those men in town who don't shave themselves. The paradox happens when we ask who shaves the Barber. He can't shave himself, because he only shaves those who don't shave themselves. Saying he doesn't shave himself but grows a three foot beard, doesn't make an escape, because the statement is that the Barber shaves those who don't shave themselves.

Now let me correctly (I pray.) apply Doron-thinking ("Visual-Spatial AND Verbal-Symbol") to this.

Doron immediately goes for what I'm calling a "binary principles" approach. This is not the same as using class concept membership, or belonging to a class of members. In this case it's two principles: separating or selecting out and not marking or selecting out anything. Lets call these two action principles Bracketing and Ignoring. Using Bracketing AND Ignoring, bracketed contents can be separated out from the field of … well, I mean there's nothing given any attention, and it's not a field. You need the Bracketing concept to say in retrospect that contents were singled out.

There's nothing to be said about the Ignoring, but once you do combine Bracketing and Ignoring, there are contents. In the story of the Barber you have a statement of the bracketing and the contents bracketed. They are of two separate meanings. The Bracketing action is "The Barber shaves." This is the gathering, the brackets: [ ]. It's in no sense a content in this context. If it were a content of some bracketing action, it would not be the bracketing, and we would be talking about something entirely different. The content here is "Only those men who don't shave themselves."

Doron's firm rule here is that you don't make a content out of what is the Bracketing. You may think that you can nestle a bracketing into another as that brackets contents. But if it's a bracketing action, you are not allowed. "The Barber shaves." is of a scope that doesn't have limitation. So you can't be bracketing it within a collection, especially when that collection does have stated limits (Only those men who don't shave themselves.).

So the two motions here don't go together. You don't collapse them into a single concept. (Yes. I realize that in talking this way about them Bracketing gets singled out. This is why I spoke of it being in its own basket. But such talk is a no no. As far as the Barber is concerned we assert that "The Barber shaves" cannot be bracketed or singled out or in of anything. And any other bracketing talk is an entirely different subject and content.

The statement stops with what it says. Who shaves the Barber is irrelevant to the statement. You have to come up with an entirely different Bracketing/Ignoring situation to talk about that.

This is the way Doron's intuitive style of cognition. Most of us have learned to nestle concepts within concepts by classification. But his is according to Doron a verbal-symbolic only style of thinking.

Again, if you are going to talk about a barber shaving as a content of a Bracketing, this is some entirety other situation where there is a different bracketing statement. The twain do not meet.

I think I may have a lurker or two still scratching their heads trying to understand how this busts the paradox. There is no paradox, because "The Barber shaves." is not a content in the statement, "The Barber shaves only the men in the town who don't shave themselves." The Barber is not and cannot be placed in the group of men shaved in this statement.

That would be thinking "bound under verbal-symbolic only." It's such flights of fancy conceptual thinking that get all wound up into pretzels of paradox.

And again I know this tears through modern Mathematics ripping it into shreds.

BTW what I'm doing in these posts is often chucking things at the wall and seeing what sticks. It's working. I know much more of what sticks with Doron now. Yes there still some things that seem to stick one time but not the next. I chalk these up to language misunderstandings. Doron has had 30 years to refine and work out the kinks in his worldview. So I don't think he's being inconsistent on anything important.

 

[jsfisher]

...
And again I know this tears through modern Mathematics ripping it into shreds.
...

No. No, it doesn't.

 

[Apathia]

No. No, it doesn't.

Great then! I'm glad to be wrong about that.
You are much more educated about Mathematics than I.

Please correct me about this.

But I think your meaning is that this is all irrelevant drivel that is as a matter of course ignored by any Mathematician, and that it doesn't count for anything that would even get mathematics wet by a single drop of spittle.

My point was that if anyone were to try to approach the discipline in the way Doron presents, s/he would have to sweep away centuries of Mathematical developments. And what then in the place of all that we have yet to get a clue about?

I'd like to see something from Doron in that direction. So far his presentation serves to illustrate the base of a philosophy. So I pursue my curiosity about that.