Deeper than primes

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jsfisher said:
By we I must assume you mean not you since you have already disqualified yourself. You freely admitted you don't understand it, so there would be nothing for you to discuss.
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jsfisher, we shell see soon who understands and who does not understand (in the real meaning of the word 'understand', about this case).
 
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ddt said:
Before you get too elated about Apathia's post, a small forewarning. Apathia's tried to do this before, and invariably, sooner or later he got burned when it turned out that his interpretation was not what Doron meant. So don't get your hopes too high up.
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:wackybiglaugh:

I must agree with that caution.
I do think I get the basic idea, but I've come to grief whenever I've tried to get a coherant view that fits all of what Doron is trying to say.
Some of this has been my own misundersrtanding.
Some the misfitting pieces Doron offers.
Sometimes Doron doesn't notice I'm saying the same thing for him, just because I'm not using his vocabulary, or current vocablary.
And in general he's not able to meet me halfway to correct me.

So, yes, here I am again trying to rope it all together again.
To mix the metaphor again, there are some pieces of his puzzle that are still not fitting for me. Of course, I'm doubting that they all fit.

But chances are that Doron will say to me a couple of posts down, "That's not it at all. That's not what I meant at all."
So, beware my attempted translations. They may be only bars of molted soap after all.

But indulge my fun, and we'll see if I can roll my boulder get any father up the mountain this time.
 
doronshadmi said:
X > 0

Let us look at (0,X] interval.

According to "up to" zooterkin and jsfisher, 0 is an immediate predecessor of (0,X].

Zooterkin and jsfisher think that there is a meaning to < relation by ignoring the content of interval [0,0] or interval (0,X].

Let us demonstrate their failure by using this diagram:

[qimg]http://www.geocities.com/complementarytheory/SportsCar.jpg[/qimg]


We can clearly see that d and e are the same value only if there is no Sports Car.

We can also see that since there are infinitely many Sports Cars between X and 0, then for any e there is d such that 0<d<e and as a result 0 cannot be an immediate predecessor of a mathematical object that is a collection of infinitely many 0<d<e relations ( infinitely many Sports Cars between X and 0, that cannot be 0 ( e=d does not hold in (0,X] )).
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Just some questions because I'm not sure I follow. In this scheme does X stand for an arbitrary value? And could interval (0, X] be the same as [0, 0]? And is this all just a roundabout way of saying that all values and intervals are expressions of zero? :boggled:
 
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AkuManiMani said:
Just some questions because I'm not sure I follow. In this scheme does X stand for an arbitrary value? And could interval (0, X] be the same as [0, 0]? And is this all just a roundabout way of saying that all values and intervals are expressions of zero? :boggled:
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Yes, X is an arbitrary value, but with the constraint X > 0. So, (0,X] is any interval at all on the number line that starts at, but does not include 0, and continues on to some arbitrary positive real number (called X).

The interval [0,0] is excluded on two counts. First, it isn't half-open on the left. Second, the X in this case isn't greater than 0.

Within the extended meaning of successor and predecessor for intervals exposed earlier in this thread, -1, -34.5, and 0 would all be examples of predecessors of the interval (0,X], and 0 would be an immediate predecessor.
 
What doronshadmi doesn't get is the standard notation. Square brackets mean "including" while curved brackets mean "excluding" when talking about points on a number line. The expression (0,x] can be written as "All numbers between zero and x, excluding zero and including x". [1,2] would be "All numbers from one to two" or "All numbers between one and two, including one and two". (-4,-3) would be "All numbers between negitive four and negitive three" or "All numbers from negitive four to negitive three, excluding negitive four and negitive three".
 
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Now I'll muck about some more.

From the very first thread Doron posted here, I had a problem with his giving Non-Locality objective, fixed content.
or another way of putting it: he attempting to make the subjective self a mathematical object.

My POV is something like the Non-Local is merely an empty stage upon which various elements enter, exit, move about, sometimes clump together, sometimes separate.
It seemed to me Doron wanted to treat these various elements as features of the stage itself, fixed in place. This amounts to me to be making of the Non-Local a realm of metaphysical objects.

But I admit that though a realm of metaphysical entities still isn't attractive to me, I didn't entirely get the Doron Method.

For me it was Non-Local:Subjective and Local:Objective
But the Dorom Method parses subjectivity and objectivity out in a different way.
There's the
Subjective Object
Objective Subject
Objective Object
Subjective Subject

This is the structure of his logic.

The purely Subjective Subject isn't a thing or an object at all.
(It's the "I” or subjective "YOU" of mysticism. And what Doron most recently labeled as the "Singularity.")
The purely Objective Object is such an exclusive thing that it cannot be related to or seen in the light of any other thing.
(Actually I'd label this the "singularity" ala black hole and the Subjective Subject as the unperturbed expanse.)
Both of these poles are outside cognition (or the "researchable" as Doron puts it).
But in conjunction they make a conceptual space where unique, essential, distinct subjective beings have a position in discourse, and mathematical objects have a metaphysical aspect.

