Deeper than primes

[The Man]

Wrong.

Given any domain, it is at least defined as [in]out

As jsfisher points out and I pointed out before it is not defined as anything until you ‘at least’ define what constitutes ‘in’ and what constitutes ‘out’ for that ‘domain’. Only then does it become a ‘domain’ of ‘in’ and a ‘domain’ of ‘out’.

Wrong again.

In order to distinguish between local element and non-local element, we define its state w.r.t a given domain.

The Man continues to use the wrong examples, and as a result cannot get the difference between locality and non-locality w.r.t a given domain.

The lines meet your given criteria for ‘local’ and ‘non-local’ and only location was required to be defined. You see that is why those words share the same Latin root ‘locus’ meaning ‘place’ or ‘spot’.

 

[doronshadmi]

But you have failed to define those things...or at least how to distinguish between the two.

No The Man.

You, The Man, have failed to get [in]out .

This is the very essence of the concept of Domain; it is used to distinguish between what's in it and what's out of it.

Let us explicitly show again how you are forcing the tautology of the Local on the tautology of the Non-local.

‘C’ would be ‘non-local’ by Dorons assertions as it is partially ‘in’ and partially ‘out’ of the defined ‘domain’.

You are wrong The Man.

Since the line segment is an atom, it is simply wrong to define it in terms "partially ‘in’ and partially ‘out’ of the defined ‘domain’".

The very notion of Non-locality w.r.t the domain is not less than in AND out w.r.t the domain, and there is nothing partial here.

Furthermore the tautology of the Non-local is shown exactly by in AND out w.r.t the domain.

Since you are forcing concepts like "partial" on the Non-local, you are not dealing anymore with the Non-local.

Furthermore, because you are forcing concepts like "partial" on the Non-local, you are actually using the tautology of the Local (in OR out) and get (in AND out) as a contradiction.

A line segment can be Local (in [_] OR out [ ]_ w.r.t the domain) OR Non-local (in [_]_ AND out [_]_ w.r.t domain).

Any attempt to force the Local on the Non-local, or to force the Non-local on the Local, leads to contradiction, simply because two distinguished states are essentially not the same thing (and so is the case of the Local OR the Non-local).

The intermediate universe (which is the result of the complementation between the Local and the Non-local) exists exactly because it is not totally Local and not totally Non-local.

This result is known as Collection, and Collection is not understood as long as its Building-blocks are not understood.

Your reasoning is "nothing more, nothing less" than X, where X is reseachable.

My reasoning is "more, less" than X, where X is reseachable.

By "more,less" reasoning we think out of the box of X, which enables us to get X better:

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

My reasoning replaces your reasoning.

 

[doronshadmi]

The lines meet your given criteria for ‘local’ and ‘non-local’ and only location was required to be defined. You see that is why those words share the same Latin root ‘locus’ meaning ‘place’ or ‘spot’.

This exactly what I do:

The Local obeys [in]out , [in]out (the tautology is in OR out).

The Non-local does not obey [in]out (the tautology is in AND out).

 

[The Man]

No The Man.

You, The Man, have failed to get [in]out .

This is the very essence of the concept of Domain; it is used to distinguish between what's in it and what's out of it.

In making that distinction of ‘in’ and ‘out’ you actually define two ‘domains’ a domain that is ‘in’ and one that is ‘out’. That fact seems to be lost on you.

Let us explicitly show again how you are forcing the tautology of the Local on the tautology of the Non-local.

Again with the misuse of the word ‘tautology’.

You are wrong The Man.

Since the line segment is an atom, it is simply wrong to define it in terms "partially ‘in’ and partially ‘out’ of the defined ‘domain’".

Would that be your assertion of an indivisible and non-composite ‘atom’ or your other assertion of your ‘atom’ composed as a division?

The very notion of Non-locality w.r.t the domain is not less than in AND out w.r.t the domain, and there is nothing partial here.

