h a l f b a k e r yWarm and Fussy
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Zeno's Arrow of Infinity is a mechanical apparatus that's physically realises the paradox called Zeno's Arrow. (if you don't know the paradox then it's best to look it up at this point)
The apparatus is comparatively simple: An Arrow is projected towards a target, which it never actually reaches.
The arrow is placed inside a clear perspex tube and is carried forward using a continuous process of magnet propulsion, exactly as per a maglev train. After an hour it has travelled exactly half the distance to the target. In the next hour, it travels half the remaining distance. Each hour is marked by the same progress rate towards the target ie half of the remaining distance always takes an hour.
A powerful microscope is positioned In front of the target so that the tip of the arrow and the target's surface are in perfect focus. Anyone so inclined can observe the progress of the arrow, which although still moving forward under its magnetic drive system, will never make contact with the target's surface no matter how long it is in operation.
This device is dedicated to Zeno: "That which is in locomotion must arrive at the half-way stage before it arrives at the goal."— as recounted by Aristotle, Physics VI:9, 239b10
[link]
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You can see a better illustration of the basic paradoxes of pre-Socratic philosophy if you work on systems integration between an accounting system and a bulk logistics system. An accounting system is the kind of system that Parmenides or Zeno would have coded, while a bulk logistics system is the kind of system that Heracleitus would have coded. |
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The middleware must therefore be at least Kantian and preferably Hegelian, but it seldom is. |
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The resultant artwork is the reddening face of a project manager who demands to know in small words how the "technical problem" can be shoehorned into his spreadsheet. |
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//They're all a load of rubbish though// I agree. You can only iterate this a finite small number of times before you are down to the diameter of an atom, and then you are into technical questions about what it means for one "thing" to touch another "thing" in terms of chemical bonds and inter-molecular interactions. I think this makes the idea incoherent long before you get to quantum effects (planck length, uncertainty of velocity and position) though it doesn't take very many divisions by two to get down there. |
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In fact you may well run into engineering tolerances well before you get to atomic interactions. Actually this is quite interesting since the accuracy on measurements tends to be expressed in % rather than absolute uncertainty, and so the point at which the tip of the arrow "touches" the target will depend much more on the accuracy of the position of the shooting mechanism and the first half-way point than on the measurement of the distance between the tip and the target a few hours later. |
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[marked -for-deletion] bad science, bad engineering, and (per [a1]) possibly also bad philosophy. |
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P.S. an arrow is "shot" not "fired". |
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It's easy to see why so many avoid the halfbakery now, making it a shadow of what it once was, given the lack of humour magnified by an enthusiasm for poisonous negativity being constantly delivered by many of its annotators now. |
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I find it hard to believe that these ancient philosophers really didn’t understand that an infinite number of ‘events’ can happen in a finite time. The inevitable conclusion then is that they just went on about these so-called paradoxes to make themselves look clever and to make it look like they weren’t just sitting around on their lazy arses all day while everybody else did all the real work. |
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Why is this getting a bonestorm? Seems to have made for conversation which is worth a bun, doesn’t seem worthy of being hated anyway so [+] |
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I didn’t give it a negative vote. The idea’s OK, but the paradox it’s based on is nonsense except as a fun thought-experiment |
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It’s a bit suspicious then that nowhere did they actually say “Oh yes, of course we know that this paradox we keep going in about is absurd. We’re only presenting it to show the unreality of events without duration” |
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OK I'll engage positively with this idea. |
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Suppose we don't shoot the arrow faster than mach 1. Let us make the launch speed just over 291 m/s. Let us begin the artwork at mid-night tonight. We need a track a bit over 1,048km long, with the target mounted exactly 1,048,576m from the tip of the arrow before it is shot. |
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Let us also make the arrow travel at constant speed for each whole hour, because my calculus is not up to a continuous decelleration. |
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For the first hour, the arrow will travel at about mach 0.85 and will cover a bit over 5 hundred kilometers. For the second hour, the arrow will fly 262km at 145 m/s. From 2pm until 3pm the arrow will travel 131km at about 36m/s. Etc. |
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From 7am to 8am the arrow will travel 4km at a bit over 1 meter per second - worth getting up to watch. Between 1pm and 2pm the arrow will be travelling at about one-and-a-half cm per second, and will move 64m over the course of the hour. |
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By 5pm the arrow will be 8m from the target, and will be moving 2mm each second - just perceptible to the naked eye close up. |
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By 9pm the arrow will be 50cm from the target and will be moving forward 1mm every 10 seconds - I think this will need the microscope suggested in order to see the movement. |
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By 2am the tip of the arrow will be 1cm from the target, and will be moving the thickness of a strand of spider silk every second. This movement may still be visible through the microscope. |
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By 6am the next morning the tip of the arrow will be 1mm from the target, and will be moving 0.3 microns every second. I'm not sure if this movement would be perceptible even through the microscope. The natural jitter in the mechanism might start to become more than the movement, meaning that the arrow will be merely vibrating gently as people walk across the gallery floor rather than actually moving towards the target. |
