iq test

Because no two objects you observe in the real world will ever be the same length, if you are willing to measure them to any arbitrary degree of precision.

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Because no two objects you observe in the real world will ever be the same length, if you are willing to measure them to any arbitrary degree of precision.

Where is this stated, postulated, theorized or proven? I must have missed something really important in my education and I'm trying to learn something here. (I'm being totally sincere - you and David seemed to have learned this and I never did. If it's true - I'd like to learn it now- and by learn I mean see proof or data that shows this concept to be true, and have the methodology by which this fact was arrived at explained to me).

Thanks.

I agree that my "proof" guarantees equality for only an instant in time, and that the measurement would have to be taken at that instant. However, I also would like to hear the explanation for why two objects can't have the same length if measured with an arbitrarily small precision. Given an object of a certain length, the probability of finding an object of the same (exact) length is zero, but that doesn't mean it's impossible. What is the impossibility (not improbability) proof?

After giving this some more thought, I wonder if anything has a constant exact length. After all, electrons are in motion.

If two processes are fired off by you, both of which make a cut on the real line between zero and one, and the cutting method gets exactly one point with a truly uniform distribution over the interval, then the probability of two cuts getting exactly the same point would be vanishingly small. Now, both processes might choose 1.5 exactly, but what are the odds if the processes are truly random?

Frankly - I do see what you're saying, but I don't think this explains or proves as fact that nothing in the real world is or can be- whether by design or randomly-equal in length to anything else.

I don't think it can be proved - because just as there may, or as you postulate, will be the slightest deviation in production - there might also, or by your theory, will be, the slightest deviation in measurement. And the only way you could prove it is to have taken the measurements of every object and compared them. Which I KNOW has never been done.

And I wasn't talking about human precision (or lack of) in terms of cutting metal - I was thinking of natural growth processes - because that's what we were talking about. I also wasn't talking about probability. Because you stated the definitive.

So again, I'm wondering if there is a postulate or thereom somewhere which would explain your belief that no two people or any other pair of entities in the real world could be equal in size.

I think your argument fails to be convincing because probability equal to zero does not imply impossibility.

Probably you're failing to consider the fact that the process is hypothesized to have a uniform distribution. I could ask you this question. Two random processes choose a number between zero and one based on a uniform distribution. What are the odds that both processes will choose a number between .499 and .501? How about between .4999 and .5001? Certainly the latter probability must be smaller.

Anyway, I think we can agree that if the length measurement process goes to the limits of quantum uncertainty, the chances of finding two people with the same height in a classroom are essentially zero.

Anyway, I think we can agree that if the length measurement process goes to the limits of quantum uncertainty, the chances of finding two people with the same height in a classroom are essentially zero.

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Anyway, I think we can agree that if the length measurement process goes to the limits of quantum uncertainty, the chances of finding two people with the same height in a classroom are essentially zero.

I can agree to that too - but I didn't see any mention in the initial question of the condition of 'the length measurement process going to the limits of quantum uncertainty.' You've changed the question.