Orchid XP v8 wrote:
> On 08/03/2011 06:40 PM, Darren New wrote:
>> Orchid XP v8 wrote:
>>> So I suppose "how many points are there on the unit square" comes down
>>> to "are the coordinates rational?"
>>
>> Draw a dot at sqrt(2),sqrt(2).
> 
> I suppose if we're not talking about real, physical space, but about 
> some mathematical abstraction, it can have whatever properties we define 
> it to have - including the point you describe not being part of the set.

Well, sure. But if you're going to start screwing with the defintion of 
"unit square" rather than using the standard "set of points whose X and Y 
are both from 0 to 1", then the answer comes out of your definition and you 
don't have to ask.

Plus, I'm not sure that physical space is actually continuous, so it's 
possible such a square doesn't have a sqrt(2),sqrt(2) point either.

>>> Oh. You mean something *outside* the mass itself causes it to become a
>>> black hole?
>>
>> Yes.
> 
> Right. So you have to take some matter and mash it somehow?

Basically.  You can do it by taking some matter and slapping it together so 
forcefully it overcomes the non-gravitational forces. I'm not sure that's 
physically possible in the universe as it exists today.

>>> But then, wouldn't that just mean that as soon as you remove the
>>> force, it wouldn't be a black hole any more?
>>
>> No. Science!
> 
> I don't know... Normally if you remove external force, pressure decreases.

It's not pressure. It's gravity.

>>>> Sure, the relative speed of light can even be superluminal.
>>>
>>> No, it cannot.
>>
>> It can travel faster than the speed of light in the medium in which it's
>> traveling.
> 
> I was under the impression that light does not require a transmission 
> medium.

It doesn't. But it does have different speeds in different media. Otherwise, 
you wouldn't have prisms and lenses and such.

>>> This is exactly what relativity states. The speed of light, no matter
>>> which way you measure it, is always constant. (Except as noted below.)
>>
>> The speed of light in a vacuum is always constant. That doesn't mean it
>> can't travel faster than the speed of light in the medium in which it is
>> traveling.
> 
> I don't understand.

The speed of light in a diamond is less than half the speed of light in free 
space/vacuum.  Hence, it's possible to move through a diamond at faster than 
the speed of light in a diamond but slower than the speed of light in a 
vacuum. Hence, superluminal travel, for some definition of that word.

http://en.wikipedia.org/wiki/Cherenkov_radiation

It's what gives the weird blue light coming out of nuclear reactors 
underwater - particles from the reactor hitting the water at speeds faster 
than the speed of light through water.

-- 
Darren New, San Diego CA, USA (PST)
  "How did he die?"   "He got shot in the hand."
     "That was fatal?"
          "He was holding a live grenade at the time."

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