08-26-2009, 03:53 AM | #81 (permalink) |
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in principle, the notion of a continually expanding universe is infinite in the same way that the series of numbers is infinite. so for any number n, there is an n + 1.
it is, i suppose, possible that our universe is an aspect of a relative trivial structure within a higher-order system or system of systems. i like to think that we're maybe part of a lima bean or part of a molecule in the upper left corner of a cheap candelabra in some giant mobile home. personally, like i said i think the infinite is a negative concept, the product of negation, a purely formal construct. what's interesting how more how it's used, so what it comes to mean for communities, how different frameworks impact upon projections as to what's Beyond or Other in this way. it's also interesting to think about why it is that not all symbolic systems include a notion of the infinite. so it's a particularity.
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08-26-2009, 10:48 AM | #82 (permalink) |
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I would like to see the proof that "math" (quoted for ubiquity) has to offer for the universe having an end.
To me it seems that if you consider the universe it could be the geometric equivalent of a ray. A start point, but no end point. Infinity doesn't always have to be in the extreme sense. Say you have a machine where you press a button and it gives you a random number. Couldn't it give you an infinite sequence?
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08-26-2009, 11:24 AM | #83 (permalink) | |
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Ironically, I just watched a naked science episode while eating lunch, where they discussed the same topic. In the end a supermassive black hole of everything, and possibly the death of the universe and the beginning of a new one when it popped. Cool. A start point of a ray implies an end, even if one end. Even in concept, not infinity. There can be no end, in either direction. By that, forwards or backwards in time, or on a linear scale of any other measure. No the machine couldn't. The machine is limited by it's physical components, and pulling the plug. If that's not enough, the machine must last forever and spit numbers forever and this realm, this universe, will not last forever. Even if the machine could overcome all obstacles of this universe, the laws that govern the universe itself would destroy it. So could it simply spit out "∞"? Sure. But that is not a number sequence. Also, the number sequence has a beginning. Say it began with 3. It couldn't be infinite, because it has a beginning in time and concept. In the end, it is still constrained by the universe around it. I assume we are talking about reality here. If not, one could devise infinity in any number of ways. We could be a simple observer, floating outside of space/time with an infinity-spitting machine, tossing numbers outside of time in a circular existence as the universe expanded and collapsed for all of your existence. But then another question comes up. How long did you exist? Heh.
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08-26-2009, 07:01 PM | #85 (permalink) |
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No roach, I was referring to Vigilante's.
Vigilante. No offense taken, but if you bring something up here you should make more of an effort to defend it than saying "google it". I mean, I could just say google this whole discussion and end this thread. I disagree with your definition of infinity. You're trying to disprove the notion based on what I consider a non-standard definition of the subject matter. Who said infinity has to go on in both directions? Also, formally, my infinite sequence machine example is such: If infinity exists There can exist such a mechanical device that will produce an infinite number sequence over an infinite amount of time. It doesn't have to be electronic. That's not fundamentally part of it. You can't say it will fail because there won't be enough time, because the statement operates under the assumption that there is infinite time. The task is to prove the opposite to form a biconditional. I feel like it's a biconditional by definition, because an infinite number sequence would take infinite amount of time. So if one exists, there must be infinity. This statement by be cyclically redundant and therefore invalid though, but I challenge somebody to formalize the opposite viewpoint.
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08-27-2009, 12:02 AM | #86 (permalink) |
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To me the statement you made on the machine, and thereby implying infinite time, is like trying to make the sky green because you want it to be so.
If you want to make your own reality, the conversation quickly loses interest (for me). I'm trying to go by what documentaries and such have discussed, not choose-your-own-adventure. That's just my take on the topic. If you want to go random on me, that's fine. I just lose interest The symbol for infinity has no beginning and no end. ∞ That is the definition of infinity I am talking about. Not a line with a starting point. "∞" has no starting point. If you start somewhere, anywhere, you have lost infinity. To me, the only thing that might have an infinite definition in this universe is gravity and other universal/molecular forces. Gravity brings about the crushing of the universe. Presumably, it is back when the big bang happens again. It can't be tested or proven, but logic dictates that it remains. Otherwise how could the big bang have occurred? Not to nag, but I have 3 hours of free time a day, and 4 if I lose sleep. I don't want to spend it researching a given topic when I could be looking at porn or something.
