Exploring the Infinitude of the Universe

[radagast]

Originally posted by Mr. Robin Parsons
Logical proofs of Infinity do NOT prove that Infinity exists, they simple demonstrate an indicator that suggests that infinity is possible, nothing more.

It depends on your definition of exists, I suppose. In a defined mental construct, such as the mathematics of real numbers, the proof of an infinite number of real numbers between the number 1.0 and 2.0 is a proof of the existence of an infinity, at least constrained to within that mathematical construct.

Since common dictionary definitions of existence and exist do encompass mental constructs as well as external reality, I see this as proof of existence within the above given context.

I do not say this says anything about external, objective reality.

 

[Mr. Robin Parsons]

Originally posted by radagast
It depends on your definition of exists, I suppose. In a defined mental construct, such as the mathematics of real numbers, the proof of an infinite number of real numbers between the number 1.0 and 2.0 is a proof of the existence of an infinity, at least constrained to within that mathematical construct.

Since common dictionary definitions of existence and exist do encompass mental constructs as well as external reality, I see this as proof of existence within the above given context.

I do not say this says anything about external, objective reality.

Since infinity cannot be a concept, it cannot be a number, other then to state that 'one' of them exists.

The emboldened is only a proof that we cannot count to infinity, but suggests to us that it is a possibility, ergo neither a conclusion, nor a proof.

 

[radagast]

Originally posted by Mr. Robin Parsons
Since infinity cannot be a concept, it cannot be a number, other then to state that 'one' of them exists.

The emboldened is only a proof that we cannot count to infinity, but suggests to us that it is a possibility, ergo neither a conclusion, nor a proof.

Agreed that, by definition, an infinity isn't and cannot be a number. Your above comment seems to fall into the category of a Bifurcation Fallacy. Implicit is the assumption that an infinity has to be a number or concept to exist. Either delineate the reasons behind this assumption, or I can't see any reason to consider that argument anything but flawed.

In trying to ascertain if an infinity exists, it's definition might be important, so I've included it below:.

Infinity
NOUN: Inflected forms: pl. in·fin·i·ties
1. The quality or condition of being infinite.
2. Unbounded space, time, or quantity.
3. An indefinitely large number or amount.
4. Mathematics The limit that a function is said to approach at x = a when (x) is larger than any preassigned number for all x sufficiently near a.
5a. A range in relation to an optical system, such as a camera lens, representing distances great enough that light rays reflected from objects within the range may be regarded as parallel. b. A distance setting, as on a camera, beyond which the entire field is in focus


Now, given (by the proof) that the numeric space, or the quantity of real numbers between 1.0 and 2.0 corrosponds to an Unbounded space, time or quantity, given (by the proof) there are An indefinitely large number or amount of real numbers between 1.0 and 2.0, and given that defn 4 also seems to apply, then, inferred from the definitions and proofs given, an infinity of real numbers exists between 1.0 and 2.0.



Being you liked the word Concept, I thought I'd explore that path too.

Concept
NOUN: 1. A general idea derived or inferred from specific instances or occurrences.
2. Something formed in the mind; a thought or notion. See synonyms at idea.
3. A scheme; a plan: “began searching for an agency to handle a new restaurant concept” (ADWEEK

From how I read the definition of infinity, defn 2 does seem to also encompass the term, given it's a thought, a notion, and/or something formed in the mind. FWIW


With regards to your second paragraph, the proof does prove that the number of real numbers from 1.0 to 2.0 is unbounded - falling into the definition of infinity.

Regards,

 

[Mr. Robin Parsons]

radagast, did you read the link that I have posted on these pages? as that explains why the "concept thingy" doesn't work at all, infinity is not conceivable, that is what my linked explanation proves!

 

[Mr. Robin Parsons]

Originally posted by Radagast

Implicit is the assumption that an infinity has to be a number or concept to exist. Either delineate the reasons behind this assumption, or I can't see any reason to consider that argument anything but flawed.

