Deeper than primes

[doronshadmi]

[qimg]http://www.threedonia.com/wp-content/uploads/2011/03/Waldo.jpg[/qimg]

I think of all the education that you've missed.
But then your homework was never quite like this!

I think of all the education that you've not missed. Maybe then your homework was never quite like this!

( http://1.bp.blogspot.com/_LS9FUwupaPM/SDTv7--j1KI/AAAAAAAAALo/rvgwNbpyJus/s320/gdfgdfg.jpeg )

This time epix's "humor" is used in order to avoid http://www.internationalskeptics.com/forums/showpost.php?p=7228839&postcount=15518 .

 

[jsfisher]

Do you have some problem to understand that if x and y points have zero distance between them, then they are actually at least 3 distinct points ?

You evaded the question. Care to try again? Where in the foundations of pseudo-metric space is location mentioned?

Acceding to Modern Mathematics' pseudometric space reasoning "need not be distinguishable" AND "distinct values x≠y" is a contradiction exactly because x and y points are indistinguishable AND distinct in the same space, no matter what name is given to that space (pseudo-metric or whatever).

...and for that matter, where are points mentioned in it all?


You are rigidly fixated on things that aren't there.

 

[doronshadmi]

You evaded the question. Care to try again? Where in the foundations of pseudo-metric space is location mentioned?



...and for that matter, where are points mentioned in it all?


You are rigidly fixated on things that aren't there.

You are rigidly fixated on not getting things that are in http://www.internationalskeptics.com/forums/showpost.php?p=7228886&postcount=15519 and explicitly provide the answers about location (by not using it) and points ( they are explicitly used in http://en.wikipedia.org/wiki/Pseudometric_space ).

This time please read all of http://www.internationalskeptics.com/forums/showpost.php?p=7228886&postcount=15519 before you reply to it.

 

[epix]

You are rigidly fixated on not getting things that are in http://www.internationalskeptics.com/forums/showpost.php?p=7228886&postcount=15519 and explicitly provide the answers about location (by not using it) and points ( they are explicitly used in http://en.wikipedia.org/wiki/Pseudometric_space ).

This time please read all of http://www.internationalskeptics.com/forums/showpost.php?p=7228886&postcount=15519 before you reply to it.

I see that you are ill-prepared to deal with the topic in a rigorous manner. There seems to be a complete void in understanding on your part of the necessary complements -- something that you need to be aware of in order to proceed.

It is proved that for each compact metric space X there exist a continuous pseudo-hairy space over X and a continuous pseudo-fan of X.

http://journals.impan.gov.pl/fm/Inf/171-2-1.html

Before you embarrass yourself once again before the eyes of the math world, please peruse the brief visual tutorial to get acquainted with the highlighted terms.

1. pseudo-hairy

2. pseudo-fan

 

[jsfisher]

This time please read all of http://www.internationalskeptics.com/forums/showpost.php?p=7228886&postcount=15519 before you reply to it.

You assume too much, as usual.

 

[jsfisher]

...explicitly provide the answers about location (by not using it)

Good. So you admit that pseudo-metric spaces do not introduce a location concept. Is it just the distance function concept that escapes you?

It's really simple. A pseudo-metric space is a set A (you may call its members points if that comforts you) and a function D from AxA to R>=0, normally referred to as distance.

Let A be the set of all integer pairs, (m,n). If (a,b) and (c,d) are in A, let D((a,b), (c,d)) be defined as |a-c|.

Don't those meet all the requirements for pseudo-metric space? Are not (1,3) and (1,6) distinct elements of A? Is not the distance between them 0?

 

[doronshadmi]

Good. So you admit that pseudo-metric spaces do not introduce a location concept.

I actually show that even if location is not introduced, still 1=3 according to pseudo-metric space reasoning.

Is it just the distance function concept that escapes you?

It's really simple. A pseudo-metric space is a set A (you may call its members points if that comforts you) and a function D from AxA to R>=0, normally referred to as distance.

Let A be the set of all integer pairs, (m,n). If (a,b) and (c,d) are in A, let D((a,b), (c,d)) be defined as |a-c|.

Don't those meet all the requirements for pseudo-metric space? Are not (1,3) and (1,6) distinct elements of A? Is not the distance between them 0?

According to pseudo-metric space the distinct x=(1,3) and y=(1,6) members are also indistinguishable.

