Deeper than primes - Continuation

The Man · Jan 20, 2012

doronshadmi said:
Let's take two arbitrary locations on the real-line.

If there is nothing between them, than the, so-called, two locations are actually the same location or in other words, nothing between location A and location B is actually A = B, which is unconditionally resulted by a single location.

So a single location is not two locations and simply labeling that singular location with two different labels "A" and "B" does not make it two locations.

doronshadmi said:
The same result (being a single location) is found even if ...=A=B=C=... expression is infinitely long.

Yes even infinitely many different labels for a singular location can not make it anything but a singular location.

doronshadmi said:
This is not the case among finite "A≠B" or infinite "...≠A≠B≠C≠..." expressions, which actually enable the existence of more than a single location exactly because "≠" expression prevents the state of nothing (notated by "=" expression) among locations.

"≠" doesn't prevent anything it simply represents the assertion of the inequality of, in this consideration, different locations.

doronshadmi said:
That is prevents the state of nothing between two locations can't be another location, because another location is always located as some end case of any given pair, no matter what scale level is considered.

No it is the continuous nature of the real number line that "prevents the state of nothing between two locations". Were the space discontinuous, as in the integers, there can be nothing between two different locations.

doronshadmi said:
Conclusion: "≠" is an expression of non-locality (known at least as 1-space), such that no amount of the form "...≠A≠B≠C≠..." completely covers a 1-space (know as a line).

Nope, ""≠" is an expression of" inequality. Attempting to conflate that expression with your "non-locality" drivel will not help you. Once again you have simply confused yourself by, apparently deliberately, positing the same location with different labels as two locations. Have you found that location (point) along the real number line where there is no point (location) yet?

doronshadmi said:
Without a loss of generality, this conclusion is extended to all spaces, such that the lower spaces are local w.r.t the higher spaces and the higher spaces are non-local w.r.t the lower spaces, where the higher spaces are represented by at least "≠" expression among the lower spaces.

Extend it where ever you want, your purported "conclusion" is patently false as is the rest or your "extended" "non-locality" nonsense. Again please at least learn something Doron.

I'll give you one last chance Doron. You can either respond to this post properly or you can attempt to ascribe any of the above assertion to your fantasy "skillers". The former will get an appropriate response while the latter will signify that you have no intent to discuss this with anyone but yourself and your fantasies and as such you will be left indulge yourself in that regard as you see fit.

doronshadmi · Jan 21, 2012

The continuous nature of the real number line that "prevents the state of nothing between two locations" can't be defined by another distinct location (whether it is one more or infinitely many more locations) between any arbitrary pair of distinct locations along the real-line, simply because no matter how many distinct locations there are on infinitely many smaller scales, they are permanently distinguished by "≠" expression, which is actually the existence of at least irreducible 1-space between distinct 0-spaces, such that each 0-space is defined simultaneously by no more than one location along the real-line, and each 1-space between arbitrary distinct 0-spaces is defined simultaneously by at least two locations along the real-line.

In other words, a collection of 0-spaces can't fully cover 1-space, because an element that is defined simultaneously by at least two locations along the real-line, is irreducible into an element that is defined simultaneously by no more than one location along the real-line.

By not ignoring the non-local nature of 1-space along the real-line, one enables to understand that the power of continuum is determined by 1-space and not by collection of 0-spaces (which are naturally local, as shown above).

In order to really get it, our local (verbal_symbolic) AND non-local (visual_spatial) brain's skills must be combined into a one comprehensive framework.

For example, by "Traditional" Mathematics (which is mostly expressed by verbal_symbolic skills) 0.111... ₂ = 0.999...₁₀ = 1 where 1 is the considered mathematical object (the number itself) and 0.111...₂ or 0.999...₁₀ are some numerals (out of many representations) that represent number 1.

By using verbal_symbolic AND visual_spatial skills as follows:

one may understand that no branch of that tree actually reaches any other branch of that tree "downward" , no matter how many levels that tree has (in other words, there is no homeomorphism between 0 dimensional space (notated by "0";"1" symbols) and 1 dimensional space (notated by "_____" spatial non-composed object)).

