World's best suggested paradox
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"Everything is something, but this is nothing."
"What happens when object that is absolutely immobile in every form and context, even to its relative surroundings. Gets hit by a object that in every form and context is unstoppable?"
"What happens when object that is absolutely immobile in every form and context, even to its relative surroundings. Gets hit by a object that in every form and context is unstoppable?"
Nope, it would not.Banana Phone said:
What you need to remember is that Relativity doesn't only give us the rule that things can't travel faster than light, it also tells us what effects happen to those objects that get very close to that speed.
In this case, the important thing is time-dilation. At very fast speeds, time slows down, and if you get very close to the speed of light, it almost stops altogether. The object may be rotating very quickly from it's own perspective but, to an onlooker, the object itself is moving forward through time much slower than it ought to be, as such, the rotation is also slowed down hugely. Avoiding the contradiction.
A simpler example is if you stand on Earth and two ships fly off at 99% light speed in opposite directions. Now, to you on Earth, neither ship is travelling faster than light, 1% slower in fact but, surely, from each other's perspective the other ship must be travelling as 198% of the speed of light. Violating two fundamental laws of Relativity, first that you can't travel faster than light and second that every inertial reference frame is equally valid.
The answer is that, thanks to the dilation effects that take place, the ships will in fact only appear to be travelling at approximately 99.99% of light speed to each other. Avoiding the violation again.
If you walk four feet north and three feet west, what have you done?NLS said:
This isn't a paradox at all. You failed in one activity, and succeeded in another.
I still don't buy this one. I understand that there is an infinitely small variance between .9999... and 1, but it is still existent, just not representable. Given the infinite number of unrepresentable numbers, how does this make sense? It isn't like you are taking a limit, or something.Maze1125 said:
Hmm, well, just after posting I did some... 'research' on this (Aka, wikipedia hehe). A few of the points there are fairly interesting, and one struck home: It questions the assumption that any given value can have only one numeric representation. This is true, and probably why I've questioned it so thoroughly.Maze1125 said:
I suppose there is probably a mathematically accepted statement such as "two numbers are equal if no numbers exist between them" or something.
Yep, in fact, there is exactly that rule (or, if you want to be pedantic, the contrapositive of it.)Zechnophobe said:
Every two distinct real numbers, x and y, have another real number between them. The obvious one being (x+y)/2.
After all, if 0.999... and 1 were distinct, what would (0.999... + 1)/2 equal?
That doesn't make sense. If you keep both apples for yourself, then you divided by one, which is essentially the equivalent of giving both apples to 1 person (you). Now imagine having both apples and being tasked to give them to nobody or nothing. That's dividing by zero.Geekosaurus said:
An entire scientific community doesn't just conclude a problem impossible "because they don't want to admit defeat." It doesn't work that way.
If a tree falls in the woods, and no one is around to hear it, and it falls on a mime, does anyone care?
Cookie for reference.
Cookie for reference.
Aw man, I thought we'd let this one go. Well seeing as you're all mathematicians, let me respond with something from my area of expertise - literature. The world's greatest detective, Sherlock Holmes, didn't know that the earth orbited the sun. Why? Because what would it matter if we orbited the moon? It would make no difference. Whether you can divide by zero or not it makes no difference to our lives.The Seldom Seen Kid said:
Yes but that's theoretical mathematics we are dealing with distance here which is precisely defined. 1cm is not the same as 9.99 mm. Presumably if you did keep halving the distance of the steps you would eventually reach a point where you have a step which is less than one planck length across. In this case eater one of two things will happen a) you cant have half a planck length and you will be forced to take a step of one planck length and thus complete the journey or b) the conditions of the original statement remain true and you some how manage to halve it and et cetra ad infanitum, thus never completing your journey and provoking the interest of quantum mechanics community considerably.Maze1125 said:
Um i hate to be a dick here but it would matter quite a lot if we orbited the moon and not the sun, there would be quite a significant difference sorry.Geekosaurus said:
oh and one more thing
This man can divide by zero
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Ahh double post fail
Rob Swire would get his ass kicked for that piece of shit called "Immersion". That's what.TerribleAssassin said:
