Deeper than primes - Continuation

doronshadmi · Dec 10, 2011

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

doronshadmi said:
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):

doronshadmi said:
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 · Dec 10, 2011

doronshadmi said:
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 · Dec 11, 2011

doronshadmi said:
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 · Dec 11, 2011

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 · Dec 11, 2011

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 · Dec 11, 2011

doronshadmi said:
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 · Dec 11, 2011

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 · Dec 11, 2011

doronshadmi said:
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 · Dec 11, 2011

doronshadmi said:
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 · Dec 11, 2011

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

doronshadmi · Dec 11, 2011

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 · Dec 12, 2011

doronshadmi said:
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 · Dec 12, 2011

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

doronshadmi said:
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 · Dec 12, 2011

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

doronshadmi · Dec 12, 2011

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 · Dec 12, 2011

doronshadmi said:
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 · Dec 12, 2011

doronshadmi said:
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 · Dec 14, 2011

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 · Dec 14, 2011

doronshadmi said:
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 · Dec 15, 2011

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.

Replying to this modbox in thread will be off topic Posted By: Cuddles

epix · Dec 15, 2011

doronshadmi said:
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.

Even Wikipedia shows that you are wrong. Here is again an example of tautology:
Let @ be some logical connective. Then

(a<b @ c<d) is True
(a<b @ c>d) is True
(a>b @ c<d) is True
(a>b @ c>d) is True

is tautology.

Your expression "r=0 ≠ r>0" lacks the necessary premise options for tautology to exist, but the main problem is that ≠ is not a logical connective. The inequality r>0 is just the only true (metrics) alternative to r≠0 and vice versa when r is a radius of a circle - the expression is not tautology, as opposed to "belongs AND doesn't belong". Remember?

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

What is "an obvious center?"
Look again at the definition of radius applied to regular polygon,
http://www.mathopenref.com/polygonradius.html
and then reconsider your inequality Radius≠Circumradius by looking at this:
http://etc.usf.edu/clipart/43400/43444/5c_43444_lg.gif
Then digest the fact that "circumradius" derives from the word "circumscribe." In both cases the magnitude of r is the same for the regular polygon and the circumscribed circle. Polygons aside, still, your initial reference to the radius was a case of insufficient definition, coz radius can apply to sphere as well as circle.

epix · Dec 16, 2011

doronshadmi said:
kaushikhit10@yahoo.co.in is available to any one, who really wishes to communicate with Dr. K. Ghosh about his work.

Why don't you communicate with Dr. K. Ghosh regarding the conjecture that you predictably skipped? He will surely help you to prove or disprove it. That gives us the opportunity to see if he would use again the non-standard descriptive means. Here it is once again:

Conjecture:

There is no prime number p such as that

p = a²+b² = c³+d³
There used to be a web site devoted to prime numbers where folks emailed related material, which was first reviewed by the webmaster mathematician. If I sent that conjecture there, then it wouldn't be very likely published, coz it is way too easy to prove or disprove - it doesn't pose much of a challenge. That means Dr. Ghosh shouldn't trip over it. Just tell him that it was a long time ago when you tinkered with number theory and if he could help you out.

doronshadmi · Dec 16, 2011

Look at these expression:

"but the main problem is that ≠ is not a logical connective."

"The inequality r>0 is just the only true (metrics) alternative to r≠0 and vice versa when r is a radius of a circle - the expression is not tautology,"

These expressions are wrong (they get things only in terms of context-dependent frameworks) because r is any value, which is not restricted to metric space or logical interpretation. By using that Cross-contexts generality the expression "r=0 ≠ r>0" is always true.

Any attempt to restrict "r=0 ≠ r>0" only to logical framework, misses the main principle of being Tautology.

Tautology at an actual universal state is a form(ula) which is true in every possible interpretation, whether the interpretation is done logically, arithmetically, or whatever.

Once again, context-dependent-only skill(ers) can't get the actuality of Tautology, which is not less than Cross-contexts.

An expression like:

"(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) )" is not Cross-contexts and therefore it is not an actual Tautology.

As for the question: "What is "an obvious center?" the answer is found in ( http://en.wikipedia.org/wiki/Radius ):

"If the object does not have an obvious center, the term may refer to its circumradius,", and this http://www.mathopenref.com/polygonradius.html is a case of circumradius.

