Deeper than primes

[epix]

Again, look up the definition of a continuous space if you want to learn how it is defined. Again, you seem to just want a space without some points. Which technically makes such a space discrete. Look up the definition of a discrete space as well if the difference still confuses you.

Doron has the uncanny ability to express in a few lines what takes others a long article with pics to explain.
http://www.phys.lsu.edu/faculty/pullin/sciam.pdf
He is well-ahead of anyone and most importantly well-ahead of himself; he can't keep up with his own insights, as he is pulled through the Vortex of Accelerated Knowledge to the next millennium. That's why he wants a space with no points at all, for he knows that having points footLeft and footRight in 2011 and point Head in 3011 no good -- it tickles.

 

[The Man]

Doron has the uncanny ability to express in a few lines what takes others a long article with pics to explain.
http://www.phys.lsu.edu/faculty/pullin/sciam.pdf
He is well-ahead of anyone and most importantly well-ahead of himself; he can't keep up with his own insights, as he is pulled through the Vortex of Accelerated Knowledge to the next millennium. That's why he wants a space with no points at all, for he knows that having points footLeft and footRight in 2011 and point Head in 3011 no good -- it tickles.

Neither the expression nor the ability is uncanny. In fact we see quite a bit of it on this forum. It is simply the expression of ones own inclinations without regard to centuries of development that have proceeded. These are innocuously referred to as 'agreed terms' or 'agreed "boxes"'. However, disagreeable 'terms' or "boxes", particularly when one just disagrees with themselves, disadvantages everyone including one's self. I expect that might just be his intent, to simply try to impose such a disadvantage upon everyone.

 

[doronshadmi]

We were all hoping that you realizing you were wrong and admitting it, as you did, would mean you were making progress. Most humans learn from their mistakes.

However, you'd know best, I suppose, so if you say you haven't made any progress in that regard, the rest of us are not in a position to argue.

Most humans learn by try to understand things beyond their current agreed knowledge, which is something that you choose not to do, so?

 

[doronshadmi]

Nope, " the concept of collection" is just, well, a concept. Now a physical collection, like my collection of ELP albums and CD's has certain physical constraints, much like a list. However, the concept of a collection is abstract as is the concept of a set (thus not a list). This is the aspect and differentiation you still seem to fail to recognize.

Again, the interval (1,2) in the natural numbers (also used as ordinal numbers) results in an "empty collection", the empty set. However, in the real numbers that same interval results in a "non-empty collection" that has an infinite number of members. The only one here that has demonstrated an inability to grasp such basic concepts is still just you.


Oh, by the way, you don't have to put "EDIT:" when you make a new post. What you have to do is just to signify such edits on a post you have already made which you have (for whatever reason) changed.

Collection is the generalization of both list or set, and if there is nothing between some considered objects of some collection, then no multiple objects exist.

This simple fact is not comprehended by your used reasoning, and once again you demonstrate that all you get about nothing or interval is valued only in terms of physical realm, which is usually comprehended by metric-space.

 

[doronshadmi]

No one, that I can recall, said that a singular point exists in "more than one location at any given space". So your argument must still be with just yourself.

Heck, that must be why a line segment is represented by a collection of points or locations in some space. Dang that self-consistency of geometry!!

In other words, the existence of singular line segment that exist at least in more than one location, is not comprehended by your reasoning, because you jump straight to the complex result, which is based on the co-existence of locality (smallest) AND non-locality (smaller).

1-dim element is the minimal expression of non-locality and 0-dim element is the minimal expression of locality, where both expressions are not limited to metric-space but used as basic building-blocks for any framework, where multiplicity is involved.

 

[doronshadmi]

Again, look up the definition of a continuous space if you want to learn how it is defined. Again, you seem to just want a space without some points. Which technically makes such a space discrete. Look up the definition of a discrete space as well if the difference still confuses you.

The agreed definitions of the continuous and the discrete space do not comprehend non-locality (smaller) as a building-block in addition to locality (smallest) under co-existence, which is resulted by multiplicity.

As a result the agreed definitions of the continuous and the discrete, are done at the level of the result of the co-existence, without the understanding of the building-blocks that enable the co-existence.

 

[doronshadmi]

Neither the expression nor the ability is uncanny. In fact we see quite a bit of it on this forum. It is simply the expression of ones own inclinations without regard to centuries of development that have proceeded. These are innocuously referred to as 'agreed terms' or 'agreed "boxes"'. However, disagreeable 'terms' or "boxes", particularly when one just disagrees with themselves, disadvantages everyone including one's self. I expect that might just be his intent, to simply try to impose such a disadvantage upon everyone.

