Deeper than primes

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The Man said:
If on the other hand we consider a 1:3 scaled down version of that R = 1 circle thus having a radius of R = 1/3 then it is still a complete circle ...
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Oppsss... you have used 1/3 and 1:3 on the same element.

Why is that?
 
zooterkin said:
So, tell me Doron, when you divide 1 by 3 what result do you get, as a decimal?
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zooterkin you take 0.333...[base 10] as some numeral expression of the rational number 1/3.

By OM 0.333...[base 10] is a non-local number < 1/3 local number.
 
doronshadmi said:
zooterkin said:
So, tell me Doron, when you divide 1 by 3 what result do you get, as a decimal?
Click to expand...

zooterkin you take 0.333...[base 10] as some numeral expression of the rational number 1/3.

By OM 0.333...[base 10] is a non-local number < 1/3 local number.
Click to expand...


I'll repeat, when you divide 1 by 3, what do you get?
 
doronshadmi said:
Oppsss... you have used 1/3 and 1:3 on the same element.

Why is that?
Click to expand...

I can understand your confusion as a circle is defined by its aspect ratio of circumference to radius and that aspect ratio is still maintained when the circle is radially divided, as in the example given. Remember a circle is defined by its radius thus when scaled it is simply a division of that singular dimension. To help you along we can consider a 3 X 6 plane, when scaled 1:3 it is a 1 X 2 plane and the 1:2 width to length aspect ratio is maintained. However this 1:3 scaled plane is only 1/9 of the original plane. This is because both dimensions must be scaled. A plane of 1 X 6 or 2 X 3 would be 1/3 of the original plane but have aspect ratios of 1:6 and 2:3 respectively so they are not scaled versions of the original plane. This is because only one dimension need be divided to get one third of a plane. Now if one is only concerned with surface area then a 30.5 X (2*30.5) plane would be 1/3 of the surface area of the original and have an aspect ratio 1:2 thus be a scaled version of the original, yet no whole number of such planes can reconstruct the original. While 9 of the 1:3 scaled planes or 3 of the one dimensionally divided planes can be used to reconstruct the original plane (as building-blocks). No whole number of the 1:3 scaled circle can reconstruct the original R=1 circle but 3 of the divided parts can.
 
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doronshadmi said:
1/infinity has nothing to to with the structural fact that no amount of k-dim elements can fully cover a 1-dim element.

Furthermore, we can't break structure 1 into more than one piece and still claim that these pieces are the same as the 1 structure, before we broke it into pieces.

So as you see, exactly because of this structural difference no amount of k-dims can fully cover n-dim.

Furthermore, no amount of more than 1 n-dims, is the same as 1 n-dim, if Structure is considered.

For example:

___ is not the same as _ + _ + _ , if Structure is considered.
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Butt, and it is a big butt, only *if* structure is considered.

So, again, you need additional constraints which would make for a more limited perception.

Unless you now state that this follows because perception is always more limited than the full faculties of the mind, in which case I would agree.
 
The Man said:
I can understand your confusion as a circle is defined by its aspect ratio of circumference to radius and that aspect ratio is still maintained when the circle is radially divided, as in the example given. Remember a circle is defined by its radius thus when scaled it is simply a division of that singular dimension. To help you along we can consider a 3 X 6 plane, when scaled 1:3 it is a 1 X 2 plane and the 1:2 width to length aspect ratio is maintained. However this 1:3 scaled plane is only 1/9 of the original plane. This is because both dimensions must be scaled. A plane of 1 X 6 or 2 X 3 would be 1/3 of the original plane but have aspect ratios of 1:6 and 2:3 respectively so they are not scaled versions of the original plane. This is because only one dimension need be divided to get one third of a plane. Now if one is only concerned with surface area then a 30.5 X (2*30.5) plane would be 1/3 of the surface area of the original and have an aspect ratio 1:2 thus be a scaled version of the original, yet no whole number of such planes can reconstruct the original. While 9 of the 1:3 scaled planes or 3 of the one dimensionally divided planes can be used to reconstruct the original plane (as building-blocks). No whole number of the 1:3 scaled circle can reconstruct the original R=1 circle but 3 of the divided parts can.
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I would like to add to this...

if we can scale it down to a 3rd of the size we should also be able to scale it down infinitely... which leads to the conclusion that there can be no smallest 1-dim element.

