Deeper than primes

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dafydd said:
Can you explain to this Homer Simpson clone the meaning of the farrago above?
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The first line is refering to the idea that if you take an object such as a point or a line out of its context, ie the universe. Its size becomes undefinable, as there is no universe around it from which to draw a relative comparison of measurement.

The second line is refering to the specific idea that a unity though formless includes in essence all things.

The inference being that if this unity is divided through dichotomy into many relative forms. These forms as a whole are the equivalent to the unity and individually to an aspect or quality of that unity.

Light is a good analogy for this, white light being the unity and the different colours in the refractive index being individual aspects of the unity.

The inclusion of infinity in the equation is more difficult to explain, so I will leave it at that for now.
 
punshhh said:
The first line is refering to the idea that if you take an object such as a point or a line out of its context, ie the universe. Its size becomes undefinable, as there is no universe around it from which to draw a relative comparison of measurement.

The second line is refering to the specific idea that a unity though formless includes in essence all things.

The inference being that if this unity is divided through dichotomy into many relative forms. These forms as a whole are the equivalent to the unity and individually to an aspect or quality of that unity.

Light is a good analogy for this, white light being the unity and the different colours in the refractive index being individual aspects of the unity.

The inclusion of infinity in the equation is more difficult to explain, so I will leave it at that for now.
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You cannot take anything out of the universe.

What does this gibberish mean?
"The second line is refering to the specific idea that a unity though formless includes in essence all things."

And this babble?
"The inference being that if this unity is divided through dichotomy into many relative forms. These forms as a whole are the equivalent to the unity and individually to an aspect or quality of that unity."

Are you using a random big word generator?

What equation? Please show it to me.
 
dafydd said:
You cannot take anything out of the universe.

What does this gibberish mean?
"The second line is refering to the specific idea that a unity though formless includes in essence all things."

And this babble?
"The inference being that if this unity is divided through dichotomy into many relative forms. These forms as a whole are the equivalent to the unity and individually to an aspect or quality of that unity."

Are you using a random big word generator?

What equation? Please show it to me.
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Oh dear I don't know what am I going to do with you.

I will explain the first idea again and see if we can agree on an understanding.

Can you imagine for the sake of argument a grain of sand or an atom.
Now imagine that the rest of the universe is taken away.

The grain of sand or atom is left on its own. Now we know how big it is as we could measure it before we removed the universe.

But consider that another hypothetical observer not aware of the universe which has been removed comes along and tries to measure its size. They would have no reference point against which to measure it, it could be any size. Infact size would have no meaning any more.

If they were viewing it through an infinitely powerful telescope it might be infinitely small or large.

Can you understand this hypothetical scenario, even in part?
 
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Originally Posted by epix
How do you remove the pair of the distinct 0-dimensional elements? By division? Or by subtraction?
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doronshadmi said:
By not using them as measurement tools of a given 1-dimensional element.
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Honey, have you seen my 2005 Bentley? I don't see see it in the garage.

What was the last time you drove it?

I guess it was like a year ago.

Then I think it's gone - removed.

:confused:

Well, if you drive your Lamborghini all the time, then the Bentley gets removed. Use it or lose it - youknowwhatimean? And quit cheating on me.

:confused:

You still have it, don't you?
 
punshhh said:
Oh dear I don't know what am I going to do with you.

I will explain the first idea again and see if we can agree on an understanding.

Can you imagine for the sake of argument a grain of sand or an atom.
Now imagine that the rest of the universe is taken away.

The grain of sand or atom is left on its own. Now we know how big it is as we could measure it before we removed the universe.

But consider that another hypothetical observer not aware of the universe which has been removed comes along and tries to measure its size. They would have no reference point against which to measure it, it could be any size. Infact size would have no meaning any more.

If they were viewing it through an infinitely powerful telescope it might be infinitely small or large.

Can you understand this hypothetical scenario, even in part?
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If my Aunt had cojones she'd be my Uncle. Let's try to adhere to reality. Got any maths to add to this thread?
 
epix said:
Honey, have you seen my 2005 Bentley? I don't see see it in the garage.