If one chooses to get some result by ignoring its fundamentals, he\she indeed have no choice but to determine such fundamentals as unnecessary, disagree with themselves, and more banalities that are used to prevent finer theoretical or practical research of the already agreed body of knowledge of the considered subject.

jsfisher, The Man, epix and most, if not all posters of this forum, are doing exactly that and no more than that, all along this philosophical thread.

They basically do not comprehend Philosophy as the natural framework where new insights are born and already agreed insights are researched.

 

[epix]

The agreed definitions of the continuous and the discrete space do not comprehend non-locality (smaller) as a building-block in addition to locality (smallest) under co-existence, which is resulted by multiplicity.

Space is divided on regular intervals [a, b], [c, d], [e, f], . . . all around.

In the space above the outside of the entrance to the inner sanctuary and on the walls at regular intervals all around the inner and outer sanctuary.
Ezekiel 41:17

 

[doronshadmi]

Space is divided on regular intervals [a, b], [c, d], [e, f], . . . all around.

In the space above the outside of the entrance to the inner sanctuary and on the walls at regular intervals all around the inner and outer sanctuary.
Ezekiel 41:17

Take an infinite zoom of the co-existence of at least 1-dim AND 0-dim, and you discover that every 0-dim is not changed under the zoom (since every 0-dim is at most smallest element), where every 1-dim is changed under the zoom (since every 1-dim is at least smaller element).

 

[epix]

Take an infinite zoom of the co-existence of at least 1-dim AND 0-dim, and you discover that every 0-dim is not changed under the zoom (since every 0-dim is at most smallest element), where every 1-dim is changed under the zoom (since every 1-dim is at least smaller element).

Seeing is believing . . .

http://en.wikipedia.org/wiki/Benoit_Mandelbrot

http://en.wikipedia.org/wiki/Gaston_Julia

 

[doronshadmi]

Seeing is believing . . .

http://en.wikipedia.org/wiki/Benoit_Mandelbrot

http://en.wikipedia.org/wiki/Gaston_Julia

Without the need of any belief, Mandelbrot set is exactly the co-existence of the smallest with the smaller upon infinitely many scales.

Furthermore the same co-existence is defined among whole numbers, where the irreducibility into the smallest is expressed by horizontal line segments, and the smallest is expressed by the vertical line segments, as demonstrated by the following fractal diagram:

 

[jsfisher]

Without the need of any belief, Mandelbrot set is exactly the co-existence of the smallest with the smaller upon infinitely many scales.

You made that up. Please stop this continual filling gaps with wrongness just because you don't understand something.

There is no smallest in Mandelbrot sets. That's the whole point, but to no ones surprise, you missed it.

 

[epix]

Without the need of any belief, Mandelbrot set is exactly the co-existence of the smallest with the smaller upon infinitely many scales.

What is the "smaller" and the "smallest" in the Mandelbrot set? Can you like add some nouns to those adjectives in order to zoom in on what exactly you are talking about?

 

[doronshadmi]

You made that up. Please stop this continual filling gaps with wrongness just because you don't understand something.

There is no smallest in Mandelbrot sets. That's the whole point, but to no ones surprise, you missed it.

Yes there are infinitely many distinct points (where a point is the smallest element) at any arbitrary scale level of Mandelbrot set, which stay distinct because among them there are always smaller elements, which are irreducible into points.

Mandelbrot set and Koch fractal are both based on the co-existence of smaller AND smallest.

Here is an example of the co-existence of smaller AND smallest at Koch fractal:

 

[ehcks]

Yes there are infinitely many distinct points (where a point is the smallest element) at any arbitrary scale level of Mandelbrot sets, which stays distinct because among them there are always smaller elements, which are irreducible into points.

Mandelbrot set and Koch fractal are both based on the co-existence of smaller AND smallest.

No, they're based on the non-existence of smallest.

 

[doronshadmi]

What is the "smaller" and the "smallest" in the Mandelbrot set? Can you like add some nouns to those adjectives in order to zoom in on what exactly you are talking about?

You still do not grasp that without the co-existence of smaller AND smallest, Mandelbrot set is collapsed into a single point (if the smaller elements are removed) or it has no distinct scale levels (if the smallest elements are removed).

 

[doronshadmi]

No, they're based on the non-existence of smallest.

Wrong, the distinct points (the smallest elements) are there at any arbitrary given scale level, and they stay distinct because there are always irreducible_to_smallest elements (known as at least smaller elements) among them, at any arbitrary given scale level.