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09-02-2009, 01:27 PM | #87 (permalink) | |
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I think infinity as a theory/practical math application exists of course. But no, to us infinity does not really exist. Everything, everywhere dies. |
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09-02-2009, 02:59 PM | #88 (permalink) |
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11 dimensional terms? If you're referring to string theory, that's not widely accepted. In fact, it's mostly believed to be false. It would not be fair to use that in this discussion because it does not fall into the set of common terms and beliefs that we all share.
Zeraph - Your approach is umm... I can't think of a better word than egotistic. I don't mean it in a negative way... just that it pertains to the ego of living things. The world was around before you were born, and will probably be around after you die my friend. So just because you're not infinite in longevity does not mean that something else cannot be.
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09-03-2009, 12:06 AM | #89 (permalink) |
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Yes, if you completely ignore the way the universe is behaving. Well duh, of course we die. The universe will too, it's just not there yet. Are you completely ignoring the observations every physicist/cosmologist/astrophysicist/etc in this field of study has made and generally agrees upon?
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09-03-2009, 07:49 AM | #90 (permalink) |
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No. But it seems I shouldn't expect you to actually read what I'm saying once you've made your mind up on what you think I mean.
My last post never made a claim that the universe is infinite. I'm simply disputing the reasoning that because people die, nothing is infinite. However, I should caution you again against the arrogance of simply believing whatever it is "every physicist/cosmologist/astrophysicist/etc" believes (and I doubt very much that every man more learned in the field than you or I believe this). After all, was it not Galileo who was punished for declaiming the flat earth theory? We never know, and as far as I'm concerned this theorizing is inconclusive, and more importantly IMPERTINENT to this discussion. So kindly, please drop it. One of us is misunderstanding this discussion. I see this as a hypothetical question of concept and potential. Your argument, as I see it, is that because the universe will end (according to popular opinion), nothing can be infinite. To this, I say, what if you have a yard stick and you cut half of it off. Is it still a yard stick? Better example: If a bullet is flying and you lift up a piece of metal and block it half way before it reaches its target. Can you not make a projection of where it would go? So even if the universe ends, precluding an infinite process, motion, etc, is it wrong to call it infinite? ---- also, @zeraph and @meri I don't think meri was being literal. It's a hypothetical principle used to outline certain flaws in logic. It was first introduced to me in calculus class when studying integration and derivation, because those deal with infinitely halving things.
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In the end we are but wisps Last edited by ManWithAPlan; 09-03-2009 at 07:52 AM.. |
09-03-2009, 10:14 AM | #91 (permalink) |
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Yeah I jumped the gun a little. My bad.
I know every person in the field does not believe the same thing. Even as I typed "every", I was thinking of a documentary involving the constant C changing over the course of the expansion of the universe. In some way perhaps the universe is infinite. If it recycles, then the forces involved would most likely remain familiar. Gravity, electromagnetism, various molecular forces, etc. have no reason to deviate, especially if when a black hole spews matter at it's collapse, the resulting energy and mass behave as everything else. Some things could deviate though, in some minor way with profound results. I don't know. The more I think about it, the more I argue with myself. Arguing with yourself can get boring real fast.
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09-03-2009, 11:35 AM | #92 (permalink) |
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The speed of light is also different through different substances. Seeing as how we know very little about what is at the 'edges' / far reaches of the universe, we can't tell for sure what the speed of light there is, or what material alters it. Black holes are also fabled to be able to bend the path of photons, which seems to me like it would modify their speed (not just velocity vector).
I don't think it's necessary to consider the universe when considering infinity. Instead of taking the object of question and casting it in the light of things we know, what we, in this thread, are doing is casting it in the light of things we actually know very little about. The concept of infinity is older than our knowledge of the universe, so surely we don't absolutely need modern science to answer the question, do we?
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09-03-2009, 11:59 AM | #93 (permalink) | |
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Unless you had something else in mind. If so, do tell Also, the speed of light is different through substances because of molecular interference. C defines light as light in a vacuum. Playing bumper cars does not change the speed of light.
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09-03-2009, 02:51 PM | #94 (permalink) | |
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09-03-2009, 05:09 PM | #95 (permalink) | |
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09-03-2009, 11:51 PM | #96 (permalink) |
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Not in this realm. Not trying to bring personal spirituality into this. Just saying.
