Deeper than primes - Continuation

Little 10 Toes · Mar 4, 2012

doronshadmi said:
Let's improve the formal novel system:

No need to even use a novel system. Cardinality doesn't care about anything other than the number of items in a set.

By the way, you can't even agree on your own definitions. Proof you may ask?

Here:

doronshadmi said:
Being aware of SOMEthing (YESthing) is an awareness at least at the level of Dichotomy, where in this case the opposite of SOMEthing is NOthing.

doronshadmi said:
EVERYthing is many SOMEthings, so the amount does no change the fact the both cases are the opposite of NOthing.

So what is the opposite?

sympathic · Mar 4, 2012

[I said:
[/I]Little 10 Toes;8080443]No need to even use a novel system. Cardinality doesn't care about anything other than the number of items in a set.

By the way, you can't even agree on your own definitions. Proof you may ask?

Here:

So what is the opposite?

LITTLE-BITthing

dafydd · Mar 4, 2012

Originally Posted by doronshadmi
Being aware of SOMEthing (YESthing) is an awareness at least at the level of Dichotomy, where in this case the opposite of SOMEthing is NOthing

Originally Posted by doronshadmi
EVERYthing is many SOMEthings, so the amount does no change the fact the both cases are the opposite of NOthing.

Punshhh is at Unity with Doron so no doubt he can explain that to us.

doronshadmi · Mar 5, 2012

Little 10 Toes said:
No need to even use a novel system. Cardinality doesn't care about anything other than the number of items in a set.

This is the concept of Cardinality under the limitations of Traditional Mathematics, so?

Organic Mathematics concept of Cardinality is novel.

Little 10 Toes said:
By the way, you can't even agree on your own definitions. Proof you may ask?

Here:

So what is the opposite?

http://www.internationalskeptics.com/forums/showpost.php?p=8079828&postcount=596 is an essential improvement of http://www.internationalskeptics.com/forums/showpost.php?p=8061757&postcount=490, such that YESthing is defined has that has no successor, which is the opposite of NOthing, which is that has no predecessor.

SOMEthing or EVERYthing are intermediate states where SOMEthing is not reducible into NOthing, which is that has no predecessor, and EVERYthing is not extensible into YESthing, which is that has no successor.

Unity (the thing) is beyond Polychotomy, where NOthing, SOMEthing, EVERYthing and YESthing are closed under Polychotomy.

Please follow after improvements from now on.

realpaladin · Mar 5, 2012

doronshadmi said:
This is the concept of Cardinality under the limitations of Traditional Mathematics, so?

Organic Mathematics concept of Cardinality is novel.

Good. Explain it from scratch, the way you would with students in the first class of the first semester of the first year.

Also, it means there is no need to point to traditional maths anymore to say what is 'wrong' there.

Let's just stick to OM.

doronshadmi said:
http://www.internationalskeptics.com/forums/showpost.php?p=8079828&postcount=596 is an essential improvement of http://www.internationalskeptics.com/forums/showpost.php?p=8061757&postcount=490, such that YESthing is defined has that has no successor, which is the opposite of NOthing, which is that has no predecessor.

SOMEthing or EVERYthing are intermediate states where SOMEthing is not reducible into NOthing, which is that has no predecessor, and EVERYthing is not extensible into YESthing, which is that has no successor.

Unity (the thing) is beyond Polychotomy, where NOthing, SOMEthing, EVERYthing and YESthing are closed under Polychotomy.

Please follow after improvements from now on.

The wording suggests this is predicate logic....

Highlighting mine: is that a mutually exclusive or, or is at an indeterminate or (i.e. 'we don't know, but either this one *or* that one must be it). Or is it an artefact of language?

Now, what does all of that *mean*? What does it *do*?

Can we predict something with it? Or explain something?

doronshadmi · Mar 5, 2012

realpaladin said:
Good. Explain it from scratch, the way you would with students in the first class of the first semester of the first year.

Already done at http://www.internationalskeptics.com/forums/showpost.php?p=8079828&postcount=596 .

realpaladin said:
Also, it means there is no need to point to traditional maths anymore to say what is 'wrong' there.

Let's just stick to OM.

