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For those that struggle with infinity — Parallax Forums

For those that struggle with infinity

zoopydogsitzoopydogsit Posts: 174
edited 2011-12-05 03:34 in General Discussion
I saw this and thought it was an excellent overview of the problems with Infinity.
If you have time it's quite enjoyable.

I quite like that Grahams Number ends in 7!

http://www.sbs.com.au/ondemand/video/2077113529/To-Infinity-And-Beyond

Comments

  • ElectricAyeElectricAye Posts: 4,561
    edited 2011-11-30 17:49
    A college acquaintance of mine used to study how many ideal holes an ideal surface could have.
    "Isn't the number infinity?" I shrugged.
    "Yes," he smirked, "But there are different kinds of infinity."
    "!?"

    http://www.scientificamerican.com/article.cfm?id=strange-but-true-infinity-comes-in-different-sizes
  • DavidSmithDavidSmith Posts: 36
    edited 2011-12-01 10:12
    If you're interested, you can get a quick idea of different infinities by checking out transfinities (Georg Cantor). Aleph zero is a countable infinity - like the cardinal numbers. Aleph 1 is an infinity that cannot be put in one to one correspondence w a countable - like the points on a line. Aleph 2 is an infinity that cannot be put in one to one w aleph 1 - like the number of lines that can be drawn through a point. It goes on up to aleph infinity (and no I don't know if that is a countable or uncountable infinity).
  • Heater.Heater. Posts: 21,230
    edited 2011-12-01 11:37
    All seems straight forward. Can't argue with Cantor's diagonal method. Although he seems to have been regarded as a bit of a nut head when he first proposed these ideas.
    Now it seems to me that an infinite amount of time must have passed before I was born. An infinite amount of time is to come after I am dead. Jeeze my life is short!
    Why do I worry about not being here for that infinite future when I was already not here for that infinite past?
  • Phil Pilgrim (PhiPi)Phil Pilgrim (PhiPi) Posts: 23,514
    edited 2011-12-01 14:14
    My first exposure to Aleph 0, Aleph 1, and their ilk came in a "Theory of Automata" class. My initial reaction was a withering, "You've got to be kidding." The class was a requirement, so I couldn't tune out or escape -- as much as I wanted to. But I didn't approach the remainder of my time there with any enthusiasm. It just wasn't hands-on enough.

    BTW, the video is off-line now. Anybody know where else to find it?

    -Phil
  • lanternfishlanternfish Posts: 366
    edited 2011-12-01 14:32
    Is this it?
  • lardomlardom Posts: 1,659
    edited 2011-12-01 14:48
    I think I found it on YouTube in six parts. The original link was off line when I first clicked on it but the YouTube face looks the same. http://youtu.be/yBdaumeA254
  • ElectricAyeElectricAye Posts: 4,561
    edited 2011-12-01 16:25
    Heater. wrote: »
    ...Jeeze my life is short!...



    Don't feel bad. Nobody lives longer than 0.7 seconds.

    You know what's going to happen about 0.1 seconds before it does.

    You know what's happening in a window of nowness that's about 0.3 seconds wide.

    And you experience what's already happened for about 0.3 seconds after it's happened.

    All else is either a memory, most likely inaccurate at that, or imaginings of things that haven't yet happened and probably won't - all of which uses up the 0.7 seconds of your life, whenever you decide to entertain such thoughts.
  • localrogerlocalroger Posts: 3,452
    edited 2011-12-01 18:11
    I got in a pretty good argument with a theoretical physicist on another forum about the whole infinities thing. While they are useful in some mathematical models that happen to describe reality, I said I don't think these infinities have a real existence of any kind. They are fictions used to probe the interaction of finite functional parts of the Universe. And the guy was like, WTF? He truly believed that these infinities are things that exist.

    I told him my first experience, before learning physics, was learning computers and very stupid computers at that, and I saw instinctively that a sufficiently good computer could be the Universe; that it might feign rules involving these infinities but that really the Universe can only ever present us with a finite amount of information (about 10^81 bits, give or take an order of magnitude, and that's assuming the Universe isn't lying its digital *** off at us, as such alternate universes as Doom, Second Life, and World of Warcraft regularly do) and it frankly made much more sense to me to think that the Universe takes economies we haven't discovered yet than that you really can get more computational power out of a few qubits than all the computers in the world.

    In the end he was shaking his head, admitted understanding how I got my worldview, but not letting go of his infinities. I have manipulated bits, they are real to me; nobody has ever seen an infinity, but those are real to him.
  • BitsBits Posts: 414
    edited 2011-12-01 18:42
    Is this thread about the existence of infinity? I am confused because some here seem to doubt it. If so I am ready to roll up my sleeves and do work.
  • ElectricAyeElectricAye Posts: 4,561
    edited 2011-12-01 18:50
    Bits wrote: »
    ... I am ready to roll up my sleeves...

    You got infinity tattooed to your arm?... or what?

    Ah, infinity...
  • BitsBits Posts: 414
    edited 2011-12-01 19:44
    That would require an infinite bottle of tattoo ink ^^ :)
  • zoopydogsitzoopydogsit Posts: 174
    edited 2011-12-02 00:51
    Hi Phil,

    It's hosted on a local TV station in Australia on their website, saying it has 4 days to go. You should be able to get it by going to;
    http://www.sbs.com.au/ondemand/
    Select under PROGRAMS documentary
    And it should appear on the page called "To Infinity And Beyond"

    Bits,

    A very Noir style documentary covering the complications of Infinity.
    I found it interesting as it's taken the field much further than I thought. I liked the infinite number of parallal universes. I'd like to believe theres one out there where I get paid to play with the propeller. But maybe that's asking too much ;-)
  • Phil Pilgrim (PhiPi)Phil Pilgrim (PhiPi) Posts: 23,514
    edited 2011-12-02 08:41
    Thanks, zoopy. I was able to catch it last night on youtube. It was an interesting presentation, to be sure. One thing that strikes me, though, is that many people say "infinite" when they mean "indefinite". There's a difference, particularly as it applies to things we experience. I also got a distinct sense that mathematicians are not grounded enough to do cosmology. :)

    -Phil
  • LoopyBytelooseLoopyByteloose Posts: 12,537
    edited 2011-12-02 08:46
    Infinity? Isn't that just the day after tomorrow?
  • DavidSmithDavidSmith Posts: 36
    edited 2011-12-02 13:04
    zoopydogsit,

    Actually, there are an ifinity of universes where you are paid to play w the propeller.

    It's just your luck this isn't one of them.
  • Bobb FwedBobb Fwed Posts: 1,119
    edited 2011-12-02 16:21
    Maybe this will help...
    -1 == infinity
    http://www.youtube.com/watch?v=kIq5CZlg8Rg
  • Heater.Heater. Posts: 21,230
    edited 2011-12-05 03:34
    Bob Fwed,

    Brilliant slight of hand there!
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