According to this framework 0.111...₂ is a number of its own < number 1 by 0.000...1₂ where the "...1" part of that number is the irreducibility of ___ 1 dimensional space into 0 dimensional space (known as a point).

By using verbal_symbolic AND visual_spatial skills one enables to distinguish between non-local numbers like 0.111...₂ or 0.000...1₂, and local numbers like 1 or 0.

Furthermore, no collection of, for example, 0 dimensional spaces or segments on 1 dimensional space has the power of the continuum of 1 dimensional space.

By understanding the power of the continuum in terms of spatial skills, one may understand that no collection of sub-spaces of a given space (mathematical or physical) has the power of the continuum of that space, or in other words, any given collection of "hosted" sub-spaces is incomplete with respect to the "host" space.

The terms "host"\"hosted" are used here in order to clarify that the the "host" and the "hosted" are defined but not made of each other.

The non-locality of 0.111...₂ or 0.000...1₂ is "naturally vague" in terms of location, and one actually discovers/invents that the Real-line has a non-empty collection of non-local numbers between 0 dimensional space and 1 dimensional space.

By generalization, given a "host" space, no collection of "hosted" spaces has the power of the "host" space.

Even a one chance must not be given to mind's that are using only verbal-symbolic skills, in order to get this fine subject.

For example look at this response, made by verbal-symbolic-only skill(er):

"≠" doesn't prevent anything it simply represents the assertion of the inequality of, in this consideration, different locations.

"≠" prevents from different variables to actually represent only a single location along the real line, but verbal-symbolic-only skill(ers)
simply can't get that ( explained in http://www.internationalskeptics.com/forums/showpost.php?p=7948514&postcount=360 ).

Furthermore, verbal-symbolic-only skill(ers) can't get the equivalence of "≠" to 1-space (as explained above) along the real-line (their inability to deal with the real-line in terms of Cross-contexts AND Contexts-dependent framework is shown in http://www.internationalskeptics.com/forums/showpost.php?p=7887931&postcount=356 and http://www.internationalskeptics.com/forums/showpost.php?p=7895512&postcount=359 ) .

The Man · Jan 21, 2012

doronshadmi said:
The continuous nature of the real number line that "prevents the state of nothing between two locations" can't be defined by another distinct location (whether it is one more or infinitely many more locations) between any arbitrary pair of distinct locations along the real-line, simply because no matter how many distinct locations there are on infinitely many smaller scales, they are permanently distinguished by "≠" expression, which is actually the existence of at least irreducible 1-space between distinct 0-spaces, such that each 0-space is defined simultaneously by no more than one location along the real-line, and each 1-space between arbitrary distinct 0-spaces is defined simultaneously by at least two locations along the real-line.

Probably why a linear continuum is defined as...

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

...a linearly ordered set S of more than one element that is densely ordered, i.e., between any two members there is another, and which "lacks gaps" in the sense that every non-empty subset with an upper bound has a least upper bound. More symbolically:

So "another distinct location" or as informally defined "between any two members there is another". Is just one aspect the "and which "lacks gaps"" is another. Both you are well aware of as they have been quoted to your before. Why do you deliberately pretend not to know what has already been explained to you and is evident in articles you have quoted yourself that expressly assert a continuum does not have what you claim it does, gaps?

doronshadmi said:
In other words, a collection of 0-spaces can't fully cover 1-space, because an element that is defined simultaneously by at least two locations along the real-line, is irreducible into an element that is defined simultaneously by no more than one location along the real-line.

So have you found that location (point) along the real number line where there is no point (location) yet?

doronshadmi said:
By not ignoring the non-local nature of 1-space along the real-line, one enables to understand that the power of continuum is determined by 1-space and not by collection of 0-spaces (which are naturally local, as shown above).

In order to really get it, our local (verbal_symbolic) AND non-local (visual_spatial) brain's skills must be combined into a one comprehensive framework.

