Not in an infinitely long string.
That's the whole problem.
Assuming the Planck Length is a reality and not a false limit for sake of the discussion, in an infinitely long string, there would be an infinite number of discrete bits.
Please go back and read my last post to you now.
it picks up on this theme.
I will think more on this tonight, as requested, but until you can convince me that a infinitely long string can not be made up of an infinite number of discrete bits, I can assure you that you have not won me over yet.
Keep trying though. I am enjoying this as well.
I found myself discussing this with my girlfriend last night.
She got bored rather quickly, but rest assured, you have at least gotten inside my head - and that's a start.
I'm not sure what the infinitely long string is doing in our discussion. I saw it creep in a few posts ago, but I was still caught up in the proof that a finite string does not have an infinite number of "bits" in it.
I will concede to you that a hypothetical string of infinite length would contain infinite "bits", but such a string is only a construct, it could never exist.
Now... if you are using the sting as a time analogy, as we have been for a few pages now, I can see that you are suggesting that infinite time would have infinite discrete bits, which I concede to you as well. But only as a hypothetical. If you will look at my proof, this is precisely what I take to be an axiom, which leads to the problems that seal god's fate (the god which I defined according to most monotheistic religions).
Here is a re-stating of the gist of my proof using your infinite string. Imagine your hand somewhere on the body of this string. Now, I want to tell you that there is a piece of string that I painted red, off to your left. I want you to go and find it. The problem is, you can't ever find it. I painted it so far to the left, that you would have to go an infinite length to get to it. No matter how far you go, the part I painted is just a little further to the left. You could travel an infinite distance, and still not approach it.
If this were time, we could use any definition of what a discrete step is. Since you are presuming that there is an infinite number of them, they can even be huge states involving many smaller states. This is the same as how an infinite ruler can be divided into an infinite number of inches, feet, or millimeters (sorry to mix standards). So don't get into the trap of thinking about seconds, minutes, years or eons. Think about god making coffee.
God makes coffee for breakfast every "day". I don't care what a day is, lets just define it as the length of time it takes for god to start making coffee again. (since we know he makes it once a day)
Over one of these cups of coffee, god decides to create the universe. Who knows how long before he gets around to doing it, that isn't important. What is important for our discussion is that there is a cup of coffee that god had... off to the "left" if we are thinking about a time-line. This cup of coffee is just like the red bit of string. No matter how far "left" you go, it is just beyond that one. Since there is an infinite number of "coffee days", this is not a mere playing with words, it isn't an abstraction, it is a feature of our hypothetical universe (and your infinite string). From this cup of coffee, which we know to have existed, all the way to the cup over which god contemplates the cosmos, there are in infinite number of cups in-between. God could not make that number of cups. And you can't use his god-like magic to weasel your way out of it. No matter how many cups he makes, there is at least one more to brew.
And I most theists I know like to say, at this point, that god just brewed an "infinite number of cups all at once". Which is the sort of ignorance and confusion you need in order to believe in a god that is made up of the three axioms I give.
Like I said in the proof, this does not mean that the future is finite, only that the past must be. Remember, the ray, not the line. The reason that this isn't impossible is because even though an infinite number of states await the cosmos, there are an infinite number of them that the universe will never reach. (most people's heads explode when they bump into this piece of logic) We could calculate that the particles and energy are approaching some asymptote of existence, but also tell that they will never quite reach them. No paradox.
The problem with an infinite past is that we are here, you and I. And an infinite cups of coffee have not been brewed. I can think of an infinite number of them that can not be reached between here and there.
Again, Sherlock Holmes is begging me to reconsider our assumptions in the face of such airtight illogic. And one of those is the assumption of the infinite past. An assumption that gives all cosmological and religious models severe problems. And it shouldn't... it is easy to consider a past with no time. And it would be less weird than other things to consider that a timeless, massless void contains the natural and overwhelming power to create all mass and time. It could be downhill in the nature of my 2nd law post. And since no time existed beforehand, it would be instantaneous. It may not have been "our" big-bang. It could have been a billion big-bangs ago. I'm not pretending to have an answer to fill the void. (pardon the pun) I'm just demonstrating that an infinite past not only doesn't make sense, it isn't even necessary.
And all gods seem to rely on this feature, which is why most gods are easily disproved.
Tell your girlfriend I said hello. And do be fair when relating my side of the issue... I'm trying to get my wife to argue your side as best she can!