Worst Inventions

[Sigi_BC84]

actually this doesn't stand up to logic, if one grants the impossibility of an effect without a cause... because no matter how you slice it, there has to be a first cause

 

added by edit: the reason there has to be a first cause has to do with the nature of infinity and the impossibility of in infinite universe (logical impossibility, that is)... if space/time is infinite, we could never logically prove we are where we are when we are

If you could elaborate further on that I would be interested.

 

To me infinity is absolute (and absolutely inconceivable).

 

--Sigi

[cherdano]

The worst invention of all time is Religion.

I have tried to refrain from commenting on this, but I can't anymore.

 

Well, I am pretty atheistic myself, but I completely fail to understand

1. how anyone could hold such a naive belief in this absoluteness, and

2. post this in a internet discussion forum with a pretty wide and diverse membership, where it will obviously insult some people.

 

For example, I think the general point raised by Richard is pretty obvious, and anyone who has never considered it, but makes such a blatant statement as above disqualifies himself from such a discussion. And Richard's point is a pretty small and pretty superficial part of the overall stabilizing effect of religion on society.

 

Gerben, have you ever met or read about a deeply religious person, whose religion obviously had a huge positive impact on his/her life? If yes, how on earth can you reconcile this with a statement like above? If no, is that because you never met someone like this (unlikely), or failed to see it when you did?

 

Anyway, it seems to me making a statement as above is only possible when you see this forum as a platform to display your opinions, not as a discussion forum for constructive discussions. Which, to be frank, is consistent with the perceived attitude in many of your posts, Gerben.

 

End of rant.

 

Arend

[keylime]

I, in the most strong of opposition tendered from my breath, disagree that religion is the worst invention. To have read that religion is this horrible, seriously undermines my respect in some people.

 

To prevent a total firestorm from erupting on here, I will refrain from discussing the whys of this. Trust me, this definitely isn't the place for what would be a firebreathing declaration - that's why God created blogs. You'll read my full response to this disgraceful attempt to discredit what I and the MAJORITY of people in the world hold dear in a couple of days.

 

I will simply state that faith is a most intimate and personal journey, and to dismiss it so readily, is to take humanity and diminish it to a mere existence based on survival, instead of truly living and emerging as a better person as the result of trials and obstacles.

 

<addendum>

 

P.S. I know where I'm going when I die, and it ISN'T down into the ground six feet deep.

[luke warm]

actually this doesn't stand up to logic, if one grants the impossibility of an effect without a cause... because no matter how you slice it, there has to be a first cause

 

added by edit: the reason there has to be a first cause has to do with the nature of infinity and the impossibility of in infinite universe (logical impossibility, that is)... if space/time is infinite, we could never logically prove we are where we are when we are

If you could elaborate further on that I would be interested.

 

To me infinity is absolute (and absolutely inconceivable).

 

--Sigi

the subject is far too vast to bore everyone with, which isn't to say that my knowledge of this area is extensive... however, in debate after debate between atheists and christian philosophers, the atheist invariably came out badly once the big bang theory became widely accepted (and acceptable)

 

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?"...

 

also, there is no logical basis for an *actual* infinite universe... this can be seen by taking a small slice of this universe, the time line, and showing that you can in fact add and subtract from it... we know when sept 11, 2001, was, we can point to it on the time line... if the universe, hence time, was infinite, there would be no way that you or i could say we live this day, this month, this year, because this particular point in time would not exist, we would never arrive "here" by adding 1 year to the next (if infinite, there are an infinite number of time intervals between one another, etc)

 

stephen hawkings has done work based on his creation of imaginary (there are those who dislike the use of that word) numbers... the use of such numbers is the only way his string theory can be supported... that theory can be used to prove an infinite universe, therefore no need for a big bang... one reason for the need of such numbers was the scientific theory of the big bang, and the resulting philosophical/religious problems it created - for those who do not believe in a creator

[han]

What if we stop offending other people and talk about bridge? First it was Gerben offending our religious members, now Luke Warm is offending those members who happen to like imaginary numbers.. me. I am certain that no imaginary number ever harmed anybody, so please leave them alone!

[Chamaco]

Hey folks, let me state my absolutistic view in this respect.

 

The worse ever invention is by far COFFEE TO GO !!!

 

As once I wrote to my gf in the US,

"For me coffee to go is like sex to go : I am sure there are many people who would not mind having it in the streets, but I think that for certain things one needs to take his time"

 

:rolleyes:

[helene_t]

there is no logical basis for an *actual* infinite universe... this can be seen by taking a small slice of this universe, the time line, and showing that you can in fact add and subtract from it... we know when sept 11, 2001, was, we can point to it on the time line... if the universe, hence time, was infinite, there would be no way that you or i could say we live this day, this month, this year, because this particular point in time would not exist, we would never arrive "here" by adding 1 year to the next (if infinite, there are an infinite number of time intervals between one another, etc)

I'm not sure if I don't understand this, or if I just disagree. It sounds to me as either of two problems:

- you cannot ask someone to think of an arbitrary integer (in this case: an arbitrary point in infinite time) because there is no probability distribution that assigns equal probabilities to all elements in an infinite set.

