Http://folding.stanford.edu/

[Siamanto]

I do realise that your conception is not a little different than mine, but more than a "little."  I will discuss about this when I have time in another thread. I will just answer about the infinity stuff for now, since we disagree in many things in our conception of the multiverse so it will take some time...

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Domino,

I'm not familiar enough with the Inflationist Theory, so I will be careful and limit myself to: "We verbalize our views in very dissimilar ways - or with very dissimilar words!"

Would you recommend any - high level - on-line paper(s?) Thanks.

 

 

 

 

I have to disagree with you about being first orther, because like I said, there is no indication that it could continue to contain itself as a member of itself(we don't know in the first place if it ever did).

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N-m i.e. the cartesian product of m first order infinite sets is a first order infinite set. In other words, if the statement:

"A set of universes is also a universe" is true; it does not mean that the set of all possible universes is a higher order infinite.

Of course, N-infinite - the cartesian product of an infinite number of infinite sets is a second order infinite.

As I have said earlier, I'm not familiar enough with the Inflationist Theory. Can you please provide some on-line references where it is rigorously defined? Thanks.

 

 

 

 

In practice aleph0 is a "countable" infinity, where every value could have its corresponding value(see Cantors "proof.") Nothing in the inflationist theory show us that there is any sort of limit to permit each values to have their correspondances.

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Cantor proved many theoremes, which one? Thanks!

Also, what do you mean by:

1- "every value could have its corresponding value" (I'm not sure if you are talking of a "mapping" or "The Axiom of Choice!")

2- "limit to permit each values to have their correspondances" (in the context of The Inflationist Theory.)

 

Thanks.

Siamanto.

[DominO123]

Siamanto, I had access to many databases of full abstract, but since this semester I will be taking somehow a forced vaccation, I can't access them anymore.

 

I don't know of any full abstracts if someone has no member provilages to databases such as sciencedirect (that site was fun, when I was fighting against Dan racial theories ). You can search Quantum fluctuation etc. on the web.

 

The inflationist theory tries to explain the appearence of universes by Quantum fluctuation in an empty space. Like the limiting borders of black holes etc.

 

True, a set of universes could be called a universe, but still, aleph0 presupposes that it still continue to contain itself as a member of itself. When I refered to Cantors "proof" I was talking about his graphical "proof," Sip brought it in the past, I don't remember in which thread. In it, there are two lines of different side, Cantor graphical demonstration shows that there are as much number in one than the other... each "values" had a corresponding value on the other line.

 

The problem with those infinies(aleph0, etc...) is that, they have a set of rules(ex. if it this, it's aleph0, if that aleph1, ... if... alephm), but there are no given rules ordering those Universes bubbles to be created, they could just appear, billions at onces, 1 at ones, or few could appear and after that time appear in that universe, in less than a nanosecond. No rules, no anyway of given any type to the infinit in question.

[Siamanto]

The inflationist theory tries to explain the appearence of universes by Quantum fluctuation in an empty space. Like the limiting borders of black holes etc.

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I have a basic understanding of it, but not enough to answer the question whether it is alepho or not! Unfortunately, I don't have enough time to acquire a deeper understanding!

 

 

 

 

True, a set of universes could be called a universe, but still, aleph0 presupposes that it still continue to contain itself as a member of itself. When I refered to Cantors "proof" I was talking about his graphical "proof," Sip brought it in the past, I don't remember in which thread. In it, there are two lines of different side, Cantor graphical demonstration shows that there are as much number in one than the other... each "values" had a corresponding value on the other line.

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I believe that you are referring to the mapping of N-2 - or Q - into N!

 

 

 

The problem with those infinies(aleph0, etc...) is that, they have a set of rules(ex. if it this, it's aleph0, if that aleph1, ... if... alephm), but there are no given rules ordering those Universes bubbles to be created, they could just appear, billions at onces, 1 at ones, or few could appear and after that time appear in that universe, in less than a nanosecond. No rules, no anyway of given any type to the infinit in question.

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If I understand you correctly, you are saying that the operator "<" is not well defined in the set of universes! But, I'm not sure if you mean, strict order, well order or just order!

In any case, if each universe comes into existence at a certain instant - whether the Time dimension is ordered or not i.e. Arrow - than there should be a way do define an order . Even if that order may not be of interest to Quantum Mechanics, it can be of interest to Set Theorist and our purpose.

 

Maybe the following will answer the question:

If the following statement is true:

(S) "For each instant t of T - the time dimension - and for each e (epsilon) in R there is a neighborhood - as defined in topology - that includes at least one universe."

Then we can conclude that the set of universes is at least as powerful as R - the domain of T - and therefore of higher order than aleph0.

(To simplify the reasoning, we can assuming that T is ordered.)

 

Is the statement (S) above true?

[DominO123]

I was not refering to N2 or Q into R, but an R into another R.

 

http://hyeforum.com/index.php?showtopic=85...indpost&p=88685

 

This is about what an aleph0 infinit is, they can be mapped, and you'll find corresponding values for each values. The condition being that by the rule you fix somehow a limit.

 

Intersting way of seing things BTW(the statment), but I don't really agree with it, this may be true for a given number of universes that shares some similarities with ours, and interact with our own, but past that, if there is no interaction, there is no way to bring any proximity notion(epsilon, neighborhood). Your notion pressuposes that each universes has a place in a giant space, no wonder you set rules for the infinit(number of them). I think I understand now why you have used aleph0, in your conception, it contains itself, well that's what you suppose with your proximity proposition. In mine(and what the inflationist theory supposes), is that unless two universes can interact(and even if they do interact this could be true), there is no way to situate a universe in comparaison with another one. They are NOT in the same space, space being a part of our universe, and there might even be universes where space does even not exist, difficult to imagine that, but the possibility exist. Suppose at the center of a black hole where the space dimensions don't exist and where you can move in the arrow of time in two or perhaps more directions.

 

The thing is that, there is no such thing as a space containing every universes, there might be a kind of space containing some subset of universes, where many universes that share things in comment are contained in it, in such cases, when giving an infinit type we could suppose that it is aleph0, but past that, for the maximum of universes, or the possibility has no limits, no bounderies, no rules, nothing... and it is even worst when considering a kind of theory where time is not a dimention but simply a phenomenen, and every possibility is just another universe and that you change universe in each fraction of second.

[Siamanto]

I was not refering to N2 or Q into R, but an R into another R.

 

http://hyeforum.com/index.php?showtopic=85...indpost&p=88685

 

This is about what an aleph0 infinit is, they can be mapped, and you'll find corresponding values for each values. The condition being that by the rule you fix somehow a limit.

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Domino,

Thanks for the link. That's a graphical "proof" that R has the same cardinality as the ]0,1[ open interval - or any interval of R.

There's a similar graphical algorithm - an infinite two dimensional matrix - that maps NxN or Q into N.

In any case, it CANNOT be about "aleph0" infinity, because R is not countable or enumerable.

First of all, the mapping shows that both have the same CARDINALITIES: the concept of aleph0 or alephi applies to ORDINALITIES.

Second of all, R is NOT aleph0. It is debatable whether it is aleph1 or not, but definitely not aleph0.

If one accepts the Axiom of Choice, then R IS aleph0; otherwise, it is unknown!

That is a very powerful, but not very intuitive axiom.

We don't know the ordinality of R because, as of today, we DON'T KNOW any well order on R. The Axiom of Choice shows that there IS/SHOULD BE at least one well order.

 

 

Intersting way of seing things BTW(the statment), but I don't really agree with it, this may be true for a given number of universes that shares some similarities with ours, and interact with our own, but past that, if there is no interaction, there is no way to bring any proximity notion(epsilon, neighborhood). Your notion pressuposes that each universes has a place in a giant space, no wonder you set rules for the infinit(number of them). I think I understand now why you have used aleph0, in your conception, it contains itself, well that's what you suppose with your proximity proposition. In mine(and what the inflationist theory supposes), is that unless two universes can interact(and even if they do interact this could be true), there is no way to situate a universe in comparaison with another one. They are NOT in the same space, space being a part of our universe, and there might even be universes where space does even not exist, difficult to imagine that, but the possibility exist. Suppose at the center of a black hole where the space dimensions don't exist and where you can move in the arrow of time in two or perhaps more directions.

 

The thing is that, there is no such thing as a space containing every universes, there might be a kind of space containing some subset of universes, where many universes that share things in comment are contained in it, in such cases, when giving an infinit type we could suppose that it is aleph0, but past that, for the maximum of universes, or the possibility has no limits, no bounderies, no rules, nothing... and it is even worst when considering a kind of theory where time is not a dimention but simply a phenomenen, and every possibility is just another universe and that you change universe in each fraction of second.

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I'll reply to this tomorrow!

For now, let me just let you know that (S) was simply an attempt to map the set of universes into R! More later!

It seemed to me that you have read too much into it. Also, the boundaries between Mathematics - formalism - and Physics - Reality - SEEM??? - I have to read more carefully - somehow fuzzy in your interpretation! Tomorrow!

