Deeper than primes - Continuation

[doronshadmi]

Here is a concrete example of the inability of verbal_symbolic-only skill(er) to understand total states.

3. "packed more tightly" has nothing to do with r = 0 (which is not less than totally packed).

Here is a typical response of some verbal_symbolic-only skill(er):

"So your "totally packed" is not "packed more tightly" than what you would consider "less than totally packed"?"

Total packed states are considered as total exactly because they can't be packed further (or more).

Non-total packed states are considered as non-total exactly because they can be packed further (or more).

For example, r = 0 is a point (totally curved space that can't be packed further), where r>0 is not a point (it is not totally-packed, and therefore it can be packed further (or more)).

What is written above actually demonstrates the invariant inability of r>0 (which is always can be packed more) to actually reach r=0 (which actually can't be packed more).

By understanding the difference between invariance r>0 and invariance r=0, one (except verbal_symbolic-only skill(ers)) easily understands the above quote.

Here is another demonstration of the limited abilities of of verbal_symbolic-only skill(ers):

4. "The limit as r approaches 0", is not actually be at the limit, and we are talking on not less than actually be at the limit, that if actually fulfilled, the result is exactly one and only one totally curved (totally packed) element, (no matter if the initial state is involved with finite or infinite collection of r>0 objects).

Here is a typical response of some verbal_symbolic-only skill(er):

"So now your claiming your line is completely covered or "(totally packed)" by points? What 'totally packs' your "one and only one totally curved (totally packed) element other than just BS?"

If r=0, then there are (finite) OR (infinitely many totally packed spaces along some unbounded and non-totally packed space), such that there is always non-totally packed space among them, because of a very simple reason:

The expression "r=0 ≠ r>0" is a tautology.

Verbal_symbolic-only skill(ers), which are luck any visual_spatial skills, simply can't get it.

 

[jsfisher]

If a given community of scholars do not distinguish between "approaches" to a given value and "reaches" a given value, then their framework is not well-established, no matter how many verbal_symbolic manipulations are written in vast quantity of their refereed journals, along the years.

You are describing a limitation of only yourself, Doron. You have demonstrated time and time again an inability to comprehend mathematical limits. Be the way, go back and reread your beloved loon's explanation of his shrinking marbles analogy. You may notice if you read very, very carefully this time, he uses the word, limit.

Even though he reaches a completely invalid conclusion, he does at least get a few things right along the way. You should try to emulate him in that regard.

Still, though, Doron, is 1/7 a rational number? We can take the questions one at a time since you have so much trouble with them all together.

1/7, rational or not?

 

[epix]

They are considered as circles only if each one of them has r > 0.

If all r's = 0 we actually left with the arbitrary chosen point, which is located on the unbounded straight line.

So Dr. Ghosh is right, and no verbal_symbolic manipulations (that do not distinguish between "approach" and "reach") can changes that.

According to your conclusion, Dr. Ghosh made a trivial and non-consequential observation, which he would surely disagree with.

You are terminally misguided. You can chose arbitrary point on the plane and then let that point become the center of a circle with some r>0. When you get tired of the inequality and choose r=0, the circle disappears, but the point remains. Big deal . . .

Look at these tangentially connected circles.

Out of all infinite number of points that can be drawn on the circumferences, one has the unlike-any-other property. That's the one through which you can travel from one circle to the other. That point is a geometric object and if it exists, then, like any other geometric object, it must be defined - otherwise it doesn't exist within the math domain. What are the defining terms? (Obviously, this point is not arbitrarily chosen.)

Even though you can't see the x and y coordinates, you can still write down a set of functions that draw the set of all similarly configured circles and derive the position of the tangent point in general terms using letters instead of particular numbers. When you chose r1=r2=0 and plug it into the defining equations for the point, they will contain some illegal property, like division by zero, or there will be no real solution for the equations. In other words, the tangent point will be undefined. As such, the point doesn't exist within the math domain.