For example, by "Traditional" Mathematics (which is mostly expressed by verbal_symbolic skills) 0.111... ₂ = 0.999...₁₀ = 1 where 1 is the considered mathematical object (the number itself) and 0.111...₂ or 0.999...₁₀ are some numerals (out of many representations) that represent number 1.

By using verbal_symbolic AND visual_spatial skills as follows:

[qimg]http://farm7.staticflickr.com/6142/5962015728_d2fe37cc5f_z.jpg[/qimg]

one may understand that no branch (including the right most branch that is not 1 branch) of that tree actually reaches any other branch of that tree "downward" , no matter how many levels that tree has (in other words, there is no homeomorphism between 0 dimensional space (notated by "0";"1" symbols) and 1 dimensional space (notated by "_____" spatial non-composed object)).

According to this framework 0.111...₂ is a number of its own < number 1 by 0.000...1₂ where the "...1" part of that number is the irreducibility of ___ 1 dimensional space into 0 dimensional space (known as a point).

By using verbal_symbolic AND visual_spatial skills one enables to distinguish between non-local numbers like 0.111...₂ or 0.000...1₂, and local numbers like 1 or 0.

Furthermore, no collection of, for example, 0 dimensional spaces or segments on 1 dimensional space has the power of the continuum of 1 dimensional space.

By understanding the power of the continuum in terms of spatial skills, one may understand that no collection of sub-spaces of a given space (mathematical or physical) has the power of the continuum of that space, or in other words, any given collection of "hosted" sub-spaces is incomplete with respect to the "host" space.

The terms "host"\"hosted" are used here in order to clarify that the the "host" and the "hosted" are defined but not made of each other.

The non-locality of 0.111...₂ or 0.000...1₂ is "naturally vague" in terms of location, and one actually discovers/invents that the Real-line has a non-empty collection of non-local numbers between 0 dimensional space and 1 dimensional space.

By generalization, given a "host" space, no collection of "hosted" spaces has the power of the "host" space.

All this blathering still gets you back to the same problem a continuum doesn't have gaps so it is by definition completely covered by points. A discrete space has gaps but you evidently just don't want to talk about a discrete space and simply insist on pretending that a continuous space can be, well, discrete.

doronshadmi · Jan 21, 2012

Verbal_symbolic-only skill(ers) do not understand that no collection has the power of the continuum.

The continuum doesn't have gaps exactly because it is not a collection. In other words, the real-line (which is not less than 1-space AND 0-spaces, or in other words, it is not only 1-space (which has the power of the continuum)) does not have the power of the continuum.

For example, the collection of all 0-spaces along 1-space does not have the power of the continuum of 1-space, exactly because such collection exists because there is always 1-space "room" between any arbitrary pair of 0-spaces along it, which is actually equivalent to "≠" expression between them.

"≠" expression enables the existence of different 0-spaces along a given 1-space, in the first place.

In that case we can ask to show even a single case, where there is no "≠" expression between 0-spaces along a given 1-space.

Once again, an element that is defined simultaneously by at least two locations along the real-line, is irreducible into an element that is defined simultaneously by no more than one location along the real-line, or in other words, the real-line is not less than 1-space AND collection of 0-spaces along it (where the term "space" is mathematical or physical), and such association (known as the real-line) does not have the power of the continuum (as 1-space has).

No Wikipedia quotes of this subject (that are currently based on Verbal_symbolic-only skills) can change this simple fact.

The Man · Jan 21, 2012

doronshadmi said:
Verbal_symbolic-only skill(ers) do not understand that no collection has the power of the continuum.

Once again if you have such problems with your fantasy "skill(ers)" then have better fantasies.

doronshadmi said:
The continuum doesn't have gaps exactly because it is not a collection. In other words, the real-line (which is not less than 1-space AND 0-spaces, or in other words, it is not only 1-space (which has the power of the continuum)) does not have the power of the continuum.

No Doron a continuum does not have gaps explicitly because a lack of such gaps is part of the definition of a continuum.

doronshadmi said:
For example, the collection of all 0-spaces along 1-space does not have the power of the continuum of 1-space, exactly because such collection exists because there is always 1-space "room" between any arbitrary pair of 0-spaces along it, which is actually equivalent to "≠" expression between them.