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09-04-2009, 06:14 AM | #98 (permalink) |
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so let's assume that there is something more to this notion of the infinite than an empty space hollowed out by the word "infinite"...
why would something infinite be singular? same kind of question: what lets us assume that there is *a* universe? why aren't there any number of them? the explanation's not in the universe, but in the word "universe" yes?
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09-04-2009, 07:16 AM | #99 (permalink) | |
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09-04-2009, 07:47 AM | #100 (permalink) |
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the universe was an example.
the point concerned the notion of infinite-ness and what relation it could possibly have to a singular process. i know the answer, really: the idea of an infinite process is a transposing of that of the number series in general, so another version of for any number n there is always n+1 i just thought it curious that we talk about "an" infinite anything. the main point is i see little in this beyond playing about with the hole created by the word infinity, which requires no referent and no knowledge of a referent, a hole generated through relatively simple acts of semantic inversion or negation. but still, how exactly does a single infinite process make sense? if the process is itself singular, it can't be infinite---it can be endless. but endless and infinite aren't the same are they? except if you adopt the position that the number series is a model for the infinite. but that seems kinda trivial, in my humble opinion. just poking around.
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09-04-2009, 08:08 AM | #101 (permalink) |
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Roachboy:
finite - Definition from the Merriam-Webster Online Dictionary infinite - Definition from the Merriam-Webster Online Dictionary Merriam Webster defines the infinite as the boundless, or endless. I think that's the most standard generic definition. There are different ones depending on the field in which you delve. Religion, mathematics, etc. have slightly different variations. So to answer your (possibly rhetorical but whatever) question: endless and infinite seem to be the same, and you don't necessarily have to exhaust all of them since it is mathematically possible to prove that something is infinite. (A universally accepted notion)
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In the end we are but wisps Last edited by ManWithAPlan; 09-04-2009 at 08:11 AM.. |
09-04-2009, 08:20 AM | #102 (permalink) |
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a merriam webster dictionary definition doesn't exactly resolve questions of meaning.
if they did, all philosophy would be is putzing about until someone in a conversation got fed up with it and decided to turn to a dictionary. i would think a finite process could theoretically be endless in the sense that it would repeat it's activities endlessly and produce whatever it produced endlessly, but that seems to me a finite situation, infinite only in the most restricted (mathematical) sense. infinite has a considerable metaphysical weight to it, a considerable history. to collapse it into it's mathematical definition requires that you define the rules of the game up front such that this is the meaning that we are talking about. the op did it to some extent long ago, but the discussion moved out from under that. such discussion as there is here at this point is really a conflict over which rules for interpretation obtain. i've been playing by the rules of philosophy of language; vigilante by something between cosmology and something else (can't remember); you by mathematics. so it's no surprise there'd be a differend. and it's no surprise that the debate would reach a point where someone would try to stipulate the rules by stipulating the genre. thing with doing that is that it makes discussion circular. you know in advance the meaning that's in question because the rules of the game spell it out for you. the philo of language is probably the only space that allows for consideration of the relation between such rule sets, words and phenomena in the world that they're made to refer to. but this is also a genre with it's own rules. so by mentioning it, i engage in the same game of trying to stipulate which game we're playing. we could go in any of these directions. but no question of any real interest is settled via merriam webster---except in the special case of one or another player in a given game not understanding the word.
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09-04-2009, 08:28 AM | #103 (permalink) |
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I don't think you can consider one without considering them all. In your head you can contemplate whatever, but as soon as it becomes interpersonal we are bound by the rules of language. If we're talking about infinity, we have to adhere to the commonly accepted definition of the word. If you or the OP mean to discuss something else, or your personal conception of infinity, then it has to be explicitly stated.
I am not taking a strictly mathematical approach. I feel like I've taken a few here, and what you just said is more or less what I've been saying. We have to start from a common ground and only use things which are understood and accepted by everyone. This is ancient philosophic theory. Perhaps, since you seem to be adequately versed in philosophy, you'd care to give us this grounding, and then we can all work together to come to some sort of conclusion. (Most likely not, but hey). Will you present us with the definition of infinity (that we should discuss) and propose a method we should use to resolve this question? There will be no more debates on what infinity means, and from there on in Infinity will be used to refer to the item defined by you.
