Printable View
Yes, when you look at it -- i.e. when the observation has taken place. But it's thesame quantum mechanics that say that when an energetic particle isn't observed, or rather, when the place is unknown, it exists at an infinite amount of coördinates in space, only to "choose" a coördinate when observed. That's superposition for you.Quote:
Originally Posted by Subway
Why infinite? It only exists at the coordinates that it can possible choose, not an infinite amount of coordinates. Where did you get the idea that it can choose an infinite amount of places?Quote:
Originally Posted by wouter999
The (imaginary) cat isn't dead, alive and everything inbetween either, it's dead and not dead at the same time or if observed, one of the two options. Same for the spin of a particle. Two options. Same for the position of an electron circling around an atomic core, it can only take one of the (relatively limted) possible positions.
Fredi
How can an electron spinning around a core have a limited amount of possible locations? As far as I know, a circle trajectory has an infinite number of possible points, it's the fundamental basics of a circle.
Yes, Schrödinger's cat is both dead and alive, and a particle is in both up and down states, but those are superpositional sets of a value 2. However there are many superpositional sets where the amount of states superimposed on eachother is infinite. Think of the double slit experiment, where one electron is shot through two slits: how can it interfere with itself if it is not in every possible location? And there are an infinite possible locations, that's a rule of any spatial body.
no one knows the size of space, so how can coordinates be finite. Sure an electron hovers around its atom because its bound by a force of some kind, but say that force is removed, it can go anywhere, be anywhere. Someone said it before, nothing is proven so we should assume infinite possibilities. And your forgetting the possibility of parallel universe's, so something is not bound by x,y,z but another value. Maybe its u value. And this value could be anything.Quote:
Originally Posted by Subway
i'm currently
x:10923084092384023844023984023480, y:123270137812039812731023981290138091283021983, z:9923878937192873987291378912873917,
u:1
But i'm also at
x:10923084092384023844023984023480, y:123270137812039812731023981290138091283021983, z:9923878937192873987291378912873917,
u:2
You can add as many dimensions as you want, as long as you don't add an infinite amount of them, anything will still be finite.
"Every possible position" is only infinite if you apply geometry (math) to it. In reality, the amount of positions is always finite, defined by the exact properties of the electron(s)/proton(s)/or whatever else you use for your experiment. Now of course you don't know the exact properties of each element, but that does'nt meen those don't exist.
If you take out (of reality) one single electron and remove any forces to it than well, it's just like math and geometry, it's imaginary, not anymore bound to reality. In reality nothing is isolated from the rest, we live in a holistic universe after all (again, quantum mechanics).
Fredi
Wow. 4 pages since yesterday evening...
This has far departed from it's original purpose. :(
exactly, so anyone saying 0.999... is absolutely equal to 1, is just as wrong as anyone saying 0.999... is absolutely Not equal to 1.Quote:
Originally Posted by swak
We are all to primitive to really know the truth.
To some it looks like 0.999...=1, to some it looks like math is flawed.
Trying to prove that math is not flawed by using more math that maybe flawed will not ever work.
No one can ever win this argument in the same way no one can prove that i exist.
I'm sorry, but those infinite zeros are fooling you. Think about the 9s. It's easier. Carry those 9s thirty times and tell me at which point you get a freakishly big nine that brings about your whole number.Quote:
Originally Posted by FlashLackey
The 9s go forever, infinitely falling short of 1. You can't subtract 0.999... from 1 and expect a reasonable answer that makes sense. It's just (in my opinion) and incorrect argument.
Infinity is abstract, while 1 is not. 0.999...is an interpretable idea - a philosophical construct even, and by its own bizarre nature, is clearly not the same thing as 1.
In your applied maths it might "more or less" equate to 1, for the purposes of ignoring a difference that has no practical effect, but the statement 1==0.999... is simply not the absolute truth.
Just stumbled over this at /. ... too funny:
Q: Do you consider photons particles or waves?
A: Yes.
:p
Another one:
:pQuote:
Most quantum computers have to be isolated from the outside world (look at them and they stop working)
So... in what fundamental way is this different from running Windows?