Quite the contrary in asserting the ‘domain’ has the distinctions of ‘in’ and ‘out’ you have in fact partitioned that ‘domain’ into those partial distinctions. What ever happened to distinction being a ‘first order property’ of your notions? You consistently fail to makes the distinctions you say your notions require.

Furthermore the tautology of the Non-local is shown exactly by in AND out w.r.t the domain.

Since you are forcing concepts like "partial" on the Non-local, you are not dealing anymore with the Non-local.


Furthermore, because you are forcing concepts like "partial" on the Non-local, you are actually using the tautology of the Local (in OR out) and get (in AND out) as a contradiction.

No one is “forcing concepts like "partial"“ you are requiring it by partitioning your domain as ‘in’ and ‘out’ distinctions, something you seem to fail to distinguish. There were no contradictions in the example I gave. If your notions result in a contradiction for you then it is a problem with your notions and what they require.

A line segment can be Local (in [_] OR out [ ]_ w.r.t the domain) OR Non-local (in [_]_ AND out [_]_ w.r.t domain).

Any attempt to force the Local on the Non-local, or to force the Non-local on the Local, leads to contradiction, simply because two distinguished states are essentially not the same thing (and so is the case of the Local OR the Non-local).

Again the lines in the example I gave conformed to your stated definitions of local and non-local, that you fail to make the distinctions you claim your notions require, is your problem. Thus the contradictions, as always, remain yours. Again they are not ‘states’ but simply locations, do you even understand what those words mean? Apparently in your notions about distinction you can not distinguish between the meanings of those two words.

The intermediate universe (which is the result of the complementation between the Local and the Non-local) exists exactly because it is not totally Local an not totally Non-local.

This result is known as Collection, and Collection is not understood as long as its Building-blocks are not understood.

Well if your ‘domain’ is the universe then it is totally ‘local‘. Again you seem to fail to understand that local and non-local are just distinctions of location (not ‘states’) that must be defined for the application being considered. Some applications consider the entire universe. Thus in that application non-local becomes some other, perhaps definable, universe. In the basic application of physics non-local is generally considered to be a space like separation in 4D space-time or an area of space not causally connected to the location you are considering due the limitations of the speed of light.

This exactly what I do:

The Local obeys [in]out , [in]out (the tautology is in OR out).

The Non-local does not obey [in]out (the tautology is in AND out).

Again with the misuse of the word “tautology”, simply calling your assertion a “tautology” does not make them so.

Now you are claiming that “The Non-local does not obey [in]out” asserting that distinction has no meaning for your ‘non-local’ yet is what you use to define your ‘non-local’. Nice way you contradict yourself again Doron.

 

[doronshadmi]

In making that distinction of ‘in’ and ‘out’ you actually define two ‘domains’ a domain that is ‘in’ and one that is ‘out’. That fact seems to be lost on you..

No, there is a one domain that has two aspects, in this case, called 'in' , 'out'.

If we are using the coin's example, then the domain is the coin and it has to sides called 'tails' , 'heads'.

We can change 'tails' , 'heads' to 'in' , 'out'.

You explore a local property w.r.t this domain, called a flip.

A flip cannot be 'in' AND 'out' w.r.t the coin (the flip's tautology is 'in' OR 'out').

I take a rubber band and put it around the coin.

A rubber band around the coin must be 'in' AND 'out' w.r.t the coin (the rubber band 's tautology is 'in' AND 'out').

The Man, you still see everything only in terms of Locality.

Furthermore, you do not understand the word "universe".

The entire universe is exactly the result of the interaction between the Local and the Non-local, but you have no chance to get it, because your reasoning is closed under Locality.

Your problem is even worse; you understand Locality and Non-locality only in terms of metric space, where OM uses these concepts as abstracts to describe things that are not limited only to metric space, for example: a logical connective is the non-local aspect of Logics and a proposition is the local aspect of Logics.

