Does Infinity Exist in the Universe?

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The discussion centers on the existence of infinity in the universe, with participants debating whether infinity is a tangible reality or merely a human concept. Some argue that empirical evidence does not support the existence of infinity, asserting that all known quantities are finite. Others suggest that the universe may be finite yet boundless, challenging the notion of a definitive beginning or end. The Big Bang is referenced as an event that describes the observable universe's expansion, but interpretations vary on whether it implies a finite or infinite universe. Ultimately, the conversation highlights the complexities of understanding infinity and existence within the framework of cosmology.
  • #31
Originally posted by Doron Shadmi

And VIOLENCE is a form of using energy to destroy complex systems indiscriminately, or in another words, to increase their entropy.

Please be aware to the difference between COMPLEX to COMPLICATED.

Complex systems are based on simple principles that give them the ability to become energy savers.

And being an energy saver means: maximum results out of minimum energy, which implies minimum entropy.

So through this point of view, the model of INFINITY is:

Nor-begining-never-ending zero-entropy that aware to itself. [/B]



Ahoy there again Doron...

and anyone else who would like to respond...

If a system is closed, is it considered stable?

Is a stable system, therefore, one which is more inclined toward entropy?

Or...

Is a stable system one which is NOT closed and is, as you put it 'in communication with' other systems, that is, in a recipricol relationship of exchange with other systems? And therefore LESS inclined toward entropy?

Can you give me examples of how this theory operates in the natural world, apart from in human interactions?

Thanks
 
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  • #32
Hi Carla,

Through my point of view, there are connections between structure's symmetry-degree and information's clarity-degree.

High Entropy means maximum level of redundancy and uncertainty, which are based on the highest symmetry-degree of some system.

For example let us say that there is a piano with 3 notes and we call it 3-system :

DO=D , RE=R , MI=M

The highest Entropy level of 3-system is the most left information's-tree, where each key has no unique value of its own, and vice verca.

Code: 
<-Redundancy->
    M   M   M  ^<----Uncertainty
    R   R   R  |    R   R
    D   D   D  |    D   D   M       D   R   M
    .   .   .  v    .   .   .       .   .   .
    |   |   |       |   |   |       |   |   |
3 = |   |   |       |___|_  |       |___|   |
    |   |   |       |       |       |       |
    |___|___|_      |_______|       |_______|
    |               |               |

An example of 4-notes piano:

DO=D , RE=R , MI=M , FA=F
Code: 
------------>>>

    F  F  F  F           F  F           F  F
    M  M  M  M           M  M           M  M
    R  R  R  R     R  R  R  R           R  R     R  R  R  R
    D  D  D  D     D  D  D  D     D  R  D  D     D  D  D  D
    .  .  .  .     .  .  .  .     .  .  .  .     .  .  .  .
    |  |  |  |     |  |  |  |     |  |  |  |     |  |  |  |
    |  |  |  |     |__|_ |  |     |__|  |  |     |__|_ |__|_
    |  |  |  |     |     |  |     |     |  |     |     |
    |  |  |  |     |     |  |     |     |  |     |     |
    |  |  |  |     |     |  |     |     |  |     |     |
    |__|__|__|_    |_____|__|_    |_____|__|_    |_____|____
    |              |              |              |

4 =
                                   M  M  M
          R  R                     R  R  R        R  R
    D  R  D  D      D  R  D  R     D  D  D  F     D  D  M  F
    .  .  .  .      .  .  .  .     .  .  .  .     .  .  .  .
    |  |  |  |      |  |  |  |     |  |  |  |     |  |  |  |
    |__|  |__|_     |__|  |__|     |  |  |  |     |__|_ |  |
    |     |         |     |        |  |  |  |     |     |  |
    |     |         |     |        |__|__|_ |     |_____|  |
    |     |         |     |        |        |     |        |
    |_____|____     |_____|____    |________|     |________|
    |               |              |              |


    D  R  M  F
    .  .  .  .
    |  |  |  |
    |__|  |  |
    |     |  |
    |_____|  |
    |        |
    |________|
    |
So, through this example, to be a creative unique person means low-entropy personality.

And by being a creative and unique person , we are no longer afraid to be opened systems to another creative and unique persons.

(please don't take what I wrote personally):wink:
 
Last edited by a moderator:
  • #33
Originally posted by Doron Shadmi
Hi Carla,

Through my point of view, there are connections between structure's symmetry-degree and information's clarity-degree.

