Orchid XP v8 wrote:
> I gather space actually has a slight negative curvature, so it strictly 
> isn't Euclidian...

Well, it isn't uniformly curved, for sure.

>>> I don't know... Normally if you remove external force, pressure
>>> decreases.
>>
>> It's not pressure. It's gravity.
> 
> I know that the way black holes normally form is because matter is 
> crushed by gravity. But you said that to make a small black hole, you'd 
> need an external force to crush it instead.

Yes. But once you have a black hole, you can take away the pressure and the 
gravity will keep it "crushed". Indeed, "black hole" is the extent to which 
you have to "crush" some amount of matter before the gravity alone is enough 
to keep it "crushed". That's kind of the definition of a black hole.

> Also, I'm still not getting how you can have [gravitational] black holes 
> of different sizes. Presumably the force required to crush matter is a 
> constant, so...?

OK, make a black hole that weighs 10x as much as the sun. Now drop 50 more 
of our sun into it. Do you think the gravity will remain the same?

>>> I don't understand.
>>
>> The speed of light in a diamond is less than half the speed of light in
>> free space/vacuum.
> 
> Really? I didn't think it was such a big difference! o_O

The index of refraction (IOR) is the ratio of the speed of light in vacuum 
to the speed of light in that material.

-- 
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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On 08/03/2011 09:14 PM, Darren New wrote:
> Orchid XP v8 wrote:
>> I gather space actually has a slight negative curvature, so it
>> strictly isn't Euclidian...
>
> Well, it isn't uniformly curved, for sure.

Oh crud, I forgot about that... >_<

> Yes. But once you have a black hole, you can take away the pressure and
> the gravity will keep it "crushed". Indeed, "black hole" is the extent
> to which you have to "crush" some amount of matter before the gravity
> alone is enough to keep it "crushed". That's kind of the definition of a
> black hole.

Right, OK.

> OK, make a black hole that weighs 10x as much as the sun. Now drop 50
> more of our sun into it. Do you think the gravity will remain the same?

You make a persuasive argument, young man.

>>> The speed of light in a diamond is less than half the speed of light in
>>> free space/vacuum.
>>
>> Really? I didn't think it was such a big difference! o_O
>
> The index of refraction (IOR) is the ratio of the speed of light in
> vacuum to the speed of light in that material.

Sure. But I thought most things had an IOR of almost exactly 1...

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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Orchid XP v8 wrote:
> Sure. But I thought most things had an IOR of almost exactly 1...

Given this is a ray-tracing newsgroup, I'm rather shocked. :-)

-- 
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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>> Umm, to keep track of what's in your account? I generally do reconcile
>> my bank statement to my register (I keep mine electronically, so it's
>> fairly simple to do)
>>
>> I think this is basic home finance 101.
>
> Wait - you actually use a sophisticated electronic accounting package
> just for your home finance?

I use a single sheet in Excel.

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>>> I think this is basic home finance 101.
>>
>> Wait - you actually use a sophisticated electronic accounting package
>> just for your home finance?
>
> I use a single sheet in Excel.

Uh... OK... but doesn't that still take a really long time?

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>> So, what, you literally sit down and check all of the thousands of
>> transactions you make, one at a time, to make sure every single one
>> matches the printed recipt?
>
> Yes, I thought everyone does that.

Well, this is the first time I've heard of it. I don't think even my 
sister does this - and she's a qualified accountant!

(Heck, my mum doesn't even bother opening her bank statements when they 
arrive. Then again, I'm pretty sure that's unique to her. Strange person...)

> So realistically, no, I don't check every single item.  But if I'm out
> shopping, I have a vague idea of how much the items I've bought come to,
> and if the receipt shows a different value than I expect, then I do get
> an adjustment.

Yeah, sure. I get that. But usually by the time you get the receipt, 
you've already paid. So I'm still not sure what use the actual piece of 
paper is. (Unless you're really going to check that the number on your 
bank statement actually matches the number on the receipt and the card 
reader...)

> I've also had occasions where a clerk has double-entered an item and not
> realized it, and I use the receipt to get that corrected as well.

That doesn't happen very often. (Fortunately!) About the only time I've 
seen this is in a busy restaurant. (This also just happens to be about 
the only place where you get an itemised list *before* you hand over the 
money.)

> It's called "money management".  If I don't have at least an awareness of
> how much I'm spending, I might end up overdrawn, and that incurs more
> fees.  People make mistakes, and a receipt is a good tool for catching
> those mistakes.

Oh hell, I have literally *no idea* how much money is in my account. My 
technique is to just avoid spending money as much as possible.

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On 09/03/2011 09:02, Invisible wrote:
>>>> I think this is basic home finance 101.
>>>
>>> Wait - you actually use a sophisticated electronic accounting package
>>> just for your home finance?
>>
>> I use a single sheet in Excel.
>
> Uh... OK... but doesn't that still take a really long time?

I only keep track of the balance in each account every month or so, I 
don't put in every transaction (I check my account online every couple 
of weeks for that).

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On Wed, 09 Mar 2011 09:07:36 +0000, Invisible wrote:

>>> So, what, you literally sit down and check all of the thousands of
>>> transactions you make, one at a time, to make sure every single one
>>> matches the printed recipt?
>>
>> Yes, I thought everyone does that.
> 
> Well, this is the first time I've heard of it. I don't think even my
> sister does this - and she's a qualified accountant!
> 
> (Heck, my mum doesn't even bother opening her bank statements when they
> arrive. Then again, I'm pretty sure that's unique to her. Strange
> person...)