Strictly speaking what is said to be in Non-Locality is neither within nor without a given locality and both within and with out that locality.
Doron posits a Local-Non-Local or a Non-Local Local.

This is a linguistic concept or device.
Trying to express it with any of the standard terms of mathematics results in a crash of contradictions, as we've seen again with the current formula for Organic Numbers.

It's more than a "new paradigm." It's an entirely different intellectual culture.
But one can find similarities in Taoist and Hindu thought.

Mathematics has a long and fascinating relationship with various schools of Mysticism and Metaphysics.
Yes, I know, Doron would rather those words not be mentioned in regard to his work.
But that's really what its about.
 
jsfisher said:
Yes, X is an arbitrary value, but with the constraint X > 0. So, (0,X] is any interval at all on the number line that starts at, but does not include 0, and continues on to some arbitrary positive real number (called X).

The interval [0,0] is excluded on two counts. First, it isn't half-open on the left. Second, the X in this case isn't greater than 0.

Within the extended meaning of successor and predecessor for intervals exposed earlier in this thread, -1, -34.5, and 0 would all be examples of predecessors of the interval (0,X], and 0 would be an immediate predecessor.
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Okay. So hes just pointing out that there's an infinite series of intervals between 0 and any value > 0. Whats all the hubbub about then? :confused:
 
AkuManiMani said:
Okay. So hes just pointing out that there's an infinite series of intervals between 0 and any value > 0. Whats all the hubbub about then? :confused:
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jsfisher claims that 0 is an immediate predecessor of the values that are > 0.

This is not the case simply because for any given value x > 0 in (0,X] interval there is d such that 0<d<x, which prevents 0 from being the immediate predecessor of x, so 0 is a predecessor of (0,X] but not an immediate predecessor of (0,X] .

Furthermore, the relation "<" in the expression [0,0] < (0,X] has a meaning only if it is used between the contents of the closed interval [0,0] and the clopen interval (0,X].

Jsfisher tries to force relation "<" between the closed interval [0,0] and the clopen interval (0,X] by ignoring their contents.

Jsfisher claims that 0 is the closest element to (0,X] which is not one of the elements of (0,X] interval.

But since (0,X] is opened w.r.t 0, then the term "closest" has no meaning exactly because for any given x there is a closer element d w.r.t to 0, and in this case 0 is not an immediate predecessor of any given x in (0,X] interval.
 
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Apathia said:
Now I'll muck about some more.

From the very first thread Doron posted here, I had a problem with his giving Non-Locality objective, fixed content.
or another way of putting it: he attempting to make the subjective self a mathematical object.

My POV is something like the Non-Local is merely an empty stage upon which various elements enter, exit, move about, sometimes clump together, sometimes separate.
It seemed to me Doron wanted to treat these various elements as features of the stage itself, fixed in place. This amounts to me to be making of the Non-Local a realm of metaphysical objects.

But I admit that though a realm of metaphysical entities still isn't attractive to me, I didn't entirely get the Doron Method.

For me it was Non-Local:Subjective and Local:Objective
But the Dorom Method parses subjectivity and objectivity out in a different way.
There's the
Subjective Object
Objective Subject
Objective Object
Subjective Subject

This is the structure of his logic.

The purely Subjective Subject isn't a thing or an object at all.
(It's the "I” or subjective "YOU" of mysticism. And what Doron most recently labeled as the "Singularity.")
The purely Objective Object is such an exclusive thing that it cannot be related to or seen in the light of any other thing.
(Actually I'd label this the "singularity" ala black hole and the Subjective Subject as the unperturbed expanse.)
Both of these poles are outside cognition (or the "researchable" as Doron puts it).
But in conjunction they make a conceptual space where unique, essential, distinct subjective beings have a position in discourse, and mathematical objects have a metaphysical aspect.

Strictly speaking what is said to be in Non-Locality is neither within nor without a given locality and both within and with out that locality.
Doron posits a Local-Non-Local or a Non-Local Local.

This is a linguistic concept or device.
Trying to express it with any of the standard terms of mathematics results in a crash of contradictions, as we've seen again with the current formula for Organic Numbers.

It's more than a "new paradigm." It's an entirely different intellectual culture.
But one can find similarities in Taoist and Hindu thought.

Mathematics has a long and fascinating relationship with various schools of Mysticism and Metaphysics.
Yes, I know, Doron would rather those words not be mentioned in regard to his work.
But that's really what its about.
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Aphatia,

First of all, thank you very much about your honest affords to understand OM.

