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A Simple Question

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Herodotus View Drop Down
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  Quote Herodotus Quote  Post ReplyReply Direct Link To This Post Topic: A Simple Question
    Posted: 24-Dec-2005 at 19:59

A droplet of water drips onto the top of a triangular structure, and for a moment, it sits perched atop the point of the triangle. To both sides are slopes of 45 degrees; both the triangular structure and the droplet of water are perfect and symetrical; the atmosphere around the actors is an absolute vacuum. The only force acting on the experiment is gravity, which pulls the droplet downward; it must fall and, because of the attraction between the water molecules, it must remain whole. 

(1) Which direction will it go, and why?

(2) What does this say about our assumptions of order, regularity, and reason in the universe?

My thoughts: First, I have no idea which way it would go, nor can I. We humans have been trained by experience and formed by nature to operate in the realm of practical, and I use that term loosley, activity. We recognize relations between spacial materials, and form patterns so as to function and survive as a species. In this scenario we have removed all those factors to which we could attribute what, at first glance, might appear to be a random action: air flow, slight fluctuations in pressure, slight irregluarites in the shape or chemcial compisition of the apparatus or of the water droplet, etc. I cannot process the notion that something happens, that the droplet falls in one particular direction, for no reason. If I were to witness this experiment, or accept its conception theoretcially, I have to recognize that nature does not work in order, nor follow our laws, nor have cause and effect. It simply does and is, but I can't know that, or what that is; nor is that something I could know. The flaw isn't that I can't see behind the veil and understand what is going on, it is that my brain makes me assume that their is something to be understood.

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Maju View Drop Down
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  Quote Maju Quote  Post ReplyReply Direct Link To This Post Posted: 24-Dec-2005 at 21:50
I assume you're talking of a triangular prismatic structure... something like a roof.

I think that the droplet will be broken when hitting the structure.

But for the rest you are right: dropping is one of the typical chaotic systems in which small unpredictable and maybe undetectable perturbations can change everything.

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  Quote Herodotus Quote  Post ReplyReply Direct Link To This Post Posted: 25-Dec-2005 at 10:18
When I say the droplet drips onto the structure, which is intended to resemble a roof, it is only falling a very short distance. Whatever aparatus the water comes from, imagine that it is only a few millimeters from the roof. In that situation, the droplet should not break. As for small unpredictable and maybe undetectable perturbations determining the direction in which the drop falls, you are missing the point. I realize that in reality my experiment could never be reproduced, but assume theorectially that the perfect conditions I described were in effect. There are NO slight pertubations to effect the droplet, nothing to explain why it would fall in one direction over the other, yet it must fall. I am not talking about chaos theory, and the minor changes in the orginal reactants that effect the eventual product. In this situation, I am describing true chaos, for lack of a better word: not a reason so intricate and on a scale so small that it's nearly beyond our comphrehension, but a system in which there truely is no reason for action, there is no cause and effect.
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  Quote Decebal Quote  Post ReplyReply Direct Link To This Post Posted: 25-Dec-2005 at 10:33
Originally posted by Herodotus

The only force acting on the experiment is gravity, which pulls the droplet downward; it must fall and, because of the attraction between the water molecules, it must remain whole. 

I think the phrase above is key. Have you considered the possibility that your assumptions are actually incompatible? Why is it necessary for the water droplet to remain whole? If it falls exactly on the edge of the 2 surfaces, depending on its mass, with no other factors playing in, it will either split in two halves (or a somewhat unequal other distribution if it's not exactly on the edge), or it will actually simply stay up there on the edge.

You have to be careful when designing your system, to make sure that your parameters are compatible with each other, that you give all necessary parameters and that you don't just jump to conclusions. You made the assumption that the droplet must necessarily drop to one side or another, but you also produced the requirement that the droplet cannot split. If the droplet cannot split, it means that it's below a critical mass, and that means that you have neglected the possibility that the droplet will simply balance itself on the edge.

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  Quote AlokaParyetra Quote  Post ReplyReply Direct Link To This Post Posted: 25-Dec-2005 at 11:02

i think the experiment proposed was meant to test randomness vs. order in nature. perhaps this experiment could do the same:

a man is seated at a table. there is another man across from him, who asks the first man this question, "one or two?" That is the whole nature of the question. there is no explanation before of after. so, it would seem the choice made would be completely random. "one" and "two" are essentially the same choice. this is then repeated exactly. absolutely nothing is changed. the time is the same, the enviroment is the same, the two men are the exact same, and the question asked is the exact same. will the same choice be made?

actually, now that i think about it, this more addresses free will/predestination, but whatever.

and as to the original question proposed, why is it necessary that the droplet drop to either side? i agree with the previous post. if dropped at exactly the tip, and is dropped so that the center of the droplet is the first to touch any surface, and the droplet cannot break, wouldn't the droplet simply stay on the top, balanced?



Edited by AlokaParyetra
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Imperator Invictus View Drop Down
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  Quote Imperator Invictus Quote  Post ReplyReply Direct Link To This Post Posted: 25-Dec-2005 at 11:17
(1) Which direction will it go, and why?


Depends on the style in which you answer the question. For example, in Quantum mechanics, we would be talking about probabilities. So in this case, the answer would be that 50% of the time, it'll fall to the left, and 50% of the times it'll fall to the right. The path of any single particle cannot be determined.

The path of each individual droplet will be determined by miniscule factors, of which there are too many to calculate, so the best answer is in probability.

(2) What does this say about our assumptions of order, regularity, and reason in the universe?

As the droplet must either go left or right, the microstages of the system increases by twofold. Therefore, the entropy (chaos) of the system is increasing.

The total entropy (chaos) of the universe is always increasing, according to classical physics.

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  Quote Maju Quote  Post ReplyReply Direct Link To This Post Posted: 25-Dec-2005 at 12:36
Herodotus:

Sorry but, if everything else is neutral, the droplet will break even if you carefully deposit it on the edge of the prism: the internal balance of gravitational forces will pull the droplet in both directions equally and therefore it should break (unless gravity is weaker than internal cohesion of the droplet, in which case it should remain in unstable balance over the edge). Try with an iron ball.

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