 

[doronshadmi]

Now you are claiming that “The Non-local does not obey [in]out” asserting that distinction has no meaning for your ‘non-local’ yet is what you use to define your ‘non-local’. Nice way you contradict yourself again Doron.

You are right about this, it has to be written like this:


The Local obeys [in]out , [in]out (the tautology is in OR out).

The Non-local does not obey [in]out , [in]out, but it obeys [in]out (the tautology is in AND out).

 

[Little 10 Toes]

Wow. I never thought that someone could not understand basic logic using a coin flip. Let's review some basic definations. If you do not agree to these terms, tell me.

coin: a flat piece of metal, typically circular, that has an equal chance on landing on either side when dropped on the ground. The edge of the coin is kept at a minimum. This coin will be a fair_coin^WP
Heads : one side of a coin
Tails : the corresponding side

Using a coin as a random result generator, you will get one of two results 100% of the time. If looking at one result, Heads in this case, you will get that result 50% of the time. Using Logic, this would be written Heads OR Tails. You will not be able to get the result of Heads and the result Tails at the same time (Heads AND Tails) since the odds are 1:2.

When placing a rubber band around the coin, you will still get Heads OR Tails when flipping the coin because those are the two results.

No, there is a one domain that has two aspects, in this case, called 'in' , 'out'.

If we are using the coin's example, then the domain is the coin and it has to sides called 'tails' , 'heads'.

We can change 'tails' , 'heads' to 'in' , 'out'.

Why use one set of terms, then change those terms, and then go back to the original terms?

You explore a local property w.r.t this domain, called a flip.

A flip cannot be 'in' AND 'out' w.r.t the coin (the flip's tautology is 'in' OR 'out').

So a local property of a coin cannot be Heads AND Tails with reguards to the coin. Doesn't make sense (or cents).

I take a rubber band and put it around the coin.

A rubber band around the coin must be 'in' AND 'out' w.r.t the coin (the rubber band 's tautology is 'in' AND 'out').

No it musn't, if there is such a word. The rubber band is not Heads AND Tails. You haven't defined "edge" in reguards to your domain and besides, you've already said that there are two aspects.

 

[The Man]

No, there is a one domain that has two aspects, in this case, called 'in' , 'out'.

If we are using the coin's example, then the domain is the coin and it has to sides called 'tails' , 'heads'.

We can change 'tails' , 'heads' to 'in' , 'out'.

You still have partitioned the coin in to two sub domains one you refer to as ‘heads’ an the other as ‘tails’ nether of these sub domains of heads or tails is the complete coin but the addition of both those are the ‘domain’ you are referring to as the ‘coin’. In fact this would make the coin as a whole ‘non-local’ with respect to itself by your requirements as it consists of both heads and tails.

You explore a local property w.r.t this domain, called a flip.

So far all the domains mentioned the ‘heads’ sub domain, the ‘tails’ sub domain, the coin’s entire domain (consisting of the heads and tails sub domains) and now the ‘flip’ domain are all local to the coin.

A flip cannot be 'in' AND 'out' w.r.t the coin (the flip's tautology is 'in' OR 'out').

An aspect that comes from the definition and partitioning of the coin as much as the definition of a flip. Were we to partition the coin differently say along it’s diameter as opposed to about it’s thickness then each side would have both sub domains of that partition. Any ‘flip’ would then always result in both sub domains and thus be non-local to the coin by your ascriptions.

I take a rubber band and put it around the coin.


A rubber band around the coin must be 'in' AND 'out' w.r.t the coin (the rubber band 's tautology is 'in' AND 'out').

Why? We can just refer to the coin as a whole. Having both the partitioned sub domains of ’heads’ and ’tails’. Why introduce some other unneeded element. In fact being around the coin your rubber band is also local to the coin (by the standard inference of ‘local’ meaning 'in the vicinity of')

The Man, you still see everything only in terms of Locality.

