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| Thread: Some facts |  This thread is pages long: 1 2 · «PREV |
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ohforfsake
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posted March 13, 2011 10:15 AM |
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Shares... WAS HERE!!! I can't believe it!!!! This is GREAT! I'm so exicted!!
Anyway. About infinity. As far as I know, it really just means unlimited.
Anything unlimited can be build up of various building blocks following some pattern, i.e. not random. Compare the patterns and you can see which one is the largest.
Yes both are unlimited, but for two different persons, taking one step on each pattern, each person have moved a different distance.
@Zenofex:
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The "infinite" you are talking about is actually quite finite To have double the amount of "infinite" numbers between 0 and 2 in comparison with the amount of numbers between 0 and 1, you have to know what is the amount of numbers between 0 and 1, i.e. to have a finite quantity which is to be "doubled".
Take each real number in the range ]0;1], it means not including zero and up to one. Put these together in a list, listing all those numbers. No doubt the list will be infinite long.
Now the list build through the same method, but for the numbers ]0;2] will be double as long. Why? Because for each time you give me any given number in the first list, I can give you the same number and the number + 1. That means I can give you two numbers for each time you can give me one.
Again. I recommend you read Hilberts Hotel, or maybe a Calculus book. Though maybe you use the term infinite differently?
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@Baklava
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Also if the Earth is round, how come nothing's upside down in Australia.
And more importantly! How come you still haven't made a single bombay video!?
@Zenofex:
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If one of them is "bigger" than the other, then the "smaller" part has to be finite, otherwise there is no base for comparison.
No. It's the components you keep repeat unlimited which will alternate in size. Basicly it means that wherever you're in one infinite set, you're at another place in another infinite set. These can be compared.
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If there are two or more infinities on the other hand, they have to co-exist in some sort of reciprocity, otherwise they will be borders for each other.
Infinity has no boarders. There's no end range. Infinity is in itself not a number, but can be used as it was.
The number 3 will always be larger than the number 2.
It doesn't change how often you repeat the comparision.
But if you compare forever, then you've compared two infinite amounts.
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ohforfsake
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posted March 13, 2011 10:46 AM |
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Anyway. That must be enough with all the infinite talk, I think it's clouding the thread unnecessarily to be honest.
So the observable universe is 15 billion light years across huh?
That's, what? ~1.5^24 km? Or ~1.5*10^30 mm I suppose.
Imagine a single letter, typed on a computer, filling exactly 1 mm.
Then to reach the edge of the observable universe, you'd need to type X=1.5*10^30 amount of letters. Or in number presentation, I suppose that would be 10^X.
In other words, typing the number 10^(1.5*10^30) would be as long as to the edge of the observable universe. That's a 1 with 1.5*10^30 zeroes.
The speed of light travels 3*10^11 letters pr. second.
I wonder, how fast can we actually reach the edge of the observable universe? Maybe it'll make 15 billion light years not seem so huge?
I mean let's try to write this number on the computer. We are not going to hold 0 down for trillions of years though. No we'll just write a single zero and then start our method.
We'll mark all. Copy all. And paste all, twice, because the marked gets overwritten. This doubles our amount of numbers from 1 to 2. From to 2 to 4, etc.
How long does it take to mark, copy and paste twice? 1 second if you're fast, I suppose, but let's just say 3 seconds.
So the formula becomes: 2^Y and for each time Y increases with 1, 3 sceonds have passed. X=2^Y, t = 3Y
At t=0 seconds, Y=0 and X=2^0 = 1 which is the single 0 we've typed.
At t=3 second, Y=1 and X=2^1 = 2 is the first time we marked, copied and pasted and pasted again.
So let's try to extrapolate. How long is it before we're at 1000 letters, equivalent to a distance of 1 meter?
Well 2^10=1024, which is approx. 1000, so here Y=10, whereby after half a minute we're already 1 meter from our distance point! Still only approx 15 billion light years to go!
Well to make it easy I'll just write 2^10=10^3.
So for each time Y=10, that's each half minute, we've moved a factor for 10^3 further. Since we're to travel 10^30 mm's, and 3 goes up in 30 10 times, we need to repeat the process which takes half a minute 10 times. That is 5 minutes.
So to the edge of the observable universe in 5 minutes here we come!
Of course this method probably won't work, because the computer will not only slow down as you're copy pasting a huge amount of data, but it'll also run out of memory.
Let's assume each letter, each 0, you type, takes up exactly 1 byte. So after a half minute you've used 1 kb. After 1 minute, it's 1 mb. After 2 minutes it's 1 terra byte!
Though 1 terra byte is certainly possible. So is 2. How fast was light again? It was 3*10^11. And how large is one terrabyte? It's 1*10^12!! Some 3 times larger than the speed of light. So if you mark, copy and paste 1 terrabyte of data in those 3 seconds you'd be faster than the speed of light!
And you could still have some memory left on your computer!
How many iterations, i.e. how many times do you need to do the process, to reach this point? Well 10 times for each time Y=10 and since 3 goes up in 12 4 times and 4 times 10 is 40, you need to do the process 40 times to reach the 1 terrabyte length.
And one more time to break the laws of physics!
Ah, I'm just kidding of course! I doubt the computer would be able to handle such a task! (I.e. repeat the process for every 3 seconds).
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Zenofex
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posted March 13, 2011 10:58 AM |
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No. It's the components you keep repeat unlimited which will alternate in size. Basicly it means that wherever you're in one infinite set, you're at another place in another infinite set. These can be compared.