Again what part of the collection is not part of the collection such that there is "room" in the collection for, well, some part of the collection?

doronshadmi said:
"≠" expression enables the existence of different 0-spaces along a given 1-space, in the first place.

Nope, a simple assertion of inequality still seems to confuse you.

doronshadmi said:
In that case we can ask to show even a single case, where there is no "≠" expression between 0-spaces along a given 1-space.

Well you can certainly ask, but I doubt most here have any need to. Once again you seem to be deliberately conflating that two different points are not equal (by that different definition) with the symbol representing inequality ("≠") as somehow 'enabling' that difference.

doronshadmi said:
Once again, an element that is defined simultaneously by at least two locations along the real-line, is irreducible into an element that is defined simultaneously by no more than one location along the real-line, or in other words, the real-line is not less than 1-space AND collection of 0-spaces along it (where the term "space" is mathematical or physical), and such association (known as the real-line) does not have the power of the continuum (as 1-space has).

No Wikipedia quotes of this subject (that are currently based on Verbal_symbolic-only skills) can change this simple fact.

For your own edification "two locations" in time are not simultaneous. Do please at least learn something Doron.

A one dimensional element is not reducible to a non-dimensional element but it can be represented as a collection of one dimensional elements, non-dimensional elements or some combinations thereof. Thank you for clearly demonstrating the advantages of mathematics over your non-local fantasies.

zooterkin · Jan 21, 2012

doronshadmi said:
Verbal_symbolic-only skill(ers) do not understand that no collection has the power of the continuum.

It's odd that you keep going on about the supposed limitations of others when you are the one who seems to be unable to grasp some fairly basic maths concepts. What do you think a continuum is?

doronshadmi · Jan 22, 2012

zooterkin said:
What do you think a continuum is?

The answer is in http://www.internationalskeptics.com/forums/showpost.php?p=7952882&postcount=364.

doronshadmi · Jan 22, 2012

Two locations in time are comparable simultaneously by memory, and yet the location in the future is potential, so Time can't be defined only in terms of collection of localities.

Step-by-step minds are tuned to get things only in terms of collections, and as a result they can't get the true nature of the continuum, which is not reducible to collections.

zooterkin · Jan 22, 2012

doronshadmi said:
The answer is in http://www.internationalskeptics.com/forums/showpost.php?p=7952882&postcount=364.

So, you don't understand what a continuum actually is. Got it.

doronshadmi · Jan 22, 2012

zooterkin said:
So, you don't understand what a continuum actually is. Got it.

No zooterkin, you do not understand that the continuum is not a collection.

zooterkin · Jan 22, 2012

doronshadmi said:
No zooterkin, you do not understand that the continuum is not a collection.

Who said it was?

doronshadmi · Jan 22, 2012

zooterkin said:
Who said it was?

Anyone who claims that there is a collection of 0-spaces with no gaps between them.

Such mind can't get:

http://www.internationalskeptics.com/forums/showpost.php?p=7878241&postcount=354

http://www.internationalskeptics.com/forums/showpost.php?p=7952072&postcount=362

http://www.internationalskeptics.com/forums/showpost.php?p=7952882&postcount=364

http://www.internationalskeptics.com/forums/showpost.php?p=7953665&postcount=368

All such mind can do is to quote Wiki and other similar sources that get the continuum in terms of collection.

Here is some nonsense given by local-only mind:

"A one dimensional element is not reducible to a non-dimensional element but it can be represented as a collection of one dimensional elements, non-dimensional elements or some combinations thereof."

And after this nonsense (which does not distinguish between 1-space and a collection of 0-spaces on it (where such collection of many 0-spaces, actually does not exist without 1-space as its "host" space)) the local-only mind writes this extra nonsense:

"Thank you for clearly demonstrating the advantages of mathematics over your non-local fantasies."

And here is another nonsense given by this local-only mind:

"Once again you seem to be deliberately conflating that two different points are not equal (by that different definition) with the symbol representing inequality ("≠") as somehow 'enabling' that difference."

