[helene_t]

luke warm, on Mar 28 2006, 01:38 PM, said:

there is no part of the universe, visible or not, which can be shown to be infinite... and helene, the simplest math model isn't the one being discussed.. it even goes by the name 'complex math'

It's possible that nothing in nature can be "shown" to be infinite, because of the problems I mentioned. This assertion may be wrong (haven't thought about it too much), or it may depend on the exact meaning of the word "show". But let's suppose, just for the sake of the argument, that you can't show that the universe is infinite. (BTW: I will assume finite=unbounded. We could also discuss whether it could be continous).

Now you may assume that the universe is finite, or that it's infinite, or you may invent some robust theory that allows for both a finite and an infinite universe. You're free to chose whatever geometry you find estetically most appealing, or allows for the easiest calculations, or whatever you find important.

Personally, I would prefer an infinite universe, because:
- I like the geometry to be Euclidian
- I like the universe to be symmetric
- A symmetric, Euclidian space in infinite

If you prefer a finite universe because you have other estetic criteria than symmetry, or because you have some data that can't be explain by Euclidian geometry (astronomers do have such data but I'm not an astromer so I don't care), then feel free to disagree with me. But that an infinite universe is impossible for purely philosofical reasons is simply not true. Consider these two models:
1) Some model for a finite universe
2) Model 1) embedeed into an infinite space with some force that prevents vissible stuff from penetrating the boundaries of 1).
The two models correspond to identical observations. If 1) agrees with observations, it's just a matter of preference.

[Sigi_BC84]

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Just to offer one alternative: maybe everything has already happened and what we perceive as "time" or "change" is not real in an absolute way.  Maybe it is just an illusion which we are prone to. 

well certainly that's possible... it's also possible that you (or i) are actually the only living entities existing... however, one must start somewhere, and since using illusion as a starting place would of necessity make it an ending place, it's probably better to not use it

"Illusion" relates to the observer, not to the facts (the absolute). You are making certain claims based on the assumption that "time" is real. Especially you are assuming that time is continuous and therefore can't be infinite (see below).

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there's a big difference between comparing 2 points in time and in actually proving one could exist in an infinite universe.. from 1/1/2005 until 1/2/2005, in an infinite universe, how many increments of time should pass? the nature of infinity is such that there are infinite points between points...

What do you assume: That time is continouus and infinite by nature, discrete by nature, discrete and finite by nature?

Let's say that time is discrete (that is, reality happens in tiny steps, each following another), maybe this has been even proved by now, I don't know. Then what's the problem in making the timeline infinitely long? You will still be able to get from then to now by counting up a googol of time quanta.

If one accepts that time is a law of nature that simply happens (like gravity simply exists), where is the problem with assuming that it is a continuous phenomenon?

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"This particular point in time" always exists, actually it is the only thing that we can absolutely sure of.  Past and future are illusions created by our mind (this is easy enough to see if you think about it).

i have thought about it, and i confess i don't see it... yesterday happened, it wasn't an illusion.. can i prove that? well no, i can't.. but this opens another whole realm of debate on knowledge and the nature of a 'functioning brain'

I fully acknowledge that "yesterday" happened, but "yesterday" does not exist. "Now" exists, nothing else.

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so whether real or illusionary, the battle of the alamo occurred at a certain point in time... and, in an infinite univers, "you can't get here from there"

Maybe you can quote somebody or give a pointer to a book, or just support this in more detail. I simply do not understand what you exactly mean by "infinite" (but also see above).

--Sigi

BTW: feel free to move this to another thread if you want to continue the discussion, I certainly do.

[david_c]

luke warm, on Mar 27 2006, 08:23 PM, said:

the reason is, it proved that the universe came into being... "from nothing nothing comes" has been a major philosophical tenet forever, and big bang gave christians the chance to ask, "what caused the singularity?"...

Ah, the fallacy of the compound question.

