Deeper than primes

[epix]

According to your provided example you are ignorant about the meaning of being Organic, where people do not harm other people exactly because they are percepting themselves and other people as organs of a one shared organism.

In other words epix, you can't comprehend http://www.internationalskeptics.com/forums/showpost.php...ostcount=15553 exactly because being flexible for you is the freedom to cut one of your legs in order to develop the framework of movement, which is based on jumping on one leg.

Your perpetual contradictory statements are leaking into anything you attempt to put forward.

Your idea of Organic line segment that cannot be entirely covered by points makes such a segment a discrete set of points and that means if point A which lies on the segment cuts its leg off, point B doesn't scream ouch, coz there is a disconnection between both points. But that contradicts the concept of shared organism that your OM feeds on. It follows that OM is riddled with inconsistencies that makes such a computing system unusable.

I recommend that you re-structure the fundamentals. Give it a break, relax, go to see a movie and then start again digging the foundations in a different place.

 

[doronshadmi]

coz there is a disconnection between both points.

Wrong, any given arbitrary pair of closer points are connected by a line segment that is simultaneously located at both points, which is a property that no point has.

You still do not comprehend the organic structure of the co-existence of locality and non-locality, which are mutually independent w.r.t each other exactly like two axioms that share the same framework without contradicting each other (exactly because they complement each other).

But that contradicts the concept of shared organism that your OM feeds on. It follows that OM is riddled with inconsistencies that makes such a computing system unusable.

The contradiction is a direct result of your weak reasoning to comprehend the co-existence of locality and non-locality that complement each other into a one organic framework.

I recommend that you re-structure the fundamentals. Give it a break, relax, go to see a movie and then start again digging the foundations in a different place.

You have no clue about the actuality of relaxation because of your noisy violent mind, as clearly can be seen in http://www.internationalskeptics.com/forums/showpost.php?p=7243339&postcount=15574 and also in your last post.

 

[epix]

Wrong, any given arbitrary pair of closer points are connected by a line segment that is simultaneously located at both points, which is a property that no point has.

I never mentioned any "given arbitrary pair of closer points." It's just your decOMposing mind that translates for you what others write.

 

[doronshadmi]

I never mentioned any "given arbitrary pair of closer points."

You don't have to.

For example, the real-line is defined in terms of metric-space.

By using metric-space please define two points that exist at the same location along the real-line.

If it can't be done, then please ask yourself why it can't be done?

 

[Trifikas]

By understanding the co-existence of sameness AND difference, the following contradiction (points are indistinguishable AND distinct) as given by

Quote:
points in a pseudometric space need not be distinguishable; that is, one may have d(x,y) = 0 for distinct values x≠y ( http://en.wikipedia.org/wiki/Pseudometric_space )

is simply avoided, because the used concepts (sameness;difference) are a generalization of concepts like distance and point.

Er, Maybe one of the more mathmatically inclined here can go into detail, but why would we want to get rid of that contradiction? Especially if, as the Wikipedia article says, "Pseudometrics arise naturally in functional analysis." Won't explaining it away by re-defining terms be only temporary, since, as a concept, it is still needed by Functional analysis?

 

[doronshadmi]

Er, Maybe one of the more mathmatically inclined here can go into detail, but why would we want to get rid of that contradiction? Especially if, as the Wikipedia article says, "Pseudometrics arise naturally in functional analysis." Won't explaining it away by re-defining terms be only temporary, since, as a concept, it is still needed by Functional analysis?

Please read http://www.internationalskeptics.com/forums/showpost.php?p=7239690&postcount=15563 .

As can be seen, the notions of Pseudometrics must not be limited only to Functional analysis, and in this case sameness is dimension and difference is the particular values of dimension.

By using this approach the mathematician's mind is educated to define the connections between the general and the particular as a one comprehensive framework.

Please look at http://www.internationalskeptics.com/forums/showpost.php?p=7243778&postcount=15576 .

 

[epix]

You don't have to.

For example, the real-line is defined in terms of metric-space.

By using metric-space please define two points that exist at the same location along the real-line.

If it can't be done, then please ask yourself why it can't be done?

I wasn't referring to the metric space but pseudo-metric space if you feel like changing the subject again.

Here is your line segment that cannot be completely covered by points, meaning there exists a positive real number that according to OM cannot be divided by another real number different from zero.