And if the so-called localities of the end-points get closer to each other then the length or the 1 dimension of that 1-dim element will be lim(0)

And hey presto, we get the 'dragging point' problem same as in standard math.

Or can Doron tell me what the smallest distance is between two 0-dim elements?

I say it is lim(0).
 
realpaladin said:
Or can Doron tell me what the smallest distance is between two 0-dim elements?
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The smallest distance between two 0-dim elements > 0-dim element.

The smallest distance between two 0-dim elements = 1-dim element.

As you see, this is a stuctural difference that stends and the basis of the concept of Distance.

In other words, Stucture is the Buiding-block of Distance, Division, Scale or any other possible change.
 
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The Man said:
I can understand your confusion as a circle is defined by its aspect ratio of circumference to radius and that aspect ratio is still maintained when the circle is radially divided, as in the example given. Remember a circle is defined by its radius thus when scaled it is simply a division of that singular dimension. To help you along we can consider a 3 X 6 plane, when scaled 1:3 it is a 1 X 2 plane and the 1:2 width to length aspect ratio is maintained. However this 1:3 scaled plane is only 1/9 of the original plane. This is because both dimensions must be scaled. A plane of 1 X 6 or 2 X 3 would be 1/3 of the original plane but have aspect ratios of 1:6 and 2:3 respectively so they are not scaled versions of the original plane. This is because only one dimension need be divided to get one third of a plane. Now if one is only concerned with surface area then a 30.5 X (2*30.5) plane would be 1/3 of the surface area of the original and have an aspect ratio 1:2 thus be a scaled version of the original, yet no whole number of such planes can reconstruct the original. While 9 of the 1:3 scaled planes or 3 of the one dimensionally divided planes can be used to reconstruct the original plane (as building-blocks). No whole number of the 1:3 scaled circle can reconstruct the original R=1 circle but 3 of the divided parts can.
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You are missing the Structural basis of both Division and Scale.

Please see http://www.internationalskeptics.com/forums/showpost.php?p=4911786&postcount=5290 .
 
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The more I think about this epic thread, Doron's posting history elsewhere, and his geocities library, the more I am convinced it all distills down to one simple issue: The basic concept of infinity. Doron does not understand it; he continually fights with it.

Part of the battle comes from him treating things as active processes. 0.999... cannot simply exist as a complete entity; it must be an on-going sequence of events, adding more 9's to the end, never to be finished. As such, it can never quite reach its destination, unity.

The process view creates the conflict, and from there he invents things or adapts things he misunderstands to resolve the conflict. 0.999... isn't 1, so there must be some difference between the two. Let's call it 0.000...1. Doron has reinvented infinitesimals. Infinitesimals fail for lack of numerical consistency, but Doron covers by declaring his infinitesimal to not be a number.

The whole local/non-local aspect of things is part of this invention to cover inconsistency. It sounds sciency, and look how easy it is to just declare 0.999... to be a non-local number and thus free it from the constraints imposed by "standard mathematics."


If I am correct in this, it would explain the difficulty people like Apathia have had trying to explore the philosophic underpinnings of some of the topics Doron has raised. Doron doesn't have any philosophic underpinnings for his local/non-local views; they are just things he has backed into to cover his misunderstanding of infinity.
 
doronshadmi said:
The smallest distance between two 0-dim elements > 0-dim element.

The smallest distance between two 0-dim elements = 1-dim element.

As you see, this is a stuctural difference that stends and the basis of the concept of Distance.

In other words, Stucture is the Buiding-block of Distance, Division, Scale or any other possible change.
Click to expand...

So “structure” is another word you do not understand. Remember these are your ‘atoms’ so they do not have “structure”. You can assert your ‘atoms’ as different but you can not assert them as ‘structurally different’ unless they have, well, structures which would make them composed of and divisible into the elements of those structures. Structure is not a “Buiding-block” it is what you have after you put two or more building-blocks or parts together.
 
jsfisher said:
The more I think about this epic thread, Doron's posting history elsewhere, and his geocities library, the more I am convinced it all distills down to one simple issue: The basic concept of infinity. Doron does not understand it; he continually fights with it.