You can't rid of the context-dependent-only paradigm.

realpaladin said:
Or is it an artefact of language?

Informal or.

I notate formal OR by italic upper case.

realpaladin said:
Now, what does all of that *mean*? What does it *do*?

Can we predict something with it? Or explain something?

We understand mathematical spaces ( http://www.internationalskeptics.com/forums/showpost.php?p=8079828&postcount=596 ).

More details are found in http://www.internationalskeptics.com/forums/showpost.php?p=8077918&postcount=589 .

realpaladin · Mar 5, 2012

doronshadmi said:
Already done at http://www.internationalskeptics.com/forums/showpost.php?p=8079828&postcount=596 .

Really? That is how you would teach freshmen pupils?

doronshadmi said:
You can't rid of the context-dependent-only paradigm.

Like them branching math thingies... right?

doronshadmi said:
We understand mathematical spaces ( http://www.internationalskeptics.com/forums/showpost.php?p=8079828&postcount=596 ).

More details are found in http://www.internationalskeptics.com/forums/showpost.php?p=8077918&postcount=589 .

I just pasted all these links below, so I can peruse them at leisure, but also for the benefit of others.

doronshadmi said:
Let's improve the formal novel system:

;||; = the cardinality of NOthing (that has no predecessor).

|;;| = the cardinality of YESthing (that has no successor).

Beyond these states there is the thing, which is the Unity beyond polychotomy.

The power of continuum is defined as the ability of a given space to be at AND beyond (not at) the domain of given lower space(s) or sub-space(s) (where sub-space(s) is\are a mixture of a given space and lower spaces, associated by Unity (by the thing)).

;|c₀|; = the cardinality of 0-space does not have the power of the continuum.

;|c₁,c₀|; = the cardinality of 1-space has the power of the continuum, but the cardinality of 0-spaces on it do not have the power of the continuum.

;|c₂,c₁,c₀|; = the cardinality of 2-space has the power of the continuum, but the cardinality of 1-spaces and 0-spaces on it do not have the power of the continuum.

;|c₃,c₂,c₁,c₀|; = the cardinality of 3-space has the power of the continuum, but the cardinality of 2-spaces,1-spaces and 0-spaces on it do not have the power of the continuum.

...

etc. ad infinitum ... where no space > 0 has the power of the continuum of YESthing (that has no successor).

In general, no collection of lower spaces or sub-spaces, has the power of the continuum of a given space.

doronshadmi said:
The subject at hand is that the power of the continuum is not satisfied in terms of collection, and this knowledge is deeper than the knowledge about primes, because it has a direct influence on our understanding of the concept of Entropy (the inability of collection of lower spaces or sub-spaces to completely cover a given space > 0, is resulted by non-entropic and therefore ever-developed (abstract or physical) realm).

As for you, you can't get, for example, http://www.internationalskeptics.com/forums/showpost.php?p=8059077&postcount=473 .

doronshadmi said:
Forces of nature are manifestations of Unity (including one's awareness), so in order to harmonically manipulate them, the manipulator must have Unity awareness. The development of The Technology of The Consciousness is exactly the development of Science, simply because real Science is not less than the harmoniums association among the developed, the developer and the used tools for development.

Wrong, the gap is actually the "host" (mathematical or physical) space, which enables "hosted" spaces or subspaces to be gathered into one organism and still leave a "room" for further complexity's development.

Once again, the "host" (mathematical or physical) space exists even if no "hosted" collection of lower spaces or subspaces exist on it.

Harmony among "hosted" (mathematical or physical) spaces.

There is no "we" without "host"\"hosted" association.

We shell not survive as ever developed responsible communicators between Simplicity and Complexity.

It is already shown in http://www.scribd.com/doc/16669828/EtikaE

and

http://farm4.staticflickr.com/3489/5842425568_4e4e18f7ee_b.jpg

doronshadmi · Mar 6, 2012

Let's look closely at some possible relations among mathematical spaces:

A given space > 0 is non-local w.r.t to lower spaces or sub-spaces (which are associated results among a given space > 0 and lower spaces) if 0 space is involved as one of the lower spaces (for example: given 1-space, it is 1-space at X-axis, but it is 0-space at Y-axis. In general, given n-space, where n>0, it has 0-space at (n+1)-axis)).

