>> 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.

Yeah, but "from 0 to 1" in which set? The integers? The rationals? The 
reals?

As you say, I guess the answer depends on how you define the question. 
(Perhaps we're not even talking about Euclidian geometry, so a unit 
"square" might not even be squarish...)

> 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.

Ah yes, the "which mathematical abstraction actually describes the 
*real* world" argument. :-D

I gather space actually has a slight negative curvature, so it strictly 
isn't Euclidian...

>> 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.

Hmm, theoretical physics for the win!

>>>> 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.

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.

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...?

>> 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.

OK.

>> 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

> Hence, it's possible to move through a diamond at
> faster than the speed of light in a diamond.

Ah, I see.

> 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.

The real world is utterly fricking weird!

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

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On Tue, 08 Mar 2011 20:20:42 +0000, Orchid XP v8 wrote:

>> and
>> yes, I do check that what I was charged is what I paid.  That's how you
>> (a) avoid getting ripped off, and (b) avoid finding yourself in an
>> overdraft situation.
> 
> 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.

> Doesn't that take an insane amount of time?

Sure, that's all I did the entire month of January.

OK, I'm being somewhat facetious here.

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.

And of course, I'm the kind of person who will say "you didn't charge me 
enough" in some circumstances.  There's a restaurant that my wife and I 
frequent, for example, and every once in a while they leave our drinks 
off, so I just have them add them back in at the register (I know they're 
not there because the bill doesn't include them).

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.

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.

>>> Why is it called a "square root"? Surely "square route" would make far
>>> more sense...
>>
>> It seems to have grown out of the old English "Rote" (there's a
>> citation circa 1425).  Etymologically it derives from the French word
>> 'racine' (which translates to 'root', natch).  "radix" also is used,
>> and that's latin for 'root'.
> 
> I knew it would be French! :-P

The OED is my friend for this type of question.  :-)  My local library 
makes the online edition available to me.

Jim

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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?

Post a reply to this message

>> 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.

Post a reply to this message

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).

Post a reply to this message

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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