3 ms·

the set of all possible events has a much, much higher cardinality than an infinite axis of time. Are you sure of that? How would you prove it? It seems intui

• jdavid 16y ago
  if they universe is composed of a single axis by which information is sorted, then infinite time should produce all possible combinations. However, if the universe has some 'structure' to it, it might become ordered at some point, exchanging chaos for order. In a universe that becomes ever more ordered and unique. This isn't like saying infinity - infinity, or infinity/infinity, this is more like there are a set of the infinite, and there is a set of the finite, and they are two distinct sets without one influencing the other. Order and Chaos need not be interchangeable. There is an interesting book called "Sync" which discusses the presence of spontaneous order from chaos. He also talks about how order can turn back into chaos, but the important part of the book is that there are cases where chaos will not turn into order, and order will not turn into chaos, meaning that the stability of the two create two distinct sets, one that contains the identity of the universe and one that allows it to change. Some of you may have read Wolframs work as well which shows that simple rules can lead to ordered stable systems. That stability is the definition of uniqueness. Sync, it's the one book I recommend all my thinking friends read. http://amzn.to/a8s5Dl http://amzn.to/a8s5Dl It changed my life, and my world view. So, I am comfortable saying that no act of randomness by any number of chimpanzees ( as they are now ) will randomly produce a work of William Shakespeare. WS, wasn't just a man, he was a man in a time with billions of events that influenced that moment when he composed those works. There was a structure and a path to those influences, and it wasn't such a frail construct that randomness happened upon it, but rather there was a beautify symmetry that occurred and allowed that to come to pass. Another way to look at it, is that random/ chaotic signals will not sum up to collapse a bridge. however an ordered marching army has in many cased taken down the bridge.
• Robin_Message 16y ago
  I have a machine that flashes a light on or off once a second, at random. You can view streams of output from the machine as possible events. Now, suppose an infinite amount of time has passed (aleph-null, by definition). Have I seen every possible sequence? Well, take the set of aleph-null length sequences (all aleph-null of them [1]) and put them in an order. Now construct the following sequence: invert bit 1 from sequence 1, invert bit 2 from sequence 2, ... etc. Note that this sequence was never produced by the machine, since we enumerated all the sequences it produced, but they are all different to this one. So, by a standard diagonalisation, the set of events is higher cardinality. [1] How many aleph-null length sequences come out of the machine? Well, they have to be continuous, so the only obvious aleph-null length sequence is the total sequence the machine produces. However, you can drop an entry from the beginning of the sequence to get another aleph-null length sequence. And so on, making a total of aleph-null.
  • hugh3 16y ago
    Interesting attempt, but I'm not convinced by the part of the argument where you divide the complete output of the flashy light box into aleph-null sequences, each of length aleph-null. Mostly, I'm unconvinced that an "event" which takes an infinitely long time to complete actually counts as an event. Usually when we talk about events they're localised in space and time.
    • theli0nheart 16y ago
      Well, it's kind of a Catch-22. This proof is dependent upon the lemma that time is infinite. On the other hand, the set of events we're looking for is the one where time ends. Therefore by assuming the lemma we have no need for the proof. OTOH, if we're looking at another event that's not so confusing (one that's not the end of time), the proof holds water. It's a pretty sweet proof that I think is similarly used to prove that the set of real numbers is uncountable.
      • hugh3 16y ago
        No, what I'm saying is that an event which takes an infinitely long time to happen (ie an infinite series of one-second flashes) isn't a proper "event", which as used at least in relativity, is something that happens in finite space and time. But there's no need to argue about the definition of event. I'll say instead that I'm interested in knowing whether infinite time implies that all finite-length events must eventually happen (and indeed, happen an infinite number of times as the paper claims).
• j_baker 16y ago
  Events happen at the same time. At any one given point in time, there are trillions (probably much more than that) of events happening. In fact, wouldn't the set of all events be uncountably infinite? Now that I think about it, we're talking about all possible events, which is even bigger. For any given event, there is theoretically an infinite amount of alternative possible events. Therefore, for each of the trillions of events at any given point in time, there is an infinite set of other possible events.
  • hugh3 16y ago
    Certainly there's an uncountably infinite number of possible events. The question is whether that's an uncountable infinity with larger cardinality than the uncountable infinity of instants in which they could be happening. As far as I'm concerned having read the thread up to this point the question is still open... though my personal prejudice is still that it's not true that every event must happen.