Points, lines, and curves are 0-dim and 1-dim objects and as such, you cannot see them drawn, coz the minimal requirement for actually seeing a geometric object is 2-dim. That's why one dimension is physically added to the line, for example, so you can draw it with your pencil. Now the line has not only length but also breadth. The problem is that the intersection of such two lines is not a unigue point but a set of points. That defies the definition of the intersection. And so the only reliable rendering of 1-dim objects is through equations and functions - the "verbal-symbolic-only" way. The 2-dim physical rendering of 1-dim objects is great for orientation, but it's the analysis of the defining functions that decides, not the "spacial-visual" requirement that you celebrate so much. But the "spacial-visual" rendering is very helpful to support certain assertions. Like we have two statements A and B where A <=> B (A is significantly related to B.)

A = (x^2+y^2+z^2<0.2)+((y^2+z^2<0.08)*(x<0.4)*(x>0))+(x^2+4*y^2<(1-abs z)*0.12)+((abs z<0.95)*(abs z>0.9)*(abs x+abs y*0.3<1))+((abs z<1)*(abs z>0.89))*((abs x<0.7)*(abs y>0.9)+(abs y<0.035)+(x>y*0.7-0.05)*(x<y*0.7+0.05)+(-x>y*0.7-0.05)*(-x<y*0.7+0.05)+((abs x+abs y*0.3<1.05)*(abs x+abs y*0.3>0.95)))

B= "Star Wars"

In order to prove A <=> B you need to execute the "verbal-symbolic-only" part and render it.

Where does that leave your "Fullness, Emptiness," and other insect that crawls through the crevices of verbal-only Doronetics?

Here is the answer: When you adjust IJPAM such as

IJPAM => IJPAM

then you need to define A so the function of that symbol is known. If it means that A is no longer present in the array, then

IJPAM => IJPAM = IJPM

Now you need to visualize the "function IJPM" so we would get some idea what configuration it renders: IJPM

Very good.

The road to City of Glory is peppered with traffic signs that aspiring genius must understand to safely arrive there. Here is very important one.

This sign says that we stir from right to left, not the other way around.

Since your native language is Hebrew, you surely got a head start.

 

[doronshadmi]

Here is another concrete demonstration of the limitations of verbal_symbolic-only skill(ers):

"You are terminally misguided. You can chose arbitrary point on the plane and then let that point become the center of a circle with some r>0. When you get tired of the inequality and choose r=0, the circle disappears, but the point remains. Big deal . . ."

The verbal_symbolic-only skill(ers) ignore the fact that we deal with actual circles (each one of them has r>0, such that (each circle is actually not totally curved space) AND (these actual circles touching each other) along an unbounded straight line (which is a space with finite curvature (0 curvature)).

The term (each circle is actually not totally curved space) AND (these actual circles touching each other) is resulted by more then one point (where a point is a space with infinite curvature) along an unbounded straight line (which is a space with finite curvature (0 curvature)) only if there is at least one case of actual circle (r>0).

If there is not at least one case of actual circle (r>0) along an unbounded straight line (which is a space with finite curvature (0 curvature)), then there is at most only one and only one space with infinite curvature (known as a point) along an unbounded straight line (which is a space with finite curvature (0 curvature)).

In other words, the multitude of points does not remain if there is not at least one case of an actual circle (r>0) along an unbounded straight line (which is a space with finite curvature (0 curvature)).

This simple beauty can be comprehended only by verbal_symbolic AND visual_spatial skill(ers).

------------------------

It must be stressed that "the circles disappear, but the points remain" only if the restriction of "touching circles" is not used.

In this case we have at least a space with finite curvature AND infinitely many infinite curvatures along it.

So the notion of a collection of spaces with infinite curvatures that totally covers a space with non-finite curvature, is a contradiction (it is always false).