Look at this expression:

"your initial reference to the radius was a case of insufficient definition, coz radius can apply to sphere as well as circle"

This is wrong since r>0 is not restricted to any dimensional space > 0.

Once again the context-dependent-only reasoning airs its fragmented view.

epix · Dec 16, 2011

doronshadmi said:
These expressions are wrong (they get things only in terms of context-dependent frameworks) because r is any value, which is not restricted to metric space or logical interpretation. By using that Cross-contexts generality the expression "r=0 ≠ r>0" is always true.

Your effort to weasel out of your erroneous statements brings in more contradictions, such as "r is any value." The left side of your doronian inequality clearly shows that r doesn't have any value, coz r=0 in there. If you switch to a particular case where r=0 and r=5, where r is the last letter of "number, then "r=0 ≠ r>0" becomes 0≠5, which is inequality, not tautology.

Any attempt to restrict "r=0 ≠ r>0" only to logical framework, misses the main principle of being Tautology.

You burned you dinner once again. The principle of tautology is an unnecessary redundancy. That means unnecessary redundancy where "unnecessary" is a redundant adjective. There is nothing redundant about 0≠5, is there?

Your attempt to come up with special math syntax, like "r=0 ≠ r>0" just reflects upon your overall confusion regarding relations. The same goes for your double-speak which is supposed to describe the result of some uncommon deep thought.

Tautology at an actual universal state is a form(ula) which is true in every possible interpretation, whether the interpretation is done logically, arithmetically, or whatever.

That's what you wish for, but tautology is applicable in well-defined domains and none of them includes arithmetics. Your effort to change that hasn't started that well, as everyone can see.

Once again, context-dependent-only skill(ers) can't get the actuality of Tautology, which is not less than Cross-contexts.

In
An expression like:

"(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) )" is not Cross-contexts and therefore it is not an actual Tautology.

That's too bad that "Cross contexts" is not an "actual" tautology, which is "not less than Cross-contexts." Since the reference to tautology in Wiki never mentions any cross-contexts, it's apparent that the relation between tautology and cross-contexts is pure Doronetics.

The Man · Dec 16, 2011

doronshadmi said:
Any attempt to restrict "r=0 ≠ r>0" only to logical framework, misses the main principle of being Tautology.

Well since a Tautology, in logic, is a proposition that is always true regardless of the truth values of its elements (the negation of a contradiction) it is obviously and deliberately you who " misses the main principle of being Tautology" in that regard.

In rhetoric a Tautology is exemplified by the repetition of meaning, as "r=0" has a different meaning than " r>0" you have missed the "main principle of being Tautology" in that regard as well.

As it is now clear that you are simply not restricting your "Tautology" to being any kind of, well, Tautology you continue on the previously noted "(totally packed)" with BS trend.

If it was your intent to demonstrate that your failure could cross contexts in the " main principle of being Tautology", you have succeeded.

By all means please Doron, do tell us what in you mind is "the main principle of being Tautology."? Simply making a true statement does not make it a tautology, in rhetoric or logic.

As already made clear to you many times before just because "r" can, or does, approach "0" does not restrict "r" from being "0", as in r ≥ 0 . Again a limit can be a member of the set it limits, though it does not have to be. Do please learn something Doron.

Oh just a little FYI, if you are formulating a response to this post then I again recommend that you address it and attribute quotes correctly, otherwise I simply will not read or reply to it.

doronshadmi · Dec 16, 2011

Context-dependent skill(ers) can't get concepts, unless they are restricted to some domain, for example:

"Well since a Tautology, in logic," means that Tautology is defined only if it is restricted (in this case) to Logic, or in other words, it can't be defined in terms of Cross-contexts principle.

Since "r=0" has a different meaning than " r>0" then r simultaneously ≥ 0 (which is a line) only if r is at and not at r=0 (where r=0 is a point) location.

Please look at these context-dependent restrictions:

"As already made clear to you many times before just because "r" can, or does, approach "0" does not restrict "r" from being "0", as in r ≥ 0 . Again a limit can be a member of the set it limits, though it does not have to be."

Case 1: at most one element:

If r only = 0, then r is a point.

If r simultaneously ≥ 0, the r is a line.

Case 2: at least two elements:

if r > OR = 0, then r is two different points, or a point and a line (the expression "r=0 ≠ r>0" is Tautology among at least two elements).

In both cases r is a point (can be only in one location) OR a line (can be in more than one location).