[Siamanto]

If the following statement is true:

  (S)  "For each instant t of T - the time dimension - and for each e (epsilon) in R there is a neighborhood - as defined in topology - that includes at least one universe."

Then we can conclude that the set of universes is at least as powerful as R - the domain of T - and therefore of higher order than aleph0.

(To simplify the reasoning, we can assuming that T is ordered.)

 

Is the statement (S) above true?

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Intersting way of seing things BTW(the statment), but I don't really agree with it, this may be true for a given number of universes that shares some similarities with ours, and interact with our own, but past that, if there is no interaction, there is no way to bring any proximity notion(epsilon, neighborhood). Your notion pressuposes that each universes has a place in a giant space, no wonder you set rules for the infinit(number of them).

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Domino,

AT NO TIME, I have talked about SPACE and PROXIMITY. Epsilon is a metrics defined in T(ime) - ordered or not - and "neighborhood" is a concept of Topology ("voisinage" in French) and has nothing to do with space!

(For instance, in R - assuming the natural distance as metrics - an interval is a "neighborhood.")

I have chosen T i.e. Time, because, based on your description, it seemed that a universe comes into existence at a certain instant and can be characterized by that instant i.e. to each instant t we can associate a set Ut of all universes that come into existence at time t.

 

 

 

 

I think I understand now why you have used aleph0, in your conception, it contains itself, well that's what you suppose with your proximity proposition.

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Nothing in the definition of aleph0 indicates that a set should - or should not - contain itself. N is the reference aleph0 and I son't see in what way it "contains itself!"

Do you mean something else?

 

 

 

In mine(and what the inflationist theory supposes), is that unless two universes can interact(and even if they do interact this could be true), there is no way to situate a universe in comparaison with another one. They are NOT in the same space, space being a part of our universe, and there might even be universes where space does even not exist, difficult to imagine that, but the possibility exist. Suppose at the center of a black hole where the space dimensions don't exist and where you can move in the arrow of time in two or perhaps more directions.

 

The thing is that, there is no such thing as a space containing every universes, there might be a kind of space containing some subset of universes, where many universes that share things in comment are contained in it, in such cases, when giving an infinit type we could suppose that it is aleph0, but past that, for the maximum of universes, or the possibility has no limits, no bounderies, no rules, nothing... and it is even worst when considering a kind of theory where time is not a dimention but simply a phenomenen, and every possibility is just another universe and that you change universe in each fraction of second.

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Please read my reply above: your reply is based on assumptions that were not implied or stated by my hypothesis! Thanks!

Edited January 12, 2005 by Siamanto

[DominO123]

Sorry that it took me so long to answer, I was discussing with an idiot denialist.

 

I think I was not clear when I brought Cantors mapping, true it is not about aleph0, but the idea of mapping is there, because any given interval will find any corresponding values and regardless of the bounderies, unless they are undeterminated. I posted more as an example of "containing itself." Cartors aleph0 equaled |N|, but the idea for him about both was the same(mapping two series of ellements).

 

AT NO TIME, I have talked about SPACE and PROXIMITY. Epsilon is a metrics defined in T(ime) - ordered or not - and "neighborhood" is a concept of Topology ("voisinage" in French) and has nothing to do with space!

(For instance, in R - assuming the natural distance as metrics - an interval is a "neighborhood.")

I have chosen T i.e. Time, because, based on your description, it seemed that a universe comes into existence at a certain instant and can be characterized by that instant i.e. to each instant t we can associate a set Ut of all universes that come into existence at time t.

 

But still, "situating" and locating like this can't be possible(I don't think so), space or time, it would not change the fact that you can not situate universes like this, "time" dimention for one set of universe could be incompatible for another set of universe, just like space, it is true that some theories supposes a compatibility of space and time, and I do agree that there are subset of universes in which there is some compatibility, but not for all of them. What you did is to somehow change the space dimention in Hilberts Space with a time dimention, but I don't think you have resolved the problem. You are probably asking yourself right now, what is a better description of all the universes other than taking all possible universes of our past present and future, and I think it was my falt for having induced you in this, because that's what I've said... but what I meant was all kind of possible universes in any possible direction of times in every time dimentions that we don't have here as well, they can be circular, hyperbolic, parabolic, sinusoidal, I don't know.

 

Nothing in the definition of aleph0 indicates that a set should - or should not - contain itself. N is the reference aleph0 and I son't see in what way it "contains itself!"

Do you mean something else?