High Entropy means maximum level of redundancy and uncertainty, which are based on the highest symmetry-degree of some system.

For example let us say that there is a piano with 3 notes and we call it 3-system :

DO=D , RE=R , MI=M

The highest Entropy level of 3-system is the most left information's-tree, where each key has no unique value of its own, and vice verca.

Code: 
<-Redundancy->
    M   M   M  ^<----Uncertainty
    R   R   R  |    R   R
    D   D   D  |    D   D   M       D   R   M
    .   .   .  v    .   .   .       .   .   .
    |   |   |       |   |   |       |   |   |
3 = |   |   |       |___|_  |       |___|   |
    |   |   |       |       |       |       |
    |___|___|_      |_______|       |_______|
    |               |               |

An example of 4-notes piano:

DO=D , RE=R , MI=M , FA=F
Code: 
------------>>>

    F  F  F  F           F  F           F  F
    M  M  M  M           M  M           M  M
    R  R  R  R     R  R  R  R           R  R     R  R  R  R
    D  D  D  D     D  D  D  D     D  R  D  D     D  D  D  D
    .  .  .  .     .  .  .  .     .  .  .  .     .  .  .  .
    |  |  |  |     |  |  |  |     |  |  |  |     |  |  |  |
    |  |  |  |     |__|_ |  |     |__|  |  |     |__|_ |__|_
    |  |  |  |     |     |  |     |     |  |     |     |
    |  |  |  |     |     |  |     |     |  |     |     |
    |  |  |  |     |     |  |     |     |  |     |     |
    |__|__|__|_    |_____|__|_    |_____|__|_    |_____|____
    |              |              |              |

4 =
                                   M  M  M
          R  R                     R  R  R        R  R
    D  R  D  D      D  R  D  R     D  D  D  F     D  D  M  F
    .  .  .  .      .  .  .  .     .  .  .  .     .  .  .  .
    |  |  |  |      |  |  |  |     |  |  |  |     |  |  |  |
    |__|  |__|_     |__|  |__|     |  |  |  |     |__|_ |  |
    |     |         |     |        |  |  |  |     |     |  |
    |     |         |     |        |__|__|_ |     |_____|  |
    |     |         |     |        |        |     |        |
    |_____|____     |_____|____    |________|     |________|
    |               |              |              |


    D  R  M  F
    .  .  .  .
    |  |  |  |
    |__|  |  |
    |     |  |
    |_____|  |
    |        |
    |________|
    |
So, through this example, to be a creative unique person means low-entropy personality.

And by being a creative and unique person , we are no longer afraid to be opened systems to another creative and unique persons.

(please don't take what I wrote personally):wink:


If I don't take what you wrote personally, what will I learn? Was there a possible insult somewhere in your words? If there was, it went right over my head. :)

I'm actually enjoying the ride immensely.
 
  • #34
Carla, can a person can't take things personally ?

By your question you give the answer.

The eye does not see itself until it is aware to its limitations, and than it can be included as an explored element.

Now please change "eye" by "personality" and read the above again.

For example, let us explore our abilities to create the Math language.


The above point of view leaded me to ask myself what are the minimal conditions that gives us the ability to identify and count things?

For example, let's examine this situation:

On the table there is finite unknown quantity of identical beads
and we have:

A) To find their sum.

B) To be able to identify each bead.

Limitation: we are not allowed to use our memory.

By trying to find the total quantity of the beads (represent the discreteness concept) without using our memory (represents the continuum concept) we find ourselves stuck in 1, so we need an association between continuum and discreteness if we want to be able to find the bead's sum.

Let's cancel our limitation, so now we know bead's sum which is, for example, value 3.

Now we try to identify each bead, but they are identical, so we identify each of them by its place on the table.

But this is an unstable solution, because if someone takes the beads, put them between his hands, then shake them and put them back on the table, then we lost their id.

Each identical bead can be the bead that was identified by us before it was mixed with the other beads.

We shall represent this situation by:

((a XOR b XOR c),(a XOR b XOR c),(a XOR b XOR c))

By notate a bead as 'c' we get:

((a XOR b),(a XOR b),c)

and by notate a bead as 'b' we get:

(a,b,c)

We satisfy condition B but (and this is the important thing) through this process we define a universe, which exists between continuum and discreteness concepts, and can be systematically explored and be used to make Math.