 

[doronshadmi]

Look at that phrase:

"You are describing a limitation of only yourself, Doron. You have demonstrated time and time again an inability to comprehend mathematical limits. Be the way, go back and reread your beloved loon's explanation of his shrinking marbles analogy. You may notice if you read very, very carefully this time, he uses the word, limit."

Dr. Ghosh and me agree about the limit point, only one case of it remains if the touching marbles actually do not exist (all there is is a one totally curved space at a non-totally curved space).

Once again the luck of understanding is clearly demonstrated if one's mind is restricted only to verbal_symbolic skills.

 

[epix]

The verbal_symbolic-only skill(ers) ignore the fact that we deal with actual circles (each one of them has r>0, such that (each circle is actually not totally curved space) AND (these actual circles touching each other) along an unbounded straight line (which is a space with finite curvature (0 curvature)).

Ubounded straight line? If a circle is special-defined as a collection of straight line segments where each segment has a lenght that approaches zero, then such a line segment is unbounded?

We deal with totally curved circles, where radius r = a and not r = a +/- some deviation caused by circumference made of straight line segments.

Also, you completely ignore the fact that the special definition of the circle defines the object as a n-sided polygon where n→ ∞ and the length of each line segment is 1/n. That means each of the line segments is bounded by two points. Nevertheless, such a circle is a polygon. Here are two touching polygons:

There exists one and only one point (red) through which you can walk from one polygon to the other. But . . .

There doesn't exist one and only one point through which you can walk through one polygon to the other.

Why do you prefer the latter case?

(Inscribe the circles.)

 

[doronshadmi]

There is no such a thing like totally curved circle, because a circle exists only if pi=circumference\diameter exists.

Furthermore, a circle is not a collection, but it is exactly one non-totally curved 1-dimensional space, which is equally curved (according to some r>0) w.r.t a totally curved space (a point, which is 0-dimensional space).

Verbal_symbolic-only skill(ers) can't get, for example, http://www.internationalskeptics.com/forums/showpost.php?p=7744770&postcount=130 .

 

[epix]

There is no such a thing like totally curved circle, because a circle exists only if pi=circumference\diameter exists.

Let me visually render you statement.
There is no such a thing like totally curved circle, because a circle exists only if pi=circumference\diameter exists.

Furthermore, a circle is not a collection, but it is exactly one non-totally curved 1-dimensional space, which is equally curved (according to some r>0) w.r.t a totally curved space (a point, which is 0-dimensional space).

I didn't say that "circle is a collection"; I said that sometimes it is convenient to define circle as a collection of line segments whose length is approaching zero. Since you can't comprehend even that, you argue that "circle is not a collection." The rest of your argument is just some declaration which lacks further non-verbal support - it's a sermon-like talk.

 

[epix]

Total packed states are considered as total exactly because they can't be packed further (or more).

Non-total packed states are considered as non-total exactly because they can be packed further (or more).

For example, r = 0 is a point (totally curved space that can't be packed further), where r>0 is not a point (it is not totally-packed, and therefore it can be packed further (or more)).

This is so hopelessly misguided idea. It completely ignores the concept of infinity and limits; it defies some of the intriguing Cantor's proofs and it's so poorly described. ("r = 0 is a point").

Not long time ago, you were arguing that a line segment, which is a 1-dim object, cannot be reduced to a 0-dim object, which is the point. Now you changed your mind. (Remember that diameter, or 2*radius, is a line segment.)

What was it that changed Doron's mind?

GOSH &* SHADMI = GOSHADMI

SHADMI &* MIND = SHADMIND

Stir harder . . .

 

[doronshadmi]

Approaching Zero is not being totally packed space (totally curved space) whether the non-totally packed (or curved) space is straight or not.

 

[doronshadmi]

Another example of the inability of verbal_symbolic-only skill(er) to understand notions that are based on verbal_symbolic AND visual_spatial skills:

"Not long time ago, you were arguing that a line segment, which is a 1-dim object, cannot be reduced to a 0-dim object, which is the point. Now you changed your mind. (Remember that diameter, or 2*radius, is a line segment.)"

