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You may be missing the subtly or the essence of this. You said 'it must arrive' but why so confident? In fact there is significant reasonable doubt here resulting from the fact that nowhere in the programming will the computer ever 'lock on' to the wall as its actual destination. Its ironic really, the computer program will allow it to go anywhere EXCEPT the wall. I am not arguing that it will hit the wall, just that it is no more likely to make it to the wall than not to. Paradox. At least in the perfect computer version and especially for the god one. I am unfamiliar with convergent or divergent series. What they are and how they may apply here and to Zeno's Paradox. Any links or clarification please? The purpose of the program was not to reach the wall so the programmer of the computer or designer of the thought experiment is not 'dumb'. The purpose was to decribe a paradox where a vehicle traveling at a constant velosity will NOT hit the wall in one hour as it must, or not...? Most of the world's populations believe in god, so what would they say if it was god instead of the robot doing this experiment, then it would really be a paradox unless you were willing to admit that god was limited in how fast he can divide by the number 2! Ya you first three respondents have it right, and it would not be possible because of the limited commuting power of the machine. Put its is still a great one with the god version! In fact I should post it over there except they might not care much about a scientific paradox...

OK step two of this possible paradox. 1 Would you agree that there is a paradox if the computer was infinitely fast and capable? 2 The vehicle would hit the wall in one hour if it did not need to slow down to give time to calculate if the computer was infinitely fast. So it would both travel the 1000 meters in one hour and at the same time never get more than half way to the wall from any point during the journey it happens to be at any given moment. 3 Einstein is allowed to have imaginary tools in his thought experiments so why not me. For example the time dilation thought experiment that is comparing the relative motions of an atomic clocks aboard a jet to one on the surface of the earth to an imaginary clock in the center of the earth. 4 And this question which seems to be a paradox just in asking. Would a computer need to be infinitely fast and capable or just good enough to keep up for one hour? If it can do its job without requiring the wheels to slow for only one hour it will hit the wall. And one hour is not infinite -hence the computer would not have to be infinitely capable... 5 Just for fun, those who believe in god then consider this variation. God takes the place of the robot and the will of god takes the place of the computer! What then, will you say? Will god slow down because he cant keep up with the demanding math! 3

I beleive I breathed life into an old concept with the following thought experiment problem. Ok, take a robotic vehicle traveling at one km per hour towards a distant wall just over one km away. The machine is aproacing a starting line drawn on the ground that marks the 1000 meters to the far wall. While the robot is aproaching at a steady crawl, it's powerfull onboard computer is preparing its plan of action to be excuted the instant it reaches the starting line. The plan that is being prepaired is as follows and is about to be exicuted is as follows and will be repeated in a loop as soon as its mission is acheived; a- before reaching the starting point, calculate the distance from the starting point to the wall. b- divide by 2 and set a virtual destination point half way to the wall from the starting point. c- travel to the virtual mid way destination at a constant one km per hour. d-before reaching the half way goal, prepare what is to occour once the destination is acheived. which will be to repeat steps a through d. With the only alteration that the definition of the 'starting point' will be replaced with the most recent 'virtual' half way destination. e-roll over virtual destinations, do not stop. (this is the purpose of pre-calculating the next leg of the journey in advance, to allow a rolling start. Maintain a constant forward velosity of one km per hour. What will happen? Will the robot reach the wall in one hour? Will the robot never get there because the computer is only allowed to set a destination goal of half way to the wall from what ever its last position was? I do not know what to think about this one, Is this a perfect paradox? What do you say and why? It is interesting to imagine what would happen with a real-world test beyond the thought experiment only realm. -