Does Infinity Exist in the Universe?

[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?

 

[BiologyForums]

No.

Contrary to what some might say, infinite does not exist in reality. There is not a single thing known to be at infinite.

No scalars, and no vectors. No speeds no quantities, no nothing. There is no empirical evidence to suggest anything in existence carries a value of infinity.

Without this evidence infinity is merely a concept created in the human mind.

 

[BiologyForums]

...and this directly fits into what you described. If we say for instance that the universe currently fits into finite amounts (which it does) then you say what about beyond the universe?

That's part of the human experience - that many cannot accept non-existance.

Beyond our universe - if we are the only one - lies ______.

I didn't say lies nothing, because it's not nothing. Technically it is not something and it is not nothing. Nothing is a lack of something - but this is so much more than a lack of nothing!

It breaches existence and pretty the ability to understand. It's like an unspoken non-coordinate. "Nothing" is in fact part of existence. But what is beyond that isn't in existence!

 

[carla]

That was a speedy reply. Thankyou.

It is a conceptual problem isn't it? Nothingness and infinity are both creations of the human mind.

But I still can not help but arrive at the conclusion that there is no end...no finality.

Being a conceptual problem, it's also a problem of language, I guess. Like the theory of parallel universes...there is only one universe, really, with possible multi-variations.

 

[BiologyForums]

Originally posted by carla
That was a speedy reply. Thankyou.

It is a conceptual problem isn't it? Nothingness and infinity are both creations of the human mind.

But I still can not help but arrive at the conclusion that there is no end...no finality.

Being a conceptual problem, it's also a problem of language, I guess. Like the theory of parallel universes...there is only one universe, really, with possible multi-variations.

Well I wouldn't say it's necessarily a problem. It's a matter of creative thinking I guess. It's a problem when people fight the truth with it :)

Well with the entire parallel universe thing, I gather what happened was the meaning of the term universe changed, or adapted I should say!

Universe meant everything, before.

Now it's used to mean the entirity of one everything. Because remember between each universe of everything is that ___ nothingness I mentioned earlier.

So we kind of moved from using it as a term for all that is, was, and will be, to a practical term distinquishes one entire closed system from another.

 

[marcus]

Originally posted by carla


...But I still can not help but arrive at the conclusion that there is no end...no finality.

Being a conceptual problem, it's also a problem of language, I guess...

I believe the root meaning of infinity is "unboundedness"

If one can specify a bound on something then it is is finite-----goes only this far and no further

If one cannot specify a bound to the thing then it is unbounded or non-finite.

Latin noun: finis----boundary, limit
Latin verb: finire----to set a bound, to limit

Some people (children, mathematicians) may speak of "infinity" as a number---as if some physical quantity could have "value equal to infinity"---but that is apt to be either a specialized technical use of the word or an innocent misconception. In its commonplace meaning, infinity is not a number but simply the absence of boundaries and limits.

It would strike me as absurdly pretentious to claim that one can assign bounds to all physical quantities or that all quantities are bounded. I don't know if anyone here is doing that.

In conventional cosmology there is no upper bound on the distance between two objects in space

if you choose two specific objects, the distance between them can be some definite quantity, but the set of possible distances is not considered to have an upper limit

assuming a limit would complicate things----unnecessary conceptual baggage

carla, I am sure you know the principle of Occam's razor, but please reassure me that you do! The unboundedness of some physical quantities is assumed, I would guess, very largely for reasons of SIMPLICITY (because introducing bounds where we do not know they exist would be to add a lot of clumsy unnecessary paraphernalia---a lot of junk).

And there are quantities actually known to be bounded, where one can specifically say what the bound is, which is great! But let's not generalize from that and pretend to know an upper limit for everything.

 

[carla]

I know what Occam's razor is now. Thanks. That's actually useful information.

 

[LURCH]

Originally posted by marcus
I believe the root meaning of infinity is "unboundedness"

In general usage I would agree. But that may be changing. In cosmology, the concept of a "finite but boundless" universe is a familiar idea. As cosmological concepts become popularised in mainstream society, the idea is making its way into the public mind.