As per my original explanation, (the link on the first page) I make no assumptions, because, all you can do is profess a belief; either it exists, or it doesn't, there is "NO proving"!

EDIT /SWITCH

 

[subtillioN]

Originally posted by Mr. Robin Parsons

The emboldened is only a proof that we cannot count to infinity, but suggests to us that it is a possibility, ergo neither a conclusion, nor a proof.

The proof that I am talking about is quite different indeed. It is not a mathematical proof but a metaphysical proof. (relating to the true nature of physical reality vs. a mere quantification of it)

 

[radagast]

Irrespective of your previous link (which I haven't read, yet), I fail to see the problem with the logic I've presented.

Just an impression, but it almost as if you're (only from the posts in this thread, since I haven't read your link), trying to define terms such that infinities cannot exist under your definitions.

 

[Mr. Robin Parsons]

Originally posted by radagast
Irrespective of your previous link (which I haven't read, yet), I fail to see the problem with the logic I've presented.

Just an impression, but it almost as if you're (only from the posts in this thread, since I haven't read your link), trying to define terms such that infinities cannot exist under your definitions.

Might I then suggest you read it, https://www.physicsforums.com/showthread.php?threadid=1438&perpage=15&pagenumber=11" at the Fourth post down, (My posting) and then you/we can discuss it better(?)

 

[radagast]

Originally posted by Mr. Robin Parsons
As per my original explanation, (the link on the first page) I make no assumptions, because, all you can do is profess a belief; either it exists, or it doesn't, there is "NO proving"!

EDIT /SWITCH

But this goes back to my initial statement that it depends on how you define exists.

Given the mathematical induction proofs, the standard definitions of the words exists, and infinity, it can be shown to exist.

Perhaps I'm missing some subtle way in which you are approaching this, but it seems fairly straightforward to me.

You do have me a little baffled at your use of words though, either it exists, or it doesn't, there is "NO proving"!

My right hand exists or it doesn't, but that doesn't keep me from proving it. You seem to be using the term exists as if it implicitly refers to objective reality, rather than (in this case) a conceptual construct, such as mathematics. If so, then I concede (and have already) that none of my arguments have been intended to reflect objective reality, with respect to infinities.

Profession of beliefs, as you use it, refers to things that cannot be known, via proof (if I get what you're saying), yet mathematical constructs are ideas delineated, with rules of interaction, which enable us to determine, thru the use of said rules, along with logic, if certain things are true or not. In this case, I cannot see anything but that it's been proven.

 

[radagast]

Having read your post, I still fail to see your point on infinities and their existence.


First:
All of the thoughts in our heads are 'delineations of space', hence we can conclude that an 'undelineated space', a 'space without boundaries', is something that we cannot conceive of.


A) the above is a definition designed to prevent a specific conclusion, I'm sure it's an argument flaw, but don't have the time to look it up at the moment. To say that all the thoughts in our heads are 'delineations of space', is not something I would concede.

Disregarding that point -
B) This may be a matter of semantics, i.e. how you define conceive differing from mine, but I have had little problem in conceiving the Euclidean 'line', which is infinite. That my mind cannot completely encompass it's entire space doesn't mean I cannot conceive of a line.

 

[Mr. Robin Parsons]

Originally posted by radagast
Having read your post, I still fail to see your point on infinities and their existence.

A) the above is a definition designed to prevent a specific conclusion, I'm sure it's an argument flaw, but don't have the time to look it up at the moment. To say that all the thoughts in our heads are 'delineations of space', is not something I would concede.

Disregarding that point -
B) This may be a matter of semantics, i.e. how you define conceive differing from mine, but I have had little problem in conceiving the Euclidean 'line', which is infinite. That my mind cannot completely encompass it's entire space doesn't mean I cannot conceive of a line.

Yes, and your concept of a line is a delineation of space, ergo "concievable"

And as per the Emboldened part of the quote of you, you sort of have that wrong it is designed to reach a specific conclusion that being the Proving of the fact of the in-conceivability of infinite.