A___ ______ ___ _________B

As you claim, Organic Mathematics is a one organism. In other words, if point A cuts its leg off, point B says ouch. But that contradicts your understanding of the real line that, according to you, cannot be completely covered by points and therefore a disconnection exists between A and B.

So tell me, Doron. A bullet leaves the gun muzzle M and hits target T twenty feet away. Which are the points between M and T that the bullet didn't travel through?

That's of course a hypothetical question, coz I don't expect any answer that would actually take into account the nature of the question.

 

[epix]

The practical technique of such development is known as meditation, which enables one's mind to systematically be aware of finer levels of his\her thinking process until he\she directly aware of the finest level of awareness, which is naturally free of any thinking process.

Just don't dump on me the idea that you, and you in particular, need to meditate in order to free your mind from any thinking process.

 

[doronshadmi]

I wasn't referring to the metric space but pseudo-metric space if you feel like changing the subject again.

And how the real-line is defined in terms of pseudo-metric space?

Please provide such traditional mathematical framework.

For non-traditional mathematical framework of this subject, please look at http://www.internationalskeptics.com/forums/showpost.php?p=7248080&postcount=15586 .

Here is your line segment that cannot be completely covered by points, meaning there exists a positive real number that according to OM cannot be divided by another real number different from zero.

A___ ______ ___ _________B

Wrong.

Here is your line segment that cannot be completely covered by points: A_______________________B, meaning that given any amount of 0-dimensional spaces, there is always a room between any arbitrary closer pair of 0-dimensional spaces for more infinitely many 0-dimensional spaces, exactly because no amount of 0-dimensional spaces has the magnitude of a 1-dimensional space (|R| < the magnitude of 1-dimensional space).

The division of two distinct real numbers > 0 is resulted by some distinct real-number > 0, but it does not change the fact that each real-number is corresponded to some 0-dimensional space along the real-line, where the real-line is not less then the co-existence of 1-dimensional space with infinitely many 0-dimensional spaces that their summed magnitude |R| < the magnitude of 1-dimensional space.

Similarly to The Man's trapped mind on the subjective level, you also can't comprehend the variation of “Hilbert's Hotel” (http://www.internationalskeptics.com/forums/showpost.php?p=7207963&postcount=15484) , which is different than the original “Hilbert's Hotel” ( http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel ).

 

[doronshadmi]

Just don't dump on me the idea ...

To really be free of any thinking process, is not an idea but a real state of mind, which is the natural source of any possible idea, where ideas are always some particular thinking process.

 

[The Man]

Here The Man's subjective-only mind uses the word "Actually" in order to express that

Here Doron tries to use his latest catch phrase (“subjective-only mind”) for simply ascribing some aspect of his own failed reasoning onto others, with no more result than all his others before (‘serial only’, ‘context dependent only’, ‘local only’….ect) . Stop simply trying to posit aspects of your own failed reasoning onto others.

Another reply of a subjective-only mind, which is trapped at level of thinking process, and as a result reality for him is only the subjective aspect of particular expressions.

Again stop simply trying to posit aspects of your own failed reasoning onto others.

Actually he has no clue about the actual meaning of cybernetics, which is not less then the simple AND non-trivial communication between the observed and the observer.

Quite the contrary, Doron, I have more than just a clue, my understanding of robotics and control systems is what earns me a living. Cybernetics is a very active and productive field of research Doron and it is not one of your buzz word fantasies.

How’s that 'OM' investment working out for you there? 20 years and still no real results, sounds like you’re the only victim of your own Ponzi scheme.

The Man's subjective-only mind can't actually comprehend http://www.internationalskeptics.com/forums/showpost.php?p=7243778&postcount=15576.

Again stop simply trying to posit aspects of your own failed reasoning onto others.

 

[epix]

And how the real-line is defined in terms of pseudo-metric space?

Please provide such traditional mathematical framework.

The real line is not defined in pseudometric space. What purpose would it serve?

Can you translate the following using your own words?

A pseudometric space (X,d) is a set X together with a non-negative real-valued function d: X x X → R _≥0 (called a pseudometric) such that, for every x, y, z in X,

1. d(x, x) = 0
2. d(x, x) = d(x, x)
3. d(x, z) ≤ d(x, y) + d(y, z)


You claimed previously that two distinct points cannot occupy the same location without even knowing that there are spaces where it can be allowed. If you want to do some hOMe improvement to math, you should get at least familiar with the subject.

The rest of your post is the usual nonsense.

 

[epix]

To really be free of any thinking process, is not an idea but a real state of mind, which is the natural source of any possible idea, where ideas are always some particular thinking process.