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09-04-2009, 08:55 AM | #104 (permalink) |
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i did already. i defined it as a negative concept, one produced through inversion of notions like finitude. it has no particular referent. to generate notions like infinity, all you need is the capacity to negation, which is a formal matter.
within christianity, negative theology came closest to addressing it's meaning: we have no access to the infinite because our understanding is finite. so if god is infinite, human beings can know nothing about this god, not even whether she exists or not, and the name "god" is nothing but a name. that repeats the act of creating a notion through negation of an existing one. but at least it's consistent. from that viewpoint, mathematical notions of the infinite are just one of any number of ways to locally define the category, one which produces some interesting effects and is useful within certain games. what i think makes the category of the infinite interesting is how it gets used and what those usages do, not what putative referent there is in the world/universe. it's interesting as a generator for speculative thinking in some contexts. but these usages are conditioned by rules, so the meta-question (to my way of thinking anyway) has to do with rules usage and phenomena in the world, how relations are established, how they condition processes of meaning generation, and how the results of these processes frame experience of the world. so i wouldn't go in the same direction as you in pursuing the question of what the infinite is, really. not that yours isn't interesting...it's just not how i'd approach it. but this all follows from the premise that the infinite is the product of an act of negation, so is the result if you like of a formal operation. in other words, it is a noun that is not a name. that's what i think the category is.
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09-04-2009, 09:01 AM | #105 (permalink) |
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Yours is an interesting approach, but perhaps I'm not fully understanding your definition, because it seems a little bit vague to me.
Is the sequence of PI infinite? Does that prove infinity? Or does this miss the point you're trying to make? Are you saying that infinity has to be spatial? (length, weight, duration) or not?
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09-04-2009, 09:06 AM | #106 (permalink) |
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I pondered the idea of infinity all night because I did not sleep.
Perhaps it's just an eternal awakeness of sorts. I no longer 'suffer' from insomnia. Now I call it, infinity. It was a fun game, while it lasted...um wait, that means I finited it. Oh well. |
09-04-2009, 09:30 AM | #107 (permalink) |
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the sequence of pi would be under the rules that are particular to mathematics, so assuming that something infinite is a series that it in principle endless.
my definition is more an explanation: if you assume the term finite, the infinite is simply it's negation. everything that is not finite, then. so it's not a name in the sense that there's nothing to point at. it's an empty signifier that way, a form that delimits. so a pure category. that's what lead me to the bit about negative theology. if you assume human understanding is finite, then the infinite would not be accessible to it. this follows from strictly applying the same operation i outlined above. the usual assumption with a noun is that one treats it as a name. there is a phenomenon in the world, you can in principle point to it, this is what that phenomenon is called, how it's referred to. what i'm saying is that this notion of the infinite comes about through another route, through inverting another noun. you could say---and people have (descartes for example)---that because i know the category "the infinite" that it follows that there is such a thing. but that supposes the noun is a name, in the sense the start of this paragraph indicates. if it's not, and it's a negation or inversion of another noun, then it's an empty space. once the category is in place, it functions to point toward this empty space (everything which is not finite). descartes' treatment of it as a name makes little sense outside the particular christian tradition he was part of. it's curious to see it wedged into the meditations on first philosophy, just after the cogito ergo sum business, so just after he attempts to ground philosophy. but there it is. you can see for yourself.
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09-21-2009, 03:26 PM | #108 (permalink) |
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I think infinity is possible and what it does is simply take you to another dimension.
An example: An infinite number of 1 dimensional lines gives you 2 dimensional plane An infinite number of 2 dimensional planes yields you in the third dimension An infinite volume of 3 dimensional models takes you to travel time through parallel worlds An infinite number of 4 dimensional time lines takes you to deal with another unit called tachyon which recently to have infinite speed(faster than light). And so forth Also to create millions of species and atom based precision in movement of planets in an order of 10 to the power who knows what span of the galaxy, you would need infinite super computing wisdom that God only has. |
09-21-2009, 03:30 PM | #109 (permalink) | |
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The second dimension does not admit the third. I know what you're trying to say, but no, that's not how it works. Otherwise you could only ever have things with infinite measurements in all dimensions. Also, please don't bring "God" into the equation, because that's a separate discussion, and it's not an element that everyone agrees on. I don't see the connection with tachyons either.
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09-21-2009, 03:52 PM | #110 (permalink) |
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Hello ManWithAPlan, sorry if I included the subject of the creator in my reply. I was just trying to be add to the subject of infinity, infinite wisdom.