For example: a given line segment is non-local (at AND not at) the domain of a given circle (which is a sub-space of 2-space) because the line segment is at AND not at the location of the intersection point (the intersection point is 0-space at (1+1)-axis of the circle's circumference 1-space) on the circle's circumference (which defines the domain of the sub-space (the circle) on a given 2-space).

dafydd · Mar 6, 2012

My Twoness theory is the correct one.

doronshadmi · Mar 6, 2012

Some correction my previous post:

EDIT: no correction is needed.

doronshadmi · Mar 6, 2012

dafydd said:
My Twoness theory is the correct one.

Twothings are undefined without the thing.

dafydd · Mar 6, 2012

doronshadmi said:
Twothings is undefined without the thing[/COLOR].

The Thing. That was a bad movie. Every positive number has a negative counterpart and vice versa so Twoness is the thing.

dafydd · Mar 6, 2012

doronshadmi said:
Some correction of the previous post:

... (the intersection point is 0-space at (2+1)-axis of the circle's circumference 1-space, which defines the domain of the sub-space (the circle) on a given 2-space).

As if that makes any difference.

doronshadmi · Mar 6, 2012

dafydd said:
Every positive number has a negative counterpart and vice versa so Twoness is the thing.

What enables -x x to be comparable, and be gathered as Twothings?

doronshadmi · Mar 6, 2012

dafydd said:
As if that makes any difference.

EDIT: I re-examined it, no correction is needed after all.

realpaladin · Mar 6, 2012

dafydd said:
The Thing. That was a bad movie. Every positive number has a negative counterpart and vice versa so Twoness is the thing.

But the color version was better.

realpaladin · Mar 6, 2012

doronshadmi said:
What enables -x x to be comparable, and be gathered as Twothings?

Don't tell me you have realised that there is a center point???

realpaladin · Mar 6, 2012

doronshadmi said:
EDIT: I re-examined it, no correction is needed after all.

That entirely depends on the context specific paradigm; now, if I were to make brownies, it would need an awful lot of correction....

dafydd · Mar 6, 2012

doronshadmi said:
What enables -x x to be comparable, and be gathered as Twothings?

The fact that they are two things.

doronshadmi · Mar 7, 2012

realpaladin said:
Don't tell me you have realised that there is a center point???

The thing is beyond polychotomy.

Some analogy: The trunk enables the polychotomy of branches AND it is beyond branches.

Some center point is an additional branch, under the polychotomy of branches.

doronshadmi · Mar 7, 2012

dafydd said:
The fact that they are two things.

This fact is impossible without the "trunk", which is not one of the -x x "branches".

You still do not under-stand my question in http://www.internationalskeptics.com/forums/showpost.php?p=8085769&postcount=614.

Please carefully look at http://www.internationalskeptics.com/forums/showpost.php?p=8088106&postcount=620.

doronshadmi · Mar 7, 2012

realpaladin said:
That entirely depends on the context specific paradigm;

Again, you can't rid of the context-dependent-only paradigm.

realpaladin · Mar 7, 2012

doronshadmi said:
The thing is beyond polychotomy.

Well, we could test the blood with a hot wire to see were it is...

doronshadmi said:
Some analogy: The trunk enables the polychotomy of branches AND it is beyond branches.

Yes, just as a center enables polychotomy AND is beyond coordinates.

doronshadmi said:
Some center point is an additional branch, under the polychotomy of branches.

Why would you say that?

realpaladin · Mar 7, 2012

doronshadmi said:
Again, you can't rid of the context-dependent-only paradigm.

I love baking brownies.

realpaladin · Mar 7, 2012

doronshadmi said:
This fact is impossible without the "trunk", which is not one of the -x x "branches".

No, the fact that a third 'branch' may be there that is not -x or x.

Relativity is well, relative. No need for an 'objective' reference point.

doronshadmi said:
You still do not under-stand my question: What enables -x x to be comparable, and be gathered as Twothings?

A center. or rather, the fact that it is:
-1*x+1*x=0

doronshadmi said:
Please carefully look at:
The thing is beyond polychotomy.

