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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Mike Raiford wrote:
> Which is why a small black hole would be short lived.

No it isn't.

> 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?

How well do you understand quantum vacuum fluctuations?

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

Yes.

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

Quicken. Or QuickBooks. Depending onw hether you need single or double-entry 
bookkeeping.

-- 
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 3/9/2011 3:07 AM, 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...)
>
>> 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...)
>

Well, you check the sum against the bank statement. If they don't match 
then, you start going through all the line items to find the mistake. It 
can happen occasionally, and can be tedious, but worth it if it means 
not overdrawing your account.

>> 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.

I'm at a loss for words ...

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On 3/9/2011 8:54 PM, Darren New wrote:
> Mike Raiford wrote:
>> Which is why a small black hole would be short lived.
>
> No it isn't.
>
>> 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?
>
> How well do you understand quantum vacuum fluctuations?
>

About as well as I understand how thoughts form. :)

>> Right, what was I thinking. Only the frequency of the light changes.
>> The speed doesn't change.
>
> Yes.
>
>> Heck no. Just a basic home finance program. Cost about US$50.
>
> Quicken. Or QuickBooks. Depending onw hether you need single or
> double-entry bookkeeping.
>

Yeah, quicken. Though intuit pisses me off.

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>> 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.

Yeah. Right until your eyes melt and you grow a third arm...

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On 10/03/2011 02:37 AM, Mike Raiford wrote:
> 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.

Set theory. Number theory is where you prove that irrational numbers 
exist. Set theory is where you prove that the set of irrational numbers 
has a strictly greater cardinal number than the set of rational numbers. 
And yes, transfinite cardinal numbers are freaking weird...

>>>> 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?

http://en.wikipedia.org/wiki/Sudoku#Variants

>> Hmm, I suppose...
>>
> Glad you see things my way for a change ;)

Hey, I'm not *that* unreasonable. :-P

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On 3/10/2011 3:19 AM, Invisible 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.
>
> Yeah. Right until your eyes melt and you grow a third arm...

He seems rather normal to me, and quite bright. He even has a kid. She's 
normal (well-- normal for a 3 year old) and doesn't seem to have any 
extra limbs or digits ;) and from what he says, she's pretty smart, too. 
I hazard she may be a bit smarter than my son in some areas.

Besides, a few stray neutrons never hurt anyone.... right? ;)

Oh, yeah, and there's that big thick plate of leaded glass between him 
and the reactor that should help.

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On 3/10/2011 3:24 AM, Invisible wrote:
> On 10/03/2011 02:37 AM, Mike Raiford wrote:
>> 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.
>
> Set theory. Number theory is where you prove that irrational numbers
> exist. Set theory is where you prove that the set of irrational numbers
> has a strictly greater cardinal number than the set of rational numbers.
> And yes, transfinite cardinal numbers are freaking weird...
>

Ah. err... Got ya.

>>>>> 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?
>
> http://en.wikipedia.org/wiki/Sudoku#Variants
>

OK, aside from nonomino they all follow a pattern of n rows x n columns 
in blocks of n. nonomino changes this a bit by making the blocks 
arbitrary in shape.

> Hey, I'm not *that* unreasonable. :-P

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> Besides, a few stray neutrons never hurt anyone.... right? ;)

No. Apparently it doesn't hurt at all. It just silently harms you. :-}

> Oh, yeah, and there's that big thick plate of leaded glass between him
> and the reactor that should help.

Wouldn't leaded glass be opaque?

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