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The Contender
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Achilles and the never ending tortoise, practical test

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Voting Style: Open Point System: 7 Point
Started: 11/2/2010 Category: Miscellaneous
Updated: 5 years ago Status: Voting Period
Viewed: 1,482 times Debate No: 13545
Debate Rounds (3)
Comments (8)
Votes (2)




This is a spin off of Zeno's classic "paradox."

What I would like to consider is in the practical testing of this paradox. Let us assume that Achilles, a very well trainned tortoise, and a 100% unbaised observer with 100% perfectly accurate measuring capabilities, set out to test this paradox.

The Paradox is - If Achilles is attempting to pass a tortoise (assuming that achilles is running faster), which has a head start of "x" feet, he will, after a certian amount of time, reach where the tortoise was, but by then, the tortoise will have moved ahead some distance. After another amount of time, Achilles will reach the tortoise's new position, but by then, the tortoise will have moved again. This process repeats indefinately in so that Achilles, can never pass the tortoise.

Now, I fully agree that Achilles will eventually catch that tortoise (and hopefully turn it into a stew so this can never happen again). However, this debate is about testing the paradox. If the paradox is tested, where achilles runs and stops where the tortoise was, and the tortoise runs and stops at the same time as achilles, just for a second, for the observer to measure and record his measurements (to ensure that the test is legitimate) before continuing again to the next stopping point (and repeaeting the process), we find that Achilles never does pass the tortoise.

I contest that by simply testing the paradox in the mannar desribed, we cannot help but find that the paradox is, indeed, true.

The goal for CON is to argue that this test does not show that the paradox is true.

Define "Paradox" - A statement that logically appears true/false, but is actaully false/true.

Please start the first round with any suggested definitions and allow arguments to begin in round 2.

Thank you.


I would first like to apologize for the lack of length in my argument as I am typing on the Ipad a device so infernal that when you are writing anything in complete sentences (or even texts due to their annoying spell check) you will feel like you are doing daft hands.
But to go back to the subject let me define two charts. The first of these is a discrete chart (1). This chart measures absolute numbers that generate automatically representing them with dots on a line graph(ex. On day one we had 15 customers on day 2 we had 16.) However a graph used on 100% of distance graphs is the continuous graph (2) one which is basically a line graph without units as they are either smaller than detectable or nonexistent. Xeno, a philosopher, would with current knowledge of Descartes and the tree in the forest problem would have agreed with me upon saying that perception is reality and if no units of basic time for a creature to move being perceived therefore none would exist.
My second argument is in fact an answer to your craving for practical testing I myself being a far weaker man than Achilles and morbidly obese raced a turtle (a tortoise was not available) and giving him a head start and a carrot for incentive proceeded to race. What followed was what I assume was the easiest race I ever committed myself to as I beat this tortoise substitute at walking distance as the turtle proceeded to defecate rather than run much although the wind did pick him up slightly forward. You may say to yourself upon this message that experiment was invalid, Achilles had a morbid fear of turtoises or that my lovable reptilian was biased against you and wanted to impede you research but for some reason this theory is farce. In fact Xeno himself considered it a curiosity as common sense dictates that Achilles would win and therefore realized it must be some unseen law of nature.
Debate Round No. 1


I thank my opponent for taking this debate, and apologize for any inconvenience that his ipad may give him.

My opponent defines two separate types of graphs. I have no issue with these graphs, but fail to see how my opponent plans on using them for his case, since the observer in our test of the paradox is already defined as being "100% unbiased" with "100% perfectly accurate measuring capabilities."

I will go ahead and show that calculus, the original method used to disprove the original paradox, will also prove that the test supports the paradox.

We can go ahead and toss some arbitrary numbers into this. Let us assume that Achilles is running at 4 mile per hour, the tortoise is running at 2 miles per hour, and the tortoise is given a 2 mile head start. Remember that these numbers are arbitrary and so long as Achilles is running faster then the tortoise, he will mathematically catch the tortoise. Conventional algebra will tell us that it will take Achilles 1 hour to catch the tortoise (Achilles will have run 4 miles, and the tortoise will have run 2 miles plus the 2 mile head start).