EDIT /switch

 

[radagast]

Yet I can conceive Euclidean line, which by definition is infinite.

 

[Mr. Robin Parsons]

Originally posted by radagast
Yet I can conceive Euclidean line, which by definition is infinite.

Yes! in your imagination you can conceive of a Euclidian line, but as anyone who studies reality, by structures, knows that the 'straight' line is a misnomer, it is a series of POINTS, as all structures, in physics, at atomic levels, currently known, are spherical.

3D

Yes, and in your imagination you can fool yourself into thinking that it is infinite, but in the reality that physics studies, well, proving that one is admitted as impossible, soooo...

 

[subtillioN]

Originally posted by Mr. Robin Parsons
Yes! in your imagination you can conceive of a Euclidian line, but as anyone who studies reality, by structures, knows that the 'straight' line is a misnomer, it is a series of POINTS, as all structures, in physics, at atomic levels, currently known, are spherical.

3D

Yes, and in your imagination you can fool yourself into thinking that it is infinite, but in the reality that physics studies, well, proving that one is admitted as impossible, soooo...

I thought the point was clear that the mind was not infinite and thus could not contain an infinite thought.

The point is then can we logically understand (not replicate in the imagination) the concept of infinity.

There is a HUGE difference here that you keep getting confused about. In the understanding of infinity one must resort to logic NOT the PURE imagination that you keep referring to...and no logic is not infinite but that is beside the point. The point is that one can define a concept in such a way that it includes the concept of boundlessness. To do this it does not have to replicate this boundlessness within itself. The same way that you can concieve of a mountain without actually trying to fit it within your brain!

 

[Mr. Robin Parsons]

Originally posted by subtillioN

(SNIP) one must resort to logic NOT the PURE imagination (SNoP)

Logic is of the ImagInatIon, inseperable.

Originally posted by subtillioN
(SNIP) The point is that one can define a concept in such a way that it includes the concept of boundlessness. (SNoP)

Not if 'one'concedes that all concepts are, inherently, "bounded" things, the only other manner is the typicono'graphic that is the word "Infinite" itself, but that word incapable of describing that which it attempts to tell of/describe. (fun eh?)

 

[subtillioN]

Originally posted by Mr. Robin Parsons
Logic is of[/b] the ImagInatIon, inseperable.

Logic is a symbolic representation. The PURE imagination is not.

There is your differentiation (not a separation as nothing can be truly separated from anything else).

Not if 'one'concedes that all concepts are, inherently, "bounded" things, the only other manner is the typicono'graphic that is the word "Infinite" itself, but that word incapable of describing that which it attempts to tell of/describe. (fun eh?)

ALL concepts are finite, that is a given.

By your reasoning then there is virtually nothing that we can truly understand because we cannot imagine the true complexity of ANY PHYSICAL THING whatsoever. The mind has to simplify everything via sensation, imagination, or logic.

 

[radagast]

Originally posted by Mr. Robin Parsons
Yes! in your imagination you can conceive of a Euclidian line, but as anyone who studies reality, by structures, knows that the 'straight' line is a misnomer, it is a series of POINTS, as all structures, in physics, at atomic levels, currently known, are spherical.

3D

By definition, points are zero dimentional. You are introducing the real world as if it were an aspect of the abstraction of Euclidean geometry (or vice versa). This is logic flaw.

It seems to be no change in positions and most of the points I've made haven't been addressed. So I feel it's time for me to withdraw from this discussion.

Kindest Regards,

 

[Mr. Robin Parsons]

Originally posted by radagast
(SNIP)By definition, points are zero dimentional. (SNoP) You are introducing the real world as if it were an aspect of the abstraction of Euclidean geometry (or vice versa).

