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[G-Flex]

Er. Yeah. I think you're right. I was thinking too much in terms of final velocity.

[Urist Imiknorris]

Suppose you go back in time and muck with history a bit. One thing leads to another and you eventually become your own parent. Weird, true, but the Guide tells us that it's a survivable thing in a relationship. How does your DNA work?

You share half of your DNA with the woman you screwed to make yourself.

[iceball3]

Suppose you go back in time and muck with history a bit. One thing leads to another and you eventually become your own parent. Weird, true, but the Guide tells us that it's a survivable thing in a relationship. How does your DNA work?

You share half of your DNA with the woman you screwed to make yourself.

Wouldn't you just end up with an infinitely small half of your original, ending up as a clone of that woman?

[Urist Imiknorris]

No, the other half is an unstable time loop - an effect without a cause. That's the portion you would pass on.


Question time:

There's this unusual little bar, where you can get a free beer if you know the secret code. The secret code works like this: You sit down at the bar. The bartender tells you a number. And you tell him another number. If it's right, you get a free beer. For example, a customer goes up to the bar and the bartender says, "Six." The customer says, "Three," and he gets his free beer. The second fellow goes up to the bar, and the bartender says, "Twelve." The customer says, "Six," and he gets his free beer! A third customer sits at the bar, and the bartender says, "Fourteen." The customer says, "Eight." He gets a free beer. You're sitting there. The bartender turns to you and says, "Twenty-two."

What do you say?

[Strife26]

Ha. I can prove it with CALCULUS!


If we graph the velocity functions of each of them, they're going to look something like this, just with bell curves instead of diagonal lines.


X:

Code: [Select]


|     
|     /-\
|----/   \--------
|
+---------------------------

Y

Code: [Select]


|     
|     
|----\   /--------
|     \-/
+---------------------------


Distance traveled at any time t (with t being on the x axis) is going to equal the integral of the function from t=0 to t=whatever the time is. For those who haven't taken Calc, the integral is the space under the graph of the function. X is clearly going to be larger.


I'm going to go tell my old Calc teacher about this.

[G-Flex]

Yeah, just graphing the velocity is the most obvious way to analyze that. All you have to do is realize that with X, it's always going at v₀ or higher, and that with Y, it's always going at speed v₀ or lower, making it clear which goes faster overall.


There's one problem with yours, though. You're clearly graphing velocity with respect to distance on the x axis, not time. So integrating won't actually get you the distance travelled, it'll get you (m/s)*m instead of (m/s)*s, which isn't particularly useful. Graphing the velocity with respect to time would be a bit more complicated and look different for each one.

[Il Palazzo]

Going back to that thingie from the Happy thread: http://www.bay12forums.com/smf/index.php?topic=42204.36465

Il Palazzo:

... What? No. Listen.

The ice cube, with the stone attached, remains floating. The stone only sinks when it becomes detached from the ice cube. None of this implies that the stone is less dense than water. If it were, it wouldn't sink at all!

The ice cube starts out floating, with the stone attached. Eventually, at some point, the stone becomes detached, yet there is still a finite volume of ice there.

Now now, where do you get the thing about there being some ice left, when the question explictly states that the stone gets released after ALL of it melts?

Rereading the question, it is worded rather poorly. The question inadvertently implies that the stone has a density infinitesimally greater than that of water, which is... pretty damn strange.

What if that is literally true, though? Then: N answer is correct at all. While the ice melts, A and D make sense, since the object is still buoyant, therefore ice melting off it won't affect the water level, for reasons I've already mentioned. The object still remains buoyant for the entirety of the ice's lifetime, since the stone apparently only sinks once all the ice is melted. Therefore, yeah, A and D are true so far, with the water level staying the same. However, after that point, with the stone sinking and the ice totally melted, no further change in the water level can even occur, since all that you have left is a rock that has already become fully submerged. In other words, if the question is interpreted like that, there is no right answer; the water level would remain the same as the object sheds water, and by the time the object has shed all its ice as water and the rock sinks down, the rock has already just become fully submerged by the process, so no further change in water level is possible.

In other words, the question doesn't make sense if you interpret it that way, but that really is what the question is asking if you interpret it literally. None of the answers are valid unless there's some ice left when the stone is released.

No. This interpretation does actually produce results as in C:
The water level would indeed remain the same, for as long as the cube stays afloat, but it is inevitably going to sink before fully melting, due to the stone increasing the average density of the stone-cube system to above that of water's. From this point onward, the water level falls as the ice melts. When it's all gone, the stone is already submerged and at the bottom of the glass, so nothing changes there.
The full time vs total volume graph would go: constant->lowers->constant, but since the question explictly asks us for only two slices of time axis: the one with ice melting, and the one when it's only stone left, we must take an average of the first two bits on the graph(constant->lowers)=lowers.

Using the interpretation you're advocating - that the ice cube remains afloat during the whole experiment - is not physically accurate.

[G-Flex]

Oh, god dammit, not this again.

No. This interpretation does actually produce results as in C:
The water level would indeed remain the same, for as long as the cube stays afloat, but it is inevitably going to sink before fully melting, due to the stone increasing the average density of the stone-cube system to above that of water's.

