The Grim Reaper Paradox

Addressing the Grim Reaper Paradox: The Short Answer: The first Grim Reaper arrives and Con is dead at 1.00 pm, exactly, it’s impossible to tell exactly when Con has died or time is quantified but still infinite. The Long Answer: Death At exactly 1.00 pm: What Pro has provided us with is a convergent series. I am sure he has heard of this before and will remain unsatisfied, but I will provide this to set the ground in the current resolution of these types of paradoxes. A reaper arrives at 30, 15, 7.5, 3.75… second intervals in preceding order. This is formally known as a convergent series (http://mathworld.wolfram.com...). A series of such will yield a finite answer This can be expressed in the following series of fractions: 60/2, 60/4, 60/8, 60/16, and so on. Each Grim Reaper n+1 has 60/2^(n) time to itself before the next reaper arrives. The time the ‘first’ reaper arrives is the last term in this infinite set. Of course this is a mathematical fallacy, but one can take the complete sum and see what the sum (x) of the infite set is by the following subtraction. 1.) x = 60/2 + 60/4 + 60/8 + 60/16… 2.) 2x =60 + 60/2 + 60/4 + 60/8 3.) 2x – x = 60 + 60/2 – 60/2 + 60/4 – 60/4 + 60/8 -60/8… Here all the terms after 60 cancel each other ad infinitum 4.) x = 60 Here we can see the sum of the infinite set tends to 60, or the full 1 minute. Therefore, the first reaper arrives exactly at 1.00 pm (1.01 – 0.01). A further justification can be made: If we take 60 seconds, and subtract an infinitesimally small fraction from it, we yield 59.99*. 0.99* is known to be equal to 1, and is trivially (and not so trivially) proven by the simple: 1.) 1/3 = 0.33 recurring 2.) 0.33 recurring x 3 = 0.99 recurring. 3.) 1/3 x 3 = 1 4.) 0.99 recurring = 1 This amongst other angles of resolution yield an answer of 1.00 pm being the time of death. From this reasoning, the question of “which Grim Reaper?” becomes a meaningless question, because there is nothing infinite number of grim reapers could arriving simultaneously at 1.00 pm. Simultaneous Causality: This of course defies intuition, however Pro stated that the job of a Grim Reaper is to check the status of the victim before killing the victim. This implied two temporally separate events. In which case we need to either accept that these events can occur simultaneously, or the victim dies at 1.00 pm + δt, where δt is an infinitesimally small period of time. In either case, the question of asking which reaper issues the death warrant when multiple/infinite grim reapers could have done so simultaniously can be answered with “The one(s) that arrive at 1.00 pm” Implications of the ‘Quantification’ of time: Each unit of time is not infinitely divisible The classical notion of time is continuous, uniform and discreet. Causes preceed effects, effects take time to execute. When time is divided beyond the Planck Time (http://en.wikipedia.org...), our current understanding of physics breaks down, along with all intuitive notions on how objects that would behave within this timescale. A theory of Quantum Gravity is required in order to resolve events that occur within this timescale. Now, if one assumes time is quantified into discreet ‘jumps’, then the problem of Grim Reaper’s paradox is immediately resolved. However that does not rule out an infinite past as Pro asserts, it only rules that the number of events that occur within a discreet amount of time must be finite. This does not rule out the past and future being finite. If there was no beginning, then there is no issue with an eternal past, and not with an eternal future. Therefore, even if I were to concede that discreet units of time are not infinitely divisible, it would not prove Pro’s contention that time cannot be infinite, such examples are modelled in cyclic models of the universe (http://en.wikipedia.org...) amongst many. I will address Pro’s Sans Causality scenario in the next round