[luke warm]

helene_t, on Mar 28 2006, 07:29 AM, said:

luke warm, on Mar 28 2006, 01:38 PM, said:

there is no part of the universe, visible or not, which can be shown to be infinite... and helene, the simplest math model isn't the one being discussed.. it even goes by the name 'complex math'

It's possible that nothing in nature can be "shown" to be infinite, because of the problems I mentioned. This assertion may be wrong (haven't thought about it too much), or it may depend on the exact meaning of the word "show".

by 'show' i mean to do more than assert... logic alone (and philosophy is, or should be, rooted in logic) can be used to prove the finite nature of the universe

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Personally, I would prefer an infinite universe, because:
- I like the geometry to be Euclidian
- I like the universe to be symmetric
- A symmetric, Euclidian space in infinite

well that's fine, we each have preferences... it just isn't what i was speaking of

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If you prefer a finite universe because you have other estetic criteria than symmetry, or because you have some data that can't be explain by Euclidian geometry (astronomers do have such data but I'm not an astromer so I don't care), then feel free to disagree with me. But that an infinite universe is impossible for purely philosofical reasons is simply not true.

it isn't that i prefer one to the other, it's that one (the infinite one) can't logically exist... i don't know what a 'purely' philosophical reason would be... i'm just saying that the universe, and all it contains, must be finite... and i don't say this on philosophical grounds, but on logical grounds... do a google for 'hilbert's paradox' to get a glimpse of what i'm talking about

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Consider these two models:
1) Some model for a finite universe

ok, i'll use the model in which we live ... the one where time itself can't be infinite

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2) Model 1) embedeed into an infinite space with some force that prevents vissible stuff from penetrating the boundaries of 1).
The two models correspond to identical observations. If 1) agrees with observations, it's just a matter of preference.

ok... can i call model 2) "eternity?" and can i say that model 2) is God's residence, and can i say that model 1) is his creation? because if i can, i do

Sigi said:

Let's say that time is discrete (that is, reality happens in tiny steps, each following another), maybe this has been even proved by now, I don't know. Then what's the problem in making the timeline infinitely long? You will still be able to get from then to now by counting up a googol of time quanta.

no, you can't get to now from then... that's the problem with any model that postulates an infinite universe... because between each googol of time quanta you quantify lies another infinite googol of time quanta, etc, etc, etc (ad, pardon me, infinitum)

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If one accepts that time is a law of nature that simply happens (like gravity simply exists), where is the problem with assuming that it is a continuous phenomenon?

i'm not sure time is a law of nature... that aside, saying that something is a continuous phenomenon is not the same thing as saying it is infinite... there are logical problems with an infinite time line... i can't say whether the same is true for a continuous time line

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I fully acknowledge that "yesterday" happened, but "yesterday" does not exist. "Now" exists, nothing else.

the very fact that you can point to yesterday proves not only that it existed, but that you have arrived at today, such arrival of necessity showing the finite nature of the path traveled... how many increments of time must have been traversed to arrive today from yesterday? now if each increment (or point) was an infinite number of such points, can you see how today would not have arrived? the very fact that we are here, now, shows the finiteness of the increments

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BTW: feel free to move this to another thread if you want to continue the discussion, I certainly do.

me too, i find it interesting... i don't know how to move these posts though, except to copy each in a new thread ... if that's the only way, i'll try to do it later

[helene_t]

luke warm, on Mar 29 2006, 04:09 AM, said:

well that's fine, we each have preferences... it just isn't what i was talking about

I think it is. There is an infinity (!) of models for the universe that agree with observations. You have to excert some preferences to avoid scizofrenia. Some people prefer models that include some object or force that could be called "God", some do not. Some people prefer a bounded universe, some prefer an unbouded one.

Personally (for what it's worth) I prefer models based on Ocam's Razor. And I think, though I might be wrong, that this leads to a rejection of the existence of God. (Kinda difficult to say since I'm not sure what "God" means. To my aunt, it means "love", which is not to suggest that atheists necesarily do not believe in love).

I prefer a space with a high degree of symmetry.

I prefer a Euclidian space but I acknowlegde that this does not agree with all observations. As far as I have understood it's still unknown whether the curvature of spacetime is positive (leading to a bounded universe) or negative (leading to an unbouded universe).

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do a google for 'hilbert's paradox' to get a glimpse of what i'm talking about

Now I'm confused - Hilbert's Hotel can exist in bounded space though not in bounded, discrete space - are you saying that the universe must be bounded and discrete? I dislike discrete spaces since they are against Ocam's Razor - they need some smallest step in time (and space), thereby adding an extra constant of nature, which should be avoided unless necesary. But we do have the Planck distance anyway, so maybe it's ok.

