Deeper than primes

[doronshadmi]

What is AND? The drawing doesn't include any AND.

It does not include any AND exactly because "constant X>0" is not "constant X > AND = 0".

There is no need for "constant X."

Worng, each one of the infinitely many Koch's forms has the same value (= constant X>0) of the upper triangle's side:

 

[jsfisher]

Cardinality is is the measurement unit of the size (or magnitude) of existence, exactly as Meter is a measurement unit of Length.

Doron, you say such marvelously ignorant things.

So, according to the master of the mathematical absurd, the size of the set {A,B,C} is 3 cardinalities.

Really, Doron. This is just dumb. Even a kindergarten student would know you are wrong, and you aspire to be as smart as a kindergartener, remember? Stop embarrassing yourself this way.

 

[jsfisher]

What is AND? The drawing doesn't include any AND.

The drawing doesn't include and X, either, and S only has meaning because of something in the text preceding the drawing. It's just another example of Doron's inability to express a complete thought. We are supposed to guess or otherwise divine what Doron may have meant.

 

[doronshadmi]

So, according to the master of the mathematical absurd, the size of the set {A,B,C} is 3 cardinalities.

{

At least 4 units of Cardinality are used to determine the "size (or magnitude) of existence" of {A,B,C}.

}

The same holds if we say that 1000 units of Meter are used to determine the "Length" of a given line.

 

[doronshadmi]

It's just another example of Doron's inability to express a complete thought.

It's just another example, of jsfisher's inability to use visual thinking, as expressed, for example in http://www.internationalskeptics.com/forums/showpost.php?p=6393884&postcount=11825 or http://www.internationalskeptics.com/forums/showpost.php?p=6398859&postcount=11841.

 

[jsfisher]

...4 units of Cardinality...

So, in doronetics, cardinality is not longer a unit? It now has units? Make up your mind, Doron. Is it a unit of a measure or is it a measure?

The 5 year olds are all laughing at you. They are also laughing at you for not realizing the cardinality of a set with three members is three.

 

[jsfisher]

It's just another example, of jsfisher's inability to use visual thinking, as expressed, for example in http://www.internationalskeptics.com/forums/showpost.php?p=6393884&postcount=11825 or http://www.internationalskeptics.com/forums/showpost.php?p=6398859&postcount=11841.

My visual abilities are apparently far superior to yours, Doron. You failed to notice that X, for example, doesn't appear anywhere in your diagram. S doesn't either, but at least you made an attempt to describe what you meant by S in text.

Doron, with your visual skills, you can see things that are not even there. Some people pay good money to induce that ability. Looks like you hallucinate without chemical assistance.

 

[jsfisher]

I missed this gem on first read:

The same holds if we say that 1000 units of Meter are used to determine the "Length" of a given line.

1000 units of Meter? Did you really write that, Doron? You've written many, many truly stupid things Doron, but this one is fantastic.

 

[Kopji]

...Analytical thinking, which is based on non-visual thinking, can't deal with the anomaly that is exposed by...

-blah blah blah-

...which demostrates that most mathematicians are unable to grasp visual thinking.

As a result the mathematical science of the past 3000 years is considered as non-visual science, just because is was developed during the years by people that are skillful by analytical thinking, which is non-visual by nature.

This warrants challenge.

If I may recommend an alternate book that easily refutes this assertion, it is Clifford A Pickover's "The Math Book", which covers 250 milestones in the history of mathematics - all accompanied by often striking visual representations and artwork.

Mathematics and the arts are certainly fellow travelers if not aspects of the same thing. Analytical thinkers who are visual, are formidable and clear thinking critics of nonsense.

 

[epix]

It does not include any AND exactly because "constant X>0" is not "constant X > AND = 0".

Worng, each one of the infinitely many Koch's forms has the same value (= constant X>0) of the upper triangle's side:

[qimg]http://farm5.static.flickr.com/4015/4430320710_daf5b36c0f_o.jpg[/qimg]

The only constant in the progressive iterations is the factor according to which the combine length of the line segments increases and the factor is 4/3. Zero iteration is a line segment with length = 1.

_________________________

You cut the line into three equidistant segments

________|________|________

and erase the middle one. Then you connect both segments with two segments of the same length, the way it is shown in the top figure, That's Iteration 1:

http://www.emeraldinsight.com/content_images/fig/0670340109062.png

You see 4 equidistant line segments, and that means the combine length = 4/3 (The length of the initial "non-bended" line is 3/3). The combine length of the segments for Iteration 2 right bellow is (4/3)², for Iteration 3 the combined length is (4/3)³ and so on. In general, the combined length of the n^th iteration is (4/3)ⁿ, where you can think of 4/3 as a constant.

