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| Philosophy General philosophy: metaphysics, ethics, the Enlightenment, and the human experience. |
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06-28-2007, 07:11 PM
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#17 (permalink) | ||
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Why do cows say MU?
Join Date: Aug 2005
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Re: disproving infinity paradoxes; Hilbert’s Hotel?
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06-29-2007, 04:11 AM
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#19 (permalink) | |
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Exercises in futility
Join Date: Oct 2005
Location: Edinburgh, scotland
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Re: disproving infinity paradoxes; Hilbert’s Hotel?
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Ok Ok Ok !! Maybe!! |
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06-29-2007, 11:16 PM
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#20 (permalink) | |
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~~~~~~~~~
Join Date: Jan 2004
Location: Gator Country, FL, USA
Posts: 3,829
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Re: disproving infinity paradoxes; Hilbert’s Hotel?
Kindest Regards, all!
Quite a thought provoking discussion you have started, z! Quote:
IF the hotel already has an infinite number of "full" rooms, then an infinite number of guests are already accommodated. That is to say, there can be no more "new" guests because they have already been "lodged" before they "arrived." As for the universe having an end or edge...who are we to say with the limited view we hold? Perhaps the universe is finite, in some sense we might agree...beginning, middle, end, and "size." However, these quantities and measures are simply too vast for us to fathom with the tools we have (our minds and our instruments). I suppose one analogy (from Christian parlance) is the number of hairs on our head, or the number of grains of sand on the seashore. Obviously, these are "numbered," but that number is relatively beyond our grasp. Today, we can calculate into astronomical terms...billions upon trillions upon quadrillions upon quintillions...but these are mostly abstract hypotheticals arrived at by calculating with far smaller numbers, extrapolating the data, and extending the sequence farther afield. Too wit, we may not know "accurately" the full number of hairs on our head, but we can take a representative sample and apply it to a measured map of our cranial anatomy. Same concept can be used to calculate "the sands of the seas." But...if one is striving for absolute factual "truth"...then one must add a "fudge factor." "We calculate that there are X number of grains of sand, plus or minus a certain percentage (fudge factor)." When it comes to calculating the width, depth and breadth of the universe (assuming "only" three dimensions), there are too many variables yet unknown to us. I feel this is why the universe is typically presented as "infinite." According to Big Bang theory popularized by Dr. Hubble, the universe at one time was an immense mass crowded into a hopelessly small size. I have heard some astronomers suggest as small as a teaspoonful. Can you imagine a universe, with all of the matter and energy known and unknown condensed to such a small size? Yet...at that point in time...what lay beyond the universe? Here is where the question of whether nothing is something may be relevant. For if "nothing" lay beyond that teaspoonful of condensed material, wow! Fast forward...is that same nothing still just beyond the outer limits of the universe? We have no way of knowing at this point in time, but I can see where it leads to all manner of speculation, such as string theory and multiple universes. Infinity is a concept we use, philosophically speaking, when the concepts are too large to grasp, too large to wrap our minds around. No matter (pardon the pun), we have enough to struggle with just dealing with the astronomically large numbers and sets we know exist and cannot fully comprehend without "educated guesses." I cannot state emphatically that the universe is a sphere 28 billion light years across at the equator...I haven't been to the edge to measure. What's more, by the time we "could" get to the edge to measure, it will have already grown even more! In that dynamic "growing" sense, I think the universe is actually infinite. Of course, then raises the quandary of more and more space filled by an unchanging amount of matter and energy... My humble two cents.  Last edited by juantoo3 : 06-30-2007 at 02:18 AM. |
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06-30-2007, 02:59 AM
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#21 (permalink) |
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Executive Member
Join Date: Oct 2005
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Re: disproving infinity paradoxes; Hilbert’s Hotel?
It occurs to me, just thinking about exponential operations, that infinity: that is the ability for there to be no end to a process, is an essential ingredient in lots of common, around the house so to speak, functions. Lot's of really common little math thingies have to do with repeating decimals. So that begs the question: why the 33 1/3 rpm LP's? Is it a matter of dynamics?
Chris |
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06-30-2007, 06:20 PM
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#22 (permalink) |
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from far far away
Join Date: Aug 2005
Location: oxfordshire
Posts: 651
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Re: disproving infinity paradoxes; Hilbert’s Hotel?
infinity is not purely conceptual in my mind. it it is then you have to replace it with something else - and that would have to have no limits too, in short you can only replace it with itself. if you don’t have infinity then what is beyond what ever we do have? there is always a beyond - but not beyond infinity.