Actually, I suspect that the whole concept of boundedness has a different meaning in relativistic space than in classical space which means that the concept, as I understand it, is meaningless in a discussion based on modern physics.

But what does this have to do with the existence of God? As an atheist I don't really care whether the universe is bounded or not.

[Sigi_BC84]

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it isn't that i prefer one to the other, it's that one (the infinite one) can't logically exist... i don't know what a 'purely' philosophical reason would be... i'm just saying that the universe, and all it contains, must be finite... and i don't say this on philosophical grounds, but on logical grounds... do a google for 'hilbert's paradox' to get a glimpse of what i'm talking about

I have just read up on it ([wikipedia] Hilbert's Grand Hotel and [wikipedia] Cosmological argument) and you are stating something for a fact that cannot be simply taken for granted. Especially Hilbert's Hotel is not necessarily a valid model for the real universe, or a proof of the impossibility that it could be infinite.

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helene said:

2) Model 1) embedeed into an infinite space with some force that prevents vissible stuff from penetrating the boundaries of 1).
The two models correspond to identical observations. If 1) agrees with observations, it's just a matter of preference.

ok... can i call model 2) "eternity?" and can i say that model 2) is God's residence, and can i say that model 1) is his creation? because if i can, i do

Now you are shooting yourself into the foot: When mentioning "eternity" you are acknowledging the possibility of infinite time.

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Sigi said:

Let's say that time is discrete (that is, reality happens in tiny steps, each following another), maybe this has been even proved by now, I don't know. Then what's the problem in making the timeline infinitely long? You will still be able to get from then to now by counting up a googol of time quanta.

no, you can't get to now from then... that's the problem with any model that postulates an infinite universe... because between each googol of time quanta you quantify lies another infinite googol of time quanta, etc, etc, etc (ad, pardon me, infinitum)

Reread the passage you have quoted: The discrete timeline consists of infinitely many, but countable time quanta, and therefore you cannot squeeze additional quanta in ad infinitum. What you described was an uncountable set.

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there are logical problems with an infinite time line... i can't say whether the same is true for a continuous time line

But you keep mixing up arguments against "continuous time" and against "infinite time".

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the very fact that you can point to yesterday proves not only that it existed, but that you have arrived at today, such arrival of necessity showing the finite nature of the path traveled... how many increments of time must have been traversed to arrive today from yesterday? now if each increment (or point) was an infinite number of such points, can you see how today would not have arrived? the very fact that we are here, now, shows the finiteness of the increments

Again you are mixing up two different things: I'm saying that one could assume that time can be quantified. You could then take an arbitrary time span and give the corresponding number of time quanta. Let's take the amount of time that passed from the moment that I submitted this posting to the very moment that you are reading this. Let's call this number "Q". So by tracing Q time quanta I arrive from then to now. The total number of (countable) time quanta that have passed so far is infinity, so is the total number of time quanta yet to happen. Where's the problem here?

The point I was trying to make about "yesterday" is something different: I'm saying that "yesterday" or "tomorrow" both do not exist. All that exists, exists now, and "yesterday" is merely a pattern visible in the current state of the universe.

--Sigi

[david_c]

luke warm, on Mar 29 2006, 03:09 AM, said:

it isn't that i prefer one to the other, it's that one (the infinite one) can't logically exist... i don't know what a 'purely' philosophical reason would be... i'm just saying that the universe, and all it contains, must be finite... and i don't say this on philosophical grounds, but on logical grounds... do a google for 'hilbert's paradox' to get a glimpse of what i'm talking about

"Hilbert's Hotel" is concerned with countable sets and so doesn't seem to be relevant. Jimmy's statement "you can't get here from there" sounds more like Zeno's paradox to me, which is well-known to be fallacious.

Infinity is a difficult subject.

Let S be a collection of subsets of the integers, such that for any A and B in S, either A is contained in B or B is contained in A. Is it possible for S to be uncountable?

[helene_t]

david_c, on Mar 29 2006, 01:17 PM, said:

Let S be a collection of subsets of the integers, such that for any A and B in S, either A is contained in B or B is contained in A. Is it possible for S to be uncountable?

It might or might not be possible. Either assumption is consistent. To get clarrification, you need to accept either the continuum hypothesis, or its negation, as an axiom.

This is called the theorem of Soloway and was proved in 1980, I think.

