• TheMadFool
    3.8k
    I got this idea from ViHart recreational mathematician

    One of Zeno's most famous paradox has to do with Achilles never being able to catch a tortoise that's been given a head start in a race because of the impossibility of having to traverse an infinite number of points between the two.

    Using the same principle on a person x born 1976 and died 2019 can we say that x is immortal given that x had to experience an infinite number of time intervals?

    Are we all immortal in some weird sense?
  • tim wood
    3k
    Are we all immortal in some weird sense?TheMadFool

    Not weird, but in the sense that it is. The weirdness is a product of insufficient knowledge wielding inadequate imagination in attempting to understand the ineffable.
  • Terrapin Station
    12.4k
    the impossibility of having to traverse an infinite number of points between the two.TheMadFool

    When you get to a point such as that in your reasoning, it's a cue to say, "Oops! I must have f-ed up somewhere, at least in some assumption I made."
  • TheMadFool
    3.8k
    Not weird, but in the sense that it is. The weirdness is a product of insufficient knowledge wielding inadequate imagination in attempting to understand the ineffable.tim wood

    Ok. That's really weird. Anyway what is ineffable in my post?
  • TheMadFool
    3.8k
    When you get to a point such as that in your reasoning, it's a cue to say, "Oops! I must have f-ed up somewhere, at least in some assumption I made.Terrapin Station

    Strangely Terrapin is a type of turtle.
  • Terrapin Station
    12.4k
    Strangely Terrapin is a type of turtle.TheMadFool

    Why is that strange?
  • TheMadFool
    3.8k
    Why is that strange?Terrapin Station

    I was talking about the tortoise and Achilles paradox and a cousin responded. Coincidence! Strange.
  • Terrapin Station
    12.4k
    I was talking about the tortoise and Achilles paradox and a cousin responded. Coincidence! Strange.TheMadFool

    Strangely "cousin" is a relational term.
  • TheMadFool
    3.8k
    Strangely "cousin" is a relational termTerrapin Station

    You should be happy your "relative" wins the race and puts the Greeks to shame. :smile:

    Anyway do you have any idea where I f***ed up in my reasoning?

    I'm not sure but I'm beginning to doubt the whole notion of infinity.
  • Terrapin Station
    12.4k
    Anyway do you have any idea where I f***ed up in my reasoning?TheMadFool

    If we're concluding that it's impossible to move then obviously we're going awry somewhere. Probably there isn't an infinite amount of points to cross.
  • TheMadFool
    3.8k
    Probably there isn't an infinite amount of points to crossTerrapin Station

    That could be it. How do you then account for the following:

    Mr x (1976 to 2019). x has to first reach 1997 and before that he has to reach 1986 and before that 1981and before that 1971 each time interval can halved indefinitely. The math says so. Is the problem with math or a subset of math infinity?
  • Terrapin Station
    12.4k
    Is the problem with math or a subset of math infinity?TheMadFool

    The problem is that mathematics is a way that we think about relations. The world isn't required to match that.
  • Forgottenticket
    160
    Yep, same thing in b-theory of time I believe. They're all Parmenidean arguments.

    So the world of reason is describing a different world to the one our senses display to us which is one of motion and change.
  • PoeticUniverse
    592
    Neither time nor distance is infinitely divisible; the Plank time and the Plank size are shortest and the smallest. The turtle loses.
  • Patulia
    26
    Can't we solve the paradox using the concept of infinits and of limits? Like, Achilles first covers half the distance from the tortoise, then he covers half of the remaining distance and so on:

    1/2 + 1/4 +1/8... Shouldn't this tend to one at infinite? Just because we add up an unlimited amount of numbers doesn't mean we'll get a finite quantity.

    Are we all immortal in some weird sense?TheMadFool

    I don't think we are immortal because it's not like we are living an unlimited amount of intervals all of the same length: it's like cutting a square shaped cake first in a half, than the remaining half in a half and so on. You'll still eat one cake.
  • fdrake
    2.5k
    Using the same principle on a person x born 1976 and died 2019 can we say that x is immortal given that x had to experience an infinite number of time intervals?TheMadFool

    No. The union of all the points in that interval still lasts 43 years.
  • TheMadFool
    3.8k
    No. The union of all the points in that interval still lasts 43 yearsfdrake

    If we take time to be on a number line how many points of time are there between 1976 and 2019? Infinite, unless you want to invoke Planck time?
  • fdrake
    2.5k
    If we take time to be on a number line how many points of time are there between 1976 and 2019? Infinite, unless you want to invoke Planck time?TheMadFool

    Wrong way to think about it. If you assume the time interval is an interval of real numbers, the measure (length) of any point is 0, but the measure of the whole interval which is the uncountable union of all points in the interval is just the usual length of the interval.

    If you assume time is discrete, then the interval length is an integer number of multiples of the plank time (rounded up or down to 1 plank time).

    Either way it's a finite time.
  • Terrapin Station
    12.4k
    If we take time to be on a number lineTheMadFool

    Then we're just being silly?

    You might as well take time to be this painting:

    Saltwater-13-2.jpg

    We could just as well say that both are a representation of time.