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By the next morning basically the arrow will be stationary. |
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By 1pm, the throngs of admirers will see the tip of the arrow head is only twice the thickness of a strand of spider silk away from the target. Looking down a powerful microscope, you will be able to see the separation of the arrowhead and the target, but you will see no movement, because the arrow head will "theoretically" only be moving at the width of one atom per second. There will be nothing to see, basically, the entire exhibit will be static. |
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Yet the gap will gradually shrink. By midnight, two days (48 hours) after the demonstration began, the arrowhead will be the width of 2 atoms away from the target. |
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At 1am it will be the width of one atom away. At 2am it will be less than the width of one atom away. By most standards this means that the tip of the arrowhead is touching the target. After this time the natural movement of the atoms caused by room temperature means that the arrow is not actually moving in any meaningful sense and so the demonstration has come to an end, just over 2 days before it began. |
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And the tortoise is allowed to move on with its life. |
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[pocmloc] Your "calculations" confirm a failure to understand the idea. Open your mind. "Fail again, fail better" Samuel Beckett. |
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Have I made an error in my calculations? It's quite possible, I was working fast. |
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It also occurred to me that Zeno's "racetrack" paradox (which per [a1]'s link is what this idea is really trying to realise), the object moving towards the finish line does not slow down. In the first hour it moves half way, in the next 1/2 hour it goes to the 3/4 mark; in the next 1/4 hour it goes to the 7/8 mark, etc |
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i.e. it moves at a constant speed and at the end of the second hour it arrives at the finish mark and continues past it at the same speed. The "paradox" is created by the person proposing the paradox not understanding calculus, not conceptually grasping that the limit of an infinite series can be a finite number - in this case the simple mathematics that 1/2 + 1/3 + 1/4 + ... + 1/n + ... = 1 |
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In your example, if "never" means "in a couple of hours" then it all makes sense, and would work as described. |
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My calculations were humouring this simple error in understanding the paradox as described, and allowing a continual (stepwise) decelleration, in which case on strictly mathematical terms "never" is correct (though also shows a lack of understanding of "approaching the limit", but you were the one who proposed actually building the machine, and so I merely tried to calculate how your proposed practical implementation would behave if constructed to spec and installed in a gallery as an exhibited work. |
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It is the same kind of error as assuming that there is a difference between 0.9999999... and 1 |
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I see you didn't pay much attention of Beckett's words - this is "fail again, fail worse". Have another go. |
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Actually they are kind of my life motto, I love it when someone points out where and how I have made an error. So please go ahead and explain what is wrong. |
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Your idea is wrong in lots of interesting ways which is why I am engaging, I am sure I am also wrong in many ways in my responses, but by engaging with our wrongness we can all learn something useful. |
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Your error lies in not accepting the fact that the arrow never reaches its destination. This is because the apparatus has been constructed in such a way as to ensure that it doesn't. This is where it differs from an arrow fired from a bow that does actually hit the target. |
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OK yes you are correct that in theory it never "reaches" its destination. |
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However, am I wrong to suggest that it only takes 48 hours to come within the width of one atom from the destination? |
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If that is correct then you will not see any separation even under a microscope. |
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Its an interesting idea for sure, but it has fatal terminal errors both in its understanding of Zeno's work, and in the proposed mechanical implementation. |
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As you intimated, it's OK to occasionally post a failed idea, and the fruitful discussion of it can help the next idea to be back to (or above) your usual high standard. |
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Now that you've made an attempt at understanding the idea, albiet begrudgingly - how about discovering some humour and abandoning that ethos of viewing every idea through the prism of a binary abacus? |
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//I tried a binary abacus once// - I think [xenzag] must have meant “…through the abacus of a binary prism”, which makes a lot more sense |
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A ternary abacus is much harder to make, because the third position of the bead must dialectically sublate the other two. But once you've got that, it would probably be easier to imprison a prism in it. |
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Pastry for the atmosphere. You appear to have "Time in a Bottle" (tm Jim Croce). |
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The "problem" with the paradox wasn't clear to me as a teenager. Although I aced Calculus 101, I had more of a problem with "as x approaches infinity" which is really Newton's contrary fudge. |
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Mmm, delicious contrary fudge! |
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It occurs to me that [a1]'s and [pocmloc]'s misgivings (who is this mis and what have they been giving?) may go some way to proving Zeno right, if we subdivide to the quantum level, etc. etc. |
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Contrary fudge is an incompressible fudge which stymies fudge packers. |
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