Most mathematicians prefer the negation of the continuum hypothesis. It is (here it comes again!) a matter of preferences.

[luke warm]

Sigi_BC84, on Mar 29 2006, 05:49 AM, said:

I have just read up on it ([wikipedia] Hilbert's Grand Hotel and [wikipedia] Cosmological argument) and you are stating something for a fact that cannot be simply taken for granted.  Especially Hilbert's Hotel is not necessarily a valid model for the real universe, or a proof of the impossibility that it could be infinite.

i didn't mention the paradox as a model for the univerese, but as an example of why time cannot be infinite

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Now you are shooting yourself into the foot: When mentioning "eternity" you are acknowledging the possibility of infinite time.

no, i don't see it that way... i'm not saying eternity has anything to do with time... as a matter of fact, time itself (if created) must exist apart from eternity... i see eternity as timeless... assume for a moment that God exists, and that heaven exists... assume heaven is located in, or is, eternity... to explain what i mean by timeless: when i die and "step" into heaven (ie, eternity), another who died 100 years prior will also be 'stepping' into heaven... see?

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Reread the passage you have quoted:  The discrete timeline consists of infinitely many, but countable time quanta, and therefore you cannot squeeze additional quanta in ad infinitum.  What you described was an uncountable set.

i think we're missing one another here... i'm saying that the very fact of arriving at point B from A shows there was not an infinite number of points between, not that such points in between are uncountable

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Let's take the amount of time that passed from the moment that I submitted this posting to the very moment that you are reading this.  Let's call this number "Q".  So by tracing Q time quanta I arrive from then to now.  The total number of (countable) time quanta that have passed so far is infinity, so is the total number of time quanta yet to happen.  Where's the problem here?

as i wrote immediately above, this seems to be where we're missing one another... in your mind, mark a point and call it "then"... mark another point and call it "now"... let's assume the 2 points are separated by a unit of measurement called 'seconds'... now then, count... how many increments, if time is infinite, are between the 1st and 2nd second? an infinite number, right? would you *ever* reach second 2 (much less 'now') from second 1, in infinity?

david said:

"Hilbert's Hotel" is concerned with countable sets and so doesn't seem to be relevant. Jimmy's statement "you can't get here from there" sounds more like Zeno's paradox to me, which is well-known to be fallacious.

no, zeno's paradox shows the flaw in the logic of an *actual* infinity existing ... yes, if one attempts to prove that an infinite number of points (meters in the hare and achilles) exist between a beginning and end, the argument is indeed fallacious, merely because a sum is available (one)... however, this is only so because an actual infinity of meters can't exist

i say hilbert's hotel is completely relevant, since it shows what to expect from an *actual* infinite as opposed to an imaginary one

helene said:

Now I'm confused - Hilbert's Hotel can exist in bounded space though not in bounded, discrete space - are you saying that the universe must be bounded and discrete?

i don't have the necessary math skills to speak much on discrete vs. indiscrete sets... i'm only speaking philosophically about a particular problem with an infinite universe... this problem has been acknowledged by others (atheists and christians) and has led to theories and arguments surrounding the origin of the universe... it's why some try to show why the singularity has always existed (which would make it infinite, by definition)... but it also shows why other theories have come into being... now i'm not saying this is the only reason for the string theory, or work in complex math, but i am saying that this logical problem certainly entered the thinking of those who try to prove the existence of a *natural* infinity (ie, one found in nature)

[david_c]

helene_t, on Mar 29 2006, 12:58 PM, said:

david_c, on Mar 29 2006, 01:17 PM, said:

Let S be a collection of subsets of the integers, such that for any A and B in S, either A is contained in B or B is contained in A. Is it possible for S to be uncountable?

It might or might not be possible. Either assumption is consistent. To get clarrification, you need to accept either the continuum hypothesis, or its negation, as an axiom.

I wish that was the correct answer, but it's not, you must have misread it. This is a question we were given in my first year at university, and doesn't require anything deeper than the definiton of countable / uncountable.

[cherdano]

helene_t, on Mar 28 2006, 02:29 PM, said:

Personally, I would prefer an infinite universe, because:
- I like the geometry to be Euclidian
- I like the universe to be symmetric
- A symmetric, Euclidian space in infinite

I don't understand any of this infinity discussion, not even this very concrete statement here... Tori look entirely symmetric and Euclidian to me, but are probably not what you call "infinite".