It's a bit dogy to describe, though, and can be said to merely move the "boundary" to a higher dimension.

 

[Integral]

Not sure where this is much about Physics, I'll bump it to math, perhaps should be in General.

 

[heusdens]

Originally posted by BiologyForums
No.

Contrary to what some might say, infinite does not exist in reality. There is not a single thing known to be at infinite.

No scalars, and no vectors. No speeds no quantities, no nothing. There is no empirical evidence to suggest anything in existence carries a value of infinity.

Without this evidence infinity is merely a concept created in the human mind.

In the empirical sense, infinity does not exist.

But what is against the idea that the universe carries onwards in time without a begin or end?

It can't be obviously measured, it can only be infered from:
- causality
- conservation of energy/mass

And a logic argument pro no-begin of time and no-end of time is this:

If the world (all that exists) is said to have had a begin in time, then all it can have begun from is from nothing.

But nothing is not a begin. Nothing is only nothing.

 

[BiologyForums]

Heusdens - the second half of your post is nonsensical. This is an argument too many people attempt to use, this "nothing can come from nothing" thing which doesn't work in the real world.

The first half is fine.

Let's recall that the big bang is the energy source of the universe expanding.

The big bang expanding created the spatial dimensions - thus the universe is finite. It's that simple.

In short - the Big Bang could not have occurred if the universe is infinite - and the Big Bang has mounds of evidence.

Originally posted by heusdens
In the empirical sense, infinity does not exist.

But what is against the idea that the universe carries onwards in time without a begin or end?

It can't be obviously measured, it can only be infered from:
- causality
- conservation of energy/mass

And a logic argument pro no-begin of time and no-end of time is this:

If the world (all that exists) is said to have had a begin in time, then all it can have begun from is from nothing.

But nothing is not a begin. Nothing is only nothing.

 

[Hurkyl]

The "Big Bang" is merely an event where the entirety of the observable universe was compressed into a highly dense volume, it is not the "creation" of the universe, as it is often misinterpreted. The big bang is consistent with, but does not require, an infinite universe.

 

[BiologyForums]

Originally posted by Hurkyl
The "Big Bang" is merely an event where the entirety of the observable universe was compressed into a highly dense volume, it is not the "creation" of the universe, as it is often misinterpreted. The big bang is consistent with, but does not require, an infinite universe.

This just sounds nonsensical with anything I have ever heard.

The Big Bang has never had anything to do with compression, but just the opposite. I've read plenty of Big Bang explanations including Hawking - never heard him mention anything but the opposite of what you just said.

And also that indeed the big bang does NOT coincide with an infinite universe.

 

[Hurkyl]

It seems my use of the word "compression" was misleading; I meant by that sentence that the observable universe was once in a highly dense region of space-time.

"A highly dense region of space-time" (which, of course, promptly expands) is certainly not prohibited from existing in an infinite universe.

 

[BiologyForums]

Well then if it was once more concentrated - and now it is less concentrated, and continueing to expand - how could it be infinite?

It can't be expanding if it's infinite, and it could never have been compressed if it isi infinite.

 

[carla]

Endless nothing. Endlessness. Nothing ad infinitum. Foreverness. Or just..endless. It's not a useful idea but something that has always fascinated me nevertheless. I know science requires concepts it can work with, which are useful to the human mind; empiricism, need to be able to be quantified in some way in order to fulfill scientific enquiry. It's a conceptual problem. It is impossible to even find words to adequately describe what is in my head. It almost slips into mysticism. Simply beyond reach.

 

[Hurkyl]

Infinite space can most certainly expand; expansion of space is defined locally, not globally. (A region of) Space is expanding iff nearby parallel geodesics tend to start diverging after a short period of time. Heuristically, it means that tiny dust clouds tend to grow in volume over time.


Anyways, BBT says nothing about the entire universe, just the observable universe. It asserts that some time in the distant past, our past light-cone enclosed a tiny volume.

