Randomly selecting from an infinite number of choices

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It does address the "finiteness of choice", by limiting the number of choices to a finite number.

 

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But you don't have such choice. If you did, and it took you longer to choose "555" than "55", I'd have to wait forever for you to choose (I never get to guess your number), in which case the problem contradicts itself.

 

Try choosing a number with 100 digits, and see if it takes you longer than choosing a number with 3 digits. Choosing a number is a process.

 

No, not so. the uncertainty principle tells us that there is no such point... at some scale, the coin's centre of mass is ill-defined. A fuzzy region, rather than a point.

 

This is true actually. A lot of people mistake heisenbergs uncertainty principle to mean simply that we can't measure with infinite precision, the position of things. What it really means is that there is no definite position at all

 

Sure, supposing you accept zero precision on the velocity of said event. Which would seem to pose a problem for the car crash, which we would presume has a velocity of exactly zero...

 

Oh, for crying out loud. There will still be a point at the exact of the region of uncertainty. The center of mass might not actually be at that particular point, but it's still a defined point that will fall randomly onto one of the infinitely many points along the ruler.

Or like quadraphonics said, do a measurement that give you zero information about the velocity.

Presumably the crash happened before you arrived to take the measurement.

 

No, I really don't think it works that way. But go further, down to the planck scale, and you'll run into more difficulties. There idea of infinite precision just doesn't seem to be built into the universe.

 

I think that mathematically what you have said is a paradox and still needs to be explained properly (although i thought I had by saying it was a countable infinity problem). However, trying to explain infinities using real life examples will always result in arguments which do not address the pure mathematical problem which you are trying to confront.

For example, you said above there will still be a point at the center of the uncertanty, but even this can be disputed. There are no real points in this universe. Particles are limited by uncertainty but even space itself is limited by Planck volume ect!

 

Regardless who goes first, any number you choose will have been selected from a finite number of choices, which doesn't adhere to the problem definition.

 

Just because particles don't have well-defined positions does not imply that a continuum of possible positions does not exist, nor that some such unique position could not be specified exactly.

To even express the idea that a particle has a finite precision in its position requires you to first assume that it is possible, in principle, to distinguish between arbitrarily-closely spaced points in space (i.e., the domain of the wave function is typically the real line).

There is a world of difference between what can be measured (definitely finite precision) and what can be specified (infinite precision).

 

That's not the reason it would. What guarantees that the number of choices is finite is that the time you took to choose the number was finite. The mere fact that you chose the number in a finite time means that your number of choices was limited to a finite number. Any choice is made in a finite time. Thus by making a choice you didn't adhere to the problem definition.

 

Right... but we're entering the realm of models of the world, the realm of abstract mathematics... which was the main thrust of my earlier post, and is what I'd actually like to be discussing.