More detailed information of my new theory of numbers, you can find here:

http://www.geocities.com/complementarytheory/CATpage.html


Yours,

Doron
 
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  • #35
Hi Doron

I had a look at your site. I got the basic gist (workings) of it. I am not a mathematician so am not sure how it will revolutionise maths. It seems to be a fractal- based system or rather, a fractal tool for exploring systems and ?efficiency. How does it differ from math as it is practised now? What have been the general reactions to your theory?
I think your efforts show some courage. You seem very excited about it!
 
  • #36
Hi Carla,

My overview describes a non-conventional perception of the continuum concept, and the minimal structure of a NUMBER.

As I wrote to you in the previous post, through my point of view, Math Langauge must include our cognition’s abilities to develop it, as a legal part of its research.

By doing this, we may avoid some possible hidden assumptions that can be in the basis of our axiomatic systems.

Through this attitude, I have found that the minimal conditions that gives us the ability to identify and count elements, is strongly based on our ability to associate between some counted elements and our memory.

If ,by analogy, "some elements" means beads, and our memory is a string, then any number which is not 0, can't be less than some necklace.

Most of the Modern Math axiomatic systems are based on the SET concept.

A SET is a finite or infinite collection of objects in which order has no significance, and multiplicity is generally also ignored.

We notate a SET by {}.

The simplest set is the empty set = {} , which means a SET with on objects.

By Math language we use the word "members" instead of "objects".

So, any non-empty set includes some finite or infinite collection of members, and its name depends on some common property of these members.

When mathematicians (the first one was Cantor) researched the properties of some infinite collections of numbers, they discovered that there is more than one level of infinite.

Actually there are infinitely many levels of infinities.

The first infinite level is called the countable infinity and the second type that have been discovered is called the uncountable infinity.

The continuum is the uncountable infinity and above it there are infinitely many levels of infinities, that Modern Math research tries to find and define.

Another question in Modern Math is the Continuum Hypothesis (CH), which tries to find if there is or there is not some infinite set between the countable and the uncountable sets.

Modern Math describes the Continuum as: "Infinitely many points with no gaps between them"

Through my research I have found that it is impossible to define the Continuum by a tool, which has exactly it opposite property.

A continuous line is a non-localized element, and a point is a localized element, so any exploration of a continuous line by infinitely many points, is as if we say:

"If you want to see the darkness, please turn on the lights".

Instead of forcing the continuum to be expressed by its opposite, I associate them without forcing one opposite property on the other, and got a new points of view on these concepts:

Continuum, Discreteness, Number, Infinity, Information, Symmetry and Cognition's abilities to create Math, as a part of Math research.


Professional mathematicians will not accept it, because I change a lot of fundamental paradigms of Modern Math, by this point of view.

Yours,

Doron
 
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  • #37
Ok guys,

I'm going to move this thread to Theory Development (which is under "theoretical physics").
 
  • #38
Carla,
I would not recommend Doron as a primary source for conventional Math/Physics. If you ever wish to learn the conventional view point you will pretty much have forget everything you have read from his material. It is unconventional to say the least.


As for your inital question, I do not believe there is any connection between an open and closed system and stability. That is an entirely separate issue.

ALL Systems are subject to entropy. Entropy is a funamental thermodynamic quantity which canbe computed for any system.
 
  • #39
Hi Carla,
Carla,
I would not recommend Doron as a primary source for conventional Math/Physics. If you ever wish to learn the conventional view point you will pretty much have forget everything you have read from his material. It is unconventional to say the least.
I agree with integral, never take any source as primary source because someone told you to do so.

It is a good idea to know the conventional picture of the above, by finding some good material on it, and then you will decide by yourself
what is your point of view on this subject.

For example, some sources to start with:

Cantor's diagonal's second proof:
http://home.ican.net/~arandall/abelard/math12/Cantor.html

The paper "Logic and Mathematics" is a survey of logic and foundations of mathematics, for the general reader by Stephan G. Simpson, a mathematician at the Pennsylvania State University:
http://www.math.psu.edu/simpson/papers/philmath.pdf

This covers a bit about what numbers are, and how to define them:
http://hemsidor.torget.se/users/m/mauritz/math/num/index.htm

University of Toronto Mathematics Network:
http://www.math.toronto.edu/mathnet/plain/answers/answers.html

The real number system:
http://www.jamesbrennan.org/algebra/numbers/real_number_system.htm

Cauchy Sequences of Rationals:
http://www.mathreference.com/top-ms,real.html

An example of formal detailed paper on the construction of the real number system:
http://www.math.nus.edu.sg/~urops/Projects/RealNumbers.pdf

Math and truth:
http://faculty.juniata.edu/esch/neatstuff/truth.html

The Infamous .999... = 1 :
http://mathforum.org/library/drmath/view/55748.html

And just for the balance, here you can find some historical non-conventional point of view on the Continuum:
http://www.angelfire.com/super/magicrobin/peirce.htm



I hope Integral will add its own list.

