Why do the majority of cartoon characters only have 8 digits instead of 10?

The unit square contains an infinite number of points. But is it 
countably or uncountably infinite?

Every Sudoku problem is a graph colouring problem. But is every graph 
colouring problem a Sudoku problem? (For suitable size and shape of 
Sudoku grid.)

A black hole forms when you have such an insanely vast amount of mass 
collected together in one place that it actually collapses under the 
sheer force of its own gravitational field, crushing itself into a space 
having zero volume and infinite density. So... how *the hell* do you 
make a /small/ black hole? Surely a small object wouldn't generate 
anywhere near enough gravity to form a black hole.

If the speed of light is constant, how the hell does light undergo 
Doppler shift?

Why do almost all species of birds bob their heads when they walk?

What is the purpose of receipts? I mean, seriously, if you're anything 
like me, you have hundreds of the damned things. What do you *do* with 
them? If I buy some petrol, and the receipt says £52.98 but they 
actually changed me £62.51, am I really going to notice? Does anybody 
actually sit down and *check* these things? For every damned purchase 
they make?! [Obviously, for high-value items that you might need to 
return, or for goods that your employer is paying for, the usefulness is 
more obvious.]

Do spiders have a sense of smell?

Why is it called a "square root"? Surely "square route" would make far 
more sense...

Why do only large feathers fall out? I mean, you often find a single 
long black tail feather. But birds must have lots of smaller feathers 
also. How come you never see any of those laying around?

Who put the dip in the dip, di-dip, di-dip?

Post a reply to this message

On 3/7/2011 4:15 AM, Invisible wrote:
> Why do the majority of cartoon characters only have 8 digits instead of 10?
>

I've heard its easier to draw 3 fingers than 4. But, really, I dunno.

> The unit square contains an infinite number of points. But is it
> countably or uncountably infinite?

I suppose you could say that it's an infinite set of all complex numbers 
in the range of [0,1+1i)?

> Every Sudoku problem is a graph colouring problem. But is every graph
> colouring problem a Sudoku problem? (For suitable size and shape of
> Sudoku grid.)

I don't necessarily think so. Sudoku has a very specific layout.

>
> A black hole forms when you have such an insanely vast amount of mass
> collected together in one place that it actually collapses under the
> sheer force of its own gravitational field, crushing itself into a space
> having zero volume and infinite density. So... how *the hell* do you
> make a /small/ black hole? Surely a small object wouldn't generate
> anywhere near enough gravity to form a black hole.
>

Take any mass and collapse it down small enough and it'll become a black 
hole. Once it reaches a critical ration of mass/volume, then you'll have 
a black hole. It may not last too long, or it may; and if it does, it 
would be rather irresponsible to create one so close to our own planet.

> If the speed of light is constant, how the hell does light undergo
> Doppler shift?
>

Same way sound Doppler shifts. the packets of light are either closer or 
further from each other depending on the relative velocity of the 
emitter and the observer.

> Why do almost all species of birds bob their heads when they walk?

Good question. I thought it was mostly just birds from the columbidae 
family that did that.

>
> What is the purpose of receipts? I mean, seriously, if you're anything
> like me, you have hundreds of the damned things. What do you *do* with
> them? If I buy some petrol, and the receipt says £52.98 but they
> actually changed me £62.51, am I really going to notice? Does anybody
> actually sit down and *check* these things? For every damned purchase
> they make?! [Obviously, for high-value items that you might need to
> return, or for goods that your employer is paying for, the usefulness is
> more obvious.]

Right, you'd need to (at least in the United States) keep certain 
receipts for tax purposes. If you purchase items on a debit card, it's 
nice to have the slip of paper to take home and enter into your account 
register. And, as you said, expense tracking is also another good 
reason. Also, you may want to keep receipts to compare against your 
account statement to make sure someone didn't pad the bill when they 
cleared the credit card transaction.