Part of the battle comes from him treating things as active processes. 0.999... cannot simply exist as a complete entity; it must be an on-going sequence of events, adding more 9's to the end, never to be finished. As such, it can never quite reach its destination, unity.

The process view creates the conflict, and from there he invents things or adapts things he misunderstands to resolve the conflict. 0.999... isn't 1, so there must be some difference between the two. Let's call it 0.000...1. Doron has reinvented infinitesimals. Infinitesimals fail for lack of numerical consistency, but Doron covers by declaring his infinitesimal to not be a number.

The whole local/non-local aspect of things is part of this invention to cover inconsistency. It sounds sciency, and look how easy it is to just declare 0.999... to be a non-local number and thus free it from the constraints imposed by "standard mathematics."


If I am correct in this, it would explain the difficulty people like Apathia have had trying to explore the philosophic underpinnings of some of the topics Doron has raised. Doron doesn't have any philosophic underpinnings for his local/non-local views; they are just things he has backed into to cover his misunderstanding of infinity.
Click to expand...

While I agree that Doron has much in common with the attitudes of Intuitionistc schools of Mathematics,
Unlike them he does assert the existance of more than just a potential infinity.

In his approach Actual Infinity is Non-Locality, Potential Infinity is of Locality.

In my opinion, what's crucial with Doron is the Non-Local/Local Interaction (or "linkage" as it's currently called.)
What he's been asserting about 1/3 not equalling .3333333333...........
in Organic Mathematics follows from his Redundancy/Uncertainty structure of Organic Numbers as seen, but not necessarily directly perceived in his Direct Perception .pdf.

Chicken or egg? I'm not certain.
But as it stands now, everything rests on the Non-Local/Local framwork.
 
Apathia said:
Chicken or egg? I'm not certain.
But as it stands now, everything rests on the Non-Local/Local framwork.
Click to expand...


I quite agree that the non-local/local concepts are ripe for interesting exploration. However, I don't think Doron is up for the exploration task. I think he backed into it rather than developed it from its foundations.
 
doronshadmi said:
The smallest distance between two 0-dim elements > 0-dim element.

The smallest distance between two 0-dim elements = 1-dim element.

As you see, this is a stuctural difference that stends and the basis of the concept of Distance.

In other words, Stucture is the Buiding-block of Distance, Division, Scale or any other possible change.
Click to expand...

You need two tomato's, I need one tomatoe...
 
jsfisher said:
The more I think about this epic thread, Doron's posting history elsewhere, and his geocities library, the more I am convinced it all distills down to one simple issue: The basic concept of infinity. Doron does not understand it; he continually fights with it.

Part of the battle comes from him treating things as active processes. 0.999... cannot simply exist as a complete entity; it must be an on-going sequence of events, adding more 9's to the end, never to be finished. As such, it can never quite reach its destination, unity.

The process view creates the conflict, and from there he invents things or adapts things he misunderstands to resolve the conflict. 0.999... isn't 1, so there must be some difference between the two. Let's call it 0.000...1. Doron has reinvented infinitesimals. Infinitesimals fail for lack of numerical consistency, but Doron covers by declaring his infinitesimal to not be a number.

The whole local/non-local aspect of things is part of this invention to cover inconsistency. It sounds sciency, and look how easy it is to just declare 0.999... to be a non-local number and thus free it from the constraints imposed by "standard mathematics."


If I am correct in this, it would explain the difficulty people like Apathia have had trying to explore the philosophic underpinnings of some of the topics Doron has raised. Doron doesn't have any philosophic underpinnings for his local/non-local views; they are just things he has backed into to cover his misunderstanding of infinity.
Click to expand...

You are absolutely right. Doron will never understand these concepts also, because he does not accept the authorities of others in this field or any field for that matter. This is probably why he will never have formal education. He says we are closed minded, but it is actually him unwilling to just accept things he does not understand.
 
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