I defiantly did not change my mind, a totally curved space is definitely different than non-totally curved space.

For example, multiplication has no impact on the size of totally curved space, but it has an impact on the size of non-totally curved AND bounded space.

 

[epix]

Another example of the inability of verbal_symbolic-only skill(er) to understand notions that are based on verbal_symbolic AND visual_spatial skills:

"Not long time ago, you were arguing that a line segment, which is a 1-dim object, cannot be reduced to a 0-dim object, which is the point. Now you changed your mind. (Remember that diameter, or 2*radius, is a line segment.)"

I defiantly did not change my mind, a totally curved space is definitely different than non-totally curved space.

I can serve the same fish on a different plate: Not long time ago, you vehemently argued that a 1-dim object couldn't be reduced to a 0-dim object. Since the circle is a 1-dim object and the point is a 0-dim object, you contradict your previous argument by saying that the circumference of a circle can be reduced to a single point.

 

[doronshadmi]

Verbal_symbolic-only skill(ers) can't get the following expression"

There is no such a thing like totally curved circle, because a circle exists only if pi=circumference\diameter exists.

A circle exists only if diameter = 2r > 0, so any value > 0 (non-totally curved space) is irreducible into 0 (totally curved space).

The difference between non-total and total is invariant at the expressed level of the associations among different curvature's degrees.

Yet Space in itself the invariant Unity among its different expressions, where by analogy it is the common "trunk" of different "branches".

Again, verbal_symbolic-only skill(ers) can't get this organic analogy, because they are not using also their visual_spatial skills.

 

[doronshadmi]

About Dr. Kaushik Ghosh, please look at http://www.sxccal.edu/xavfms/faculty/science.htm#Physics

 

[doronshadmi]

For verbal_symbolic-only skill(ers), here is a good exercise that may stimulate your mind to get how only one curved space is left on a non-curved space:

If you get that, you can stimulate your mind by more advanced visual_spatial exercise:

https://lh6.googleusercontent.com/-...ACps/3wrxrhikIN0/w401/Hats_Micael_Reynaud.gif

 

[The Man]

Here is a concrete example of the inability of verbal_symbolic-only skill(er) to understand total states.



Here is a typical response of some verbal_symbolic-only skill(er):

"So your "totally packed" is not "packed more tightly" than what you would consider "less than totally packed"?"

Total packed states are considered as total exactly because they can't be packed further (or more).

Non-total packed states are considered as non-total exactly because they can be packed further (or more).

For example, r = 0 is a point (totally curved space that can't be packed further), where r>0 is not a point (it is not totally-packed, and therefore it can be packed further (or more)).

What is written above actually demonstrates the invariant inability of r>0 (which is always can be packed more) to actually reach r=0 (which actually can't be packed more).

By understanding the difference between invariance r>0 and invariance r=0, one (except verbal_symbolic-only skill(ers)) easily understands the above quote.

Here is another demonstration of the limited abilities of of verbal_symbolic-only skill(ers):



Here is a typical response of some verbal_symbolic-only skill(er):

"So now your claiming your line is completely covered or "(totally packed)" by points? What 'totally packs' your "one and only one totally curved (totally packed) element other than just BS?"

If r=0, then there are (finite) OR (infinitely many totally packed spaces along some unbounded and non-totally packed space), such that there is always non-totally packed space among them, because of a very simple reason:

The expression "r=0 ≠ r>0" is a tautology.

Verbal_symbolic-only skill(ers), which are luck any visual_spatial skills, simply can't get it.

Once again Doron, if you find your fantasy “verbal_symbolic-only skill(er):” so troubling, then I suggest you have better fantasies. If, on the other hand, this post is intended as your redress to some question actually asked on this thread then I recommend that you address both the quote and your response properly. Otherwise you may just find yourself left simply to the disposition of your own fantasies that you find so troubling.