What was the last time you drove it?

I guess it was like a year ago.

Then I think it's gone - removed.

:confused:

Well, if you drive your Lamborghini all the time, then the Bentley gets removed. Use it or lose it - youknowwhatimean? And quit cheating on me.

:confused:

You still have it, don't you?
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"Still crazy after all these years" (Paul Simon) http://www.youtube.com/watch?v=46bkXgxb66E
 
punshhh said:
Oh dear I don't know what am I going to do with you.

I will explain the first idea again and see if we can agree on an understanding.

Can you imagine for the sake of argument a grain of sand or an atom.
Now imagine that the rest of the universe is taken away.

The grain of sand or atom is left on its own. Now we know how big it is as we could measure it before we removed the universe.

But consider that another hypothetical observer not aware of the universe which has been removed comes along and tries to measure its size. They would have no reference point against which to measure it, it could be any size. Infact size would have no meaning any more.

If they were viewing it through an infinitely powerful telescope it might be infinitely small or large.

Can you understand this hypothetical scenario, even in part?
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You cannot 'take away' the rest of the universe and leave behind a grain of sand. There would be nowhere for the sand to exist,let alone a hypothetical observer. Can you understand that?
 
jsfisher said:
You claimed |S| = |P(S)| for any set S, finite or infinite. You also claimed there to be a bijection between the elements of any set S and its power set.

Either retract these bogus claims, or perform the impossible by providing a bijection between the elements of the null set and its power set.​
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cantheor.png


I think that pretty much settles it.


shadtheor.png


:confused:

Now I don't know what to believe.
I think I take a cruise to the Alapago Islands and get aptized there to become an atheoremist.
 
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dafydd said:
You cannot 'take away' the rest of the universe and leave behind a grain of sand. There would be nowhere for the sand to exist,let alone a hypothetical observer. Can you understand that?
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In that case universe = a grain of sand.

Since the source of any possible universe is Unity, the grain of sand is actually some manifestation of that source, exactly as a wave is some inseparable manifestation of the calm level of the ocean.

The ocean is the same, whether it is calm or not.
 
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doronshadmi said:
The ocean is the same, whether it is calm or not.
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That's right. The ocean is always the same like you are regardless of whether you make sense or not -- and no violent storm over the Pacific can change that.
Pacify me, atlantize me, I will always be the same . . .
 
dafydd said:
You cannot 'take away' the rest of the universe and leave behind a grain of sand. There would be nowhere for the sand to exist,let alone a hypothetical observer. Can you understand that?
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Yes I know that Dafydd, it is a thought exercise. The purpose of which is to illustrate the idea that outside of time and space the size of a point is indefinite. As there is nothing to compare it against to establish its size.

Can you understand that?
 
punshhh said:
Yes I know that Dafydd, it is a thought exercise. The purpose of which is to illustrate the idea that outside of time and space the size of a point is indefinite. As there is nothing to compare it against to establish its size.
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A point has no size.

Can you understand that?
 
zooterkin said:
A point has no size.

Can you understand that?
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Yes, this point you refer to is a thought construct in the human mind.

Are there any points which have no size outside the human mind (or possibly a computer)?

ie, do points with no size actually exist?
 
epix said:
That's right. The ocean is always the same like you are regardless of whether you make sense or not -- and no violent storm over the Pacific can change that.
Pacify me, atlantize me, I will always be the same . . .
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Is the Ocean is not the Ocean, whether it is calm or not?

Furthermore, do you understand that the Ocean is still the Ocean even if it is both calm (at the bottom level) AND not calm (at the surface level)?

The Western logic is too weak in order to get the Unity of the Ocean.

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

S is an infinite set.

In order to define the all P(S) members, without missing even a single member, we are using |P(S)| different cases of mappings, where each case (of these |P(S)| different mappings) is done between all S members and |S| amount of P(S) members.

Such each case defines an explicit P(S) member, which is not one of the |S| P(S) members that are used in that given case.

Since there are |P(S)| different cases of such mappings, we actually construct the all P(S) members, without missing even a single P(S) member.