Or maybe I don't understand what "infinite" is supposed to mean here?

Arend

[helene_t]

david_c, on Mar 29 2006, 02:11 PM, said:

helene_t, on Mar 29 2006, 12:58 PM, said:

david_c, on Mar 29 2006, 01:17 PM, said:

Let S be a collection of subsets of the integers, such that for any A and B in S, either A is contained in B or B is contained in A. Is it possible for S to be uncountable?

It might or might not be possible. Either assumption is consistent. To get clarrification, you need to accept either the continuum hypothesis, or its negation, as an axiom.

I wish that was the correct answer, but it's not, you must have misread it. This is a question we were given in my first year at university, and doesn't require anything deeper than the definiton of countable / uncountable.

You're right, sorry. I thought you were refering to:
R= (the set of all subsets of N)
S=(some subset of R for which there is no surjective mapping S -> R)
Question: can S be mapped injectively -> N?

[helene_t]

cherdano, on Mar 29 2006, 02:18 PM, said:

helene_t, on Mar 28 2006, 02:29 PM, said:

Personally, I would prefer an infinite universe, because:
- I like the geometry to be Euclidian
- I like the universe to be symmetric
- A symmetric, Euclidian space in infinite

I don't understand any of this infinity discussion, not even this very concrete statement here... Tori look entirely symmetric and Euclidian to me, but are probably not what you call "infinite".

Or maybe I don't understand what "infinite" is supposed to mean here?

Arend

If the universe is a torus, Euclidian geometry does not apply. But I thought we were discussing boundedness, I should use that word instead of "infinite".

Let's suppose the vissible universe a 3-dimensional thorus embeded into 4-dimensional euclidian space. Now you could say that the "universe" is the visible universe, hence not euclidian. Or you could say the "universe" is the space in which the thorus is embeded, hence unbounded (or assymetrical, if you prefer).

[helene_t]

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mark a point and call it "then"... mark another point and call it "now"... let's assume the 2 points are separated by a unit of measurement called 'seconds'... now then, count... how many increments, if time is infinite, are between the 1st and 2nd second? an infinite number, right? would you *ever* reach second 2 (much less 'now') from second 1, in infinity?

This is Zeno's paradox and it is not a problem. It's true that we can't observe an infinity of events between "then" and "now". But that doesn't say that there can't be an infinity of time points.

In fact, it is very difficult (to me at least) to immagine space to be discrete. There would have to be some grid of points in space, meaning that you can't travel in certain directions because you wouldn't enounter any points then. Or straight lines must allways be zig-zag lines at the microscopic level (how to explain that light travels with the same speed in all directions, then?) or the grid would have to bend itself to addapt to traveling objects. The math would be quite difficult. So please, give me a continuus space unless you have very strong arguments for something else.

[helene_t]

luke warm, on Mar 29 2006, 02:01 PM, said:

but i am saying that this logical problem certainly entered the thinking of those who try to prove the existence of a *natural* infinity (ie, one found in nature)

I'm not saying that infinity can be "found" in nature - if infinite sets exist we can never observe them. This is more related to our limited perception than to nature.

Much less am I saying that the existence of such sets can be proven.

But theories about non-observable things are everywhere in science. They are even part of human nature - children have been shown spontaneously to develop the concept of "existence" as something independant of "observed".

And many scientific theories require infinite sets for convenient mathematical modeling.

[david_c]

helene_t, on Mar 29 2006, 01:24 PM, said:

If the universe is a torus, Euclidian geometry does not apply.

The natural geometry of the torus is Euclidean: indeed it is a quotient of Euclidean space. Admittedly, you don't "see" this if you try to embed the torus into (n+1)-dimensional Euclidean space, but why would you want to do that?

[helene_t]

david_c, on Mar 29 2006, 02:59 PM, said:

helene_t, on Mar 29 2006, 01:24 PM, said:

If the universe is a torus, Euclidian geometry does not apply.

The natural geometry of the torus is Euclidean: indeed it is a quotient of Euclidean space. Admittedly, you don't "see" this if you try to embed the torus into (n+1)-dimensional Euclidean space, but why would you want to do that?

Right. Arend told me the same. I thought that the fact that straight lines bide themselves in the tail makes a thorus non-euclidian. But now that I think about it I'm not sure if it violates any of Euclides axioms.