EDIT:

The co-existence of smaller AND smallest is the logical condition of the existence of any given fractal ( please see http://www.internationalskeptics.com/forums/showpost.php?p=7140559&postcount=15292 ).

 

[The Man]

Collection is the generalization of both list or set, and if there is nothing between some considered objects of some collection, then no multiple objects exist.

“both list or set,”? “or” is not consistent with “both”. Again what is your “interval” between the letters A and B in the alphabet?

This simple fact is not comprehended by your used reasoning,

Your ridiculous and self-contradictory assertions still do not constitute facts.

and once again you demonstrate that all you get about nothing or interval is valued only in terms of physical realm, which is usually comprehended by metric-space.

Once again I have made no assertions that “interval is valued only in terms of physical realm” nor requiring a “metric-space” and have repeatedly informed you of this fact, so stop simply lying.

In other words, the existence of singular line segment that exist at least in more than one location, is not comprehended by your reasoning, because you jump straight to the complex result, which is based on the co-existence of locality (smallest) AND non-locality (smaller).

1-dim element is the minimal expression of non-locality and 0-dim element is the minimal expression of locality, where both expressions are not limited to metric-space but used as basic building-blocks for any framework, where multiplicity is involved.

Doron “multiplicity is involved” and required by your “singular line segment that exist at least in more than one location” which of course also requires your “0-dim element” that you call “location”. So the only one jumping all over the place in your nonsense assertions is still just you.

The agreed definitions of the continuous and the discrete space do not comprehend non-locality (smaller) as a building-block in addition to locality (smallest) under co-existence, which is resulted by multiplicity.
As a result the agreed definitions of the continuous and the discrete, are done at the level of the result of the co-existence, without the understanding of the building-blocks that enable the co-existence.

Doron you “do not comprehend” your own “non-locality (smaller) as a building-block in addition to locality (smallest) under co-existence, which is resulted by multiplicity.” nonsensical and self contradictory assertions.

“(smaller)”? Smaller than what? Without your “multiplicity” what can it be smaller than? Your “non-locality (smaller)” also by your own assertions specifically requires “more than one location” which of course requires your “locality (smallest)”. So the lack of comprehension, even just about your own nonsense assertions, remains demonstrably yours

If one chooses to get some result by ignoring its fundamentals, he\she indeed have no choice but to determine such fundamentals as unnecessary, disagree with themselves, and more banalities that are used to prevent finer theoretical or practical research of the already agreed body of knowledge of the considered subject.

jsfisher, The Man, epix and most, if not all posters of this forum, are doing exactly that and no more than that, all along this philosophical thread.

They basically do not comprehend Philosophy as the natural framework where new insights are born and already agreed insights are researched.

Doron you still just can’t comprehend that your “Philosophy” of simply making up self-contradictory nonsense and calling it “fundamentals” isn’t “theoretical or practical research” of any subject. The banalities remain simply and entirely yours.

 

[epix]

Mandelbrot set and Koch fractal are both based on the co-existence of smaller AND smallest.

Here is an example of the co-existence of smaller AND smallest at Koch fractal:

[qimg]http://farm3.static.flickr.com/2707/4408536446_ce60c7d35f_z.jpg?zz=1[/qimg]

Mandelbrot set and Koch fractal don't live under one roof: The former is in C whereas the latter in R to begin with. They represent completely different ways of fractal generations, but most importantly, they won't let your buddies Smaller and Smallest screw up both concepts. We've seen Emptiness and Fullness on the Olympus and now those deities are joined by Smaller and Smallest -- the daughters of Tiny and Micronesia.

 

[epix]

“Doron you “do not comprehend” your own “non-locality (smaller) as a building-block in addition to locality (smallest) under co-existence, which is resulted by multiplicity.” nonsensical and self contradictory assertions.

Can you make some sense of this

Wrong, the distinct points (the smallest elements) are there at any arbitrary given scale level, and they stay distinct because there are always irreducible_to_smallest elements (known as at least smaller elements) among them, at any arbitrary given scale level.

so Doron could upgrade from making chaotic statements to making fallacious statements?

I think that the above statement harbors a merciful contradiction, namely that "the distinct points (the smallest elements)" are always irreducible to those "at least smaller elements." It implies to me that those at least smaller elements are actually smaller than those smallest elements, but in that case the smallest elements/points cannot be the smallest in the . . . well, in the framework (messwork?).

But there is also a good chance that Doron's definition of "reduction" may not agree with the commonly used one, and Doron sees the smallest elements as incapable of dissolving and blending with those "irreducible_to_smallest elements" -- presumably line segments. The options in the interpretation are numerous and as always frightening.