Deeper than primes

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doronshadmi said:
Think about a complex thing like your body.

Is the number of cells of your body gives you the knowledge about the parallel\serial linkage among the cells?
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Well, Doron, I have countless uncounted cells.
In parallel they are, till I count them and dirive a serial quantity.

If I group them into organs and count the organs, I get a different serial quantity.

Traditional Math merely derives a quantity at the count. 3 is no more than the three items counted.
It's a set that contains only 3 items till another count is made and with it a new set.

Organic Number though has a permanent, single, ever used Set.
It has all possible quantities in membership.

Traditional Math talks about, say, the set of the sum of 3 plus 2.
{5}
5 is it's sole occupant.
However, the Set in Organic Mathematics is not so limited.
It always includes any numeral, any quantity from infinitude.
You can select the 5 alone, but you do so at limitation and ignorance of all the rest of the members of The Set.

Another way to put this is that Organic Mathematics deals with what we might call, "Metanumerals."
They dwell in the Meta, non-local, parallel realm till a quantity is determined.

The empty set strictly serially speaking has no members.
But metanumerically it's membership is ∞.

Or you could say as a "set" it has no members, but as The Set it has all members.

This positing of a distinct meta domain of Metanumerals and The Set is the key element of Doron's escape from Zeno's and Russel's paradoxes.

So numerals can be in parallel or serial aspect.
A numeral in parallel aspect is in non-local locality.

Can we calculate metanumerically?
I don't see how.
Calculating makes a determination.
And a determination is a limitation.
When Set (which should be in mind instead of set) prior contains all possible results, there is nothing to calculate.
Calculation is only a matter of the serial limitation.

Mertanumerical thinking is not "step-by-step."
It's not linear. It has no algorithms.

It intuits from Unitary Consciousness.

The best way to do Organic Mathematics is to "just sit" in meditation.
Or to dismiss all serial classifications to appreciate the bottom line "Complexity' of all the individual cells.
 
To continue:

OM posits the single, Non-Local, eternal, transcendent, metanumerical Set that includes in its membership all numerals in Non-Local locality.

It’s not that Traditional Mathematics has nothing to do with Non-Locality.
It's simply that in Traditional Math, the Non-Local isn't a locality populated by permanent metanmerals.
It's merely an empty background before which new localities, sets, numerals, and quantities come into and then pass out of existence.

Constant change is its flexibility. New sets to fit new circumstances are created as needed.

In Organic Mathematics new results aren't created but exist already.
All potential results of calculation already exist in The Set.
Its flexibility is in saying that that no one of them is the definitive answer.
They all belong in the moment.

In OM to deny any numeral it's membership in a set is limiting.

In Traditional Mathematics to hold set as a permanent, unchanging container would be thought limiting.

We have to go back to Pythagoras to find mathematics regarding numbers as metaphysical entities.
 
Apathia said:
This positing of a distinct meta domain of Metanumerals and The Set is the key element of Doron's escape from Zeno's and Russel's paradoxes.
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I'm having trouble with this statement. Doron has consistently denied any sort of hierarchical structuring of his non-localities. At best he can move Russell's paradox out of the local, but it still gets stuck in the non-local.

As for Zeno's paradox, I don't see it getting addressed at all.
 
jsfisher said:
I'm having trouble with this statement. Doron has consistently denied any sort of hierarchical structuring of his non-localities. At best he can move Russell's paradox out of the local, but it still gets stuck in the non-local.

As for Zeno's paradox, I don't see it getting addressed at all.
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At the least his M.O. is to separate the Finite and the Infinite into two separate domains. His Metaphysical (so to speak) Infinity remains inviolable.


Perhaps that just shoves it under the carpet, and then we roll the lump in the carpet under the couch.

I've yet to completely work through this, which is why I bowed out of the Zeno discussion.
 
Apathia said:
...In OM to deny any numeral it's membership in a set is limiting.
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Numerical emancipation of set participation - not a vote-winner.