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

But wait a minute!

If we are using Cantor's construction method also on all S members that are mapped with the all constructed P(S) members, we define another P(S) member and another S member, etc... ad infinitum ...

Conclusion:

Our initial assertion that there is a complete infinite set, is false.

Yet there is no S member the is not mapped with P(S) member (Dedekind infinite holds).
 
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punshhh said:
Yes I know that Dafydd, it is a thought exercise. The purpose of which is to illustrate the idea that outside of time and space the size of a point is indefinite. As there is nothing to compare it against to establish its size.

Can you understand that?
Click to expand...

What is the point? I prefer to deal with reality. You ought to try your hand at writing fantasy stories, I mean that.
 
punshhh said:
Yes, this point you refer to is a thought construct in the human mind.

Are there any points which have no size outside the human mind (or possibly a computer)?

ie, do points with no size actually exist?
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In geometry yes. Didn't you hear about Euclid when you were in school.
Def. 1.1. A point is that which has no part.
Def. 1.2. A line is a breadthless length.
Def. 1.3. The extremities of lines are points.
Def. 1.4. A straight line lies equally with respect to the points on itself.
 
dafydd said:
In geometry yes. Didn't you hear about Euclid when you were in school.
Def. 1.1. A point is that which has no part.
Def. 1.2. A line is a breadthless length.
Def. 1.3. The extremities of lines are points.
Def. 1.4. A straight line lies equally with respect to the points on itself.
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These exist as thought constructs in the human mind and can only be represented by another thought construct, mathematics.
 
doronshadmi said:
Conclusion:

Our initial assertion that there is a complete infinite set, is false.
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You mean YOUR INITIAL ASSERTION. The evolution of human species has been merciful enough to extinct the part of the brain where the notion of "complete infinite set" could later materialize. That's why Homo habilis never made it to China, except for two: male and female.
 
dafydd said:
Lerk?
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This must be the result of me trying to debate something with you, rather like banging my head against a brick wall.

I suggest we stop banging our heads against this brick wall and take a more light hearted approach.

I was interested to hear how many instruments you play, do you play a folk repertoire?
My brother plays fiddle and guitar in a folk band doing gigs around the midlands.
 
punshhh said:
This must be the result of me trying to debate something with you, rather like banging my head against a brick wall.

I suggest we stop banging our heads against this brick wall and take a more light hearted approach.

I was interested to hear how many instruments you play, do you play a folk repertoire?
My brother plays fiddle and guitar in a folk band doing gigs around the midlands.
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Have you ever visited a crop circle?
 
epix said:
Have you ever visited a crop circle?
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Yes, although at the time I didn't know what a crop circle was. It was before they were publicised.
I remember being puzzled, but didn't think much about it and carried on my walk.
 
punshhh said:
Yes, although at the time I didn't know what a crop circle was. It was before they were publicised.
I remember being puzzled, but didn't think much about it and carried on my walk.
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What made you to enter the field? The curious indent or something else?
 
epix said:
What made you to enter the field? The curious indent or something else?
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I was walking through a field of wheat off the path, not something folk do these days, but at the time I would walk anywhere.
I didn't see it until I walked into a straight part of the design about 2 feet wide.

Now I think about it I can't place the time or place, which is odd as I can see clearly in my memory the wheat lying flat on the ground.
 
punshhh said:
I was walking through a field of wheat off the path, not something folk do these days, but at the time I would walk anywhere.
I didn't see it until I walked into a straight part of the design about 2 feet wide.

Now I think about it I can't place the time or place, which is odd as I can see clearly in my memory the wheat lying flat on the ground.
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So you didn't walk along the tramline. But what made you to enter the field in the first place?
 
epix said:
So you didn't walk along the tramline. But what made you to enter the field in the first place?
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I did walk the tramline 10 or 20metres, I don't know if there were any other parts to it.

I really can't remember the occassion, it might have been walking Offa's Dyke path in the summer of 1981, on the Welsh borders.
 
epix said:
You mean YOUR INITIAL ASSERTION. The evolution of human species has been merciful enough to extinct the part of the brain where the notion of "complete infinite set" could later materialize.
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This part exists, for example, in The Man's and jsfisher's brains.

