| From: vorpal_sword | 7/05/99
12:47:20 |
| Subject: Infinite universe? | post id:
10154 |
| If the universe is still
expanding, how can it be infinite if there is room for
expansion? | |
| From: George | 7/05/99
12:49:29 |
| Subject: re: Infinite universe? | post id:
10156 |
| The universe is really really big
but not infinite (snicker-snack) | |
| From: Manfred | 7/05/99
13:02:27 |
| Subject: re: Infinite universe? | post id:
10159 |
| You should not think of the
universe like blowing up balloon in a room. There is no outside to the
universe, no perimeter. It expands by creating more space. You can never
reach it's boundaries because it has none. Traveling in a straight line
will take you back to where you started from,
eventually. | |
| From: George | 7/05/99
13:14:58 |
| Subject: re: Infinite universe? | post id:
10161 |
| really really big: self
evident. not infinite: do you accept that the universe is expanding? if so, then it cannot be infinite. Seriously, this topic has been done to death in this forum - please check earlier posts from many of the regulars who have explained this much more convincingly than I ever could. | |
| From: James Richmond (Avatar) | 7/05/99
13:22:05 |
| Subject: re: Infinite universe? | post id:
10164 |
| That's the funny thing about
infinity. If you take something infinite and double its size, it's still
infinite. Actually, it's still the same order of infinity, too. For example, consider Hilbert's Hotel. This hotel is unusual in that it has an infinite number of rooms. Now, suppose every room is occupied. A new guest arrives and asks for a room. The guy at the desk says "No problem. You can take room 1. The person currently in room 1 can move to room 2. The person in room 2 moves to room 3, and so on. Since we have an infinite number of rooms, no-one will be left without a room." Now suppose an infinite number of new guests turn up and ask for rooms. The guy at the desk says "No problem. All the people currently in the hotel can be moved to double their current room number (e.g. the person in room 8 moves to room 16). This means that all the odd numbered rooms will be free, and we can fit in the extra infinity of guests." Notice that at no time in the process do we need to change the size of the hotel - it remains the same sized infinity. Now, the interesting thing is that there are actually different sizes of infinity, but that's another topic. JR | |
| From: Sue | 7/05/99
13:30:14 |
| Subject: re: Infinite universe? | post id:
10166 |
| How can infinity be doubled?
Surely the definition of infinity prohibits
this! | |
| From: Manfred | 7/05/99
13:37:22 |
| Subject: re: Infinite universe? | post id:
10168 |
| I agree. Infinity is just that.
Double it and you get the same thing. I don't consider the universe
infinite. We just can't easily comprehend that it has no boundaries. It is
not a 3D object. As I said earlier you can travel in a straight line and
end up back where you started from. You cannot leave the universe. At
least not from what we know. The universe is a closed system. Even if we
could live at the time of the big crunch we could not escape it. no matter
what direction we took, we would face it.
| |
| From: Chris (Avatar) | 7/05/99
14:17:40 |
| Subject: re: Infinite universe? | post id:
10179 |
Actually James is spot on right here. There are a variety of infinite numbers, and you can perform real math with them. For example consider the infinite number which is the sum of all positive integers: 1 + 2 + 3 + 4 + ... so on. Now take each member of the set of integers above and double it. Add them up. Compare this new infinite number with the first one - which is bigger? James' hotel example is a hint... Chris | |
| From: Manfred | 7/05/99
14:41:56 |
| Subject: re: Infinite universe? | post id:
10190 |
| This sounds like nonsense to me.
Even if you multiplied all the integers instead of adding them you would
still end up with the same answer, infinity. Even if you raised infinity
to the power of infinity, it is still infinity.