Here's what I mean about the second dimension. If you have an infinite number of planes with Angstrom width they will add together to a certain definable width which you define depending on the number of planes and the variables in question. As in: A = A number going to Angstrom ( I stress going to) B = A number going to Infinity = 1/A Hence Width = constant * A * B = k * A * 1/A = K = a certain volume definable |
09-21-2009, 03:54 PM | #111 (permalink) |
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I think the question of whether infinity exists has a lot in common with the question of whether god exists in that there really isn't any proof either way, but folks tend to come down on either side of the fence anyway.
Why would anything tangible be infinite? Why wouldn't it? I challenge anyone to answer either of these questions affirmatively with anything other than a handful of wishes. |
09-21-2009, 03:56 PM | #112 (permalink) |
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Oh regarding Tachyons its a hypothesis of mine about infinity. An infinite number of time lines in the forth dimension yields you in the dimension where you are in comparable speed to the (x where x goes to infinity) speed of the Tachyons which I think in my humble opinion is the 5th dimension.
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09-21-2009, 04:27 PM | #113 (permalink) |
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@cellfactor: No need to apologize. It isn't as though you've offended me. I'm simply trying to keep us on track. There are rules in philosophy. You can't try to explain something in terms other than those that everyone accepts. For instance, I may not accept that god is infinitely wise, or I may not know he is, so it's not a good way to try to prove something.
A two dimensional plane does not have a height. You can theoretically position them (theoretically, read: academically) in 3-space such that the origin of each will have a z-coordinate, but they still won't have a height, so you could not stack them. If you're talking about an infinite amount of pieces of paper or something that is like a 2d plane but has the height of an angstrom, then the height of the stack is infinite. I don't know what you mean by "going to". I assume you mean "approaching", as in limits, which is also a theoretical concept, and not something observable. I also don't understand what your equation is trying to show. Of course if you pick three things, set two of them to be inverses, and multiply them, you'll be left with the third. It doesn't seem to show anything at all. @filtherton - who says only tangible things can be infinite? The way I see it is you have 3 levels of abstraction: tangible, observable, conceivable. Let us reserve tangibility to our concrete perceptions. We can see and feel a yardstick. It has an innate spatial length. Let observable be the set of properties which we can observe though are not innate to an entity. Like a cycle, a planet's orbit, a trajectory, the passage of time, a wheel's rotation Let conceivable be the set of concepts which we can imagine with our minds but not experience directly for one reason or another. Seeing as how our lives are limited, we cannot experience infinite time. We also cannot experience breathing underwater without the aid of SCUBA gear... we cannot experience being a bird. But that doesn't mean those things don't exist. As our senses are limited, we cannot experience infinite length or distance. We also cannot see all the way to china from the usa, but that doesn't mean that china doesn't exist. We can however talk about these things, including infinity, so it must exist. If there is no example of it in the universe, it exists only conceptually. but if there is no experiential example, then it can still exist on one of the other two levels; we just can't see it. "Why" implies teleology. Can you prove that things have a purpose? If not, then you can't ask that question. Something might be infinite simply by coincidence. To revive an old challenge - If the universe is not infinite, then what do we call the thing in which the universe sits? Is that infinite? Does a non-infinite universe imply multiple universes? Are they infinite? If so, does that not mean that the thing that contains them has to be infinite? And ultimately, if the universes are not infinite, what acts as a boundary between them that prevents us from saying that they are really just one universe? edit: I've also just thought of something that I think pretty much ends this debate: Infinity exists. Time is infinite. Time is always measured from a frame of reference. If the universe is infinite (in time), and has no end, then time within the universe is infinite and infinity exists. If the universe is finite, there must be another frame of reference which can admit that*, which seems to me has to be infinite** * Meaning, can see the beginning and end of the universe. ** Unless that thing also comes to an end, in which case there must be something else, etc. edit 2: Can you link me to your Tachyon theory? I could try to find it myself but I want to make sure I get the exact one that you mean.
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In the end we are but wisps Last edited by ManWithAPlan; 09-21-2009 at 04:42 PM.. |
09-21-2009, 05:45 PM | #114 (permalink) | ||||
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Your argument here depends on some pretty arbitrary notions about what must exist outside of the universe. |
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09-21-2009, 06:49 PM | #115 (permalink) |
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It's not teleology to say that the universe must reside in something. It's just logical. If you have something that is not infinite, then what happens when you go outside it? Note: I'm not saying it does reside in something because I'm not saying it's finite. But if we take as given that it's finite, and we can traverse it, then that means there must be such a point where we cease to be in the universe and must be in _something else_.