Points only approach a given limit (whether it belongs OR does not belong to a given set).

Lines can actually reach a given limit (whether it belongs OR does not belong to a given set).

Please look at the restrictions of context-dependent-only skill(er):

"Oh just a little FYI, if you are formulating a response to this post then I again recommend that you address it and attribute quotes correctly, otherwise I simply will not read or reply to it."

Once again the limited (formal or informal) reasoning of Context-dependent-only skill(ers) is strictly demonstrated.

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

The expression "0≠5" is always true, no matter what context is used.

Please look at this expression:

"Since the reference to tautology in Wiki never mentions any cross-contexts, it's apparent that the relation between tautology and cross-contexts is pure Doronetics."

Wiki describes only already agreed marital, so relation between tautology and cross-contexts (which is a paradigm-shift of the already agreed marital) can't be found in Wiki.

epix · Dec 16, 2011

The Man said:
Oh just a little FYI, if you are formulating a response to this post then I again recommend that you address it and attribute quotes correctly, otherwise I simply will not read or reply to it.

Doronetics and tautology are very closely related. No matter what kind of options you take to instruct Doron, the outcome will be the same.

doronshadmi · Dec 17, 2011

Pi is a dimensionless size, because it is not impacted by the sizes of all existing circles.

Zero circumference or diameter do not allow the existence of Pi as a dimensionless size.

epix · Dec 17, 2011

Pi is a collection of two letters. They are the 19th and the 20th letters in a text. What text?

Oh, Lord! What have I done that would deserve punisment like that, for the Heavens know that no mortal soul of the world can match Your omniscience.

In that case I shall send an angel to assist your non-omniscient mind . . .

doronshadmi said:
Pi is a dimensionless size, because it is not impacted by the sizes of all existing circles.

Zero circumference or diameter do not allow the existence of Pi as a dimensionless size.

(Let's see... 19+20=39, and there are 39 books in The Old Testament.)
The text is a part of the Bible - it is in The Old Testament, my Lord.

You must put more rigor into your effort, my son, to please my heart.

rolleyes: It looks like a brute force search to me . . .)
I have analytically arrived at the answer, my Lord.

Please, reveal it to Me.

With his own spear you pierced his head
when his warriors stormed out to scatter us,
gloating as though about to devour
the wretched who were in hiding.
Habakkuk 3:14

I'm done, Doron. You can fly away. Thanks for the assistence. Btw, if you see an Atheist temple on your way back, let me know. I feel like converting.

Little 10 Toes · Dec 17, 2011

doronshadmi said:
Pi is a dimensionless size, because it is not impacted by the sizes of all existing circles.

Zero circumference or diameter do not allow the existence of Pi as a dimensionless size.

Who ever said pi is a) dimensionless, b) a size, or c) a dimensionless size?

Pi is a ratio between a circle's circumference and it's diameter.

The Man · Dec 17, 2011

epix said:
Doronetics and tautology are very closely related. No matter what kind of options you take to instruct Doron, the outcome will be the same.

Indeed, but at least I gave him the chance and the choice. What he does with it is up to him alone.

The Man · Dec 17, 2011

Little 10 Toes said:
doronshadmi said:

Pi is a dimensionless size, because it is not impacted by the sizes of all existing circles.

Zero circumference or diameter do not allow the existence of Pi as a dimensionless size.

Click to expand...

Who ever said pi is a) dimensionless, b) a size, or c) a dimensionless size?

Pi is a ratio between a circle's circumference and it's diameter.

Technically Pi is a dimensionless quantity, whatever Doron actually means by “size” let alone “dimensionless size” is really irrelevant as it will vary whenever it suits him.

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

Little 10 Toes · Dec 18, 2011

The Man said:
Technically Pi is a dimensionless quantity, whatever Doron actually means by “size” let alone “dimensionless size” is really irrelevant as it will vary whenever it suits him.

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

Well, I was using pi^WP for my info. So neener.

epix · Dec 18, 2011

The Man said:
Technically Pi is a dimensionless quantity, whatever Doron actually means by “size” let alone “dimensionless size” is really irrelevant as it will vary whenever it suits him.

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

Wiki quote:

In dimensional analysis, a dimensionless quantity or quantity of dimension one is a quantity without an associated physical dimension. It is thus a "pure" number, and as such always has a dimension of 1. Dimensionless quantities are widely used in mathematics, physics, engineering, economics, and in everyday life (such as in counting). Numerous well-known quantities, such as π, e, and φ, are dimensionless.