Some analogy: The trunk enables the polychotomy of branches AND it is beyond branches.

Some center point is an additional branch, under the polychotomy of branches.

You can not even explain as to why that should be. And it is handled above.

doronshadmi · Mar 7, 2012

realpaladin said:
No, the fact that a third 'branch' may be there that is not -x or x.

"Branches" are the polychotomous expression of the "trunk" (Unity).

doronshadmi · Mar 7, 2012

realpaladin said:
No need for an 'objective' reference point.

Unity is the source of objective\subjective polychotomous expression.

realpaladin said:
Why would you say that?

realpaladin said:
A center.

|{-x,+x,0}| = 3 "branches"

realpaladin said:
You can not even explain as to why that should be. And it is handled above.

You can't rid of context-dependent-only and polychotomy paradigm, so what you have said is restricted to these limitations.

doronshadmi · Mar 7, 2012

I have said that if there is NOthing between X and Y, where X or Y is SOMEthing, then X=Y (there is only SOMEthing).

In terms of polychotomy NOthing and YESthing are not the same because polychotomy is not the thing (Unity).

realpaladin · Mar 7, 2012

Btw. I was correct in that your sidekick Punshhh has mosied off.

Weeeeee're off to see the wizard.... :eusa_boohoo:

doronshadmi · Mar 7, 2012

realpaladin said:
Btw. I was correct in that your sidekick Punshhh has mosied off.

Weeeeee're off to see the wizard....

You do not have to be in "bla bla ..." state in order be in agreement with someone.

doronshadmi · Mar 7, 2012

A point at a given (k=0 to ∞)+1 flat space can be in the same distance > 0 from a given (k=0 to ∞) curved space.

keyfeatures · Mar 7, 2012

doronshadmi said:
A point at a given (k=0 to ∞)+1 flat space can be in the same distance > 0 from a given (k=0 to ∞) curved space.

Really interesting discussion. Thoroughly enjoying your links. Have been thinking along similar lines recently but didn't know about organic mathematics - nor am I a mathematician. But this one-many / non-locality relates to and bounds locality etc makes sense to me. That's all for now. You say it better.

PiedPiper · Mar 7, 2012

doronshadmi said:
I have said that if there is NOthing between X and Y, where X or Y is SOMEthing, then X=Y...

If there's nothing between x and y then x=y. Is there some deeper meaning I'm supposed to be gleaning from this? It seems very obvious.

doronshadmi · Mar 7, 2012

PiedPiper said:
If there's nothing between x and y then x=y. Is there some deeper meaning I'm supposed to be gleaning from this? It seems very obvious.

It is not obvious for traditional mathematicians, since they are claiming that an infinite collection of distinct points (0-dimensional spaces) actually completely cover a given line (1-dimensional space) such that there are no gaps (there is nothing) between them.

I disagree with the traditional mathematicians, and claim that there are always gaps between distinct points along a given line, no matter how many points are involved.

By this notion no collection of lower spaces or sub-spaces (where a sub-space is a mixture of some lower space and a given space > 0) has the power of the continuum of a given space > 0.

doronshadmi · Mar 7, 2012

keyfeatures said:
Really interesting discussion. Thoroughly enjoying your links. Have been thinking along similar lines recently but didn't know about organic mathematics - nor am I a mathematician. But this one-many / non-locality relates to and bounds locality etc makes sense to me. That's all for now. You say it better.

First of all keyfeatures, welcome.

I am glade to know that.

Please feel free to share your ideas.

zooterkin · Mar 7, 2012

PiedPiper said:
If there's nothing between x and y then x=y. Is there some deeper meaning I'm supposed to be gleaning from this? It seems very obvious.

Actually, Doron is equivocating. If we are dealing with integers, then there is nothing between 3 and 4. That does not mean that 3=4.

keyfeatures · Mar 7, 2012

zooterkin said:
Actually, Doron is equivocating. If we are dealing with integers, then there is nothing between 3 and 4. That does not mean that 3=4.