BBT does not require that tiny volume to have been the entirety of the universe, nor does it require that the entire universe to "simultaneously" be similarly dense.

 

[BiologyForums]

You it is "our" light-cone, meaning we are lying in a region of space which comes from the expansion of this light-cone.

If our light-cone was enclosed in a tiny volume, and is now NOT in that tiny volume - it has expanded. Locally.

And if our local space-section is expanding, it cannot be infinite.

Thus if the universe were to be infinite, it could not ONLY be the results of our own expanding light-cone.

But because our expanding light defines the spatial properties and thus the universe of our expansion (because there were no spatial dimensions in this location before the existence of the matter - this comes from Greene) could not possibly be infinite.

Even if it collided with zillions of other universes, none of them could be infinite, thus the total could not be infinite.

Originally posted by Hurkyl
Infinite space can most certainly expand; expansion of space is defined locally, not globally. (A region of) Space is expanding iff nearby parallel geodesics tend to start diverging after a short period of time. Heuristically, it means that tiny dust clouds tend to grow in volume over time.


Anyways, BBT says nothing about the entire universe, just the observable universe. It asserts that some time in the distant past, our past light-cone enclosed a tiny volume.

BBT does not require that tiny volume to have been the entirety of the universe, nor does it require that the entire universe to "simultaneously" be similarly dense.

 

[Hurkyl]

But because our expanding light defines the spatial properties and thus the universe of our expansion (because there were no spatial dimensions in this location before the existence of the matter - this comes from Greene) could not possibly be infinite.

I will agree that the observable universe must be finite...

But I'm troubled by "because there were no spatial dimensions in this location before the existence of the matter - this comes from Greene"; I presume this is a statement of some sort of relativity that you can't make measurements without a reference to compare them against, but the gravitational field itself can serve to be a reference, even in the absense of matter.

It's also curious why you would bring this up anyways; BBT does not claim matter did not exist before the BB, yet you seem to imply that you think otherwise.

Even if it collided with zillions of other universes, none of them could be infinite, thus the total could not be infinite.

I'm not sure what you mean by colliding...

And while it is true that a finite collection of finite objects is finite, why would you think that the collection is finite?

 

[Doron Shadmi]

Hi Carla,


I think that Quantum Mechanics gave us a very important insight about ourselves.

We are no longer observers but full participators in our world, and there is a complementary relation between our internal end external sides.

To every thinkable concept there is an opposite and among any system of opposites there is a potential balance.

And beyond any balance the unthinkable.

And beyond the unthinkable

And beyond


Yours,

Doron

 

[carla]

Originally posted by Doron Shadmi
Hi Carla,


I think that Quantum Mechanics gave us a very important insight about ourselves.

We are no longer observers but full participators in our world, and there is a complementary relation between our internal end external sides.

To every thinkable concept there is an opposite and among any system of opposites there is a potential balance.

And beyond any balance the unthinkable.

And beyond the unthinkable

And beyond


Yours,

Doron

Hi Doron...

I'm not sure what this means. It sounds very Zen, which is not a bad thing, of course. But when I say what is 'in my head' borders on the mystical, it's not that I want it that way. It's like a truth I know is true but can not ..oh dear, I feel a kick to philosophy thread coming on... :)

 

[Doron Shadmi]

..oh dear, I feel a kick to philosophy thread coming on... :)

This is not a philosophy .


For example, there is a difference between any model that
answer to the question: "What is silence ?" , and silence itself.

Any model is on the silence, but never the silence itself.


You can change "silence" by "infinity" and 'in your head' you try
to find a model of infinity.

But again, any model is on something and never the something.

 

[carla]

Originally posted by Doron Shadmi
This is not a philosophy .


For example, there is a difference between any model that
answer to the question: "What is silence ?" , and silence itself.

Any model is on the silence, but never the silence itself.


You can change "silence" by "infinity" and 'in your head' you try
to find a model of infinity.

But again, any model is on something and never the something.