All taken from this quantum computer post: http://science.slashdot.org/science/.../1355255.shtml
Fredi
This is sadly where it falls to semantics. You can't tell me I'm wrong, because you can't prove it. You can only cite maths that relies on the same belief it tries to prove. It's circular and meaningless.
Random has it nailed in this regard.
Oh wait, that quantum joke works perfectly for this thread:
Q: Is 0.999... less or equal than one?
A: Yes
:p
Fredi
Quote:
Originally Posted by plang
I don't get how you can keep saying that when the number 1 is non-existent. No matter what you're not going to be walking along one day and say "hey look, it's number one!" and be referring to something other than a symbol. 1 is just as abstract as infinity but infinity is just too much for us to grasp because everything we can see or feel is finite. Even outer space can only be finitely. The best way I can imagination space is as an ever expanding object.Quote:
Originally Posted by http://www.google.com/search?q=define%3A+abstract&ie=utf-8&oe=utf-8&rls=org.mozilla:en-US:official&client=firefox-a
Going by math, calculating 1=0.999... is just as abstract as stating that 1=0.999... I think that the argument can either be determined by saying: "Look 1 does not equal 0.999... they are two completely different numbers separated by a minuscule difference." or "1=0.999... is a fact because by the same math that we use to calculate gravity and some other physics we can determine that they do equal each other. 1/3 * 3 or 3/3 = 1 and 1/3=0.333...*3=1 or 0.999.... Pretty much the only way you can say that 1!=0.999... is by disregarding our most fundamental math system which in turn forces us to disregard anything that results from it such as calculating gravity or calculating the proportions of a building. I think that there is really no real way to resolve this because we are dealing with the abstract and no experiment will determine one way or another. I also think that this will be debated till the end of time with each new generation until it becomes widely known and agreed upon and accepted. This has already been debated before and yet, here we are debating it some more.
This is interesting though, it's a good debate. Debating is interesting and this is a great debatable subject to engage in. I wish that I had more debates like this in school but I don't think that I'd do as good unless I know what I'm debating about pretty well.
By the way..."Infinitely small" was relative to the number 1. A 'number' greater than 1, but by an infinitely small margin. If you don't believe in this number, then you should also not believe in the existence of 0.999... Because the sum of the two equals 1.
Try to think about it in terms of a jigsaw puzzle. 0.999... has a very tiny piece missing - infinitely tiny infact (wow!). It needs that infinitely tiny piece to become whole again.
Makes my head spin, but I can see it.
Btw, just noticed your postcount. Is it 0 or the difference between 0.999... and 1, I can't tell. :pQuote:
Originally Posted by plang
Oh and a new one for the next six pages of circling discussions:
1 == 0.999...1
Fredi
Yes, saying that 1 is not abstract was a poor choice of words, you're right. What I meant was that 1 is something that has real, clear ties to the very fabric of how we count, calculate, etc...Infinity on the other hand is just something else.Quote:
Originally Posted by swak
And re:debating. I'm not here to try and change the world. I'm just here, in this debate, to challenge my own mind, and to have something to think about, and so on. I accept that I could be wrong, but while I believe that I;m not I'll argue my point with conviction, as long as I have something to say :).
It doesn't really interest me that the debate has been done before. I've never discussed it before, hence it's interesting to me.
Even one of those links that some one posted as a supporting article for 0.999...==1 stated in its first paragraph that the following rationalizations required certain things to be taken on faith.
I don't know about anyone else, but I think FlashLackey and I agreeing on anything is harder to believe than 1 = 0.999...
Heh :). Hey, I forgot my old Flashkit login. Sue me.Quote:
Originally Posted by Subway
Have a look for my infinitely small post though. It's profound.
I was just joking, just to make that clear. Btw, most of my posts are made-up. There was a recount where all CL posts were removed from anyones postcount and the mods got the chance to get those removed ones back. As I did'nt know exactly how many I had, I just guessed a number, so my postcount is at least as imaginary as infinity outside of math. :D
Fredi
I don't think I had many posts on my old account anyway, to be fair :)... When I started learning Flash a couple years ago, I had a brief period of self learning before being thrown in the deep end at a web company. After that I stopped going to forums much because I had all the help and discussion I could handle at work.
Might have to make regular visits to the lounge though if interesting stuff like this comes up. I'll see how long I can keep my post count 0. Simple things amuse me :)