You have to be more careful when you try to give a fixed title like "subjective" to Non-locality or "objective" to Locality.

For example, the laws of Physics are considered as objective exactly because they are non-local, or in other words, we can define them by using a well-defined experiment only if they do not depend on the location of the laboratory (the results hold iff they are independent of the location of the experiment).

I already wrote to you about Non-locality and Locality in http://www.internationalskeptics.com/forums/showpost.php?p=4726464&postcount=2899 (please ignore my rough language to you in this post).

About Ethics and Logic, one of OM's main afford to define the common and non-local foundations of both Ethics and Logics, exactly because Logics is non-local w.r.t any culture and Ethics is local w.r.t any culture.

This is exactly the reason of why the current scientific paradigm is so dangerous to our own survival, because it easily enables a realm where a mass destruction weapon, that used made by using non-local methods like Logic\Technology are used by people that have a Ethics that is local by culture.
 
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Little 10 Toes said:
What doronshadmi doesn't get is the standard notation. Square brackets mean "including" while curved brackets mean "excluding" when talking about points on a number line. The expression (0,x] can be written as "All numbers between zero and x, excluding zero and including x". [1,2] would be "All numbers from one to two" or "All numbers between one and two, including one and two". (-4,-3) would be "All numbers between negitive four and negitive three" or "All numbers from negitive four to negitive three, excluding negitive four and negitive three".
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What you and jsfisher do not get is the notion.

Notations have no meaning without notions, and you and jsfisher are using here notations and names, without understand the meaning of the relation "<" of 0<X expression in the case of (0,X] clopen interval.

By determine 0 as an immediate predecessor of (0,X] a very important mathematical universe is ignored and not researched (for example you are using the word "all" without understand that the is no such a thing like the non-finite collection of all X, simply because no collection has the magnitude of existence of the real-line itself, which is a non-local ur-element).

Please look at http://www.internationalskeptics.com/forums/showpost.php?p=4844439&postcount=3950 .
 
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doronshadmi said:
By determine 0 as an immediate predecessor of (0,X] a very important mathematical universe is ignored and not researched (for example you are using the word "all" without understand that the is no such a thing like the non-finite collection of all X, simply because no collection has the magnitude of existence of the real-line itself, which is a non-local ur-element).
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Are you simply objecting to applying the word 'all' to an infinite collection of numbers even though it is well-defined?
 
zooterkin said:
Are you simply objecting to applying the word 'all' to an infinite collection of numbers even though it is well-defined?
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It is not well-defined, because first you have to undertand with what you deal before you try to define it by some string of words.
 
doronshadmi said:
jsfisher claims that 0 is an immediate predecessor of the values that are > 0.
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Nope. This has never been my claim.

This is not the case simply because for any given value x > 0 in (0,X] interval there is d such that 0<d<x, which prevents 0 from being the immediate predecessor of x, so 0 is a predecessor of (0,X] but not an immediate predecessor of (0,X] .
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Nope, this is just Doron not understanding some basic Mathematics terminology and definitions then substituting wrong meanings for things he doesn't understand.

Furthermore, the relation "<" in the expression [0,0] < (0,X] has a meaning only if it is used between the contents of the closed interval [0,0] and the clopen interval (0,X].
Click to expand...

Ditto.

...
Click to expand...

...and so on.
 
doronshadmi said:
It is not well-defined, because first you have to undertand with what you deal before you try to define it by some string of words.
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In what way is (0, X] not well-defined? For any number, it is clear whether it is in the interval or not. Why on earth can you not use 'all' to refer to every number that is in the interval?
 
jsfisher said:
Nope. This has never been my claim.



Nope, this is just Doron not understanding some basic Mathematics terminology and definitions then substituting wrong meanings for things he doesn't understand.



Ditto.



...and so on.
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jsfisher thinks that there is difference in the use of "<" relation between 0 or [0,0] w.r.t (0,X].

This is a good example of playing with notations without notions.
 
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zooterkin said:
In what way is (0, X] not well-defined? For any number, it is clear whether it is in the interval or not.
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So what? it does not mean that this collection has the magnitue of existence of the real-line itself (no collection of 0-dim beads is a string).
 
doronshadmi said:
So what? it does not mean that this collection has the magnitue of existence of the real-line itself (no collection of 0-dim beads is a string).
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What does that have to do with anything? Please explain why you cannot use the phrase "all the numbers in the interval", if that is what you are objecting to.
 
zooterkin said:
What does that have to do with anything? Please explain why you cannot use the phrase "all the numbers in the interval", if that is what you are objecting to.
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What does that have to do with anything? Please explain why you don't get that infinitely many objects cannot be a complete one object (again think about infinitely many 0-dim beads that have to completely cover a one string).
 
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