LOL.
A little distraction would also raise the question why a quantity without dimension has been assigned a dimension of 1. Just stick with the initial part of the definition and don't assign any dimension to it. Right?

If pi is a dimensionless quantity, then what is number pi?

I guess it has to be a dimensionless number.

And what is a dimensionless number?

A number representing a property of a physical system, but not measured on a scale of physical units (as of time, mass, or distance).

That's why we don't see around expressions, like pi miles/h, pi mV, and so on.

The Wikipedia writers usually never do any explaining by example for those who know a little about a given subject but are not completely ignorant. Doron, as usually, sees things differently:

Pi is a dimensionless size, because it is not impacted by the sizes of all existing circles.

doronshadmi · Dec 18, 2011

Pi has a physical size as distance along the real line but it is dimensionless in terms of an invariant ratio among all circles.

In other words, Pi is Cross-contexts w.r.t all circles' curvature degrees, and without such Cross-contexts property circles with different curvature degrees can't be gathered into a one class.

Yet being gathered into a one class does not mean that all in terms of finite cardinality is equivalent to all in terms of transfinite cardinality, simply because the expression "+1" is an invariant Cross-contexts property w.r.t all infinite collections, exactly as Pi is Cross-contexts w.r.t all circles' curvature degrees.

In other words, the incompleteness of infinite collections is their "+1" expression (in terms of cardinality) as an invariant Cross-contexts property.

epix · Dec 19, 2011

doronshadmi said:
Pi has a physical size as distance along the real line but it is dimensionless in terms of an invariant ratio among all circles.

In other words,

pi is a constant ratio when associated with circles.

Pi is Cross-contexts w.r.t all circles' curvature degrees, and without such Cross-contexts property circles with different curvature degrees can't be gathered into a one class.

Yet being gathered into a one class does not mean that all in terms of finite cardinality is equivalent to all in terms of transfinite cardinality, simply because the expression "+1" is an invariant Cross-contexts property w.r.t all infinite collections, exactly as Pi is Cross-contexts w.r.t all circles' curvature degrees.

In other words, the incompleteness of infinite collections is their "+1" expression (in terms of cardinality) as an invariant Cross-contexts property.

If you think so . . .

The Man · Dec 19, 2011

epix said:
Wiki quote:

LOL.
A little distraction would also raise the question why a quantity without dimension has been assigned a dimension of 1. Just stick with the initial part of the definition and don't assign any dimension to it. Right?

From the first referance in that article….

^ "1.8 (1.6) quantity of dimension one dimensionless quantity". International vocabulary of metrology — Basic and general concepts and associated terms (VIM). ISO. 2008. http://www.iso.org/sites/JCGM/VIM/JCGM_200e_FILES/MAIN_JCGM_200e/01_e.html#L_1_8. Retrieved 2011-03-22.

1.8 (1.6)
quantity of dimension one
dimensionless quantity
quantity for which all the exponents of the factors corresponding to the base quantities in its quantity dimension are zero
NOTE 1 The term “dimensionless quantity” is commonly used and is kept here for historical reasons. It stems from the fact that all exponents are zero in the symbolic representation of the dimension for such quantities. The term “quantity of dimension one” reflects the convention in which the symbolic representation of the dimension for such quantities is the symbol 1 (see ISO 31 0:1992, 2.2.6).
NOTE 2 The measurement units and values of quantities of dimension one are numbers, but such quantities convey more information than a number.
NOTE 3 Some quantities of dimension one are defined as the ratios of two quantities of the same kind.
EXAMPLES Plane angle, solid angle, refractive index, relative permeability, mass fraction, friction factor, Mach number.
NOTE 4 Numbers of entities are quantities of dimension one.
EXAMPLES Number of turns in a coil, number of molecules in a given sample, degeneracy of the energy levels of a quantum system.

Actually the initial part of the definition (as you quoted) does say “or quantity of dimension one”

epix said:
If pi is a dimensionless quantity, then what is number pi?

I guess it has to be a dimensionless number.

And what is a dimensionless number?

A “quantity of dimension one”

epix said:
That's why we don't see around expressions, like pi miles/h, pi mV, and so on.

The Wikipedia writers usually never do any explaining by example for those who know a little about a given subject but are not completely ignorant.