Well when you are speaking of local and non-local you are speaking "in terms of Locality”. perhaps it is simply that you do not realize or choose to not accept that fact.

Furthermore, you do not understand the word "universe".

The entire universe is exactly the result of the interaction between the Local and the Non-local, but you have no chance to get it, because your reasoning is closed under Locality.

Only if you choose to partition the universe in such a fashion and then it is simply trivial that what you have partitioned is the sum of the results of your partition.

Your problem is even worse; you understand Locality and Non-locality only in terms of metric space, where OM uses these concepts as abstracts to describe things that are not limited only to metric space, for example: a logical connective is the non-local aspect of Logics and a proposition is the local aspect of Logics.

Again doron ‘abstraction’ does not mean simply making up what ever you want to claim. Particularly about concepts already well established and defined. Again locality and non-locality are about one thing, defining location, whether that be the result of some applied metric in some space or the association of elements in logic.

 

[doronshadmi]

You still have partitioned the coin in to two sub domains one you refer to as ‘heads’ an the other as ‘tails’ nether of these sub domains of heads or tails is the complete coin but the addition of both those are the ‘domain’ you are referring to as the ‘coin’. In fact this would make the coin as a whole ‘non-local’ with respect to itself by your requirements as it consists of both heads and tails.

The domain called coin is indeed a whole\parts domain.

If you are using a flip, then you are focused only on its parts aspect (the tautology of this use is 'tails' OR 'heads', where a flip cannot be simultaneously 'tails' AND 'heads' (this is a contradiction from flip's (Local) point of view)).

If you are using a rubber band, then you are focused only on its whole aspect (the tautology of this use is 'tails' AND 'heads', where a rubber band must be simultaneously 'tails' AND 'heads' (NOT('tails' AND 'heads') is a contradiction from rubber band's (Non-local) point of view)).

Let us do it simpler.

X has two opposite aspects.

If Y obeys simultaneously to one and only one aspect of X, then Y is Local w.r.t X.

If Y obeys simultaneously to more than a one aspect of X, then Y is Non-local w.r.t X.

Well when you are speaking of local and non-local you are speaking "in terms of Locality”. perhaps it is simply that you do not realize or choose to not accept that fact.

No, Locality obeys simultaneously to one and only one aspect of X.

You choose to get things only in terms of Locality.

Only if you choose to partition the universe in such a fashion and then it is simply trivial that what you have partitioned is the sum of the results of your partition.

Since any universe is not less than a whole\parts domain (uni=whole, verse=part), it must be an interaction between Non-locality and Locality.

 

[The Man]

The domain called coin is indeed a whole\parts domain.

If you are using a flip, then you are focused only on its parts aspect (the tautology of this use is 'tails' OR 'heads', where a flip cannot be simultaneously 'tails' AND 'heads' (this is a contradiction from flip's (Local) point of view)).

Doron, once you partition the coin you are focused ‘on its parts aspect‘, since that is the purpose of the partition to distinguish ‘parts’. Otherwise that partition has no utility.

If you are using a rubber band, then you are focused only on its whole aspect (the tautology of this use is 'tails' AND 'heads', where a rubber band must be simultaneously 'tails' AND 'heads' (NOT('tails' AND 'heads') is a contradiction from rubber band's (Non-local) point of view)).

If you are using the rubber band in relation to your partitioned ‘parts’ then you are still ‘focused on the parts aspect‘. In fact that focus on ‘the parts aspects’ is fundamental to your definition of 'non-local', that it must include both ‘parts’. Again this still makes your coin 'non-local' to itself by your own definitions. Similarly if you do not choose to partition the coin then it is always ‘local‘ to itself by your definitions. Also as I mentioned before if you partition the coin differently then any ‘flip‘ can also be 'non-local' by your definitions. Again Doron, local and non-local, even by your own definitions, are simply a matter of how one chooses to define those or partition some locations.

