Deeper than primes

[punshhh]

Can you explain to this Homer Simpson clone the meaning of the farrago above?

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.

 

[dafydd]

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.

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.

 

[punshhh]

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.

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?

 

[epix]

Originally Posted by epix
How do you remove the pair of the distinct 0-dimensional elements? By division? Or by subtraction?

By not using them as measurement tools of a given 1-dimensional element.

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.



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.



You still have it, don't you?

 

[dafydd]

Can you understand this hypothetical scenario, even in part?

Why? Let us imagine that my left foot can pick up Classic FM. What about the equation that you mentioned?

 

[dafydd]

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?

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?

 

[doronshadmi]

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.



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.



You still have it, don't you?

"Still crazy after all these years" (Paul Simon) http://www.youtube.com/watch?v=46bkXgxb66E

 

[dafydd]

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?

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?

 

[dafydd]

"Still crazy after all these years" (Paul Simon) http://www.youtube.com/watch?v=46bkXgxb66E

Is that your theme tune?

 

[epix]

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.​

I think that pretty much settles it.

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.

 

[doronshadmi]

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?

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.

 

[epix]

The ocean is the same, whether it is calm or not.

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 . . .

 

[punshhh]

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?

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?

 

[zooterkin]

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.

A point has no size.

Can you understand that?

 

[punshhh]

A point has no size.

Can you understand that?

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?

 

[doronshadmi]

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 . . .

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).

 

[dafydd]

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?

What is the point? I prefer to deal with reality. You ought to try your hand at writing fantasy stories, I mean that.

 

[dafydd]

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?

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.

 

[punshhh]

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.

These exist as thought constructs in the human mind and can only be represented by another thought construct, mathematics.

 

[punshhh]

What is the point? I prefer to deal with reality. You ought to try your hand at writing fantasy stories, I mean that.

I don't see the point either, maybe we should lerk from each other for a while.