While that may be the case in some instances, it is not (see the later examples cited below) in this and reference as well as additional links are usually provided in most cases.

http://en.wikipedia.org/wiki/Dimensionless_number#Example

Example
The power consumption of a stirrer with a given shape is a function of the density and the viscosity of the fluid to be stirred, the size of the stirrer given by its diameter, and the speed of the stirrer. Therefore, we have n = 5 variables representing our example.
Those n = 5 variables are built up from k = 3 dimensions which are:
• Length: L (m)
• Time: T (s)
• Mass: M (kg).
According to the π-theorem, the n = 5 variables can be reduced by the k = 3 dimensions to form p = n − k = 5 − 3 = 2 independent dimensionless numbers which are, in case of the stirrer:
• Reynolds number (a dimensionless number describing the fluid flow regime)
• Power number (describing the stirrer and also involves the density of the fluid)

ExamplesConsider this example: Sarah says, "Out of every 10 apples I gather, 1 is rotten.". The rotten-to-gathered ratio is (1 apple) / (10 apples) = 0.1 = 10%, which is a dimensionless quantity.

Another more typical example in physics and engineering is the measure of plane angles. An angle is measured as the ratio of the length of a circle's arc subtended by an angle whose vertex is the centre of the circle to some other length. The ratio, length divided by length, is dimensionless. When using radians as the unit, the length that is compared is the length of the radius of the circle. When using degree as the units, the arc's length is compared to 1/360 of the circumference of the circle.

In the case of the dimensionless quantity π, being the ratio of a circle's circumference to its diameter, the number would be constant regardless of what unit is used to measure a circle's circumference and diameter (eg. centimetres, miles, light-years, etc), as long as the same unit is used for both.

See also.

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

epix said:
Doron, as usually, sees things differently:

Well that will probably always be the case.

The Man · Dec 19, 2011

doronshadmi said:
Pi has a physical size as distance along the real line but it is dimensionless in terms of an invariant ratio among all circles.

Really a “physical size”, what “size”? Keeping in mind that 100cm has a smaller “physical size” than 10m

doronshadmi said:
In other words, Pi is Cross-contexts w.r.t all circles' curvature degrees, and without such Cross-contexts property circles with different curvature degrees can't be gathered into a one class.

In the same words as before unless you are using the word “circles” in some other context there is simply and still nothing that crosses any context in your purported “Cross-contexts”. Learn the meaning of the word context at least, please Doron.

doronshadmi said:
Yet being gathered into a one class does not mean that all in terms of finite cardinality is equivalent to all in terms of transfinite cardinality, simply because the expression "+1" is an invariant Cross-contexts property w.r.t all infinite collections, exactly as Pi is Cross-contexts w.r.t all circles' curvature degrees.

In other words, the incompleteness of infinite collections is their "+1" expression (in terms of cardinality) as an invariant Cross-contexts property.

OK, who ordered this word salad?

doronshadmi · Dec 19, 2011

A typical response of Context-dependent-only skill(er):

"Really a “physical size”, what “size”? Keeping in mind that 100cm has a smaller “physical size” than 10m"

He\she can't comprehend Pi as a Cross-contexts value among all circles, where curvature's value > 0 AND < ∞ is context-dependent among all circles.

zooterkin · Dec 19, 2011

doronshadmi said:
A typical response of Context-dependent-only skill(er):

"Really a “physical size”, what “size”? Keeping in mind that 100cm has a smaller “physical size” than 10m"

He\she can't comprehend the concept of Distance, unless it is defined by some particular value.

What units do you measure pi in? Are you familiar with what a ratio is?

Deeper than primes - Continuation

Penultimate Amazing

ETcorngods survivor

Banned

Penultimate Amazing

Penultimate Amazing

Banned

Penultimate Amazing

Banned

Banned

Penultimate Amazing

Penultimate Amazing

Banned

Penultimate Amazing

Penultimate Amazing

Penultimate Amazing

Unbanned zombie poster

Banned

Penultimate Amazing

Banned

Penultimate Amazing

Banned

Banned

Penultimate Amazing

Banned

Unbanned zombie poster

Penultimate Amazing

Banned

Penultimate Amazing

Banned

Master Poster

Unbanned zombie poster

Unbanned zombie poster

Master Poster

Banned

Penultimate Amazing

Banned

Unbanned zombie poster

Unbanned zombie poster

Penultimate Amazing

Nitpicking dilettante, Administrator