Because of this part they will ask you: "Please show a natural number that is not a member of the set of all natural numbers".

My answer is:

"Even if all natural numbers are the members of the set of all natural numbers, this set exists exactly because there is an unclosed interval among the natural numbers, which guarantees the distinct existence of all natural numbers.

This unclosed interval demonstrates the incompleteness of any collection of distinct members, which enables the existence of distinct members, in the first place.

This fact is true for the set of all natural numbers, exactly as it is true for any possible collection with distinct objects, where one of these possible collections is the set of all real numbers.

Also this set has distinct members exactly because of the unclosed interval among the real numbers, which guarantees the distinct existence of all real numbers."

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

In other words, actual completeness is exactly the unclosed interval, and no collection of distinct objects can close it simply because actual infinity is beyond the magnitude of any given collection of distinct members.

Cantor missed The Actual infinity exactly because he wrongly defined it in terms another number system, called Transfinite numbers, which are still closed under the notion of collection of distinct objects.

But also among the Transfinite numbers there is an unclosed interval, which guarantees the distinct existence of all of them.
 
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punshhh said:
This must be the result of me trying to debate something with you, rather like banging my head against a brick wall.

I suggest we stop banging our heads against this brick wall and take a more light hearted approach.

I was interested to hear how many instruments you play, do you play a folk repertoire?
My brother plays fiddle and guitar in a folk band doing gigs around the midlands.
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Good on him.
 
punshhh said:
Sounds like your riding on the back of a turtle.

Anyone else going to join you?
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I have asserted no turtles, so whatever “Sounds” you are referring to in that regard certainly weren’t coming from me.

punshhh said:
Anyone else going to join you?
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Join me in what? Something you simply want to ascribe to me? Looks like you have already joined Doron in that particular propensity.


doronshadmi said:
The Man's awareness is floating upon the surface of thoughts (emotionally and intellectually).

He does not have the needed simplicity to transcendent beyond the thoughts' process in order to be aware of the simplest state of awareness, which is the un manifested unified source of both physical and spiritual manifestations as a one organic realm.
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See what I mean. Simply trying to ascribe some particular aspect of his own nonsense to someone else is already Doron’s forte. So unless you just want to join him in that, punshhh, I would recommend that you take a different tact.
 
doronshadmi said:
This part exists, for example, in The Man's and jsfisher's brains.

Because of this part they will ask you: "Please show a natural number that is not a member of the set of all natural numbers".

My answer is:

"Even if all natural numbers are the members of the set of all natural numbers, this set exists exactly because there is an unclosed interval among the natural numbers, which guarantees the distinct existence of all natural numbers.

This unclosed interval demonstrates the incompleteness of any collection of distinct members, which enables the existence of distinct members, in the first place.

This fact is true for the set of all natural numbers, exactly as it is true for any possible collection with distinct objects, where one of these possible collections is the set of all real numbers.

Also this set has distinct members exactly because of the unclosed interval among the real numbers, which guarantees the distinct existence of all real numbers."

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

In other words, actual completeness is exactly the unclosed interval, and no collection of distinct objects can close it simply because actual infinity is beyond the magnitude of any given collection of distinct members.

Cantor missed The Actual infinity exactly because he wrongly defined it in terms another number system, called Transfinite numbers, which are still closed under the notion of collection of distinct objects.

But also among the Transfinite numbers there is an unclosed interval, which guarantees the distinct existence of all of them.
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“In other words” simply meaning Doron has now replaced his “uncovered” line or line segment with an “unclosed interval” while still deliberately misusing the word “incompleteness” in reference to “any collection of distinct members”. Additionally once again, apparently deliberately, ignoring that the set of all natural numbers is closed under an integer operation of succession, which is why “all natural numbers are the members of the set of all natural numbers”.