The use of sums, in standard calculus, in the first iteration of the paradox, Achilles runs 2 miles (to where the tortoise was) and it takes him 1/2 an hour, and the tortoise will have run 1 mile. In the next iteration, Achilles runs 1 mile (to where the tortoise was) and it takes him 1/4 an hour (so total time is 1/2 + 1/4 = 3/4 hours), and the tortoise will have run 1/2 a mile. As we keep going through these iterations, we start to see a pattern, 1/2 + 1/4 + 1/8 + 1/16 + ... + (1/2)^n + (1/2)^(n+1) + ... When we add these countless iterations, we see that they get closer and closer and closer to 1 hour (the same result we get from the algebra solution, thus showing consistency). This is called a convergent series (as all the terms are added, they converge upon a single number).

Now, in our test, we must remember that at each iteration, Achilles and the tortoise stop for a second so that the observer can measure the paradox. This means that for each iteration, along with the time of running, there is also 1 second added for measuring. So the first iteration take 1/2 an hour and 1 second, or 1,801 seconds. The second iteration takes 1/4 an hour and 1 second, or 901 seconds (for a total of 2,702 seconds when combined with the first iteration). This may seem like an insignificant amount however it does begin to add up. If we show it with the pattern (now measured in seconds, not hours, like the first one), it come out to (3600/2 + 1) + (3600/4 + 1) + (3600/8 + 1) + (3600/16 + 1) + ... + (3600/(2)^n + 1) + ... If we add these together, we'll see that they don't appear to be coming to any particular number. As it turns out, that little +1 second on each iteration turns a convergent series, into a divergent series (meaning that it does not converge on any number and goes to infinity).

So our testers find that when they test this paradox through measurement, that even after an infinite amount of time, Achilles does not pass that blasted tortoise.

Thank you,


I'ld like to ask what your trying to prove. The fact the paradox exists (which it does.) or the fact that it's true (which common sense dictates is not.) The definition of a paradox is when two things are not equal when a mathematical equation says they are I.e. The mathematic equation and real life. If that is the case than logically something is not accounted for in the equation and if real life is false than our senses dictate otherwise according to Descartes-esque logic. You asked for a practical solution and I gave you one.
And the second of recording you implied would be needless as the most un-biased observer, a computer would make the calculations without a second of rest.
The most damning evidence of all is that jesse owns beat a horse in a hundred meter dash. The horse was given a headstart.
Debate Round No. 2


I thank my opponent for his last round.

My opponent states "...the second of recording you implied would be needless as the most un-biased observer, a computer would make the calculations without a second of rest." However, even the fastest computer in the world still takes some time to calculate every iteration. And since it still takes some time (even if only a millionith of a nano second per iteration), it still holds true that upon testing the paradox by calculating every iteration yields that there still is a paradox and that Achilles will not pass that tortoise.

We all know that the Achilles will, in fact, pass the tortoise, that much is common sense, but why is it that this paradox, which also, on a mathematical level, makes sense in saying the opposite, that Achilles will not pass the tortoise? Even when we test the paradox (not the race, but the actual paradox, that requires us to calculate each iteration) that the paradox holds? Even using the calculus that originally showed that the paradox is not really a paradox, backs up the paradox when actually tested. This has been shown by both the logic of the paradox itself, and by the very math that was suppose to disprove it.

Thank you very much.


You must remember that you wanted throughout the argument you asked for a practical test. I have given you two each of them being more than applicable. You are trying to prove a statement disproved by logic, experience and not to mention nothing says there is no hidden variable to the mathematic equation. You have proven nothing and have no ground to stand on with an obvious answer to who is the winner. To a contest which has been beaten by the probably weaker Jesse Owens against the obviously faster horse.
Debate Round No. 3
8 comments have been posted on this debate. Showing 1 through 8 records.
Posted by Ore_Ele 5 years ago
pretty well actually. Though it is tortoise soup, so it may turn out a little tough.
Posted by losedotexe 5 years ago
How's the turtle soup coming along?
Posted by Kiwi13cubed 5 years ago
I don't think Con ever really grasped the point OreEle was trying to make...
Posted by Kiwi13cubed 5 years ago
oh, this seems so familiar. haha.
Posted by Sonofkong 5 years ago
Two things to say.
1) By the very nature of this argument I racially decline to define paradox
2) I have reported your previous comment for lying about your flexibility.
Posted by Sonofkong 5 years ago
Last (for now)
Posted by Ore_Ele 5 years ago
Also, if someone wants to suggest different definitions for paradox, I'm really flexible.
Posted by m93samman 5 years ago

2 votes have been placed for this debate. Showing 1 through 2 records.
Vote Placed by gavin.ogden 5 years ago
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Vote Placed by Kiwi13cubed 5 years ago
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