I prefer your other suggestion - just to sit and consider 'OM'.

Say, that sounds kind of familiar...
 
Apathia,

Thank you for your beautiful replies.

Here are some remarks:

Apathia said:
In Organic Mathematics new results aren't created but exist already
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Exactly the opposite, at OM new results are a permanent fact exactly because no set is complete externally (by extrapolation) or internally (by interpolation).

Standard Math is the framework that forces completeness on Sets by using the quantifier "for all" on the existence of the members of some non-empty and infinite set.

Furthermore, Standard Math does it only on the first level of the existing members and by doing this it get a ridiculous framework that does not understand the existence of the measured things twice: not by Complexity (only the first level of members is considered) and not by Cardinality (completeness is forced on infinite collections exactly because of the luck of understanding of the independent existence of Set from the existence of any collection members, exactly as a stage exists independently of the players on it, and no amount of players is Stage).

Apathia said:
However, the Set in Organic Mathematics is not so limited.
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The set of OM is:

1) ATOM

2) The result of the linkage between the non-local AND local versions of ATOM.

3) ATOM is not researchable.

4)Non-locality\Locality Linkage is researchable.

We can use Cardinality in order to limit Non-locality\Locality Linkage, for example please read pages 7-8 of http://www.scribd.com/doc/17504323/WZATRP8 .

Apathia said:
Can we calculate metanumerically?
I don't see how.
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Apathia, numerals are different representations of the same number.

By using OM I show that the place-value system is a system of numbers and not numerals (as Standard Math understands it).

As a result Complexity can be measured by numbers, where one of the possible complexities is the place-value system.

We can do the same calculations as we do by Standard Math, but since we do not ignore Complexity, we get finer results that are beyond the scope of Standard Math, for example:

1 – 0.999… = 0.000…1 , where the "1" of "0.000…1" is exactly the non-locality that is not covered by any amount of locales "9" of "0.999…".

Furthermore, for example by Standard Math 2+3=5. By OM we get the same result if we ignore Complexity, but at OM we can also not ignore Complexity and in this case we have to ask what complex 2 + what complex 3 we are using, in order to get complex 5.

Apathia said:
The best way to do Organic Mathematics is to "just sit" in meditation.
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Wrong.

Please see http://www.internationalskeptics.com/forums/showpost.php?p=4896208&postcount=5009
 
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Just for the record, I like Apathia's version better. It has a ring of consistency about it and the potential for utility. Doronshadmi's, not so much.
 
Apathia said:
Still lurking, holding my tongue, and slapping my hand that wants to type out that quotation of Humpty Dumpty in Through The Looking Glass,

Have a happy B-Day Fisher.
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dlorde said:
It's Humpty's self-referential 'explanation' of his ipse-dixitisms.
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"When I use a word” Humpty Dumpty said, "...it means just what I choose it to mean-neither more nor less."
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OK , see the difference between Locality (Humpty Dumpty Local game with words) and Non-locality in http://www.internationalskeptics.com/forums/showpost.php?p=5000005&postcount=5665 .
 
doronshadmi said:
Exactly the opposite, at OM new results are a permanent fact exactly because no set is complete externally (by extrapolation) or internally (by interpolation).
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"The truth is out there."

Standard Math is the framework that forces completeness on Sets by using the quantifier "for all" on the existence of the members of some non-empty and infinite set.
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I mentioned Russell's paradox. Actually this is the way you address it; by the removal of universal quantifiers.

Furthermore, for example by Standard Math 2+3=5. By OM we get the same result if we ignore Complexity, but at OM we can also not ignore Complexity and in this case we have to ask what complex 2 + what complex 3 we are using, in order to get complex 5.
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Ah but this can become quite cumbersome. Imagine my Bank of America monthly statement if it had to acount for all groupings and possible groupings of transactions involving every dollar in BOA.

It seems we can do that already if so desired, selecting however we want to configure the data.

But would OM force us to do all levels of complexity and does it provide the tecniques to handle all that?