Of course, I was kidding, hopefully you caught that in the rest of my 
reply. :-)

>> So realistically, no, I don't check every single item.  But if I'm out
>> shopping, I have a vague idea of how much the items I've bought come
>> to, and if the receipt shows a different value than I expect, then I do
>> get an adjustment.
> 
> Yeah, sure. I get that. But usually by the time you get the receipt,
> you've already paid. So I'm still not sure what use the actual piece of
> paper is. (Unless you're really going to check that the number on your
> bank statement actually matches the number on the receipt and the card
> reader...)

If I know I only bought one widget at CostCo and they charged me for 2, 
then I know there's something wrong, and I can get it corrected before I 
leave the store.

>> I've also had occasions where a clerk has double-entered an item and
>> not realized it, and I use the receipt to get that corrected as well.
> 
> That doesn't happen very often. (Fortunately!) About the only time I've
> seen this is in a busy restaurant. (This also just happens to be about
> the only place where you get an itemised list *before* you hand over the
> money.)

You'd be surprised at how often it really happens.  It's more common in 
places that use a barcode scanner to scan items into the register, 
sometimes it gets double-scanned (I've seen that more frequently than I 
would have expected), or when an item is scanned and then a quantity 
entered (for example, you buy 5 frozen pizzas and the clerk miskeys and 
hits '8' instead).

>> It's called "money management".  If I don't have at least an awareness
>> of how much I'm spending, I might end up overdrawn, and that incurs
>> more fees.  People make mistakes, and a receipt is a good tool for
>> catching those mistakes.
> 
> Oh hell, I have literally *no idea* how much money is in my account. My
> technique is to just avoid spending money as much as possible.

Well, surely that is one way that could work, as long as you don't go 
into overdraft.  A better way is to check your account balance 
periodically (I do that as well) to make sure there's still money there.

Otherwise you also wouldn't know if someone fraudulently used your 
account for something.

Jim

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On 3/8/2011 12:29 PM, Orchid XP v8 wrote:
>>> It is undeniably infinite. But is it countable?
>>
>> Tell me when you're done counting from 0 to 1 in infinitesimally small
>> intervals.
>
> "Countable" doesn't mean that you can actually count them in finite
> time. It means that you can assign a unique positive integer to each one.
>
> Now, between 0 and 1 in the rationals, there are a countable infinity of
> values. But in the reals (which inclused irrational numbers), there is
> an uncountably infinite supply of values.
>
> So I suppose "how many points are there on the unit square" comes down
> to "are the coordinates rational?"
>

Hmm... I don't have a strong enough grasp of number theory, apparently.

>>> Sure. Regular Sudoku is 9x9. But you can make 'em other sizes (with
>>> other numbers of unique symbols).
>>
>> Right, but, even if it were 25x25 it still has a specific layout.
>
> You can make them rectangular, you know. ;-)
>

This would work? How?

>> Graph
>> coloring problems don't necessarily have a consistent number of borders.
>
> True...
>
>>> But if you have a small mass, why would it be crushed to a small size?
>>
>> An incredible amount of force acted upon that mass?
>
> Oh. You mean something *outside* the mass itself causes it to become a
> black hole?
>
> But then, wouldn't that just mean that as soon as you remove the force,
> it wouldn't be a black hole any more?
>

Which is why a small black hole would be short lived. But, then, it does 
have an event horizon, and nothing can escape a black hole. So, wouldn't 
it remain a black hole after being compacted?

>>> But the speed of sound is /not/ constant. It changes depending on the
>>> motion of the source and the receiver. Light, on the other hand, has the
>>> seemingly impossible property that the relative motion of source and
>>> receiver somehow makes no difference to the apparent velocity of the
>>> light... but somehow *does* affect its wavelength? WTF?
>>
>> For the purposes of Doppler shift, it has a constant rate in the medium
>> it is in. The actual speed the waves move through the medium doesn't
>> change. The /relative/ speed does change, however. And is the same for
>> light. Sure, the relative speed of light can even be superluminal.
>
> No, it cannot.
>

Right, what was I thinking. Only the frequency of the light changes. The 
speed doesn't change.

>> Umm, to keep track of what's in your account? I generally do reconcile
>> my bank statement to my register (I keep mine electronically, so it's
>> fairly simple to do)
>>
>> I think this is basic home finance 101.
>
> Wait - you actually use a sophisticated electronic accounting package
> just for your home finance?
>

Heck no. Just a basic home finance program. Cost about US$50.

>>> A "root" is generally a part of a plant. Whereas a "route", as in, "this
>>> is how you get to this square number", would logically make more sense.
>>
>> Isn't the root considered the base of something? A Plants roots are at
>> its base, for example. for example the root word of unbelievable is
>> believe. You wouldn't say route in that context, would you?
>
> Hmm, I suppose...
>
Glad you see things my way for a change ;)

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On 3/8/2011 2:24 PM, Darren New wrote:

>
> 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.
>

On a completely unrelated note, I know someone who has witnessed this 
with his own eyes. Dang cool, if you ask me.

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