Your triangle restricts the progression of the combined length given by the exponential growth. Can you compute the combined length for each iteration inscribed into the triangle? You need to do that to come up with the constant you are talking about. See, Pi is a constant, and as such, it has its numeric representation. Your constant X should have numerical representation as well. What's that number, Doron? And what is the combined length of the line segments for each iteration inscribed into the eq. triangle if its side s = 1? Do some number crunching for a change.

Btw, there is no cardinality, only papacy.

 

[doronshadmi]

My visual abilities are apparently far superior to yours, Doron. You failed to notice that X, for example, doesn't appear anywhere in your diagram.

In other words, you can't see anything in the following diagram, that has orange color:

 

[doronshadmi]

epix

S=2(a+b+c+d+...) and the finite constant value > 0, do not exist in:

S=2(a+b+c+d+...) and the finite constant value > 0, exist in:

 

[doronshadmi]

Analytical thinkers who are visual, are formidable and clear thinking critics of nonsense.

I agree with you that the best is to be both Analytical and Visual thinker.

But this is not the case with parsons like jsfisher or The Man.

 

[epix]

epix

S=2(a+b+c+d+...) and the finite constant value > 0, do not exist in:
[qimg]http://www.emeraldinsight.com/content_images/fig/0670340109062.png[/qimg]

S=2(a+b+c+d+...) and the finite constant value > 0, exist in:
[qimg]http://farm5.static.flickr.com/4015/4430320710_daf5b36c0f_o.jpg[/qimg]

What is the numerical value of the "constant" that you claim exists in your drawing providing the side of the triangle = 1? LOL

 

[doronshadmi]

What is the numerical value of the "constant" that you claim exists in your drawing providing the side of the triangle = 1? LOL

It does not matter, it can be any constant and finite value > 0.

jsfisher or The Man may claim that there exists Koch's form with infinite constant value.

In that case there must be a form of constant size > 0, that is entirely defined by forms of 0 sizes, which is definably Reductio ad absurdum, because no amount of only 0 sizes defines a size (finite or not), which is > 0.

 

[epix]

It does not matter, it can be any constant and finite value > 0.

jsfisher or The Man may claim that there exists Koch's form with infinite constant value.

In that case there must be a form of constant size > 0, that is entirely defined by forms of 0 sizes, which is definably Reductio ad absurdum, because no amount of only 0 sizes defines a size (finite or not), which is > 0.

Any iteration can be reduced in such a way that the combined length of the line segments would equal to certain value, such as 1. You can see such a reduction in your drawing where the length of the segments for all cases keep constant. But you need to prove it, and what you came up with isn't the proof.

 

[doronshadmi]

So, in doronetics, cardinality is not longer a unit?

It is not my problem that the English language has limitations about this subject.

In Hebrew, it is perfectly legal to say, for example: 5 Meter, 20 Mater, 70 Amma (an old measurement unit, that can be found in the Bible) etc...

jsfisher, you waste your energy on insignificant details.

 

[doronshadmi]

Any iteration can be reduced in such a way that the combined length of the line segments would equal to certain value, such as 1. You can see such a reduction in your drawing where the length of the segments for all cases keep constant. But you need to prove it, and what you came up with isn't the proof.

Take a 1-dim element with finite size X.

Bend it and get 4 equal sides along it.

Since the size between the opposite edges is changed to the sum of only 3 sides, and since the number of the sides after the first bending is 4 sides, we have to multiply the bended 1-dim element by 1/(the number of the sides after some bending), in order to get back the finite constant size X > 0, etc ... ad infinitum ... , as shown in the diagram below.

As a result each bended 1-dim element has finite constant size X > 0, but the size between its opposite edges becomes smaller (it converges), and used to define S=2(a+b+c+d+...) .

In general, S size is unsatisfied because the bended 1-dim element has finite constant size X > 0 upon infinitely many bended levels of:

 

[DazzaD]

In general, this convergent series of 1/(the number of the bended sides) is resulted by 1/1+1/4+1/16+1/64+1/256+... , which has no limit exactly because length X is invariant upon infinitely many convergent scales of that series:

Really?

So the sum of a geometric series with a common ratio less than 1 does not have a limit?

...

 

[doronshadmi]

Really?

So the sum of a geometric series with a common ratio less than 1 does not have a limit?

...

Please look at S in http://www.internationalskeptics.com/forums/showpost.php?p=6400287&postcount=11858.

Its does not have a sum if the series 2(a+b+c+d+...) is infinite.