the infinity lamp this puzzle is a lot simpler than the hotel one, and i think we can resolve a few issues with it. quote: Question. Consider a very durable ceiling lamp that has an on-off pull string. Say that the string is to be pulled at noon every day, for the rest of time. If the lamp starts out off, will it be on or off after an infinite number of days have passed? Answer. The lamp could in fact be either on or off after infinitely many days. Information about its state after any finite number of days is not enough to enable us to extrapolate past infinity. What makes this question interesting is that it is possible give an argument that seems to indicate the lamp will be on, as well as an argument that seems to indicate the lamp will be off. On: "The light starts out off, and then we turn it on. Each time we turn it off again, we immediately turn it back on. Therefore it must ultimately be on." Off.- "Each time we turn the light on, we immediately turn it back off. Therefore it must ultimately be off." This type of lamp is called a Thompson Lamp. firstly we may ask; what exactly is an infinite number set? in maths surely we are actually talking about open number systems! it is presumed that you can have an infinite set of natural numbers, yet in truth what is visualised is a very large number without end.this means that you can add for instance; injective or bijective sets, to the original infinite number set - add infinitum. you can keep adding sets because infinity is thought of as without end, thus another set can be added without detracting from that space [the open end]. in short then you cannot have an infinite number set, nor add sets to it. you can have open ended number systems or potential infinities just as we can have theoretical geometric shapes which begin and end at infinity. thus you cannot have a lamp that can be switched on or off infinitely, nor an infinite amount of days to perform this task in. |
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06-30-2007, 09:29 PM
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#23 (permalink) | |
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~~~~~~~~~
Join Date: Jan 2004
Location: Gator Country, FL, USA
Posts: 3,829
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Re: disproving infinity paradoxes; Hilbert’s Hotel?
Only got a minute, Z...
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Let us consider from a somewhat different perspective, that of zero. What is zero? Zero is one of the most powerful forces in the universe...let us place your imaginary lamp into the black hole of zero, and play the on-off game for an infinite amount of time, and what will the outcome be? Zero.  |
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07-01-2007, 04:49 PM
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#24 (permalink) | |
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Why do cows say MU?
Join Date: Aug 2005
Location: Pacific Ring of Fire
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Re: disproving infinity paradoxes; Hilbert’s Hotel?
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Therefore, the best answer would be a question: Is the lamp on or off now? Yes, it is either on, or off. The funny thing is, where ever you are, it is "now." |
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07-01-2007, 06:00 PM
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#25 (permalink) | ||
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~~~~~~~~~
Join Date: Jan 2004
Location: Gator Country, FL, USA
Posts: 3,829
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Re: disproving infinity paradoxes; Hilbert’s Hotel?
Kindest Regards, Seattlegal!
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07-01-2007, 06:55 PM
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#26 (permalink) | |||
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Why do cows say MU?
Join Date: Aug 2005
Location: Pacific Ring of Fire
Posts: 1,583
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Re: disproving infinity paradoxes; Hilbert’s Hotel?
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07-01-2007, 08:42 PM
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#27 (permalink) | |
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from far far away
Join Date: Aug 2005
Location: oxfordshire
Posts: 651
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Re: disproving infinity paradoxes; Hilbert’s Hotel?
juantoo3
excellent description which completely agrees with where i am going here - thank you! i have had a seven page battle with mathematicians at another forum and they just don’t get it. zero is interesting, someone said that the combined value of all energy in the universe is zero. the interesting thing about infinity is that you may produce as many zero’s as you like as long as they have no value they don’t create a paradox, then when we consider the above, that the universe itself emanates from zero, then infinity become a fascinating and interesting field of exploration - for me this includes creation and eminationary notions. seattlegal Quote:
so hands off science it belongs to us |
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07-02-2007, 01:42 PM
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#28 (permalink) |
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Exercises in futility
Join Date: Oct 2005
Location: Edinburgh, scotland
Posts: 2,490
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Re: disproving infinity paradoxes; Hilbert’s Hotel?
So infinity is always beyond all efforts to observe as a whole. So is it like the cat and expands with observation, is infinity dependent on the observer? And what about the reverse of outward looking infinity, what about going inward through the microscope? Is there infinite space there too?
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07-02-2007, 05:50 PM
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#29 (permalink) | |
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Why do cows say MU?
Join Date: Aug 2005
Location: Pacific Ring of Fire
Posts: 1,583
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Re: disproving infinity paradoxes; Hilbert’s Hotel?
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n=any nonzero number |
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07-02-2007, 08:36 PM
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#30 (permalink) | |||
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from far far away
Join Date: Aug 2005
Location: oxfordshire
Posts: 651
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Re: disproving infinity paradoxes; Hilbert’s Hotel?
tao equus
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well that is how i see it anyhow. Quote:
seattlegal Quote:
i have considered similar notions, very interesting - thank you. when we consider the totality of energy = 0 then it makes more sense as a real ‘force’ of creation/emanation. i would consider it so that from this base all things would arise autotelically [see below] i.e. all entities either actual or in terms of law and principle, would arize from their base ‘0’ value! [1] autotelic philosophy; possessing internal purpose: describes an entity or event that has within itself the purpose of its existence or occurrence. |
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