 

N is in N, Neumanns Hierarchy shows us that N is inclusive of itself as a member of itselfs, it includes and contains itselfs, by the same token, we can as well say the same for |N|, so as aleph0.

Edited January 12, 2005 by Fadix

[Siamanto]

I think I was not clear when I brought Cantors mapping, true it is not about aleph0, but the idea of mapping is there, because any given interval will find any corresponding values and regardless of the bounderies, unless they are undeterminated. I posted more as an example of "containing itself." Cartors aleph0 equaled |N|, but the idea for him about both was the same(mapping two series of ellements).

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1- What do you mean by "undeterminated?" What is an "undeterminated" interval or set?

2- Would you please define "containing itself?" Thanks!

My impression is that at times you use it as in the "union of sets of a set" and at times as "having same cardinality as a subset!"

Let's please agree on a definition and stick to it! The confusion is misleading!

3- The "graphical proof" you have mentioned CANNOT be about aleph0 or N! It assumes continuity and is obviously a mapping from R - for instance - into R!

4- There are mappings of subsets of N into N such as from {2n| where n is in N} into N. Such subsets are called "ideals" in Group Theory.

 

 

 

 

But still, "situating" and locating like this can't be possible(I don't think so), space or time, it would not change the fact that you can not situate universes like this, "time" dimention for one set of universe could be incompatible for another set of universe, just like space, it is true that some theories supposes a compatibility of space and time, and I do agree that there are subset of universes in which there is some compatibility, but not for all of them. What you did is to somehow change the space dimention in Hilberts Space with a time dimention, but I don't think you have resolved the problem. You are probably asking yourself right now, what is a better description of all the universes other than taking all possible universes of our past present and future, and I think it was my falt for having induced you in this, because that's what I've said... but what I meant was all kind of possible universes in any possible direction of times in every time dimentions that we don't have here as well, they can be circular, hyperbolic, parabolic, sinusoidal, I don't know.

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Again, you are reading too much into the statement that I have submitted to either prove or disprove!

Let's get there step by step without jumping too high!

 

1- You have stated that universes come into existence and "pop up." That means that they can be CHARACTERIZED - not IDENTIFIED - by the instant t of T when they come into existence.

In other words:

(P1) There is a mapping from U - the set of universes - into T i.e. Time.

(Note, I did not say from T into U. I'm not sure there exists a mapping from T into U!)

Before we continue, do you agree that (P1) is true?

 

 

 

N is in N, Neumanns Hierarchy shows us that N is inclusive of itself as a member of itselfs, it includes and contains itselfs, by the same token, we can as well say the same for |N|, so as aleph0.

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I'm not sure what you mean!

Von Neumann showed that starting with the empty set, we can construct - using the "union of sets of a set" - a set that has the same structure as N.

Some of those who believe in Von Neumann's Set Theory, deny the existence of aleph0! Let's not get there!

[DominO123]

Siamanto, I will be answering you in another thread if you don`t mind.

[DominO123]

http://statsman.info/folding2stats/html/39937.html

 

I don't like it, it isn't enough.

[vava]

Seems we're stalling around 660... Domino, have you stopped promoting??

[DominO123]

Sorry Vava for my late answer.

 

No one seems to really care about it. Perhaps someone could install them in Armenian school computers?

 

How many there is in LA? Azatig?

[vava]

Sorry Vava for my late answer.

 

No one seems to really care about it. Perhaps someone could install them in Armenian school computers? 

 

How many there is in LA? Azatig?

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I'm not sure how many cared, (really cared, I mean) at the beginning. But we came together under your banner & vision. If you stop promoting/cheerleading, everyone will simply stop eventually. You are the key, Mr. Fadixian.

[ExtraHye]

I have a dumb question. Why is my score only 5173? Thought it would be higher with 54 WU's?

[DominO123]

I have a dumb question.  Why is my score only 5173?  Thought it would be higher with 54 WU's? 

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All WU are not equal.

 

BTW Vava, what you think of using chain emails?

[vava]

BTW Vava, what you think of using chain emails?

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Chain e-mails? I'm not a fan - i think they discredit whatever 'cause' they're meant to serve. A well managed 'e-campaign' is another question.

[DominO123]

Chain e-mails? I'm not a fan - i think they discredit whatever 'cause' they're meant to serve. A well managed 'e-campaign' is another question.

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And where is the list of email address that I shall sent the message to?

 

BTW, we are at about 600 simething, we need only few dozens of new CPUs, and we could be top 100, and a little better, and we could even expect number 1.