I've already mentioned one of my favorite things to think about, the infinitely sticky substance (Fish!). Yesterday I came up with another one, an infinitely elastic object. Meaning that it bounces off of things perfectly. Now, I don't claim to understand collisions very well, but the first consideration that comes to mind is whether this object (let's say it's a ball) is hard or soft. If it were rubbery, it would absorb force and then use it to propel itself backwards on collision. If the rebound were perfect, it would bounce off with the same amount of force as it entered with. But on the other hand, if it were hard, it seems like it would bounce off better. The same way that a basketball bounces better than a ball of pizza dough.
On second thought, it would have to be rubbery. It has to deform slightly on impact with another object, doesn't it? Otherwise (and I'm just going on intuition here; I don't have any other tools to work with), it feels like it would shatter on impact, because the forces on the ball would have to go somewhere, cause some change. It has to do with impact, which is force times time. An infinitely hard ball would take no time at all to bounce, so the impact would also be zero. But that doesn't say anything about the force. It could be anything and still satisfy the equation. The other thing that impact is is the change in momentum, and the ball is certainly changing its momentum. After all, it's switching directions entirely. Hmm... I can't remember what kind of a proof that is-assuming one thing, finding that assumption's consequences, and finding a contradiction in them. Here, I assumed that the ball was infinitely hard, and had a contradiction in the magnitude of impact, so I can safely conclude that the ball is not infinitely hard. (I think that's a valid proof)
So we have a rubbery ball that is perfectly elastic and bounces off of things without slowing down in the slightest. If we dropped it to the floor, it would perpetually bounce up to the height we dropped it from and back down to the ground. In other words, there would be no loss of energy. Conclusion: perpetual motion!
The key to this substance is the perfect rebound. This, I suppose, means that it has to rebound in the same time it absorbed the force. It seems like it needs to have a very set shape which it wants to return to with all possible speed. Hmm...but that sounds a lot like a very hard substance. Shoot. I'll leave that question alone for a bit.
What would it be useful/annoying for? Certainly it would be useful for museum exhibits and scientific papers, simply because of its inherent weirdness, but without knowing a bit more about what it would actually be like (hard, soft, etc.), I don't know enough to really tell what it would likely be used for.
Another interesting thing about it is that it cannot possibly make any noise on impact. That is, the ball can't. The wall or floor it hits can. Unless that, too, is made of the elastic material. This is a weird material. I'm starting to see why physics would object to the existence of such matter.
I am thankful for my unbelievably awesome family.
Showing posts with label speculation. Show all posts
Showing posts with label speculation. Show all posts
Sunday, November 14, 2010
Tuesday, November 9, 2010
Fish!
Continuing in my trend of being a complete copycat, I now have fish!!
<-- See, over there?
Yeah, they're pretty cool. And, if you're interested, I have an invisible fish...or two...or three. So, for those of you looking to kill some time, can you see them? And how many are there?
I maintain the right to remove them at any time and completely forget about changing this post. If so, sorry, you'll just have to live with it.
I also got some practice converting to hexadecimal for the coloring, which was quite enjoyable. It's always fun to do strange problems like that. I can do two digits fairly easily. Three becomes much trickier, because I fundamentally do not think in base-16.
On a vaguely related note, does base 1 work? I've had a teacher tell me that to express, say, 8 in base 1, you need: 11111111. But at the same time, isn't one of the defining characteristics of a number system the existence of the placeholder, the number zero? And base one certainly doesn't have a zero. Or if it does, it doesn't have a one, and thus can't express numbers... It's thoroughly confusing. But also very fun to think about.