| |
| From: Sue | 7/05/99
15:05:51 |
| Subject: re: Infinite universe? | post id:
10201 |
| I'm unconvinced that this is
anything other than an artifact of mathematical theory. I suppose it
depends on your definition of
infinity. | |
| From: Rhys | 7/05/99
15:29:17 |
| Subject: re: Infinite universe? | post id:
10205 |
| Vorpal_Sword.. hmmm, not the same
Vorpal sword that slew the dreaded Jabberwock? Calloo Callay! Perhaps too this is the same Vorpal Sword who took residence for so long in the hallowed halls of battle.net? Is the universe infinite? Some parts of it are. For example, we must say that the universe equals the sum of all the universe's many aspects. Time is a universal aspect, as is space and matter. These can be mathematically shown to be finite. However, one must also say that life is a universal aspect, and ipso facto so must be thought. The realm of the thinking mind has infinite dimensions... there are no boundaries or limitation on what we can think. Therefore, thought is infinite, therefore a part of the universe is infinite. It has already been shown that infinity exists in the realm of math, and since math is a part of the universe (many would say an integral part), there we have another aspect of the universe which allows for infinity. But we have already said that the physical dimensions of the universe are indeed finite.. so we have a TARDIS situation. The infinite is dwelling within the finite. rhys | |
| From: Terry Frankcombe | 7/05/99
16:02:40 |
| Subject: re: Infinite universe? | post id:
10213 |
| The realm of the
thinking mind has infinite dimensions... there are no boundaries or
limitation on what we can think. Therefore, thought is
infinite Can you prove this? | |
| From: James Richmond (Avatar) | 7/05/99
18:16:11 |
| Subject: re: Infinite universe? | post id:
10271 |
| Infinity is a difficult concept
to get your mind around. Sue asks "How can infinity be doubled? Surely the
definition of infinity prohibits this!" Manfred
agrees. Mathematicians have thought a lot about infinity. They define infinite quantities in two ways, which give us ordinal numbers and cardinal numbers. Ordinal numbers are based on counting. When we write a+b, it means count to a then count b steps further. Similarly, a*b means count up to a b times in a row. For finite numbers a+b=b+a and a*b=b*a. However, for infinite numbers this is not true. Suppose we write a number as an equivalent number of x's in a row. Then, for example 3+5 = 5+3 = 8 would be written as: xxx + xxxxx = xxxxx + xxx = xxxxxxxx But consider: 1 + infinity = x + xxxx.... = xxxxx.... = infinity as compared to infinity + 1 = xxxx.... + x = xxxx.....x = the next number after infinity! Similarly 2*infinity = xx + xx + xx + xx + .... = xxxx..... = infinity but infinity*2 = xxxx.... + xxxx.... = xxxx....xxxx.... = a bigger ordinal. Cardinal numbers are based on correspondences between sets. If two sets (or ordinals) can be put into one-to-one correspondence they are said to have the same cardinality. All finite numbers have different cardinality. This is obvious since you can never put a group of, say, 3 objects into one-to-one correspondence with a group of 2 objects. But many infinite ordinals have the same cardinality. For example, in the Hotel example we can fit an extra infinity of guests into the hotel without increasing the number of rooms, just by shifting people around so that we get a one person to one room correspondence. This tells us that infinity + infinity (or infinity*2) has the same cardinality as infinity. Mathematicians call this number - the smallest infinite cardinal - Alef zero. Using the Hotel example, you can show that infinity*infinity and infinity to the power of infinity also have cardinality Alef zero. But, there are bigger infinities. The next bigger one is called Alef one. It is impossible to fit Alef one guests into our Alef zero hotel. And we can easily define bigger cardinals than Alef one. The cardinality of the integers (counting numbers) is Alef zero. Most people think that the cardinality of real numbers is Alef one. In other words, there are more real numbers than natural numbers. Note however, that the cardinality of the rational numbers (fractions) is Alef zero. There are as many integers as numbers which can be written as fractions. ------ Regarding whether the universe is infinite: we don't know yet. We don't know if you would end up back where you started if you set out in a straight line. It's possible, but not necessarily the case. There may never be a big crunch. The universe may be actually infinite in extent. JR | |
| From: Helen | 7/05/99
18:29:03 |
| Subject: re: Infinite universe? | post id:
10274 |
| OK - Postmodern Woman takes the
floor.... I'm assuming that by 'thought' you mean 'cognition' (There are other possible definitions, and if you intended one of those, I'm afraid this isn't going to make much sense... but I digress). Thought/cognition cannot be infinite since the human mind tends to be bound to certain conventions by which we create meaning and therefore comprehension. The most fundamental of these conventions is experience/metaphor. I know what 'hot' means because when I was a child someone used the word hot to describe the weather/a heater etc. which I could experience and relate to the word. My experience provided meaning to an otherwise meaningless collection of sounds. This becomes clearest when we're trying to explain concepts which are based on highly personal experiences such as emotion. Try to explain how you feel to someone, and you'll invariably find yourself using metaphor - helping them to understand your meaning by relating it to another experience. Consequently, thought cannot be infinite - it is bound by our experience. Thanks. I'm done. | |
| From: Terry Frankcombe | 7/05/99
19:00:37 |
| Subject: re: Infinite universe? | post id:
10289 |
| I would disagree. I would argue
that the human brain definitely has the capability to move outside our
collective experience. (One could almost point to religion as an example.)