Doron later asserts his “actual completeness is exactly” his “unclosed interval” the very aspect that he claims “demonstrates the incompleteness of any collection of distinct members”. So once again Doron simply, and perhaps deliberately, contradicts himself by claming that having his “unclosed interval” meaning his “actual completeness” , which he also claims is “beyond the magnitude of any given collection of distinct members”, is what “demonstrates the incompleteness of any collection of distinct members”. On the one hand “there is an unclosed interval among the natural numbers” that “demonstrates the incompleteness of any collection of distinct members”. While on the other hand his “actual completeness is exactly” that “unclosed interval” that is “beyond the magnitude of any given collection of distinct members.” As usual Doron remains the staunchest of just his own notions.
 
Originally Posted by epix
You mean YOUR INITIAL ASSERTION. The evolution of human species has been merciful enough to extinct the part of the brain where the notion of "complete infinite set" could later materialize.
Click to expand...



doronshadmi said:
This part exists, for example, in The Man's and jsfisher's brains.

Because of this part they will ask you: "Please show a natural number that is not a member of the set of all natural numbers".
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Your problem is that you don't read about math stuff enough to know that "all" doesn't have the sole function of a limiting quantifier, as it is almost always the case with the word's common use.
Examples of ALL:

I've been waiting all week to see her.

He had to walk all the way home.

She works all year round.

He'll need all the help he can get.

Someone took all the candy.
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In math, especially in the set theory, "all" is not used as an explicit quantifier -- it is replaced by the word "finite" -- but it is used as a qualifier. Once you define an object, such a natural number, "all", as an adjective, relates to a set of those objects that have the property described by their definition. So the term "the set of all prime numbers" doesn't mean that Euclid got his proof regarding the infinitude of primes wrong and that The Man and jsfisher can't navigate around, as you believe so.
 
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The Man said:
“In other words” simply meaning Doron has now replaced his “uncovered” line or line segment with an “unclosed interval” while still deliberately misusing the word “incompleteness” in reference to “any collection of distinct members”. Additionally once again, apparently deliberately, ignoring that the set of all natural numbers is closed under an integer operation of succession, which is why “all natural numbers are the members of the set of all natural numbers”.


Doron later asserts his “actual completeness is exactly” his “unclosed interval” the very aspect that he claims “demonstrates the incompleteness of any collection of distinct members”. So once again Doron simply, and perhaps deliberately, contradicts himself by claming that having his “unclosed interval” meaning his “actual completeness” , which he also claims is “beyond the magnitude of any given collection of distinct members”, is what “demonstrates the incompleteness of any collection of distinct members”. On the one hand “there is an unclosed interval among the natural numbers” that “demonstrates the incompleteness of any collection of distinct members”. While on the other hand his “actual completeness is exactly” that “unclosed interval” that is “beyond the magnitude of any given collection of distinct members.” As usual Doron remains the staunchest of just his own notions.
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The Man, you simply can't comprehend that "1-dimensional element" , "line", "unclosed interval", etc... is the same magnitude that enable smaller magnitudes to be distinguished from each other.

You get only the level of the smaller magnitudes, without being aware of the magnitude that actually enables the distinction of their elements.

Once again you demonstrate your weak logic, which can't get the co-existence of the non-local and the local as fundamental agents of Unity, which enable the existence of finite or infinite complexity.

Please read also http://www.internationalskeptics.com/forums/showpost.php?p=7111214&postcount=15197 .

The Man said:
Says a person that evidently has no knowledge about meaning of the word 'science'.
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Without this fundamental understanding your science is no more than the surface level of the ocean of knowledge.

For example, by your surface-only reasoning you can't comprehend the following:

The Ocean is still the Ocean even if it is both calm (at the bottom level) AND not calm (at the surface level).
 
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epix said:
Your problem is that you don't read about math stuff enough to know that "all" doesn't have the sole function of a limiting quantifier, as it is almost always the case with the word's common use.


In math, especially in the set theory, "all" is not used as an explicit quantifier -- it is replaced by the word "finite" -- but it is used as a qualifier. Once you define an object, such a natural number, "all", as an adjective, relates to a set of those objects that have the property described by their definition. So the term "the set of all prime numbers" doesn't mean that Euclid got his proof regarding the infinitude of primes wrong and that The Man and jsfisher can't navigate around, as you believe so.
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epix, please read about Universal quantification ( http://en.wikipedia.org/wiki/Universal_quantification ), before you air your view about this subject.