This is funny, by this mind "≠" expression among collection of unique values (for example R members) does not naturally related to their inequality w.r.t each other (this local-only mind does no get that "≠" is not transformable to "=" among R members without eliminating their unique values w.r.t each other, which is resulted by no more than a single 0-space).

Actually, this is another example of the inability of this local-only mind to get, for example, http://www.internationalskeptics.com/forums/showpost.php?p=7948514&postcount=360.

doronshadmi · Jan 22, 2012

Here is another nonsense of this local-only mind:

"Were the space discontinuous, as in the integers, there can be nothing between two different locations."

Nothing between value A and value B is expressed as "A = B", which is defiantly not two things (locations, quantities, sizes or whatever).

This is another example of the inability of this local-only mind to get, for example, http://www.internationalskeptics.com/forums/showpost.php?p=7948514&postcount=360.

Here is another nonsense:

"Once again you have simply confused yourself by, apparently deliberately, positing the same location with different labels as two locations."

A = B is exactly the same thing, so the phrase above simply exposes the inability of this local-only mind to get what I wrote in http://www.internationalskeptics.com/forums/showpost.php?p=7948514&postcount=360.

zooterkin · Jan 22, 2012

doronshadmi said:
Here is another nonsense of this local-only mind:

"Were the space discontinuous, as in the integers, there can be nothing between two different locations."

Nothing between value A and value B is expressed as "A = B", which is defiantly not two things (locations, quantities, sizes or whatever).

I see your confusion. It doesn't mean that at all. For example, talking of integers, there is no value that is an integer between 3 and 4. That doesn't mean that 3=4.

Here is another nonsense:

"Once again you have simply confused yourself by, apparently deliberately, positing the same location with different labels as two locations."

A = B is exactly the same thing, so the phrase above simply exposes the inability of this local-only mind to get what I wrote in http://www.internationalskeptics.com/forums/showpost.php?p=7948514&postcount=360.

If A and B are points, and A=B, then A and B are two labels for the same thing.

doronshadmi · Jan 23, 2012

zooterkin said:
I see your confusion. It doesn't mean that at all. For example, talking of integers, there is no value that is an integer between 3 and 4. That doesn't mean that 3=4.

I see your confusion. "there is no value that is an integer between 3 and 4" doesn't mean that there is nothing between 3 and 4, and in this case "there is a difference between 3 and 4" (notated by ≠) ,such that "3=4" is a false expression.

Your understanding of Nothing is not comprehensive.

zooterkin said:
If A and B are points, and A=B, then A and B are two labels for the same thing.

If A=B, than the variables are two labels for the same thing, whether it is a point, a line, or any possible (abstract or not) thing.

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

Let us talk about points. You are invited to show two points, such that there is nothing (understood also as no-gap) between them.

If you do that, then I agree that 1-space is completely covered by 0-spaces.

jsfisher · Jan 23, 2012

doronshadmi said:
Let us talk about points. You are invited to show two points, such that there is nothing between them.

Bundled into your confusion are all sorts of assumptions about those points. In your muddle, you fail to recognize all these hidden assumptions, and so you leap to very wrong conclusions. Ironic, too, you continuing to miss hidden assumptions, but we've come to expect no less of you.

For the case at hand, if I define the integers as my universe of points and apply their natural ordering, then point 3 and point 4 are two distinct points in this universe. There is nothing, however, between point 3 and point 4.

The Man · Jan 24, 2012

Well Dorn, I did caution you about misattributing quotes to your fantasies, so enjoy your self-indulgent fantasies as that is evidently all you want.

Little 10 Toes · Jan 24, 2012

doronshadmi said:
I see your confusion. "there is no value that is an integer between 3 and 4" doesn't mean that there is nothing between 3 and 4, and in this case "there is a difference between 3 and 4" (notated by ≠) ,such that "3=4" is a false expression.