17/07/2003

So you think that a point can be defined as “Zero Dimensions”, perhaps in (imaginary) mathematics, but not in reality, as reality defines a point as 'solid', having existence, "Being There", (sounds like the title of a movie doesn't it?) and "Zero Dimensions" is definitely NOT there.

A "Zero dimension point" is an oxymoron. (as anything other then an Imaginary item)

As I recall it, in Physics, we describe reality, that which "is".

It is respectfully suggested that you adhere to your own observation, which is easily seen as being that of your own self-perception, reflected off of me, and presented by you as...

Originally posted by radagast
(SNIP) This is logic flaw. (SNoP)

Then again, as you seem to have indicated your departure, this has no Point! (Pardons the pun!)

 

[subtillioN]

Originally posted by Mr. Robin Parsons
17/07/2003

So you think that a point can be defined as “Zero Dimensions”, perhaps in (imaginary) mathematics, but not in reality, as reality defines a point as 'solid', having existence, "Being There", (sounds like the title of a movie doesn't it?) and "Zero Dimensions" is definitely NOT there.

A "Zero dimension point" is an oxymoron. (as anything other then an Imaginary item)

As I recall it, in Physics, we describe reality, that which "is".

EXACTLY! Mathematics is imaginary and not equivalent to reality. This deep confusion between mathematics and reality is the sickness of modern physics!

Infinity exists independently of mathematics and any logic system.

 

[Mr. Robin Parsons]

Originally posted by subtillioN
Logic is a symbolic representation. The PURE imagination is not.
PURE imagination is a BLANK PAGE!

There is your differentiation (not a separation as nothing can be truly separated from anything else).



ALL concepts are finite, that is a given.

By your reasoning then there is virtually nothing that we can truly understand because we cannot imagine the true complexity of ANY PHYSICAL THING whatsoever. The mind has to simplify everything via sensation, imagination, or logic.

From whence in "My Reasoning" do you find what follows in your statement; "cannot imagine the true complexity of ANY PHYSICAL THING whatsoever" , where?? where in what I have said do you see that?? where??

In that "unascribed quotation" (of me!) I speak ONLY of the 'thing' "Infinity" and how we use a typicono'graphic to tag/name that which we realize we cannot conceive of.

Where do you find that thing about the inability to imagine anything of any true complexity?? where??

 

[russ_watters]

Originally posted by Mr. Robin Parsons
that a point can be defined as “Zero Dimensions”, perhaps in (imaginary) mathematics, but not in reality, as reality defines a point as 'solid', having existence, "Being There", (sounds like the title of a movie doesn't it?) and "Zero Dimensions" is definitely NOT there.

A "Zero dimension point" is an oxymoron. (as anything other then an Imaginary item)

As I recall it, in Physics, we describe reality, that which "is".

This is the first thing you learn in 8th grade geometry. A point is zero dimensional (ie, it has no length, width, or height), a line is one dimensional (it has length but no width or height), a shape such as a square is two dimensional (length and width but no height, and an object such as a box is three dimensional (length, width, and height).

It sounds like you two are mistaking the point itself being zero dimensional for its LOCATION being zero dimensional. Its location can be expressed in any amount of dimensions you wish depending on the situation (ie, points on a map are located two dimensionally, points in space three dimensionally).

EXACTLY! Mathematics is imaginary and not equivalent to reality. This deep confusion between mathematics and reality is the sickness of modern physics!

Thats a separate and often controversial issue. Is that the root of your distaste for "standard" physics? That would explain an awful lot about where your misconceptions come from.

Virtually everything derived mathematically about physics has later been confirmed by observation to be physically real. This often leads to uncomfortable discoveries - black holes for example were a source of debate on this grounds until they were discovered (their existence was predicted through mathematical derivation long before HST found the first one). Much of quantum mechanics has had the same type of controversy though to my knowledge NOTHING implied by the math has yet to be found inconsistent with physical reality. Ie, nothing that has ever been predicted mathematically by QM has ever been found to be at odds with later experimentation. Even the uncomfortable implications.