Another of my favorite contemplations is an infinitely sticky substance. That is, it sticks to anything it touches. Anything. A single point particle of it would bring anything it touches to absolute zero, because everything it touched would be unable to move away from it or along it (since it's a point particle). Luckily, not many things would be able to touch a single particle of it because it would have a limited area around it. Once filled by particles, the clump of particles would behave like a single (very strange) particle. It would be a very strange clump, a hodgepodge of charge, mass, and strange interactions, but a particle nonetheless. And if there were a lot of this sticky substance, you could get to the point where you have a macroscopic particle, immobile and probably rather stringy, since chances are that few sticky particles are only stuck to other sticky particles. So we have a fantastically dense, entirely indivisible, fractal-like construct. What would you be able to do with such an object? Because it is indivisible, it would be infinitely harder than diamonds. It could not break. Could it bend? Perhaps. It would involve the rearrangement of the particles around the sticky particle, which I suppose could be possible, so long as they could slide by each other easily. Charge or space-filling-ness (I'm sure there's a word for that, but I can't think of it) would change their ability to change positions. But what if one of the particles swinging around was a sticky particle? If it got close enough to another sticky particle, they'd stick and not be able to rotate again. So over time, if any rotation were possible, the stickiness would slowly gravitate towards the center, creating a very nearly spherical macroscopic particle. But...no. Because then you have suddenly much less surface area for the same number of particles stuck to the outside, which means that some would have to come disconnected, which is against our initial condition. So probably if there's any room for rotation or bending, then the sticky particles are not yet fully saturated. Since saturation would occur pretty much instantaneously, this is impossible. We're left with an infinitely strong, completely unbreakable root network.
Any other interesting ideas for random ramblings? Let me know!! I'm almost invariably willing to think about interesting topics.
And today, I'm grateful for warm tea on chilly nights.
<-- See, over there?
Yeah, they're pretty cool. And, if you're interested, I have an invisible fish...or two...or three. So, for those of you looking to kill some time, can you see them? And how many are there?
I maintain the right to remove them at any time and completely forget about changing this post. If so, sorry, you'll just have to live with it.
I also got some practice converting to hexadecimal for the coloring, which was quite enjoyable. It's always fun to do strange problems like that. I can do two digits fairly easily. Three becomes much trickier, because I fundamentally do not think in base-16.
On a vaguely related note, does base 1 work? I've had a teacher tell me that to express, say, 8 in base 1, you need: 11111111. But at the same time, isn't one of the defining characteristics of a number system the existence of the placeholder, the number zero? And base one certainly doesn't have a zero. Or if it does, it doesn't have a one, and thus can't express numbers... It's thoroughly confusing. But also very fun to think about.
Another of my favorite contemplations is an infinitely sticky substance. That is, it sticks to anything it touches. Anything. A single point particle of it would bring anything it touches to absolute zero, because everything it touched would be unable to move away from it or along it (since it's a point particle). Luckily, not many things would be able to touch a single particle of it because it would have a limited area around it. Once filled by particles, the clump of particles would behave like a single (very strange) particle. It would be a very strange clump, a hodgepodge of charge, mass, and strange interactions, but a particle nonetheless. And if there were a lot of this sticky substance, you could get to the point where you have a macroscopic particle, immobile and probably rather stringy, since chances are that few sticky particles are only stuck to other sticky particles. So we have a fantastically dense, entirely indivisible, fractal-like construct. What would you be able to do with such an object? Because it is indivisible, it would be infinitely harder than diamonds. It could not break. Could it bend? Perhaps. It would involve the rearrangement of the particles around the sticky particle, which I suppose could be possible, so long as they could slide by each other easily. Charge or space-filling-ness (I'm sure there's a word for that, but I can't think of it) would change their ability to change positions. But what if one of the particles swinging around was a sticky particle? If it got close enough to another sticky particle, they'd stick and not be able to rotate again. So over time, if any rotation were possible, the stickiness would slowly gravitate towards the center, creating a very nearly spherical macroscopic particle. But...no. Because then you have suddenly much less surface area for the same number of particles stuck to the outside, which means that some would have to come disconnected, which is against our initial condition. So probably if there's any room for rotation or bending, then the sticky particles are not yet fully saturated. Since saturation would occur pretty much instantaneously, this is impossible. We're left with an infinitely strong, completely unbreakable root network.
Any other interesting ideas for random ramblings? Let me know!! I'm almost invariably willing to think about interesting topics.
And today, I'm grateful for warm tea on chilly nights.
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