Well, placement (or position) is something else and here comparison is possible, but this itself does not prove that one of the infinities is "bigger" than the other but only that what is station on spot X - say 0.5 for "infinite 0 to 1", is stationed on spot Y for "infinite 0 to 2".
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Infinity has no boarders. There's no end range. Infinity is in itself not a number, but can be used as it was.
That's part of what I'm saying. Mathematically in the end it turns out that there is an infinite amount of infinities which is only one self-sustaining infinity with infinite amount of variables. I think I've read something similar written by Stephen Hawking when it comes to the predetermination ("destiny"?) - that it could turn out that there is something like that but it can not be calculated or "foreseen" due to the nature of the infinite variables. With today's instruments anyway.
As for the Hilberts Hotel - it's about infinitely positioning one infinity (number of guests) within another (number of rooms) but by itself it does not prove that the number of guests is smaller than the number of rooms and other other way around.
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Jabanoss
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posted March 13, 2011 11:06 AM |
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Edited by Jabanoss at 11:13, 13 Mar 2011.
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If you have studied Limits in school you should know that there's indeed is a difference between infinity and infinity.
For example Inf/Inf does not "have" equal 1. It can equal one, but in most cases it doesn't.
Concerning the OP, nice list and cool info. 
I always knew my teachers were wrong.
Edit: Hmm in retrospective that link didn't give a clear idea of what I mean but nvm...
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- Meroe
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Zenofex
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posted March 13, 2011 11:57 AM |
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Anyway, move along - I guess we'll proceed on PMs.
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ohforfsake
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posted March 14, 2011 08:13 PM |
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Corribus
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posted March 16, 2011 09:17 PM |
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Edited by Corribus at 21:24, 16 Mar 2011.
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@Adrius
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I have a hard time grasping the non-existence of time but I think I get what you're saying...
The problem is that the human mind isn't really well-equipped to deal with the physics of extreme systems. The non-constancy of time is particularly troublesome because it is so far outside of everyday experience. (I've seen the same disbelief in students when I've tried to explain how an electron can interfere with itself - essentially being at two places at the same time.) The real problem for laypeople is that they try to take these ideas and filter them through their empirical experience and common sense, which is primarily constructed upon Newtonian Physics - and that just doesn't work in situations which require quantum or relativity theory. Hell, even for myself, a person who understands quantum theory quite well, if I think about it too hard, I get a headache.
For instance, OhForFSake wrote a little later in the thread:
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For what I know. Time, as we know it, starts at the moment of the big bang. The cause of the Big Bang, if such exists, is unknown.
It would seem to make sense to use words like "cause" and "start" surrounding a singular event like the Big Bang, because from our personal experience we know that any given event has a singular cause, and time extends in both directions away from said event. Our experience has taught us to rely on this basic fact of physics: for every event there is a before and there is an after. The universe, according to human experience, is deterministic. This is not the case in the quantum world, where a singular event does not necessarily have a single, singular cause. Moreover, it may not be so in the relativistic world. The flow of time is related to space-time curvature, and in a singularity that curvature is so great that time actually flows infinitely slow. In essence, time would be undefined at zero time - essentially the same as dividing by zero. So therefore what meaning do words like "cause" and "start" and "before" and "after" really have?
Admittedly, this is philosophical conjecture on my part more than any sort of scientific analysis. I'm not a cosmologist and my understanding of advanced relativity is limited. Nevertheless, what I do know is that the physics of singularities, the harmonization of quantum theory with relativity, and the first femtoseconds of the Big Bang are still a matter of intense research and debate; moreover I do know that quantities that we often regard as constant and reliable from personal experience are not often so in esoteric systems. So my point is only that what we think we know about the world may not apply in situations that are so far removed from the world we think we know. And we should be very careful about making any sort of grand conclusions about the universe while scientific work is still under way. In particular, any sort of justification of the supernatural borne out of pseudoscientific reasoning (e.g., this nonsense about something coming from nothing, first cause, 2nd law of thermodynamics etc.) is mere hogwash and demonstrates a complete inability to appreciate how utterly Newtonian physics fails - and how useless knowledge obtained through empirical observation of our world is - when it comes to understanding the very small, the very fast, the very heavy and the very (very) long ago.
(Ok, that last little bit was a bit of a rant, one clearly not directed at you, Adrius. )
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JollyJoker
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posted March 27, 2011 05:20 PM |
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What I always find amazing is how everyone is accepting the "Big Bang" as a given, allegedly understanding the process, when it is perfectly clear that the information as such - provided it is even correct - doesn't explain anything.
The reason is, that a "state" is assumed - the "starting point" -, with neither space or time existing, since all "energy" (or mass or gravitation or a mix of all) is compressed into something called singularity - a Black Hole.
I mean, what would that explanation gain?
For me, at least, this would make sense only as a SECONDARY phenomenon: something happened in a larger-dimensional "realm" RESULTING in a Bang. Comparable somewhat to an underwater volcanic eruption leading to the surfacing of a volcanic island in the ocean.
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xerox
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posted March 27, 2011 07:31 PM |
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Well, the big bang is just a theory.
Personally I don't think we ever will fully understand how the universe began, if it even had a begin (yes, I know such things as eternity and infinity are hard to imagine for humans xD)
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Corribus
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posted March 28, 2011 03:26 PM |
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... is just a theory.
That's becoming such a ridiculous cliche. 
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Macintosh
Tavern Dweller
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posted April 02, 2011 04:34 PM |
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Very much appreciated,
Very very nice post.
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