 

[subtillioN]

Originally posted by Mr. Robin Parsons
PURE imagination is a BLANK PAGE!

No, PURE imagination is syntax independent. It's "symbols" are not part of a rigorous logic system.

From whence in "My Reasoning" do you find what follows in your statement; "cannot imagine the true complexity of ANY PHYSICAL THING whatsoever" , where?? where in what I have said do you see that?? where??

You are saying that since we cannot imagine the fullness of infinity then we cannot understand it whatsoever. The fact is that we cannot imagine the fullness of ANYTHING in this physical world, so by your logic we can't understand anything.

 

[Mr. Robin Parsons]

Originally posted by russ_watters
This is the first thing you learn in 8th grade geometry. A point is zero dimensional (ie, it has no lenght, width, or height), a line is one dimensional (it has length but no width or height), a shape such as a square is two dimensional (length and width but no height, and an object such as a box is three dimensional (length, width, and height).

It sounds like you two are mistaking the point itself being zero dimensional for its LOCATION being zero dimensional. Its location can be expressed in any amount of dimensions you wish depending on the situation (ie, points on a map are located two dimensionally, points in space three dimensionally).

Yes russ in Imaginary realms things can be whatever you would like them to be, concepts in math are included in being things that can contain imaginary elements, but in this discourse we are supposed to be talking about REALITY, Hence tangiblity becomes a critical factor in whether, or not, what you talking about, is real, or not.

It seems that the point being missed is exactly that, the differentiation between what your imagination can do, and what reality does do! It should be noted that your imagination does "imaginary", reality DOES NOT!

EDIT SP!??

 

[subtillioN]

Originally posted by russ_watters
This is the first thing you learn in 8th grade geometry. A point is zero dimensional (ie, it has no length, width, or height), a line is one dimensional (it has length but no width or height), a shape such as a square is two dimensional (length and width but no height, and an object such as a box is three dimensional (length, width, and height).

So we have a symbol system for quantifying reality.

It sounds like you two are mistaking the point itself being zero dimensional for its LOCATION being zero dimensional.

no such confusion here.

Thats a separate and often controversial issue. Is that the root of your distaste for "standard" physics? That would explain an awful lot about where your misconceptions come from.

No, the root of my distaste is that standard model is wrong at the core. This is only visible if you get outside the system and can see it from another comparable system. The reason we have resorted to pure mathematics as a causal description is that we have no other choice in the standard model. This is because the roots are faulty and they cannot be thrown out. Too much infrastructure and too painfull.

Virtually everything derived mathematically about physics has later been confirmed by observation to be physically real.

Nope. It is all just an interpretation of the data. There are other more coherent and comprehensive interpretations for which these things are "proof" as well.

This often leads to uncomfortable discoveries - black holes for example were a source of debate on this grounds until they were discovered (their existence was predicted through mathematical derivation long before HST found the first one).

They have not been discovered. They are used to fill in the holes of the standard model, LITERALLY!

Much of quantum mechanics has had the same type of controversy though to my knowledge NOTHING implied by the math has yet to be found inconsistent with physical reality.

It is constantly being retro-fitted to the surprising new data, how could it ever be proven wrong? The only way to supplant it is to show a simpler more coherent system, which already exists.

Ie, nothing that has ever been predicted mathematically by QM has ever been found to be at odds with later experimentation. Even the uncomfortable implications.

Yeah right. These constant suprises are simply dealt with in the standard manner of retro-fitting the theory to new contradictory data so that now it can "predict" them! An abuse of the term "predict' if you ask me!

 

[russ_watters]

Originally posted by Mr. Robin Parsons
Yes russ in Imaginary realms things can be whatever you would like them to be, concepts in math are included in being things that can contain imaginary elements, but in this discourse we are supposed to be talking about REALITY, Hence tangiblity becomes a critical factor in whether, or not, what you talking about, is real, or not.