I see your confusion. You don't know what an integer^WP is. If I have a number line made only of integers, and you ask me place 2.5 on it, I will say you can't because there is nothing between 3 and 4 that is an integer. There is no integer between 3 and 4. 3 and 4 are different.

doronshadmi said:
Your understanding of Nothing is not comprehensive.

Your understanding of integers is not comprehensive.

doronshadmi said:
If A=B, than the variables are two labels for the same thing, whether it is a point, a line, or any possible (abstract or not) thing.

So then you agree that A=B. Thank you.

doronshadmi said:
Let us talk about points. You are invited to show two points, such that there is nothing (understood also as no-gap) between them.

If you do that, then I agree that 1-space is completely covered by 0-spaces.

Okay then. I have a number line made up of integers. What is between 3 and 4?

doronshadmi · Jan 24, 2012

Little 10 Toes said:
Okay then. I have a number line made up of integers. What is between 3 and 4?

The difference between 3 and 4 is notated as 3≠4 or 3__4, where ___ is the line and 3 and 4 are two different values along it.

For more details, please look at page 3 in http://www.scribd.com/doc/17039028/OMDP .

Some local-only mind may say: "if I define the integers as my universe of points and apply their natural ordering, then point 3 and point 4 are two distinct points in this universe. There is nothing, however, between point 3 and point 4."

Filtering out elements does not mean that they do not exist, for example ...__-4__-3__-2__-1__0__1__2__3__4__... is an example of the form of points if only the integers are considered along the real-line, which is, again, not less than Non-locality (at least 1-space) AND a collection of localities (0-spaces), where the term "space" can be mathematical or physical.

What you see above is not limited to Geometry, but it is Formalism that is based of verbal_symbolic AND visual_spatial skills.

----------

Once again, you are invited to show two points, such that there is nothing (understood also as no-gap) between them.

If you do that, then I agree that 1-space is completely covered by 0-spaces.

jsfisher · Jan 24, 2012

doronshadmi said:
The difference between 3 and 4 is notated as 3≠4 or 3__4, where ___ is the line and 3 and 4 are two different values along it.

That's just supreme silliness. The difference between 3 and 4 is notated as |3 - 4|.

However, difference between does not have the same meaning as between, so you have again demonstrated your weakness in reading comprehension. Please try again.

doronshadmi · Jan 24, 2012

Verbal_symbolic-only skill(ers) may claim this:

"That's just supreme silliness. The difference between 3 and 4 is notated as |3 - 4|."

This claim clearly shows that they simply can't associate verbal_symbolic AND visual_spatial skills as a one comprehensive framework.

Let's look at this:

"However, difference between does not have the same meaning as between, so you have again demonstrated your weakness in reading comprehension. Please try again."

Anyone who claims such a thing, gets everything only in terms of Reading comprehension, which is actually based only on verbal_symbolic skills (but verbal_symbolic-only skill(er) is not aware of his\her own limitation).

But the truth is that the number line is not less than the association among different mathematical or physical spaces, such that the lower space can't completely cover the higher space.

jsfisher · Jan 24, 2012

Don't give up, Doron. You may eventually get it right.

doronshadmi · Jan 25, 2012

Little 10 Toes said:
Okay then. I have a number line made up of integers. What is between 3 and 4?

Whether it is known as number line, or any other possible collection, the objects of any possible collection can't be extended beyond Cardinality 1 if at least two spaces (mathematical or physical) are not associated with each other in terms of "Host"\"Hosted" states, such that they are defined but not made of each other (actually, this is the exact meaning of being "Host"\"Hosted" spaces (mathematical or physical) w.r.t each other).

Since the "host" space is defined but not made of "hosted" spaces, no Cardinality of "hosted" spaces has the power of the continuum of the "host" space.

In order to be aware of this fact, the mind has no choice but to use at least its verbal_symbolic AND visual_spatial skills, where again, visual_spatial skills are not limited to Geometry.

Little 10 Toes · Jan 25, 2012

No, thanks. I'm on a word-salad-free diet. Try using words that have definitions other than those that you only assign to them.

doronshadmi · Jan 26, 2012

Little 10 Toes said:
No, thanks. I'm on a word-salad-free diet. Try using words that have definitions other than those that you only assign to them.