So maybe, if Jimmy insists the universe be bounded and I insist it being symmetric and eucidian, we could compromize on a thorus. But in the meantime I've realized that what Jimmy does not believe in is the continous space rather than unbounded space.

Not sure what this has to do with God, though.

[luke warm]

helene_t, on Mar 29 2006, 07:34 AM, said:

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mark a point and call it "then"... mark another point and call it "now"... let's assume the 2 points are separated by a unit of measurement called 'seconds'... now then, count... how many increments, if time is infinite, are between the 1st and 2nd second? an infinite number, right? would you *ever* reach second 2 (much less 'now') from second 1, in infinity?

This is Zeno's paradox and it is not a problem. It's true that we can't observe an infinity of events between "then" and "now". But that doesn't say that there can't be an infinity of time points.

but we can observe the passage of time, correct? that's all i was trying to say..

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I'm not saying that infinity can be "found" in nature - if infinite sets exist we can never observe them. This is more related to our limited perception than to nature.

perhaps my use of the word "natural" was unfortunate... what i meant by it was "actual"... so in case my position hasn't been clear, it's simply this: to say that time is infinite is to say that an *actual* infinity exists... this cannot be shown (proven) to be true by logic, mathmatics, or even simple observance... i come at this from the philosophical side

[Sigi_BC84]

luke warm, on Mar 29 2006, 06:26 PM, said:

perhaps my use of the word "natural" was unfortunate... what i meant by it was "actual"... so in case my position hasn't been clear, it's simply this: to say that time is infinite is to say that an *actual* infinity exists... this cannot be shown (proven) to be true by logic, mathmatics, or even simple observance... i come at this from the philosophical side

OK, I cancel my previous claim that time is infinite (ie. that there is no beginning of time) and that this is logical. I replace it by "I assume that time is infinite and that there is no beginning of time" without claiming that this follows from logic.

However, I also do not accept any claims of the opposite (ie. that time cannot be infinite). Now, if you still want to uphold your claim that time cannot be infinite, then please give accurate reasoning (or provide some links to sources that do so).

Helene has mentioned Occam's Razor already (which in a nutshell says that of two otherwise equally satisfying theories the simpler one is to be preferred). I'm applying this here. If the Big Bang did actually happen, it was replacing something before the singularity, which is beyond our possibilities for observation. Maybe an earlier universe had collapsed into the singularity just to be reborn into the present one, so time never actually ceased to exist -- I do not know.

After all, assuming a creator of the world and a beginning of time is not necessary in my eyes and only makes the theory more complicated without explaining more.

--Sigi

[luke warm]

Sigi_BC84, on Mar 30 2006, 02:50 AM, said:

If the Big Bang did actually happen, it was replacing something before the singularity, which is beyond our possibilities for observation.  Maybe an earlier universe had collapsed into the singularity just to be reborn into the present one, so time never actually ceased to exist -- I do not know.

After all, assuming a creator of the world and a beginning of time is not necessary in my eyes and only makes the theory more complicated without explaining more.

--Sigi

but sigi, this is merely an assertion on your part stated as a fact... as i've stated, an actual inifinity needs imaginary numbers used in complex math... as for stating sources, we're each free to draw our own conclusions from debates held by others... as for me, when hawking says (in 'a brief history in time')

"The idea that space and time may form a closed surface without boundary also has profound implications for the role of God in the affairs of the universe. With the success of scientific theories in describing events, most people have come to believe that God allows the universe to evolve according to a set of laws and does not intervene in the universe to break these laws. However, the laws do not tell us what the universe should have looked like when it started – it would still be up to God to wind up the clockwork and choose how to start it off. So long as the universe had a beginning, we could suppose it had a creator. But if the universe is really completely self-contained, having no boundary or edge, it would have neither beginning nor end: it would simply be. What place, then, for a creator?"

it makes it obvious (to me at least) why it was imperative to prove the existence of an infinite universe... and if the only way to do that was to use imaginary numbers, well that's better than having to use God, right? notice that even hawkings admits that if there was a beginning, God (or at least a creator) exists... to me hawkings is saying that the universe is either infinite or created... since it can't be created (his mindset), ergo ...

so while you contend that assuming a creator makes the matter more complicated, i contend the opposite - what could be simpler?