Do you even understand your own interpretation of the question? The interpretation I'm talking about is interpreting the question literally, as I thought you were doing: That the stone only sinks when all the ice is melted. If this were true, then the ice can't sink before fully melting because it would take the stone with it.

Using the interpretation you're advocating - that the ice cube remains afloat during the whole experiment - is not physically accurate.

What do you mean "not physically accurate"? My interpretation is that the ice cube remains afloat for the entire time that the stone is attached to it, and that the stone becomes detached from it while the object as a whole is still floating. There is nothing physically wrong with this, and the literal interpretation of the question (that the stone only detaches once the ice is completely melted) leads to no given answer being possibly true. I explained why.

[Il Palazzo]

Because I can interpret it as there being no such case when there exist ice and stone separatedly, while the "sink to the bottom" is still technically true, because it's where the stone is at the end of the experiment.

Eh, man, let's just drop. It's became just a matter of arguing what the question "really" says, which part should be taken literally, and which shouldn't, and we could do this forever. If anything I'm sure we can agree that the wording of the problem is not perfect.

Here, let me give you a riddle as well.

Imagine a gigantic guillotine(i.e.two blades, one slightly angled), spanning infinitely large distance from side to side.
It's cutting blade's angle is very small(let's say, infinitely small).
Now if the blade falls, the cutting point at the intersection of the two blades starts traveling alongside the guillotine's length.
Can it travel faster than the speed of light? Why it can, or why it cannot?

Now, imagine an eqally gigantic pair of scissors. As with all scissors, the farther you go alongside the cutting arms, the faster they move towards each other as you make a cut. If you start depressing the handles*(or whatever that not-cutting end is called in English), will there be a pair of points alongside the scissor arms that is traveling faster than the speed of light, and why there is or isn't?

*We are assuming that the material they're made of won't break under any pressure, and that you've got a hand large and strong enough to actually make use of the scissors.

[G-Flex]

Now, imagine an eqally gigantic pair of scissors. As with all scissors, the farther you go alongside the cutting arms, the faster they move towards each other as you make a cut. If you start depressing the handles*(or whatever that not-cutting end is called in English), will there be a pair of points alongside the scissor arms that is traveling faster than the speed of light, and why there is or isn't?

*We are assuming that the material they're made of won't break under any pressure, and that you've got a hand large and strong enough to actually make use of the scissors.

Of course no part of it will move past the speed of light. Nothing can. If it were that easy to disprove modern scientific theory, we'd be in big trouble if nobody qualified had done it already. Keep in mind you still have to put energy into the scissors in order to make them move, and that in order to make any part of it move at the speed of light, you'd need to be putting literally infinite energy into it... which you aren't going to do. Newtonian laws of motion simply don't work on such large scales, so you can't use simple laws of leverage to figure out how to make something move faster than the speed of light.

Simply put, even if you the force propagates through the entire pair of scissors instantaneously (which it won't), it gets harder and harder to press on them as the blades move faster, and it's infinitely hard to get any small part of it to the speed of light.

[Il Palazzo]

That's correct. What about the guillotine case then?

[G-Flex]

I honestly don't even understand your first question. What are you asking is moving faster than the speed of light, exactly? And why does it have two blades?

At any rate, no, nothing about it will move faster than (or at) the speed of light, because that just plain can't happen.

[Il Palazzo]

Hmm, you know how does a guillotine look like? Two blades, one horizontal, one angled, the angled one falling at the other.
If you look at the intersection point between those two(the cutting point), is it at all possible for it to move faster than the speed of light?

ed: Ninja quote:

At any rate, no, nothing about it will move faster than (or at) the speed of light, because that just plain can't happen.

Is that so? Any other explanations, anybody?

[iceball3]

At any rate, no, nothing about it will move faster than (or at) the speed of light, because that just plain can't happen.

Eh. Regarding the scissors problem. Couldn't there be the possibility that there is just a shitload of tunneling occurring on the blades or something? When something tunnels through a vacuum or matter it essentially ends up on the other side of whatever it tunnel instantaneously. So I guess the best explanation of the scissors question would be that any points past the speed of light would essentially begin to "lag" through the air/vacuum. It would still be moving the speed of light, but it would be compensating by teleporting to catch up.

[Leafsnail]

For the guillotine... nothing's actually moving horizontally, is it?  We just perceive a kindof wave moving along the bottom.  So perhaps you could create an illusion of faster than light travel in this manner.

Er. Yeah. I think you're right. I was thinking too much in terms of final velocity.

That's pretty much the basic trap with this question, yeah.

Friction would make it more complicated to work out, but I don't think it'd actually change the answer.

Is it time for an evil question?  I think it's time for an evil question.

You have one piece of cheese.  Using only straight slices, what is the lowest number of slices you can use to cut it into 8 parts?

I think I'll also present the clues that came with this question...
You can only do this because it's cheese.  If you tried to do this with a birthday cake, there would be a huge fight.
It's impossible to cut or break this cheese with anything other than a knife.
You can only cut in straight lines, but you can cut wherever you want.
The cheese is of a normal shape, one which you can buy in a shop.