Note the scenario where all space is bent such that when traveling to the outer reaches of the universe you end up wrapping around. This would be something like a hyper-sphere effect where the dimension is folded up upon itself. To me, that would be infinite, but that's another topic, sort of. Why do you need a frame of reference? Because that's how time is measured. Theory of relativity?
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In the end we are but wisps Last edited by ManWithAPlan; 09-21-2009 at 06:52 PM.. |
09-21-2009, 07:09 PM | #116 (permalink) |
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If time needs a reference in order to be measured, then outside of that reference, time does not exist, therefore applying some notion of infinity to it seems illogical since it can't be measured outside of a reference.
I believe infinity exists simply because I can't see a reason not to believe it exists. However, proving it becomes paradoxical because we would need an infinite existence to prove it.
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09-21-2009, 07:10 PM | #117 (permalink) | |||
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The mathematical line has zero thickness not angstrom thickness however when we talk about reality there is no such thing as zero thickness. No matter how small even if it is smaller than a quark it will have a thickness. Now volume, matter, and time are reality hence their equations are those created by variables that have their extra dimension not being zero hence its the closest number to zero. the closest number to zero is angstrom hence angstrom applies to dimensions in reality. Imagine it like this. I want to draw two dots A and B on a line. Dot A and Dot B are each on certain centimeters from Zero point. Dot width: 0.000000000000001cm Dot A pos: 0.000000000000001cm from Zero Dot B pos: 0.000000000000001cm from Zero they will still be on the same spot so i want to make them on different spots Dot width: 0.00000000000000000000000000000001cm Dot A pos: 0.00000000000000000000000000000001cm from Zero Dot B pos: 0.00000000000000000000000000000001cm from Zero Still on the same spot so: Dot width: 0.00000000000000000000000000000000000000001cm Dot A pos: 0.00000000000000000000000000000000000000001cm from Zero Dot B pos: 0.00000000000000000000000000000000000000001cm from Zero ok so I do like this Dot width: 0.0000000000000000000000000000000000000000000000001cm Dot A pos: 0.0000000000000000000000000000000000000000000000001cm from Zero Dot B pos: 0.0000000000000000000000000000000000000000000000002cm from Zero Now they are not on the same spot but they're: 0.0000000000000000000000000000000000000000000000001cm from each other So what it means if you have to have 2 points that are distinct from each other and you want to line them up near each other in physical space then the 2 points have to not lie on top of each other. meaning the points should be angstrom apart from each other. this means the closest space between 2 points is angstrom. now if we put an infinite number of angstroms near each other they will get you a certain value as defined earlier. If you have time perhaps you can ask a math teacher about it. Quote:
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09-21-2009, 08:03 PM | #118 (permalink) |
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Location: M[ass]achusetts
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I know what an angstrom is. For any number n | n > 0; n * infinity = infinity.
If you have an infinite amount of angstroms, it will give you infinity. JumpinJesus - I'm not sure I understand what your point is. There are lots of references that we use... such as "time from event A", but there's also relativistic time, as in the theory of relativity. If something has a motion, its trajectory can be plotted with a reference point to something. If something has a duration (a defined beginning or ending), then its being can be plotted with a reference point to SOMETHING. Otherwise it doesn't make sense and that first something must not have an end point.
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09-22-2009, 01:58 AM | #119 (permalink) | |
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x where x decreases ever * y where y increases ever = k why k, its because k is to be a constant since x and y are in the same dimension. You see lengths of 2 units would increase at the same speed in the same dimension if you put them under the same effect, hence linear difference. Its like a car with an engine A and a car with an engine B, the cars maximum speeds are at linear amount from each other because they both use the same combustion technology. Now if you use a car with hybrid technology, thats another dimension. |
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09-22-2009, 03:02 AM | #120 (permalink) | |
Junkie
Location: In the land of ice and snow.
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If the universe was finite, it probably wouldn't need its finiteness measured. It's quite possible that it would remain finite without any sort of frame of reference to measure it. Time passes while we sleep, after all. |
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exist, infinity |
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