Let us do it simpler.

X has two opposite aspects.

If Y obeys simultaneously to one and only one aspect of X, then Y is Local w.r.t X.

If Y obeys simultaneously to more than a one aspect of X, then Y is Non-local w.r.t X.

No, Locality obeys simultaneously to one and only one aspect of X.

You choose to get things only in terms of Locality.

Again Doron the examples I gave meet your requirements of local and non-local, there were no contradictions and only locations were required to be defined. Your problems with your own notions and definitions are yours alone simply because you choose to think references to location like local and non-local must infer something other then simply location.

So as usual finding yourself unable to defend your claims you now introduce another word you apparently do not know the meaning of or how to apply, ‘simultaneously’. In my example line ‘C’ ‘simultaneously’ meets the requirements of the ‘in’ and ‘out’ definitions and thus your previous and now your current requirement for being ‘non-local’.

Since any universe is not less than a whole\parts domain (uni=whole, verse=part), it must be an interaction between Non-locality and Locality.

Again doron only if you choose to partition it that way and it is simple and trivial that what you partition must be the sum of the results of your partition. Again you fail to understand the significance of making specific definitions and then the requirement to work within those definitions.

ETA;

Try looking up the origins or words instead of just makin up your own.


http://dictionary.reference.com/browse/universe

Origin:
1325–75; ME < OF univers < L ūniversum, n. use of neut. of ūniversus entire, all, lit., turned into one, equiv. to ūni- uni- + versus (ptp. of vertere to trun)

So it is not a combination of ‘whole’ and ‘part’ as you claim but ‘one’ and ‘to turn’ or as sated ‘turned into one’. Stop making up crap and do some darn research.

 

[doronshadmi]

You call it Whole\Parts.

I call it Non-locality\Locality.


We are talking on the same thing, but you ignore the Whole and use only its Part's view.


[in]out = Whole = Non-locality

[in]out , [in]out = Parts = Locality


( ([in]out) = (in AND out) = the tautology of Non-locality ) ≠ ( ([in]out , [in]out) = (in OR out) = the tautology of Locality )

 

[The Man]

You call it Whole\Parts.

I call it Non-locality\Locality.


We are talking on the same thing, but you ignore the Whole and use only its Part's view.

Says the man who uses only the 'parts view' as the basis of his definitions of 'local' and 'non-local'.

No Doron we are not 'talking on the same thing', I am taking about definable and supportable cliams, you are just talking about your fantasies.

 

[doronshadmi]

If you are using the rubber band in relation to your partitioned ‘parts’ then you are still ‘focused on the parts aspect‘. In fact that focus on ‘the parts aspects’ is fundamental to your definition of 'non-local', that it must include both ‘parts’.

Here you have missed it again. "In relation to …" means that we are focused on the relation aspect (the non-local aspect) that exists between the parts.

Again this still makes your coin 'non-local' to itself by your own definitions.

No The Man, The coin is exactly a Whole\Parts thing or Non-local\Local thing. You simply do not get this simple beauty and continue to force your partial X OR Y Local-only reasoning on the coin.

Similarly if you do not choose to partition the coin then it is always ‘local‘ to itself by your definitions.

Again, NO.

The coin is exactly a Whole\Parts thing or Non-local\Local thing.

Also as I mentioned before if you partition the coin differently then any ‘flip‘ can also be 'non-local' by your definitions.

Wrong. A flip cannot be in more than a one and only one part's state of the coin.

Again Doron, local and non-local, even by your own definitions, are simply a matter of how one chooses to define those or partition some locations.

No.

A rubber band shows the non-local aspect of the coin.

A flip shows the local aspect of the coin.

The coin itself is not totally non-local and not totally local.

The coin itself is exactly non-local\local thing (a whole\parts thing in your language).

Says the man who uses only the 'parts view' as the basis of his definitions of 'local' and 'non-local'.