Yes, that makes sense. Does this discrepancy between the thing itself and the model have a name in the scientific world?

 

[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

 

[carla]

Originally posted by Doron Shadmi
Hi Carla,


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

As is language itself, perhaps.

 

[Doron Shadmi]

Yes, language itself is first of all a form of participation through communication.

If there is no communication we become closed systems, and closed systems find their death by entropy.


Please let me show you some interesting insight through Hebrew language (my language).

Hebrew belongs to a family of languages that are built on 'roots'.

It means that any word is built on some combination of letters, which is not a specific word.

For example: in Hebrew the words ELEM(=MUTENESS) and ALIMOOT(=VIOLENCE) are built on the same root, which is Aleph.Lamed.Mem .

Through this common root we get the insight that the one how can't express himself (=MUTE=ILEM) through communication, becomes VIOLENT(=ALIM).

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.

 

[carla]

Originally posted by Doron Shadmi
Yes, language itself is first of all a form of participation through communication.

If there is no communication we become closed systems, and closed systems find their death by entropy.


Please let me show you some interesting insight through Hebrew language (my language).

Hebrew belongs to a family of languages that are built on 'roots'.

It means that any word is built on some combination of letters, which is not a specific word.

For example: in Hebrew the words ELEM(=MUTENESS) and ALIMOOT(=VIOLENCE) are built on the same root, which is Aleph.Lamed.Mem .

Through this common root we get the insight that the one how can't express himself (=MUTE=ILEM) through communication, becomes VIOLENT(=ALIM).

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.

That is a FANTASTIC insight Doron! I'd like to sit with that for quite a good long while! Doron, here, or in another thread, could you please enlighten me as to the full implications, background and meaning of the Hebrew term 'YHWH' or Yahweh? I have been sitting with that one too. As I understand it, its etiological background was of the Sacred and Holiest Name which could not be spoken by a human tongue, which no image could be ascribed to but IS.

As for your insightful contribution, I have been thinking that human cruelty and brutality is indeed an expression of excess Cerebral cortex matter with 'no place to go'...if that makes sense. Hence the importance of Art and creative expression in general.

 

[Doron Shadmi]

Dear Carla,


Thank you for let me be understood.


The word “YEHOVA” means: HAYAH(=WAS)_HOVE(=IS)_YIHIYE(=WILL BE).


I think that one deep reason of not to say its name, is connected somehow to the difference between any thinkable model to the thing itself.

And in this case, the thing itself is the most simple, and may be we can be opened to it by being aware to this simplicity, within the most fine levels of each of us.

I think that another deep reason for not to say its name, is connected to the inflation concept, which means no uniqueness.

We care about rare or unique things (they are more close to our heart and mind) and vice versa.

May be those two examples are connected somehow to each other, to direct us to find some unique simplicity, which may be is the source of any original creativity.

And by creativity I mean in any aspect of our life on this planet (and may be beyond it).

I think that the internet is the beginning of some possibility to share our point of views with each others, without any "broker" like education systems, politicians, or any other human authority that try to tell us what is the "right" way to be a creative person.



Yours,

Doron

 

[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...

 

[clicky]

Every body is finite if it is to exist, including the universe.

 

[carla]

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

 

[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.

<-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

------------>>>

    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)

 

[carla]

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.

<-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

------------>>>

    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)

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.

 

[Doron Shadmi]

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

 

[carla]

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!

 

[Doron Shadmi]

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

 

[ahrkron]

Ok guys,

I'm going to move this thread to Theory Development (which is under "theoretical physics").

 

[Integral]

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.

 

[Doron Shadmi]

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

 

[pmb]

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

 

[carla]

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.

 

[PRodQuanta]

Game, set, match.
Paden Roder

 

[Mr. Robin Parsons]

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)

 

[Michael F. Dmitriyev]

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?

 

[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.

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.

 

[Michael F. Dmitriyev]

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.

 

[Michael F. Dmitriyev]

One only existing infinity is the infinity of information.