    It just that neither would imply anything in particular about what time is like objectively.
  • TheMadFool
    3.8k


    I guess an explanation for Zeno's paradox would apply here. A convergent infinite series.
  • Arne
    416
    Zeno's paradox, like your paradox, presumes the universe to be analog. However, if the universe is digital, then there is a discrete (finite) number of states between Achilles and the tortoise. So long as Achilles can "jump" discrete states faster that the tortoise, he will catch the tortoise.
  • noAxioms
    750
    Neither time nor distance is infinitely divisible; the Plank time and the Plank size are shortest and the smallest.PoeticUniverse
    This assertion is of course nonsense since there is no evidence whatsoever that neither time nor distance cannot be divided after some point. It's just below the ability to measure after a point.

    So the argument nevertheless ties into the wording of the OP: There is very much a finite time interval (well above the Planck time) below which no 'experience' can take place, therefore shorter durations are not experienced. You have a finite number of 'experiences' in your life, and when they've run out, you're done.

    Mr x (1976 to 2019). x has to first reach 1997 and before that he has to reach 1986 and before that 1981and before that 1971 each time interval can halved indefinitely. The math says so. Is the problem with math or a subset of math infinity?TheMadFool
    The math also says that you can cut the cheese as many times as you like and it doesn't give you more cheese. You f***ed up when you drew a different conclusion from the mathematics.

    I also don't think Mr X ever needed to reach 1971, but that's just a nit.
  • Filipe
    25
    Time in itself is relative to the experiencer, exactly because infinity is relative, there are infinite numbers between 0 and 1, but it is intrinsical that there are more numbers between 0 and 2 and if you apply the same logic to all types of infinity including Time you will realize that every second is a mathematical impossibility of an infinite amount if infinities happening (what is the last number before 1 second? would it be 0,0000000001? or 0,00000000000000001 or even 1X10^-8474?) Living is an improbability, the odds of existence are so incredibly low but yet it feels so certain that is scary so finally Living is being immortal (at least to some degree)
  • Pattern-chaser
    1.8k
    The story of the tortoise only seems paradoxical because, with each observation of the hare's position, we allow half the time interval since the last observation. The hare isn't speeding up or slowing down, we are taking more and more observations in shorter and shorter intervals. And assuming that time isn't quantised ("Planck time" has been mentioned earlier), we can carry on ad infinitum. But there's no paradox, or even confusion. Just a strangely set up story (which Zeno did deliberately, I assume :chin:).
  • Shamshir
    675
    One of Zeno's most famous paradox has to do with Achilles never being able to catch a tortoise that's been given a head start in a race because of the impossibility of having to traverse an infinite number of points between the two.

    Using the same principle on a person x born 1976 and died 2019 can we say that x is immortal given that x had to experience an infinite number of time intervals?
    TheMadFool
    The amount of partitions does no matter, provided you take the inertia in to account - it still takes the same amount of time for Achilles to catch the tortoise and to reach 2019 from 1976.

    The trick is in the conflation of speed and distance.
  • TheMadFool
    3.8k
    The amount of partitions does no matter, provided you take the inertia in to account - it still takes the same amount of time for Achilles to catch the tortoise and to reach 2019 from 1976.

    The trick is in the conflation of speed and distance.
    Shamshir

    Perhaps there's a problem with the model we're using - the number line. I mean if we do the math sure there's always a number between any two numbers but when you use a physical line to represent that idea we somehow end up with paradoxes.
  • khaled
    1k
    That could be it. How do you then account for the following:

    Mr x (1976 to 2019). x has to first reach 1997 and before that he has to reach 1986 and before that 1981and before that 1971 each time interval can halved indefinitely. The math says so. Is the problem with math or a subset of math infinity?
    TheMadFool

    Neither. The problem is it could just simply be that there is a "smallest time". As in the smallest amount of time that could exist. Similar to how the smallest amount of an element that could exist is called an "atom". I'm not very knowledgeable on this but from what I understand there is such a time. It's called planck's time. Look it up.
  • Shamshir
    675
    Perhaps there's a problem with the model we're using - the number line.TheMadFool
    I don't see a problem with the model, moreso with its presentation.
    A lens can magnify or reduce the size of an object, so you can manipulate its relative size.

    If you zoom in, the length seems long - too long; but if you zoom out for instance, it'll look curiously short.
  • Gregory
    52
    If the plank length is the smallest length, than it not zero. Therefore you can make a right triangle with it. Half the hypotenuse is smaller than the Plank length. There you go
  • TheMadFool
    3.8k
    I don't see a problem with the model,Shamshir

    Numbers are infinitely divisible.
    A line is infinitely divisible??? Zeno's paradox

    If the plank length is the smallest length, than it not zero. Therefore you can make a right triangle with it. Half the hypotenuse is smaller than the Plank length. There you goGregory

    That illustrates what I mean by the model being inadequate for the purpose. Physical lines have limits. Mathematical lines don't
  • Shamshir
    675
    Numbers are infinitely divisible.
    A line is infinitely divisible??? Zeno's paradox
    TheMadFool
    Where's the issue?
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