Thank you.

Indeed "the man uses only the 'parts view' as the basis of his definitions of 'local' and 'non-local'".

No Doron we are not 'talking on the same thing', I am taking about definable and supportable cliams, you are just talking about your fantasies.

No The Man, you do not get your own words.

 

[doronshadmi]

The Man,

It is all based on your misunderstanding of the concept called "universe".

As a result you do not get a universe or domain like a coin.

It is clear now why you can't get, for example, a paper like that:

http://www.geocities.com/complementarytheory/BasicOM-E.pdf

Pay attention that this paper is only the serial case of Organic Numbers, but you will not get also the the serial case, because you are not able to get "universe" as parallel\serial thing exactly as you don't get it as a whole\parts thing.

 

[doronshadmi]

So it is not a combination of ‘whole’ and ‘part’ as you claim but ‘one’ and ‘to turn’ or as sated ‘turned into one’. Stop making up crap and do some darn research.

"turned into one" is simply the viewpoint from the Parts to the Whole. The universre is also ""turned into many" or the viewpoint from the Whole to the Parts.

Stop forcing us a pertial-only, local-only and serial-only view of the concept of Universe.

 

[zooterkin]

Sorry if I've missed it, but what breakthroughs have you been able to make as a result of your use of Organic Numbers? In what way is your system better than the tried and tested conventional mathematics?

 

[catbasket]

Sorry if I've missed it, but what breakthroughs have you been able to make as a result of your use of Organic Numbers? In what way is your system better than the tried and tested conventional mathematics?

It's a lot easier to prove the Hokey Cokey true in doronetics -

[snip]

[in]out = Whole = Non-locality

[in]out , [in]out = Parts = Locality


( ([in]out) = (in AND out) = the tautology of Non-locality ) ≠ ( ([in]out , [in]out) = (in OR out) = the tautology of Locality )

Therefore -

[in]out + [in]out = shake it all about

 

[doronshadmi]

It's a lot easier to prove the Hokey Cokey true in doronetics -



Therefore -

[in]out + [in]out = shake it all about

'+' is the non-local aspect and 'in' or 'out' is the local aspect of the reseached domain, so you proved me right.

 

[doronshadmi]

Sorry if I've missed it, but what breakthroughs have you been able to make as a result of your use of Organic Numbers? In what way is your system better than the tried and tested conventional mathematics?

ON use Distinction as their first-order properties, where conventional mathematics is nothing but the particular case of crisp Distinction, as if it is the universal principle of the foundations of this science.

 

[catbasket]

'+' is the non-local aspect and 'in' or 'out' is the local aspect of the reseached domain, so you proved me right.

How on earth does what I posted support your claim this proves you right? Is there some non-local aspect of OM logic which you haven't yet introduced?

Clearly you are incapable of getting that under catbasket revised Organic Mathematics the '+' is merely a local representation of the non-local aspect!

Your Standard Model of Organic Mathematics is puny in comparison to catbasket revised Organic Mathematics!


SMOM < (cbr)OM

... and this is true for both the local and non-local aspects of OM, whether the outdated SM or (cbr).

ON use Distinction as their first-order properties, where conventional mathematics is nothing but the particular case of crisp Distinction, as if it is the universal principle of the foundations of this science.

Whereas (cbr)OM clearly proves that SMOM is nothing but the particular case of soggy Distinction, as if it is the universal principle of the foundations of this science!

It is now clear to me that you simply cannot get that the distinction of Distinction (doD) into merely standard and crisp Distinction is incomplete unless and only unless you don't fail to not get that these represent only the local and non-local aspects of Researchable Totality. To further abuse the coin 'Heads' AND/OR 'Tails' (NOT) analogy - you have completely failed to get the elastic band!

This really should be obvious to anyone who has, as you claim, been researching the unresearchable for more than twenty years. I suspect you simply haven't thought this through thoroughly enough.