However, this does not prove that the potential for thought and/or
cognition are infinite. | |
| From: Rhys | 7/05/99
21:20:50 |
| Subject: re: Infinite universe? | post id:
10331 |
| Yep, I knew as soon as I'd posted
it that thoughtas infinite would cause some concerns. Terry asks me to
prove it, and now the theory has been challenged by a post modern
female! (And to you people who say time travel isn't possible.. how do you
explain "post modernism?") Firstly, to Terry. I probably can't prove it, which is a real shame as I'd really like to do so. The basis of my theory derives from the human ability to form unique abstractions and concepts. The imagination of humankind has not shown any limits to me thus far, and in fact the larger our base of knowledge, so too do the possibilities of the imagination grow. The other argument I have up my sleeve comes from what Helen was saying. Yes, we do indeed conceptualise the world through a rigid worldview which is learned. If this is the case, then we might be able to state that the breadth of human thought is limited to the amount of differing world views. To suggest this, however, suggests that there is a finite amount possible world views an individual could subscribe to, and I'm afraid this just doesn't seem right at all. We cannot predict the world views of folk from the future, or even really have a great idea of the world view of folks in the distant past. Every individual has the ability to change their world view at will; sometimes these changes are subtle, often they are like bombs in an individual's life. Anyway, it seems to be one of those unprovable situations. Is thought infinite? Are there an infinite amount of concepts which the human mind can deal with? Perhaps it's analogous to music. Is there a limited amount of different songs that could be produced? With so many variables, I find it hard to imagine (but I should add, not impossible!:) I read somewhere of a bloke who worked out how many different arrangements of pixels there could be on a monitor in a given resolution at a given color depth. The figure given could fill the Encyclopedia Britannica, but his argument was that within that number lay every possible picture displayable on a monitor. This, I find impossible. rhys | |
| From: Terry Frankcombe | 7/05/99
22:02:09 |
| Subject: re: Infinite universe? | post id:
10340 |
| Are there an
infinite amount of concepts which the human mind can deal
with? This indeed is the crux of the question. A tricky one. The human brain is finite, with a finite (though large) number of neurons and synapses. But then surely quantum effects count in the human brain, which (we think) introduces an infinite number of possibilities. There is also the issue of emergent complexity, and whether this can become infinite. Perhaps it's analogous to music. Is there a limited amount of different songs that could be produced? With so many variables, I find it hard to imagine (but I should add, not impossible!:) Ahh, but now you're cheating. You can keep you song going for all of eternity. Then again, if you got really tricky then you could produce an infinite number of different songs just by varying the length of the second note between 1 and 2 seconds. Assuming that time is continuous, that is. I read somewhere of a bloke who worked out how many different arrangements of pixels there could be on a monitor in a given resolution at a given color depth. The figure given could fill the Encyclopedia Britannica, but his argument was that within that number lay every possible picture displayable on a monitor. This, I find impossible. Too easy! The number is (number of colours)(number of pixels = X resolution x Y resolution). Provided the number of colours and the two resolution limits are finite, this is finite (though again, potentially very very big). To give you an idea how big, for 5 colours and a 10x10 screen gives around 7.9x1069 possible 'pictures'. | |
| From: Rhys | 7/05/99
22:13:50 |
| Subject: re: Infinite universe? | post id:
10343 |
| nice colurs, Terry. I always feel
so important when quoted in purple :o) I understand the that equation is relevant. But the implication is that any photo that could be taken, any picture that could be drawn.. in fact an visual image at all which is displayable on a monitor (and this must cover the vast bulk of them, if not all)is accounted for within one of those numbers. Does this then put a limit on what can be drawn or photgraphed? Surely it would be feasible to write program which drew any one of the possibilites on command, thus eliminating the need for artists... | |
| From: Terry Frankcombe | 8/05/99
19:45:09 |
| Subject: re: Infinite universe? | post id:
10529 |
| Does this
then put a limit on what can be drawn or photgraphed? On what can be drawn, probably no, as this is essentially an analogue process. What can be photographed, probably! There are only a limited number of crystals on a photographic plate. Though the number of possible colours may give you an infinite range of possibilities. Surely it would be feasible to write program which drew any one of the possibilites on command, thus eliminating the need for artists... Entirely feasible, and actually easy. The problem comes with selecting the correct one. Think about how crude a 10x10 picture in five colours is. And there are 1070 possibilities. There are an awful number of completely meaningless noise pictures in that. | |