It seems it comes back to the same number crunching, just more numbers to crunch.


Wrong.

Please see http://www.internationalskeptics.com/forums/showpost.php?p=4896208&postcount=5009
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This isn't the place to discuss various school and styles of meditation.
But the Soto Zen "Just Sitting" is quite compatable with your bleaching analogy.
 
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jsfisher said:
Just for the record, I like Apathia's version better. It has a ring of consistency about it and the potential for utility. Doronshadmi's, not so much.
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Could you eleborate what you find has potential in my "shadow" version of Doron's OM.

Or did mean my characterization of Traditional Math as a panoply of changes?
 
Apathia said:
I mentioned Russell's paradox. Actually this is the way you address it; by the removal of universal quantifiers.
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Consistency would require the removal of the existential quantifier as well. Since

[latex]$$$ (\neg \exists x \, P(x)) \equiv (\forall x \, \neg P(x))$$$[/latex]​

The disqualification of both quantifiers is a serious restriction.
 
jsfisher said:
Consistency would require the removal of the existential quantifier as well. Since

[latex]$$$ (\neg \exists x \, P(x)) \equiv (\forall x \, \neg P(x))$$$[/latex]​

The disqualification of both quantifiers is a serious restriction.
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A fatal one to all Mathematics since Pythagoras.
 
Apathia said:
"The truth is out there."
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What do you mean?


Apathia said:
I mentioned Russell's paradox. Actually this is the way you address it; by the removal of universal quantifiers.
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Only in the infinite case, becaue the Cardinality of a non-finite collection is not fixed as the finite Cardinality.

Both cases do not have the Cardinality of Set itself (the stage analogy), but the finite case is fixed and "for all" can be used in the finite case.

As for Russell's paradox, it simply avoided at the moment that you get Set as Membership.

Again, as long as one does not understand Non-locality (which its Cardinality is exactly ∞) one forces on it local only point of view, and as a result one does not understand that membership (non-locality) cannot be a member (locality) and vise versa.

Look at this:

The outer "{" "}" is membership.

Anything under membership is a member but membership is Non-local w.r.t any given member.

A set that it is its own member has, for example, this structure:

{…{{{…{} …}}}…} and as you see membership is beyond the non-finite interpolation\extrapolation of members, or in other words, membership is not one of the members (the outer "{" "}" is not a member of itself) and as a result, for examples, the set of all idas is not a member of itself exactly as the empty set is not a member of itself (the outer "{" "}" is not a member and still the empty set exists, and this existence is represented by the outer "{" "}" ).

So is the case with the Set of ideas, since its existence is greater than any member it cannot be fully its oun member, because any member is local w.r.t the Set itself (represented by the outer "{" "}" ).


Apathia said:
Ah but this can become quite cumbersome. Imagine my Bank of America monthly statement if it had to acount for all groupings and possible groupings of transactions involving every dollar in BOA.
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Again, we do not have to use maximum Complexity. We use it according to our needs, but now we are aware of our limitations and do not take them as general cases.

Actually Organic Numbers is an open Complexity and my current system is also a limit case of Complexity exactly because no structure of localities is Non-locality.
 
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doronshadmi said:
Only in the infinite case, becaue the Cardinality of a non-finite collection is not fixed as the finite Cardinality.
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How will you be able to identify an infinite set in this your private mathematics of yours? For that matter, how do you propose to build a set theory that even includes infinite sets?
 
jsfisher said:
How will you be able to identify an infinite set in this your private mathematics of yours? For that matter, how do you propose to build a set theory that even includes infinite sets?
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Very easy:

{} or {{}} are examples of finite sets.

{a,b,c,..} or {{a,b,c,...}} are examples of infinite sets.

In both cases Set (represented by the outer "{" "}" ) is not a member of itself (its existence is non-local w.r.t any collection (finite or not) of members.

jsfisher, at the moment that you get Non-locality you start to get OM.
 
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