- you cannot construct a language that can denote an uncountable number of elements. So allthough mathematicians talk about the "existence" of uncountable sets, those sets necesarily consist largely of elements that can never be described.

 

But this does not show that infinite sets, such as infinite number of time points, do not "exist", unless you define the word "existing" as "observable". Of course, the visible universe will allways be finite. The idea that the universe is infinite merely says that it is the simplest mathematical model that agrees with observations (or the most beautiful mathematical model, or whatever optimization criteria one prefers).

[Sigi_BC84]

also, there is no logical basis for an *actual* infinite universe... this can be seen by taking a small slice of this universe, the time line, and showing that you can in fact add and subtract from it... we know when sept 11, 2001, was, we can point to it on the time line... if the universe, hence time, was infinite, there would be no way that you or i could say we live this day, this month, this year, because this particular point in time would not exist, we would never arrive "here" by adding 1 year to the next (if infinite, there are an infinite number of time intervals between one another, etc)

I'm completely unable to see your point here.

 

First of all, one should be very careful with assumptions about the nature of "time". Especially one should not equal time to the physical notion of time.

 

In physics, time is used to measure the rate at which changes occur. To be able to handle it mathematically, time is quantified (by observing nature and creating a reference point that way).

 

Now, the physicist's notion of time as a "line" where you can mark events (which undoubtely makes a lot of sense) or as a fourth dimension (which ostensibly makes a lot of sense as well, although I don't have an intuitive grasp of that concept) has become so deeply ingrained in us that we believe that this actually is time.

 

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. Maybe the people who claim to be clairvoyants have found a way to see more in the pattern of things-that-have-already-happened than the ordinary person. This is very speculative and only used here to illustrate my point that taking the concept of "time line" for granted and deriving statements about the impossibility of an infininite existence from it is shortsighted, in my eyes (no offense, Luke).

 

Apart from that I also don't get why, even if the timeline is real in an absolute sense, it could not be infinite in both directions. The set of real numbers is infinite (not even enumerable) and still you can easily compare two given real numbers in size. Likewise you can compare two given points in time to eachother, no matter where they are on the timeline.

 

"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).

 

--Sigi

[luke warm]

- you cannot ask someone to think of an arbitrary integer (in this case: an arbitrary point in infinite time) because there is no probability distribution that assigns equal probabilities to all elements in an infinite set.

- you cannot construct a language that can denote an uncountable number of elements. So allthough mathematicians talk about the "existence" of uncountable sets, those sets necesarily consist largely of elements that can never be described.

well certainly a person is free to imagine whatever s/he wants... that's not quite the case here... not only did the numbers have to be made up, there had to be imaginary rules applied to their use (in formulas, for example)...

 

But this does not show that infinite sets, such as infinite number of time points, do not "exist", unless you define the word "existing" as "observable". Of course, the visible universe will allways be finite. The idea that the universe is infinite merely says that it is the simplest mathematical model that agrees with observations (or the most beautiful mathematical model, or whatever optimization criteria one prefers).

"time" is part of the universe and is not visibile.. however, it is also not infinite... 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'

[luke warm]

I'm completely unable to see your point here.

 

First of all, one should be very careful with assumptions about the nature of "time".  Especially one should not equal time to the physical notion of time.

 

In physics, time is used to measure the rate at which changes occur.  To be able to handle it mathematically, time is quantified (by observing nature and creating a reference point that way).

but sigi, *it does not matter* ... the fact remains that if time itself were infitine, we could never arrive here, now... this isn't something i'm saying just to be clever, even those who wish it were otherwise agree with

 

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

 

Apart from that I also don't get why, even if the timeline is real in an absolute sense, it could not be infinite in both directions.  The set of real numbers is infinite (not even enumerable) and still you can easily compare two given real numbers in size.  Likewise you can compare two given points in time to eachother, no matter where they are on the timeline.

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...

"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'

 

anyone can assert that anything dreamed up by his mind is real... unfortunately, those dreams don't lend themselves well to rational discussion, unless all people share them (in which case they'd be real anyway).. 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"

[helene_t]

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]

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).

 

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?

 

"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.

 

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]

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]

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

 

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

 

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

 

Consider these two models:

1) Some model for a finite universe

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

 

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

 

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)

 

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

 

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

 

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]

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).

 

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]

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.

 

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.

 

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.

 

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".

 

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]

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]

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]

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

 

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?

 

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

 

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?

 

"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

 

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]

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]

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]

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]

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]

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]

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.