The Universal quantification "for all" gets only the property of the quantity of distinct objects of some collection, without the needed understanding of what enables them to be distinct from each other, in the first place.

For example: The set of all real numbers does not exist if there is no co-existence between the non-local property of being real number AND the local property of being a particular real number.

This non-local property of being real number, is equivalent to the unclosed interval among particular real numbers.

In other words, no amount of particular real numbers is the non-particular (or non-local) property of being real number.

The rule is stronger than any collection of some particular expressions of it, which is a notion that can't be comprehended by a reasoning that gets only the amount of the particular expressions (the co-existence of rule\rule's expression is not understood by the quantitative-only western logic, which according to it, the rule is the sum of its particular expressions).
 
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doronshadmi said:
epix, please read about Universal quantification ( http://en.wikipedia.org/wiki/Universal_quantification ), before you air your view about this subject.

The Universal quantification "for all" gets only the property of the quantity of distinct objects of some collection, without the needed understanding of what enables them to be distinct from each other, in the first place.

For example: The set of all real numbers does not exist if there is no co-existence between the non-local property of being real number AND the local property of being a particular real number.
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This is sheer nonsense. Saying that A(upsidedown) gets only the property of the quantity of distinct objects of some collection," is inparsable, unless you define the term, "property of quantity," coz no such term exists outside your scribble.

Your example involving the set real numbers depends on your invention and general incorporation of locality, which needs a narrow definition.

Suppose that I say that there IS a coexistence between the non-local property of being real number AND the local property of being a particular real number. How are you going to prove otherwise without reverting to the argument of "serial-only, weak resoning?" You just can't formulate your statment in such a way that it would lead to a comprehensive proof.
 
The Man said:
Additionally once again, apparently deliberately, ignoring that the set of all natural numbers is closed under an integer operation of succession, which is why “all natural numbers are the members of the set of all natural numbers”.
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Here is some concrete example of The Man's "reasoning":

"the set of all natural numbers is closed under an integer operation of succession"

The proposition is wrong simply because any collection is actually open if succession is its inherent property, and this openness it true whether the succession is immediate, in the case of integers, or not immediate, in the case of rational or irrational numbers.

So, next time if some professional mathematician asks you to show some object that is not a member of its set, please ask him\her to show you the complete infinite set of these members, without ignoring the following facts:

1) One example at a time of some object that belongs to some infinite set, does not prove the completeness of that set.

2) Any infinite set exists exactly because succession (immediate or not) is its inherent property.

3) Succession among objects is possible only if there is an unclosed interval among them, otherwise there is not room for Succession, in the first place.

4) Without the interval among objects, there are no distinct objects in the first place, and the only possible set is the empty set.
 
epix said:
This is sheer nonsense. Saying that A(upsidedown) gets only the property of the quantity of distinct objects of some collection," is inparsable, unless you define the term, "property of quantity," coz no such term exists outside your scribble.
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Really?

Please define the set of real numbers by ignoring the unclosed interval among then, which enables their distinction from each other.

epix said:
Your example involving the set real numbers depends on your invention and general incorporation of locality, which needs a narrow definition.
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You are talking about the set of real numbers, without providing the must have terms, which enable their existence in the first place, exactly because you are unable to understand the co-existence of a rule (non-locality) and its particular expressions (localities).

epix said:
Suppose that I say that there IS a coexistence between the non-local property of being real number AND the local property of being a particular real number. How are you going to prove otherwise without reverting to the argument of "serial-only, weak resoning?" You just can't formulate your statment in such a way that it would lead to a comprehensive proof.
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The rule exists at-once, in parallel, as non-locality among particular expressions (localities) of it, where no particular expression (locality) or collection of particular expressions (localities) is the non-local rule.

EDIT:

Any reasoning that ignores this co-existence, has no, so called, comprehensive proof(s) of this fine subject.
 
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