You are still missing that according to pseudo-metric space x and y are indistinguishable AND distinct, as follows:

Unlike a metric space, points in a pseudometric space need not be distinguishable; that is, one may have d(x,y) = 0 for distinct values x≠y

Points are not any member, they are exactly the smallest existing members, and this property is significant, so your "(you may call its members points if that comforts you)" nonsense simply demonstrates your ignorance about members that have the property of the smallest existing things.

Furthermore, you actually claimed that points are not involved in pseudo-metric space, according to this question:

..and for that matter, where are points mentioned in it all?

It demonstrates that you do not read the considered subject ( in this case http://en.wikipedia.org/wiki/Pseudometric_space ) before you reply.

Are not (1,3) and (1,6) distinct elements of A? Is not the distance between them 0?

(1,3) and (1,6) are distinct members of A and your abs(1-1)=0 ignores the fact that these members are at least A={(1,3),(1,6)} such that |A|=2, or in other words, you can't break the members into pieces , because according to the notion of set theory, the identity of a given member is defined as a whole.

In this case the wholes are two distinct points that have distance 3 between them in 2-dimensional space.

Moreover, if abs(1-1)=0 is considered as distance, then also abs(3-6)=3 is considered as distance, or in other words, there is no 0 distance between (1,3) and (1,6) members of A set.

 

[epix]

It demonstrates that you do not read the considered subject ( in this case http://en.wikipedia.org/wiki/Pseudometric_space ) before you reply.

The application is not there and you never find an instance where a problem must be solved with pseudometrics. But I give you a clue. A sphere has two distinct points N and S (North and South). When you reduce the dimension of the sphere to 2-dim without junking N xor S, then there is a zero distance between N and S.

The difference between pseudometrics and metrics is entirely topological. That is, a pseudometric is a metric if and only if the topology it generates is T0 (i.e. distinct points are topologically distinguishable).

Sit down, Waldo!

 

[doronshadmi]

..., then there is a zero distance between N and S.

EDIT:

..., then there no two things like S and N, because:

1) If S and N are distinct, then so is the zero distance between them, and in this case we have 3 distinct things.

2) If S and N are indistinguishable, then so is the zero distance between them, and in this case we have a 1 distinct thing.


Pseudometrics is entirely nonsense as clearly also seen in http://www.internationalskeptics.com/forums/showpost.php?p=7203810&postcount=15474 exactly because it asserts that S and N are indistinguishable AND distinct.

epix, you take pieces of information and use them without the needed knowledge that enables to gather them into a one comprehensive framework.

Once again you quote things without their reference.

 

[doronshadmi]

I would add that if jsfisher is a reliable example of Modern Math reasoning, we can clearly understand why he can't get OM.

1) He does not understand the difference between 0-dimensional element and 1-dimensional element.

2) He can't comprehend membership in terms of Locality (x in XOR out w.r.t S) or Non-locality (x in AND out w.r.t S).

3) He claims that "x in AND out w.r.t S" is a contradiction but "x and y are indistinguishable AND distinct" is consistent.

 

[doronshadmi]

Also it has to be stressed that a point (and a point is a 0-dimensional element, no matter how many coordinates a used to define it) can't be indistinguishable AND distinct w.r.t any given point, because then they are belong AND do not belong to a given 0-dimensional space, which is a property that only a given k>0-dimensional element has.

Once again we see how Modern Math prevents form one's mind the understand the difference between Locality and Non-locality right at the level of 0-dimensional elements, and it does it by braking the coordinates that define the points, which is simply nonsense because if one breaks the coordinates that define a given point, he\she does not have a point at all, and no definition about points is possible anymore.

Furthermore, let's see how jsfisher uses its traditional reasoning in order to define a pseudo-metric space by using only one coordinate that define the considered points, for example A={(a),(b)} such that "|a-b|=0" AND "(a) is distinct from (b) and vice versa".

 

[jsfisher]

I would add that if jsfisher is a reliable example of Modern Math reasoning, we can clearly understand why he can't get OM.

You presume too much, doron. I do understand a fair amount of Mathematics, and I also understand a fair about of the nonsense you pedal as OM. However, what I can see in your nonsense--something to which you are totally blind--is its contradiction, inconsistency, and just plain irrelevance.

We are still waiting for something relevant, doron. Got anything?

 

[doronshadmi]

You presume too much, doron. I do understand a fair amount of Mathematics, and I also understand a fair about of the nonsense you pedal as OM. However, what I can see in your nonsense--something to which you are totally blind--is its contradiction, inconsistency, and just plain irrelevance.

We are still waiting for something relevant, doron. Got anything?