 

[epix]

About Dr. Kaushik Ghosh, please look at http://www.sxccal.edu/xavfms/faculty/science.htm#Physics

Gosh! There is a whole family listed!

Dr. Subhankar Ghosh
Dr. Soma Ghosh
Dr. Kaushik Ghosh
Dr. Partha Pratim Ghosh
Dr. Rina Ghosh
Mr. Amit Kumar Ghosh
Dr. Mahasweta Mitra Ghosh
Dr. Jaydip Ghosh
Ms. Jayati Ghosh Dastidar

Well, let's join the family dinner and listen what uncle Kaushik has to say about not-totally curved circles and totally stuffed snakes . . .

 

[doronshadmi]

The expression "r=0 ≠ r>0" is a tautology, whether the amount of totally curved space (r=0) on non-totally curved space (r>0) is 1 or infinite.

In both cases a collection of r=0 spaces ≠ non-totally curved space r>0, or in other words, no collection of r=0 spaces completely covers non-totally curved space r>0.

The power of the continuum of a given (mathematical or physical) space is fulfilled beyond the amount of all possible collections, which are no more than "hosted" spaces w.r.t its "host" power.

There is no value to such vulgar question:

"So now your claiming your line is completely covered or "(totally packed)" by points? What 'totally packs' your "one and only one totally curved (totally packed) element other than just BS?"

but the rude mind that spited it out does not know that.

 

[epix]

The expression "r=0 ≠ r>0" is a tautology, whether the amount of totally curved space (r=0) on non-totally curved space (r>0) is 1 or infinite.

No, it is not tautology, coz it lacks the third element.

A tautology is a logical statement in which the conclusion is equivalent to the premise. More colloquially, it is formula in propositional calculus which is always true.

That also includes

A sentence whose truth table contains only 'T' is called a tautology.

As you know, the truth table is made of three columns, not only two. To conclude this part, YES≠NO is not tautology.

Your Phantasmagoricum Abstractum includes two propositions:

1. When radius r equals zero, space is totally curved.

2. When radius r is greater than zero, space is not totally curved.

As always, there is the omnipresent failure to include the description of the object that the radius refers to, coz radius is used with other objects than circles - with polygons, for example.
http://www.mathopenref.com/polygonradius.html

Since you are not aware of the options mentioned above, 'r' very likely refers to the radius of a circle, which is a geometric object, or just object having Hausdorff dimension 1. We know that the circumference of a circle is a curve and so one would expect that the propositions would refer to the circumference, but they don't. Instead, there is the mentioning of "curved space."

Einstein's theory of general relativity describes space as curved, with the "curved space" being the four-dimensional space-time conceived of by Minkowski.

http://www.fi.edu/learn/case-files/einstein/curved.html

By referring to the curved space, are you up to the advancement of the theory of relativity via the radius of the universe just before the big bang?

Your mentor Dr. Gosh used a non-standard math language when describing his idea and that's very suspicious. Maybe he was thinking about his favorite and totally curved dish at the time of writing.

 

[doronshadmi]

The expression "r=0 ≠ r>0" is always resulted by T as its truth value, or in other words, it is a tautology (In logic, a tautology (from the Greek word ταυτολογία) is a formula which is true in every possible interpretation (http://en.wikipedia.org/wiki/Tautology_(logic))).

If one does not agree about it, he has to provide a False result to "r=0 ≠ r>0" expression.


Also Circumradius (does not related to an obvious center) ≠ Radius (does related to an obvious center), and also this case is a tautology.

As for totally curved space, there can't be more than one case without the existence of non-totally curved space in the same universe (mathematical or physical).

http://media-2.web.britannica.com/eb-media/64/91964-004-30C6274D.gif

http://cosmology.com/images/BlackHoleNeutron.gif

http://cosmology.com/images/singularityBlackHole.jpg

Breach of rule 5 removed. Do not hotlink images from other sites without permission.

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