I'm risking punching way above my weight here - and excuse my lack of familiarity with mathematical expressions. But this is what has been puzzling me. If we consider the universe as an expressed whole, then how do we get sense by starting at zero and marching forth with infinite integers? Surely what we have is (partly perceived) internal division? Therefore (increasing) complexity? The set is 1. Conservation rules suggest the set to be finite. You can only know the value of the unit if you know the value of the rest of the excluded set. Fractions not integers? I'm trying to make sense of Russell to resolve this. Quite possibly my inability to so is due to personal limitations.

I don't wish to derail the thread, so if I'm talking nonsense please feel free to ignore me.

realpaladin · Mar 7, 2012

zooterkin said:
Actually, Doron is equivocating. If we are dealing with integers, then there is nothing between 3 and 4. That does not mean that 3=4.

And this is also the main source of his erroneous concoction of a theory:

He thinks that if we use integers as coordinates on a line, there is a 'gap' between them.
But there is not; since there are no coordinates left between 3 and 4 there can not be a gap (as there is nothing to be a gap *in*), and thus the line is completely filled.

Then he becomes all cross because he has a problem thinking about infinity in the context of integers.

But the whole thing is fractal; the closer you zoom into it, the 'finergrained' the coordinates become and they will *always* fill the line.

realpaladin · Mar 7, 2012

keyfeatures said:
I'm risking punching way above my weight here - and excuse my lack of familiarity with mathematical expressions.

keyfeatures said:
But this is what has been puzzling me. If we consider the universe as an expressed whole,

And that is already where Doron also makes his first mistake; mathematics does not deal with the universe.
The universe has constraints like Planck time and quanta etc. physics.

keyfeatures said:
then how do we get sense by starting at zero and marching forth with infinite integers?

No idea what that question asks.

keyfeatures said:
Surely what we have is (partly perceived) internal division?

No idea what that question asks.

keyfeatures said:
Therefore (increasing) complexity?

Don't get all messed up by trying to understand math via physics... it is the other way around.

keyfeatures said:
The set is 1. Conservation rules suggest the set to be finite.

Physics, not math.

keyfeatures said:
You can only know the value of the unit if you know the value of the rest of the excluded set.

No, we know values of unit by inference. Like 0 < 1 < 2 < .. < n-1 < n < n+1

Mathematics has algorithms that can be proven in this manner. So the knowledge of the 'full answer' is not necessary.

keyfeatures said:
Fractions not integers? I'm trying to make sense of Russell to resolve this. Quite possibly my inability to so is due to personal limitations.

Nah, we all try to make sense of Doron's ramblings for over 2 years now (or more...) and he tells us it is because of personal limitations on our side.

keyfeatures said:
I don't wish to derail the thread, so if I'm talking nonsense please feel free to ignore me.

You will be ignored when appropriate.

keyfeatures · Mar 7, 2012

realpaladin said:
Don't get all messed up by trying to understand math via physics... it is the other way around.

Thanks for the reply.

But what is the point of maths that does not, or cannot, describe / relate to physical reality? To me, infinite integers are faith-think without evidence of infinite physical reality. If you use terms with no evidence they relate to something real you risk writing nonsense poems. Obviously at the level of counting etc. they have proved a useful communicative tool but in terms of a framework of reality I have my doubts. A man not distracted by sums stuck electricity and magnetism back together (not forgetting it was observer bias that separated them in the first place). My mind is far from being made up but this thread is providing valuable food for thought.

Anyway, I shall type less and read more.

Deeper than primes - Continuation

Master Poster

Critical Thinker

Banned

Penultimate Amazing

Master Poster

Penultimate Amazing

Master Poster

Penultimate Amazing

Banned

Penultimate Amazing

Penultimate Amazing

Banned

Banned

Penultimate Amazing

Penultimate Amazing

Master Poster

Master Poster

Master Poster

Banned

Penultimate Amazing

Penultimate Amazing

Penultimate Amazing

Master Poster

Master Poster

Master Poster

Penultimate Amazing

Penultimate Amazing

Penultimate Amazing

Master Poster

Penultimate Amazing

Penultimate Amazing

Critical Thinker

Thinker

Penultimate Amazing

Penultimate Amazing

Nitpicking dilettante, Administrator

Critical Thinker

Master Poster

Master Poster

Critical Thinker