It seems that the point being missed is exactly that, the differentiation between what your imagination can do, and what reality does do! It should be noted that your imagination does "imaginary", reality DOES NOT!

So then the fact that a square has length and width is a figment of my imagination?

Whoa.

Nevermind. There is no point (no pun intended) to continuing this discussion.

edit: One thing I must note, and I think its been addressed before, but you and Sub are using circular and arbitrary definitions. Ie, by definition A=B, therefore A=B. Then someone points out that either in the real world or by mathematical derivation, A does NOT equal B, you go back to your definition.

 

[Mr. Robin Parsons]

Originally posted by russ_watters
(SNIP) So then the fact that a square has length and width is a figment of my imagination?

Whoa. (SNoP)

Just outa curiosity, just where, in what you quote from me, do you derive the idea that something tangible is now a figment of your imagination??

 

[russ_watters]

Originally posted by Mr. Robin Parsons
Just outa curiosity, just where, in what you quote from me, do you derive the idea that something tangible is now a figment of your imagination??

Ok, I guess you have sucked me in. Let's start with a clarification:

Does a square have a physically real length and width?

 

[subtillioN]

Originally posted by russ_watters
Ok, I guess you have sucked me in. Let's start with a clarification:

Does a square have a physically real length and width?

There is metrical extension and there is physical extension.

Is the square physical? Or is it a figment of your imagination?

Let's start with a physical cube instead. This cube has a real physical extension, which can be assigned an arbitrary set of dimensional values depending on the unit system employed. The dimensioning system is imaginary but the physical extension is real and independent of any dimensional system.

 

[russ_watters]

Originally posted by subtillioN
There is metrical extension and there is physical extension.

Is the square physical? Or is it a figment of your imagination?

Let's start with a physical cube instead. This cube has a real physical extension, which can be assigned an arbitrary set of dimensional values depending on the unit system employed. The dimensioning system is imaginary but the physical extension is real and independent of any dimensional system.

Ok, that's still not clear. Does the cube have 3 physically real dimensions or not?

You seem to be implying (whether or not MRP agrees, I'll leave up to him) that the dimensions exist only in my mind. So a cube does NOT have 3 real physical dimensions?

How then do you know that its a cube? Hell, how do you even know its real - that it even exists?

 

[Hurkyl]

A more pressing question is how do we verify whether or not something has physical extension? What measurable properties does physical extension have?

 

[subtillioN]

Originally posted by russ_watters
Ok, that's still not clear. Does the cube have 3 physically real dimensions or not?

Dimensions are not physically real.

You seem to be implying (whether or not MRP agrees, I'll leave up to him) that the dimensions exist only in my mind. So a cube does NOT have 3 real physical dimensions?

exactly

How then do you know that its a cube? Hell, how do you even know its real - that it even exists? [/B]

I can see it. Do you have to measure something and categorize it to know it exists?

 

[subtillioN]

Originally posted by Hurkyl
A more pressing question is how do we verify whether or not something has physical extension? What measurable properties does physical extension have?

Everything real has physical extension. Depends on what it is and the measurement tools at our disposal.

 

[chroot]

Originally posted by subtillioN
I can see it. Do you have to measure something and categorize it to know it exists?

You could know the thing exists; but you couldn't know what the thing was. You wouldn't know if it was a cube, square, gallon of milk, or Carmen Electra, if you (or your visual cortex, on behalf of you) weren't able to measure its properties.

- Warren

 

[Hurkyl]

Everything real has physical extension. Depends on what it is and the measurement tools at our disposal.

How do we know if something is real? Unless we have a way to know if something is real, this does not provide a way to verify if it has physical extension.

What if the measurement tools are atomic clocks and light beams?

 

[subtillioN]

Originally posted by chroot
You could know the thing exists; but you couldn't know what the thing was. You wouldn't know if it was a cube, square, gallon of milk, or Carmen Electra, if you (or your visual cortex, on behalf of you) weren't able to measure its properties.

- Warren

My eyes work just fine thank you