Yours,

Doron
 
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  • #40


Originally posted by carla
Hi

In terms of the cosmos, which I think is the right word I need to describe 'what's out there', would it be fair to say that infinity exists? I mean, even if the universe was not infinite and was some sort of expanding phenomena, or was circular, it must be expanding against something or, if circular, surrounded by something. So 'somethingness' just goes on and on and on...maybe changing shape or form or just void...but infinity, in this sense, exists?
It's possible that the universe is infinitely large. As such it's also possible that the universe has an infinite amount of matter in it. But no, the universe is not expanding against anything and its not surrounded by anything.

Pete
 
  • #41
Integral : I never intended to take anyone's word as being true beyond all dispute. I gratefully accept your warning in that light. I come here to learn what I can with the understanding that even conventional science and all of its members, are usually in heated debate over one theory or another. I guess the term 'mad scientist' did not come to usage without any basis. You could probably name more historical figures in science and maths than I could, however, who by their daring and illogic in the face of conventional understanding and knowledge, added to that understanding and knowledge.
 
  • #42
Game, set, match.
Paden Roder
 
  • #43
Originally posted by quantum
The concept of infinity must exist in some form, even if not yet discovered. I personally believe that the universe is infinite, and in that case infinity exists in a very obvious form, but when we suppose that the universe is finite it is significantly more difficult to spot latent infinities... Possibly somewhere in string theory or something related there may lie infinities...
That statement is actually the problem, 'thinking' that "infinite" is (somehow) a concept, it isn't, it is unconceivable.

Otherwise, please explain to me how you can 'think' of anything that is "boundless", it simple doesn't work, cause infinity is an "ideal" that we cannot substantiate, nor prove as unsubstantial.
(Not to go off the off topic)
 
  • #44
Originally posted by Doron Shadmi
Hi Carla,

I think that the closest thing is the relation between theory and experiment
in applied science, and consistent axiomatic systems in pure science.

They are all related in some deep connections between our internal and external sides.

In both applied and pure methods there is the seek after some elegant simplicity, that on one hand can help us to survive as complex systems, and on the other hand can give us the reasons to be a part of its wonders.

One of the most beautiful things in science is its language: Mathematics.

This is the most powerful tool that was developed by the evolution process.

But this tool, without open heart and mind to ourselves as participators in this world, is the most deadly tool.

Yours,

Doron
To create exact model of object and to create object itself is an equivalent. The mathematics has very few opportunities of success in this process. At all its importance, mathematics is an applied science. In my opinion, all attempts to describe the universe by formulas are useless expenditure of time (by the way time has no any mathematical definition). To predict behavior of complex system intuitively or to calculate under some invented formulas. What is more effective?
 
  • #45
Hi Michael F. Dmitriyev ,

As I understand it, any model of X is never X itself, so in my opinion, this "gap" between the model of X and X, is going to stay forever.

Mathematics is first of all a kind of language, and any language has this beautiful ability to connect between unique self awared systems.

Like any lanugage, we cannot know exactly how mathematics is going
to be developed in the next years, because there are a lot of insights
that are coming from a lot of different close an far areas, that can change this language deeply.

For example look at my website:

http://www.geocities.com/complementarytheory/CATpage.html

where you can find a non-standard point of view on the discreteness and the continuum concepts in the Mathematics language.
 
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  • #46
Originally posted by Doron Shadmi
Hi Michael F. Dmitriyev ,

As I understand it, any model of X is never X itself, so in my opinion, this "gap" between the model of X and X, is going to stay forever.
Hi Doron Shadmi.
You are right in part. Your statement is fair for X, created by the nature. Here we try to create model of existing object. For objects created by the person, a “gap” between X and the model of X is absent. The sequence of actions in this case is inverse. First we create the model of object, and then we reproduce this model as object.
 
  • #47
One only existing infinity is the infinity of information.
 

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