Another typical reply of jsfisher, which avoids detailed replies to:

http://www.internationalskeptics.com/forums/showpost.php?p=7233789&postcount=15527

http://www.internationalskeptics.com/forums/showpost.php?p=7233941&postcount=15529

http://www.internationalskeptics.com/forums/showpost.php?p=7234231&postcount=15530

http://www.internationalskeptics.com/forums/showpost.php?p=7234821&postcount=15531

 

[doronshadmi]

In http://www.kahany.com/mathematics/metricspace.html we define this:

It is always an application that decides our choice of an axiom-set and the flavor of the mathematics used. There is nothing inherently right or wrong about one mathematical system as against another based on a different axiom-set. One application may require us to work in a metric space, while another may require a pseudo-metric. Our mathematics must bend to the will of Mother Nature.

The problem is that pseudo-metric space is inherently wrong, without any need to compare it to other axiomatic systems, simply because according to pseudo-metric space a pair of points are indistinguishable AND distinct, which is a contradiction.

"Mother nature" does not support contradiction.

Let's look at http://ai.stanford.edu/~ang/papers/icml04-onlinemetric.pdf (the end of page 2) :

... we predict that the pair is dissimilar. Otherwise, we say that the pair is similar.

In other words, if a given pair is similar, for example (1,1), then there is redundancy between them, which is essentially different than "nothing between 1 and 1" that is actually (1).

Anyway if 1 is used in order to define the existence of 0-dimensional element, and there is redundancy between 1 and 1, then since 0 distance is also an 0-dimensional element, we actually have redundancy among 3 0-dimensional elements.

Pseudo-metric reasoning misses it, because it is focused only on the contradiction of "similar (indistinguishable)" AND "dissimilar (distinct)".

Also be aware that Pseudo-metric reasoning does not work on (a) form, which is less than a pair.

 

[doronshadmi]

Please be aware that there are applications which use Pseudo-metric reasoning but this is like "using a fork in order to put a butter on a slice of bread", it can be done, but one misses the right understanding and efficient functionality of both knife and fork.

 

[doronshadmi]

We are still waiting for something relevant, doron. Got anything?

Start by the relevancy of the irreducibility of 1-dimensional element into a 0-dimensional element, and the non-extendability of 0-dimensional element into 1-dimensional element (there is no homeomorphism between them).

By understanding these simple facts, please research the real-line.

 

[zooterkin]

Another typical reply of jsfisher, which avoids detailed replies to:

http://www.internationalskeptics.com/forums/showpost.php?p=7233789&postcount=15527

http://www.internationalskeptics.com/forums/showpost.php?p=7233941&postcount=15529

http://www.internationalskeptics.com/forums/showpost.php?p=7234231&postcount=15530

http://www.internationalskeptics.com/forums/showpost.php?p=7234821&postcount=15531

Another typical reply from doronshadmi. Once again, ignoring the request for some demonstration of the utility of OM, and giving bare links to posts which explain nothing.

 

[epix]

The problem is that pseudo-metric space is inherently wrong, without any need to compare it to other axiomatic systems, simply because according to pseudo-metric space a pair of points are indistinguishable AND distinct, which is a contradiction.

"Mother nature" does not support contradiction.

Really? Consider two distinct points S and M in natural 3-dim space. The distance between both points can never be equal to zero as seen below.

Under special circumstances, when both points appear in the local 2-dim viewing frame, the distance between both points can become zero, otherwise there is no eclipse.

Constellations are also mapped in 2-dim space where the possible superimposition of two distinct stars results in zero difference.

It's remarkable that your in-kitchen acquired stereotypes failed to guide you toward grasping the simple concepts of advanced topology.

When the pancake eclipses the plate, one mind thinks syrup, the other thinks pseudo-metric space. Yours thinks syrup every time pancakes are served.

 

[doronshadmi]

Under special circumstances, when both points appear in the local 2-dim viewing frame, the distance between both points can become zero, otherwise there is no eclipse.

Wrong, the points in 2-dimensional space have two coordinates each, and there is 0 distance between 2 points only of there is actually a one pair of coordinates, or in other words, only a one point.

For example, by set theory {(1,3),(1,3)}={(1,3)} where (1,3) is a single point in a 2-dimensional space.

It is amazing that you can't get such a simple fact.

 

[doronshadmi]

Another typical reply from doronshadmi. Once again, ignoring the request for some demonstration of the utility of OM, and giving bare links to posts which explain nothing.

http://www.internationalskeptics.com/forums/showpost.php?p=7236473&postcount=15536