My words are easily defined if verbal_symbolic AND visual_spatial skills are used.

Little 10 Toes · Jan 28, 2012

No they're not. Please spend some time and clearly define "your" words. Maybe even post them here.

doronshadmi · Jan 29, 2012

Little 10 Toes said:
No they're not. Please spend some time and clearly define "your" words. Maybe even post them here.

Please spend some time to use your verbal_symbolic AND visual_spatial skills in order to get the considered subject.

jsfisher · Jan 29, 2012

doronshadmi said:
Please spend some time to use your verbal_symbolic AND visual_spatial skills in order to get the considered subject.

Translation: Nanner, nanner, pooh-pooh.

doronshadmi · Jan 30, 2012

"pooh-shmoo" or any other verbal-symbolic_only nonsense simply can't change the fact that no amount of "hosted" (mathematical or physical) spaces or subspaces of a given "host" (mathematical or physical) space, have the power of the continuum of the "host" (mathematical or physical) space.

Once again, "Host"\"Hosted" spaces are defined but not made of each other.

This is the exact meaning of being "Host"\"Hosted" spaces (mathematical or physical) w.r.t each other, and it is known only if verbal_symbolic AND visual_spatial skills are actually used in one's mind.

jsfisher · Jan 30, 2012

doronshadmi said:
"pooh-shmoo" or any other verbal-symbolic_only nonsense simply can't change the fact that no amount of "hosted" (mathematical or physical) spaces or subspaces of a given "host" (mathematical or physical) space, have the power of the continuum of the "host" (mathematical or physical) space.

Once again, "Host"\"Hosted" spaces are defined but not made of each other.

This is the exact meaning of being "Host"\"Hosted" spaces (mathematical or physical) w.r.t each other, and it is known only if verbal_symbolic AND visual_spatial skills are actually used in one's mind.

Now, click you heels together three times....

Don't forget Toto.

doronshadmi · Feb 8, 2012

Little 10 Toes said:
No, thanks. I'm on a word-salad-free diet. Try using words that have definitions other than those that you only assign to them.

Nothing between A and B means that A and B are variables of the same thing.

This simple notion fits also your word-salad-free diet.

In the case of natural numbers, if there is nothing between variable A and B, then A and B are actually the same natural number.

What holds among natural numbers holds among any possible number system.

zooterkin · Feb 8, 2012

doronshadmi said:
Nothing between A and B means that A and B are variables of the same thing.

This simple notion fits also your word-salad-free diet.

In the case of natural numbers, if there is nothing between variable A and B, then A and B are actually the same natural number.

What holds among natural numbers holds among any possible number system.

So, dealing with integers, what is between 3 and 4?

doronshadmi · Feb 8, 2012

zooterkin said:
So, dealing with integers, what is between 3 and 4?

Their difference w.r.t each other.

If it was nothing, then 3=4, which is false.

Little 10 Toes · Feb 8, 2012

zooterkin said:
So, dealing with integers, what is between 3 and 4?

doronshadmi said:
Their difference w.r.t each other.

If it was nothing, then 3=4, which is false.

Try again.

The question is "what is between 3 and 4?"

Little 10 Toes · Feb 8, 2012

doronshadmi said:
Nothing between A and B means that A and B are variables of the same thing.

This simple notion fits also your word-salad-free diet.

In the case of natural numbers, if there is nothing between variable A and B, then A and B are actually the same natural number.

What holds among natural numbers holds among any possible number system.

No. You are wrong.

Please review the definition of Natural Numbers. You'll then see that there is nothing between two natural numbers. And then you'll realize that your statement of "What holds among natural numbers holds among any possible number system" is wrong as well.

doronshadmi · Feb 9, 2012

Little 10 Toes said:
No. You are wrong.

Please review the definition of Natural Numbers. You'll then see that there is nothing between two natural numbers. And then you'll realize that your statement of "What holds among natural numbers holds among any possible number system" is wrong as well.

