Deeper than primes

[ddt]

I'll ask Moshe to make a registration.

How is that going along? Has he signed up for the forum?

It is going to be an interesting dialog with you, more than you expect, especially because your ignorance about Organic Numbers is going to be exposed and maybe the members of this thread will learn something about you and about Organic Numbers.

I'm looking forward to it.

Remember, we are talking about http://www.internationalskeptics.com/forums/showpost.php?p=4839507&postcount=3906 , and also do not forget that Moshe's English writing skills is less than my English writing skills, but English is not the case here.

Is that possible - less than your English skills?

You are invited to show the errors in http://www.internationalskeptics.com/forums/showpost.php?p=4839507&postcount=3906 .

I have some comments about Moshe's explanation, point 3. I wait for Moshe to appear in this thread with asking it.

Not at all, Drake's equation is about us, in this case.

Please read http://www.internationalskeptics.com/forums/showpost.php?p=4840972&postcount=3923 .

Nowhere does it say so. Drake's equation is about how much intelligent life there is in the universe, period. The L is about how long it takes for a civilization to release detectable signals into space. That's not confined to mankind. And you seem to forget that mankind only released detectable signals into space for about a century - from around 1900 when radio was developed. That period has now virtually ended, now all radio and TV broadcast converts to digital terrestrial broadcast.

 

[ddt]

What doronshadmi doesn't get is the standard notation. Square brackets mean "including" while curved brackets mean "excluding" when talking about points on a number line.

I got the impression that the problem is more that Doron insists there are more numbers than the real numbers. As with his insistence that 0.999999..... is another number than 1.

But maybe I'm wrong, I only skimmed the thread the last month or so.

 

[doronshadmi]

Nowhere does it say so. Drake's equation is about how much intelligent life there is in the universe, period. The L is about how long it takes for a civilization to release detectable signals into space. That's not confined to mankind. And you seem to forget that mankind only released detectable signals into space for about a century - from around 1900 when radio was developed. That period has now virtually ended, now all radio and TV broadcast converts to digital terrestrial broadcast.

ddt,

Your English skills do not help you to understand that L is about any civilization, including us.

This is by the way one of the reasons that you don't get OM.

You, as an observer, exclude yourself from the research, and this is your fundamental mistake all along this thread.

The claim that our current and future technologies are completely silent is simply nonsense.

 

[doronshadmi]

I got the impression that the problem is more that Doron insists there are more numbers than the real numbers. As with his insistence that 0.999999..... is another number than 1.

But maybe I'm wrong, I only skimmed the thread the last month or so.

It is first of all about notions , for example http://www.internationalskeptics.com/forums/showpost.php?p=4844666&postcount=3960 , only then notations are used in order to address the notions.

 

[zooterkin]

Please explain why you don't get that infinitely many objects cannot be a complete one object (again think about infinitely many 0-dim beads that have to completely cover a one string).

Because it can?

 

[Apathia]

Aphatia,

First of all, thank you very much about your honest affords to understand OM.

You have to be more careful when you try to give a fixed title like "subjective" to Non-locality or "objective" to Locality.

For example, the laws of Physics are considered as objective exactly because they are non-local, or in other words, we can define them by using a well-defined experiment only if they do not depend on the location of the laboratory (the results hold iff they are independent of the location of the experiment).

I already wrote to you about Non-locality and Locality in http://www.internationalskeptics.com/forums/showpost.php?p=4726464&postcount=2899 (please ignore my rough language to you in this post).

About Ethics and Logic, one of OM's main afford to define the common and non-local foundations of both Ethics and Logics, exactly because Logics is non-local w.r.t any culture and Ethics is local w.r.t any culture.

This is exactly the reason of why the current scientific paradigm is so dangerous to our own survival, because it easily enables a realm where a mass destruction weapon, that used made by using non-local methods like Logic\Technology are used by people that have a Ethics that is local by culture.

You're right. I should be careful because of the starkly different usages of the words "subjective" and "objective." I see your meaning in the above in which the non-local is the objective stance.
I was speaking of "persons" as opposed to "things."