I think it would be better if you show how that meditation works. There is a unit circle (radius=1) inscribed in an isosceles triangle -- one of the infinitely many which a unit circle can be inscribed to.

But infinitely many cases doesn't mean that the cases are all equal -- there is always a criterion of choice that makes a particular selection(s) unlike any other and therefore unique or special (more than one but very few in comparison with the whole).

In this particular case, the specialty lies in the relationship between 2-dim objects (areas) and 1-dim objects (lines) and the question is this: What is the altitude h so that the area of the unit circle equals the area not in the circle (lighter blue).

Now start meditating upon the strategy of the solution -- you may learn something about the real points. This way I can get a pretty good picture of what you meant in your reply. You can try to google help. Just show that the OM solution is superior to the one that traditional math can fetch.

 

[doronshadmi]

I think it would be better if you show how that meditation works.

It can be done only by your ability to be aware of finer levels of your thinking process (no matter what meaning you give it) until you are aware of the finest state of awareness, which is naturally free of any thinking process.

The development of your awareness is its ability to be aware of its finest level without losing it during the thinking process, such that both calmness and activity are present in your mind without prevent each other.

By developing such state of mind, you are in the optimal conditions to express your abilities in any wished way, which is naturally free of contradiction w.r.t other expressions, exactly because your mind expresses itself right from the source of all possible expressions.

Organic Mathematics is first of all a systematic method that uses mathematical insights in order to open the mathematician's mind to the Unity of simplicity (calmness) and activity (complex expressions).

Your currently active-only state of mind still unables to get the analogy of 1-dimensional space as the Unity of both straight-line (calmness) and curved-lines (complex expressions), as provided by the following diagram:

Please this time try to gently grasp the following diagram, before you try to analyze and define it by some already agreed mathematical tools.

If you do that your mind naturally begins to be opened to its non-subjective level of awareness (illustrated by the straight line), at least at the level of the analogy (which is not the actual non-subjective state of mind).

 

[doronshadmi]

Quite the contrary, Doron, I have more than just a clue, my understanding of robotics and control systems is what earns me a living.

Thank you for sharing an actual aspect of your life.

Please share with the posters of this thread your view of current and future development of Robotics.

 

[epix]

Organic Mathematics is first of all a systematic method that uses mathematical insights in order to open the mathematician's mind to the Unity of simplicity (calmness) and activity (complex expressions).

I can't wait to see it in action:
http://www.internationalskeptics.com/forums/showpost.php?p=7251673&postcount=15593

 

[epix]

Your currently active-only state of mind still unables to get the analogy of 1-dimensional space as the Unity of both straight-line (calmness) and curved-lines (complex expressions), as provided by the following diagram:

[qimg]http://farm4.static.flickr.com/3296/5721561558_c5b78c3152_b.jpg[/qimg]

Please this time try to gently grasp the following diagram, before you try to analyze and define it by some already agreed mathematical tools.

Gently? That diagram of yours is a mutilated version of Cantor set

which you've dismembered in a frenzy of irreversible desire to forcefully separate, chop, cut and tear apart. "Mother! Have you seen the red gas can? I think I hear a 75 Chevy pulling up in our yard; I think we have guests to take care of."

 

[PadainFain]

I was actually quite lost in the original explanation of the theory... and there was me thinking the my Physics degree counted for something. But **** me... ORGANIC numbers? Since when did numbers in their purist sense become associated with carbon atoms?

 

[jsfisher]

I was actually quite lost in the original explanation of the theory... and there was me thinking the my Physics degree counted for something. But **** me... ORGANIC numbers? Since when did numbers in their purist sense become associated with carbon atoms?

If I recall correctly, it arises from an address given by Hilbert that Doron completely misunderstood. Hilbert spoke of the organic nature of Mathematics, alluding to characteristics of its interconnectedness and evolution.

 

[PadainFain]

If I recall correctly, it arises from an address given by Hilbert that Doron completely misunderstood. Hilbert spoke of the organic nature of Mathematics, alluding to characteristics of its interconnectedness and evolution.

JFC... I hate the use of Organic in foods (because what food is NOT Organic!?), but in numbers! Now I have a new thing to hate! Based on observation, evidence hypotheses and reason of course!

I am also someone who wants to preserve language. I hate the way it "evolves". This whole concept of "Organic" meaning wholesome or interconnectedness is simply wrong from the outset.