You are wrong Little 10 Toes.

If there is nothing between considered things (numbers or whatever) then there is actually one and only one thing, for example:

There is an endless straight line, which is actually one and only one thing.

Now, there is a point which is located along it, end as a result we are able to distinguish between, for example, left and right rays w.r.t the considered point, even if the point has 0 dimensional space, so 0 dimensional space is not nothing, because if it is omitted, we get a single endless straight line.

But it is also known that a 1 dimensional space (whether it is a ray or an endless straight line) is not reducible to 0 dimensional space, such that it is located AND not located at the location of some arbitrary point (0 dimensional space) along it.

The irreducibility of some higher space to some lower space defines the "host"\"hosted" state of these (mathematical or physical) spaces w.r.t each other, such that they are defined but not made of each other (end this is exactly the meaning of being "host"\"hosted" w.r.t each other).

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

If the term Number is considered, then it is distinguished according Quantity and\or Size and\or Order differences, which is defiantly not Nothing.

So by using Distinction as a fundamental term among Number systems, if there is Nothing between them, then their different objects are not known.

It is also has to be stressed that superposition of ids among things (including numbers) is still distinguished according to Uncertainty x Redundancy Distinction Trees (URDT) ( more details about URDT are seen in http://www.internationalskeptics.com/forums/showpost.php?p=7721309&postcount=64 ).

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

The motivation of this thread is given in http://www.internationalskeptics.com/forums/showpost.php?p=7676943&postcount=5 .

Mudcat · Feb 9, 2012

I have been kinda lurking on this thread for sometime now, hoping that it would start making sense. Could someone maybe explain it to me in simple, easy to understand terms along with how it wound up in th RnP section?

Thanks in advance.

doronshadmi · Feb 9, 2012

Mudcat said:
I have been kinda lurking on this thread for sometime now, hoping that it would start making sense. Could someone maybe explain it to me in simple, easy to understand terms along with how it wound up in th RnP section?

Thanks in advance.

EDIT: Hi Mudcat,

My goal in this thread is to represent the first sketches of a new framework, which develops Mathematics beyond its current formal paradigm, in order to develop practical method that may enable to extend human consciousness, in order to define the harmony among its subjective and objective aspects.

The current paradigm of the mathematical science is based on context-dependent frameworks, such that each framework has its own consistent rules.

The new paradigm of this science (called Organic Mathematics) is based on Cross-contexts AND Context-dependent rules that if carefully developed, may achieve the considered goal.

One of the main principles of this development is to use verbal_symbolic AND visual-spatial brain's skills (the current development of the mathematical science is based mostly on verbal_symbolic brain's skills).

Mudcat · Feb 9, 2012

doronshadmi said:
Hi ~~Mutcat~~ Mudcat

Made your first mistake here. Don't worry, I fixed it for you.

doronshadmi said:
My goal in this thread is to represent the first sketches of a new framework, which develops Mathematics beyond its current formal paradigm, in order to develop practical method that may enable to extend human consciousness, in order to define the harmony among its subjective and objective aspects.

The current paradigm of the mathematical science is based on context-dependent frameworks, such that each framework has its own consistent rules.

What part of "simple and easy to understand" don't you get? You say you want develop a practical method, but fail to provide in what way is it of practical use.

That would be a good way to start.

doronshadmi said:
The new paradigm of this science (called Organic Mathematics) is based on Cross-contexts AND Context-dependent rules that if carefully developed, may achieve the considered goal.

I see the word science in there, but nothing that adheres to time honored scientific practices, and I suspect you think it means something it does not.

doronshadmi · Feb 9, 2012

Mudcat said:
Made your first mistake here. Don't worry, I fixed it for you.

What part of "simple and easy to understand" don't you get? You say you want develop a practical method, but fail to provide in what way is it of practical use.

That would be a good way to start.

I see the word science in there, but nothing that adheres to time honored scientific practices, and I suspect you think it means something it does not.

Please look at http://www.internationalskeptics.com/forums/showpost.php?p=7672352&postcount=16583 .

Deeper than primes - Continuation

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