Also I wasn't meaning by "non-local" being in another than than a designated location, or a broader field.
There's a confusion that happens here when the non-local becomes just a different space or the background space. Taking the metaphor literally quickly goes to crash and burn.

Perhaps that's why you took up speaking about element/relation interaction instead.

 

[AkuManiMani]

jsfisher claims that 0 is an immediate predecessor of the values that are > 0.

This is not the case simply because for any given value x > 0 in (0,X] interval there is d such that 0<d<x, which prevents 0 from being the immediate predecessor of x, so 0 is a predecessor of (0,X] but not an immediate predecessor of (0,X] .

Furthermore, the relation "<" in the expression [0,0] < (0,X] has a meaning only if it is used between the contents of the closed interval [0,0] and the clopen interval (0,X].

Jsfisher tries to force relation "<" between the closed interval [0,0] and the clopen interval (0,X] by ignoring their contents.

Jsfisher claims that 0 is the closest element to (0,X] which is not one of the elements of (0,X] interval.

But since (0,X] is opened w.r.t 0, then the term "closest" has no meaning exactly because for any given x there is a closer element d w.r.t to 0, and in this case 0 is not an immediate predecessor of any given x in (0,X] interval.

Alright. So X is always > 0. But because any value greater than 0 also has an infinite number of intervals between it an zero, zero cannot be an immediate predecessor to any value. In fact, no value can be an immediate predecessor to any other w/o ignoring the continuum of values between it and some other value. That about the gist of what you're saying?

 

[Little 10 Toes]

What you and jsfisher do not get is the notion.

Yes we do.

Notations have no meaning without notions, and you and jsfisher are using here notations and names, without understand the meaning of the relation "<" of 0<X expression in the case of (0,X] clopen interval.

The "X" in the expression of "(0,X]" is a variable. We define X to be greater than zero because on a number line, the larger number is on the right hand side of the number line. We can start using actual numbers if you want.

By determine 0 as an immediate predecessor of (0,X] a very important mathematical universe is ignored and not researched (for example you are using the word "all" without understand that the is no such a thing like the non-finite collection of all X, simply because no collection has the magnitude of existence of the real-line itself, which is a non-local ur-element).

What "mathematical universe" is ignored? X is not a "non-finite collection", it's a variable. The rest of the paragraph is based on error and your misunderstanding.

Please look at http://www.internationalskeptics.com/forums/showpost.php?p=4844439&postcount=3950 .

And again, that post is based on error and your misunderstanding. We, jsfisher (who is a better math person than I) and I, don't care about the X in (0,X], but we are talking about the zero.

Since you are stuck on the X, let's use actual numbers. I believe that the immediate predecessor of (0,1] is zero.

 

[AkuManiMani]

What "mathematical universe" is ignored? X is not a "non-finite collection", it's a variable. The rest of the paragraph is based on error and your misunderstanding.

And again, that post is based on error and your misunderstanding. We, jsfisher (who is a better math person than I) and I, don't care about the X in (0,X], but we are talking about the zero.

Since you are stuck on the X, let's use actual numbers. I believe that the immediate predecessor of (0,1] is zero.

I think what hes saying is that one cannot determine the difference between interval [0, 0] and interval (0, 1].

 

[The Man]

I think what hes saying is that one cannot determine the difference between interval [0, 0] and interval (0, 1].

The difference is still the interval (0,1]. As 0 is the only member of the interval [0,0] and 0 is not an element of the interval (0, 1]. Were we to say the difference between the interval [1,1] and (0,1] one could claim that it is (0,1). Again the confusion comes down to boundaries and the possible elements of an interval. The open interval (0, 1) does not include the boundaries of 0 and 1. For any number we might select that falls within that interval there will always be some other number between the selected number and a boundary that is also in that interval. However when we refer to the interval we are referring to all members of the interval and not any specific one, finite group or even infinite (for an interval in the reals) group, simply all members. Thus there are no numbers between the boundaries of the interval (0,1) that are not in that interval. So no numbers exist between the intervals [0,0] and (0,1] in the reals. If Doron believes that is not the case he can simply show such a number between the interval [0,0] and (0,1]. I have repeatedly ask him to do this, but he continues to simply ignore this question.

 

[doronshadmi]

If Doron believes that is not the case he can simply show such a number between the interval [0,0] and (0,1]. I have repeatedly ask him to do this, but he continues to simply ignore this question.

The answer was clearly given also in http://www.internationalskeptics.com/forums/showpost.php?p=4844439&postcount=3950 .

There is no meaning to "<" relation without the numbers, so the question "what number exists between interval A and interval B is meaningless because all we have is only about the relations between numbers, if "<" relation is used.

At the moment that this simple and rigorous notion is understood, we immediately understand that no real number is an immediate predecessor (or successor) of another real number, because -x<-d<0<d<x is a permanent state that is not changed also by infinitely many real numbers.

The illusionary use of intervals as objects that are not related to their contents, is a perfect example of playing with notations without notions.

 

[doronshadmi]

I think what hes saying is that one cannot determine the difference between interval [0, 0] and interval (0, 1].

The whole idea of "<" relation between intervals is nothing but an illusionary game with notations, simply because "<" relation has a meaning only between the elements that are used as the contents of these intervals.

As this simple notion is understood, it is easy to show that [0,0] is not an immediate predecessor interval of (0,X], because no real number is an immediate predecessor of another real number.

jsfisher said that I have no imagination about the validity of the use of "<" or ">" relations between intervals.

Well, he does not distinguish between imagination and illusionary game with notations without notions.

 

[doronshadmi]

Because it can?

Do you claim that you can completly cover a 1-dim element by infinitely many 0-dim elements?

If your answer is yes, you are invited to show it.

 

[zooterkin]

Do you claim that you can completly cover a 1-dim element by infinitely many 0-dim elements?

If your answer is yes, you are invited to show it.

I was responding to the first part of your post, "Please explain why you don't get that infinitely many objects cannot be a complete one object". The second part is a non sequitur.

 

[doronshadmi]

I was responding to the first part of your post, "Please explain why you don't get that infinitely many objects cannot be a complete one object". The second part is a non sequitur.

Please answer by yes or no:

Do you claim that you can completly cover a 1-dim element by infinitely many 0-dim elements?

 

[AkuManiMani]

If Doron believes that is not the case he can simply show such a number between the interval [0,0] and (0,1]. I have repeatedly ask him to do this, but he continues to simply ignore this question.

That's just the thing. Even assuming that 0 is the immediate predecessor of (0, 1], it means that there is no real difference between them.

 

[zooterkin]

Please answer by yes or no:

Do you claim that you can completly cover a 1-dim element by infinitely many 0-dim elements?

No, and I'm at a loss to understand why you think I would.

Remember how this started; you object to using the term 'all' to refer to all the numbers in an interval.

 

[doronshadmi]

That's just the thing. Even assuming that 0 is the immediate predecessor of (0, 1], it means that there is no real difference between them.

Let us play the game of the intervals like this:

X>0

[0,0]<[X,X]

Now, it does not matter what X is, [0,0] is not an immediate predecessor of [X,X] because no real number is an immediate predecessor of another real number.

Things are not changed also in the case of [0,0]<(0,X]. Also in this case [0,0] is not an immediate predecessor of any X of (0,X] interval.

And indeed if there is no real number between [0,0] and (0,X] then 0 must be X and "<" relation between [0,0] and (0,X] is nothing but gibberish.

 

[doronshadmi]

No, and I'm at a loss to understand why you think I would.

Remember how this started; you object to using the term 'all' to refer to all the numbers in an interval.

"all" holds only if infinitely many 0-dim elements can completely cover a 1-dim element.

Remember, we are talking here about infinitely many 0-dim elements, so if there are always uncovered domains along the 1-dim element, it means that there is no such a thing like the complete collection of "all" 0-dim elements that completely cover a 1-dim element.

 

[zooterkin]

"all" holds only if infinitely many 0-dim elements can completely cover a 1-dim element.

Er, why? What definition of 'all' are you using?

ETA: Doron, this is simple English. I can use 'all' to refer to all the numbers in a particular interval even if there is an infinite number of them; I do not need to specify each individual one.