>
> Do spiders have a sense of smell?
>

I'm sure they do, but not as we do. I imagine their palps have some sort 
of chemical sense that can pick molecules out of the air. Especially the 
free roaming varieties that don't set up a web. They also might need a 
sense of smell to find a suitable mate.

> Why is it called a "square root"? Surely "square route" would make far
> more sense...

Wouldn't the square route be the perimeter of the square? Square root 
because it is the root of exponentiation operation. The big number on 
the bottom is the root, the little number on the top is the exponent. So 
square root makes sense, as does cube root, 4th root, nth root, etc... :)

> Why do only large feathers fall out? I mean, you often find a single
> long black tail feather. But birds must have lots of smaller feathers
> also. How come you never see any of those laying around?

They're rather light and tend to drift around. I've seen lots of smaller 
feathers. Go find a place where birds roost. You'll see all variety of 
feathers, especially when they're molting.

> Who put the dip in the dip, di-dip, di-dip?
>

The 1950's?

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>> The unit square contains an infinite number of points. But is it
>> countably or uncountably infinite?
>
> I suppose you could say that it's an infinite set of all complex numbers
> in the range of [0,1+1i)?

It is undeniably infinite. But is it countable?

>> Every Sudoku problem is a graph colouring problem. But is every graph
>> colouring problem a Sudoku problem? (For suitable size and shape of
>> Sudoku grid.)
>
> I don't necessarily think so. Sudoku has a very specific layout.

Sure. Regular Sudoku is 9x9. But you can make 'em other sizes (with 
other numbers of unique symbols).

>> A black hole forms when you have such an insanely vast amount of mass
>> collected together in one place that it actually collapses under the
>> sheer force of its own gravitational field, crushing itself into a space
>> having zero volume and infinite density. So... how *the hell* do you
>> make a /small/ black hole? Surely a small object wouldn't generate
>> anywhere near enough gravity to form a black hole.
>>
>
> Take any mass and collapse it down small enough and it'll become a black
> hole. Once it reaches a critical ration of mass/volume, then you'll have
> a black hole. It may not last too long, or it may; and if it does, it
> would be rather irresponsible to create one so close to our own planet.

But if you have a small mass, why would it be crushed to a small size?

>> If the speed of light is constant, how the hell does light undergo
>> Doppler shift?
>>
>
> Same way sound Doppler shifts.

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?

>> Why do almost all species of birds bob their heads when they walk?
>
> Good question. I thought it was mostly just birds from the columbidae
> family that did that.

Seen a chicken walk recently? ;-)

>> What is the purpose of receipts?
>
> Right, you'd need to (at least in the United States) keep certain
> receipts for tax purposes. If you purchase items on a debit card, it's
> nice to have the slip of paper to take home and enter into your account
> register. And, as you said, expense tracking is also another good
> reason. Also, you may want to keep receipts to compare against your
> account statement to make sure someone didn't pad the bill when they
> cleared the credit card transaction.

Who the heck has an "account register" just for their personal stuff? 
For business expenses, sure. But just for, like, "I went to the corner 
shop yesterday and bought a loaf of bread", are you *really* going to 
check your bank statement to see if every single transaction like that 
was correctly charged? Who does this?

>> Do spiders have a sense of smell?
>
> I'm sure they do, but not as we do. I imagine their palps have some sort
> of chemical sense that can pick molecules out of the air. Especially the
> free roaming varieties that don't set up a web. They also might need a
> sense of smell to find a suitable mate.

Hmm, you're probably right. I think I recall something about a female 
wolf spider's silk having a special taste to it...

>> Why is it called a "square root"? Surely "square route" would make far
>> more sense...
>
> Wouldn't the square route be the perimeter of the square?

It's the "route" to that square.

> Square root because it is the root of exponentiation operation.

Which just means that the term is used elsewhere too.

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.

Probably means the original mathematician who worked all this out was 
French or something... :-P

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Le 2011-03-07 05:15, Invisible a écrit :
>
> If the speed of light is constant, how the hell does light undergo
> Doppler shift?

Doppler shift is a shift in wavelength, not a shift in the speed the 
wave travels.

>
> Why do almost all species of birds bob their heads when they walk?
>

http://www.loc.gov/rr/scitech/mysteries/pigeon.html

> What is the purpose of receipts? I mean, seriously, if you're anything
> like me, you have hundreds of the damned things. What do you *do* with
> them? If I buy some petrol, and the receipt says £52.98 but they
> actually changed me £62.51, am I really going to notice? Does anybody
> actually sit down and *check* these things? For every damned purchase
> they make?! [Obviously, for high-value items that you might need to
> return, or for goods that your employer is paying for, the usefulness is
> more obvious.]

Proof of purchase.  Let's say the store clerk reported someone leaving 
without paying.  You can show the cops your receipt and say "not me!"

Since another copy of the receipt is printed by the cash register, it 
also makes sure that the store owner will be able to keep an accurate 
inventory, as well as give the govt the sales taxes he collected from you.

What you do with the receipt once you've left the store is, of course, 
up to you.

>
> Do spiders have a sense of smell?
>

http://findarticles.com/p/articles/mi_m0EPG/is_n7_v29/ai_17027826/

-- 
/*Francois Labreque*/#local a=x+y;#local b=x+a;#local c=a+b;#macro P(F//
/*    flabreque    */L)polygon{5,F,F+z,L+z,L,F pigment{rgb 9}}#end union
/*        @        */{P(0,a)P(a,b)P(b,c)P(2*a,2*b)P(2*b,b+c)P(b+c,<2,3>)
/*   gmail.com     */}camera{orthographic location<6,1.25,-6>look_at a }

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Invisible wrote:
> Why do the majority of cartoon characters only have 8 digits instead of 10?

It's easier to draw.

> The unit square contains an infinite number of points. But is it 
> countably or uncountably infinite?

Uncountable. Even the numbers between 0 and 1 are uncountable.

> make a /small/ black hole? 

Squeeze something small very hard. Like, during the big bang era, or inside 
a nova or something like that.

 > Surely a small object wouldn't generate
> anywhere near enough gravity to form a black hole.

You have to help.

> If the speed of light is constant, how the hell does light undergo 
> Doppler shift?

The frequency of light (so to speak) is related to the energy of the photon. 
If you're moving towards the source of the photons, they'll have more energy 
and hence look more blue. If you're moving away, they'll have less energy 
and look read.

> Why do almost all species of birds bob their heads when they walk?

If I had to guess, I'd say it's to keep their eyes still while they're 
walking, like a dancer spotting during a spin. However, that's entirely a guess.

> What is the purpose of receipts? 

To give you a record of what and when and how much you paid for something.

-- 
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."

Post a reply to this message

On 3/7/2011 7:26 AM, Invisible wrote:
>>> The unit square contains an infinite number of points. But is it
>>> countably or uncountably infinite?
>>
>> I suppose you could say that it's an infinite set of all complex numbers
>> in the range of [0,1+1i)?
>
> It is undeniably infinite. But is it countable?
>

Tell me when you're done counting from 0 to 1 in infinitesimally small 
intervals.


> 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. Graph 
coloring problems don't necessarily have a consistent number of borders.

>
> 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?

>
> 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. And, 
light does travel at different rates in different media. C is simply the 
speed of light in a vacuum.

>>> Why do almost all species of birds bob their heads when they walk?
>>
>> Good question. I thought it was mostly just birds from the columbidae
>> family that did that.
>
> Seen a chicken walk recently? ;-)
>

Oh, right. I'm thinking columbidae is unique in how they can tuck their 
head ...

>
> Who the heck has an "account register" just for their personal stuff?
> For business expenses, sure. But just for, like, "I went to the corner
> shop yesterday and bought a loaf of bread", are you *really* going to
> check your bank statement to see if every single transaction like that
> was correctly charged? Who does this?
>

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.


>
> It's the "route" to that square.
>
>> Square root because it is the root of exponentiation operation.
>
> Which just means that the term is used elsewhere too.
>
> 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?



-- 
~Mike

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On Mon, 07 Mar 2011 10:15:42 +0000, Invisible wrote:

> What is the purpose of receipts? I mean, seriously, if you're anything
> like me, you have hundreds of the damned things. What do you *do* with
> them? If I buy some petrol, and the receipt says £52.98 but they
> actually changed me £62.51, am I really going to notice? Does anybody
> actually sit down and *check* these things? For every damned purchase
> they make?! [Obviously, for high-value items that you might need to
> return, or for goods that your employer is paying for, the usefulness is
> more obvious.]

Receipts are useful for expense reports (nee required in most cases), 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.

> 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'.

Jim

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> > The unit square contains an infinite number of points. But is it
> > countably or uncountably infinite?
>
> Uncountable. Even the numbers between 0 and 1 are uncountable.

That depends on what numbers you are using. The number of points in the unit
square of rational numbers is countable, the number of points in the unit square
of irrational numbers is not.

By the way, IIRC, it is actually possible to constuct a bijection from [0,1]
onto the unit square, meaning there is actually the same number of points in the
unit square as there are points between 0 and 1.

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Roman Reiner wrote:
> That depends on what numbers you are using. The number of points in the unit
> square of rational numbers is countable, the number of points in the unit square
> of irrational numbers is not.

Well, of course, yes. And the unit square of integers has a finite number of 
points in it. :-P

> By the way, IIRC, it is actually possible to constuct a bijection from [0,1]
> onto the unit square, meaning there is actually the same number of points in the
> unit square as there are points between 0 and 1.

Yep. There's really only two infinities you get when you talk about 
"numbers" - Aleph0 and Aleph1.

-- 
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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> Yep. There's really only two infinities you get when you talk about
> "numbers" - Aleph0 and Aleph1.

Wasn't the question whether there is a set that is larger than a countable
infinite set and smaller than an uncountable infinite set proven to be
unprovable?

Lovely sentence, isn't it? :D

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Roman Reiner wrote:
>> Yep. There's really only two infinities you get when you talk about
>> "numbers" - Aleph0 and Aleph1.
> 
> Wasn't the question whether there is a set that is larger than a countable
> infinite set and smaller than an uncountable infinite set proven to be
> unprovable?

My memory is that it was thought to be unprovable but later proven to not be 
so. However, wikipedia (Cardinal_numbers) agrees with you. Not that it's 
unprovable, but that its provability depends on the axioms of set theory you 
accept. I suspect it depends in part on things like the axiom of choice, etc.

-- 
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."

Post a reply to this message

On 08/03/2011 06:07 PM, Darren New wrote:
>> Wasn't the question whether there is a set that is larger than a
>> countable
>> infinite set and smaller than an uncountable infinite set proven to be
>> unprovable?
>
> My memory is that it was thought to be unprovable but later proven to
> not be so. However, wikipedia (Cardinal_numbers) agrees with you. Not
> that it's unprovable, but that its provability depends on the axioms of
> set theory you accept. I suspect it depends in part on things like the
> axiom of choice, etc.

That was my recollection - that the question is provably "independent" 
of the standard axioms of set theory. (I believe the axiom of choice is 
specifically implicated - although I have no idea WTF the axiom of 
choice is.)

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

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Am 07.03.2011 12:58, schrieb Mike Raiford:

> Take any mass and collapse it down small enough and it'll become a black
> hole. Once it reaches a critical ration of mass/volume, then you'll have
> a black hole. It may not last too long, or it may; and if it does, it
> would be rather irresponsible to create one so close to our own planet.

Don't worry - if such an experiment can be conducted by man (and some 
say that with the newest CERN particle accelerator it might be 
possible), then nature does it all the time as well, thereby having 
already proven it a harmless prank.

Essentially, any success in creating an artificial black hole in a 
controlled environment with current technology would prove that black 
holes do decay over time, as otherwise our universe would already be 
full of them.

(I personally favor the idea that leptons, quarks and the like might be 
black holes themselves; kind of like the smallest black holes you can 
possibly get.)

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>> 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?"

>> 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. ;-)

> 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?

>> 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.

This is exactly what relativity states. The speed of light, no matter 
which way you measure it, is always constant. (Except as noted below.)

> And, light does travel at different rates in different media.

This part is correct. And I would expect light entering or leaving a 
different medium to exhibit Doppler shift as a result (although it 
doesn't seem to do this...)

> 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?

>> 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...

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

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Orchid XP v8 wrote:
> although I have no idea WTF the axiom of 
> choice is.)

The axiom of choice essentially says that if you have an infinite set each 
of whose elements is a set, you can construct a new set by picking one 
element from each of the elements of the infinite set.

-- 
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."

Post a reply to this message

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).

> Oh. You mean something *outside* the mass itself causes it to become a 
> black hole?

Yes.

> 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!

(Altho there's arguments over whether quantum effects would eventually make 
a black hole too small to form on its own evaporate, but I didn't take that 
to be what you meant.)

>> 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.

> 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.

> This part is correct. And I would expect light entering or leaving a 
> different medium to exhibit Doppler shift as a result (although it 
> doesn't seem to do this...)

That's not how light slows down. Light slows because it is being absorbed 
and re-emitted, not because the speed per se is different in different 
media.  The train always travels the same speed - but sometimes it stops at 
more stations.

> Wait - you actually use a sophisticated electronic accounting package 
> just for your home finance?

Yes. It's not all that sophisticated.

-- 
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."

Post a reply to this message

Am 07.03.2011 14:26, schrieb Invisible:

>> Take any mass and collapse it down small enough and it'll become a black
>> hole. Once it reaches a critical ration of mass/volume, then you'll have
>> a black hole. It may not last too long, or it may; and if it does, it
>> would be rather irresponsible to create one so close to our own planet.
>
> But if you have a small mass, why would it be crushed to a small size?

Non-gravitational external force. Smash two particles into each other 
hard enough, and you /might/ get them close enough together that they 
can't escape each other's gravitational well anymore.

>>> If the speed of light is constant, how the hell does light undergo
>>> Doppler shift?
>>
>> Same way sound Doppler shifts.
>
> 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?

That's one of the fun things about Einstein's theory of relativity 
(don't know if this one falls into the domain of special or general 
relativity).

You can put it like this: In your frame of reference, things buzzing 
towards you simply have a faster-ticking clock than things buzzing away 
from you (presuming that you define "now" based on when light from 
"somewhere" reaches you, rather than "when" it was emitted).

>>> Do spiders have a sense of smell?

Insects do, so I guess spiders do as well - though if they follow the 
insect way, then their "noses" are on their legs.

> 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.

Even more generally, a "root" is something from which something bigger 
grows, so it does make sense. Also note that if it was "route", it would 
be "route to", rather than "root of".

> Probably means the original mathematician who worked all this out was
> French or something... :-P

Maybe, but he spoke (or at least) wrote Latin. The original word was 
"radix" (latin for - guess what - "root"). In German it's "Wurzel", 
which also means "root".

Post a reply to this message

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.

>> 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?

>> 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.

>>> 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.

>> 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.

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

Post a reply to this message

On 08/03/2011 01:36 AM, Jim Henderson wrote:

> Receipts are useful for expense reports (nee required in most cases),

Agreed. In a commercial context, you want to keep track of this kind of 
thing.

> 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?

Doesn't that take an insane amount of time?

>> 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

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

Post a reply to this message

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."

Post a reply to this message

>> 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*

Post a reply to this message

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

Post a reply to this message

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."

Post a reply to this message

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*

Post a reply to this message

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."

Post a reply to this message

>> 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.

Post a reply to this message

>>> 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

Post a reply to this message

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 ;)

Post a reply to this message

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.

Post a reply to this message

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."

Post a reply to this message

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 ...

Post a reply to this message

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.

Post a reply to this message

>> 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...

Post a reply to this message

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

Post a reply to this message

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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>>>> 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.

I've seen ones that are 3x2 blocks arranged in a 2x3 grid, so you need 
1-6 in each block, row and column.

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Le 10/03/2011 12:44, Invisible a écrit :
>> Besides, a few stray neutrons never hurt anyone.... right? ;)
> 
> No. Apparently it doesn't hurt at all. It just silently harms you. :-}

There is no nerves on the ADN, so no dolors!

> 
>> 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?

Ever seen some Bohemian glass ?
(Prague is well-known...)

Glass with 30% of PbO (lead oxyd), and very clear!

Household cristal is between 18 and 38 % PbO (% weight)

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Mike Raiford wrote:
> Yeah, quicken. Though intuit pisses me off.

Me too. But what do you expect from a company with a monopoly on such useful 
software?

-- 
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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Orchid XP v8 <voi### [at] devnull> wrote:
> 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?

  Remember that little detail that nothing can come out of the black hole?
That means that the black hole cannot stop being a black hole because the
material it's made of cannot come out. (Hawking radiation notwithstanding.)

-- 
                                                          - Warp

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Mike Raiford <"m[raiford]!at"@gmail.com> wrote:
> > 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.

  A black hole cannot stop being a black hole (according to GR) because
nothing can come out. Once it has become a black hole, it will be like
that forever. (Quantum mechanics might cause something else to happen,
but from a purely GR point of view.)

> 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?

  There's no other possibility (in GR). A black hole can only grow (if
more matter is fed to it), not shrink.

-- 
                                                          - Warp

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clipka <ano### [at] anonymousorg> wrote:
> Am 07.03.2011 14:26, schrieb Invisible:

> >> Take any mass and collapse it down small enough and it'll become a black
> >> hole. Once it reaches a critical ration of mass/volume, then you'll have
> >> a black hole. It may not last too long, or it may; and if it does, it
> >> would be rather irresponsible to create one so close to our own planet.
> >
> > But if you have a small mass, why would it be crushed to a small size?

> Non-gravitational external force. Smash two particles into each other 
> hard enough, and you /might/ get them close enough together that they 
> can't escape each other's gravitational well anymore.

  I'm not sure how that would work. All the mass in those particles would
need to be compressed into a volume smaller than the Schwarzschild radius
of those masses, which is really, really small. Could we be hitting the
limits of planck volumes?

  And this assumes that the "volume" of the particles (if that term even
makes sense at quantum levels) gets smaller when particles hit each other.
It's not like particles are little balls that get compressed when they hit
each other.

  Perhaps if you get enough particles close enough to each other by
colliding them all at the same time, you could get a mass that is so
dense that it's smaller than its own Schwarzschild radius.

  Btw, AFAIK in theory eg. a black hole with the mass and charge of an
electron (assuming such a thing is physically possible) would basically
be indistinguishable from a normal electron. (Ok, maybe it would behave
differently in collisions with other particles. I don't know enough of
physics to say for sure.)

-- 
                                                          - Warp

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clipka <ano### [at] anonymousorg> wrote:
> (I personally favor the idea that leptons, quarks and the like might be 
> black holes themselves; kind of like the smallest black holes you can 
> possibly get.)

  Hawking would probably disagree with that.

-- 
                                                          - Warp

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Roman Reiner <lim### [at] gmxde> wrote:
> That depends on what numbers you are using. The number of points in the unit
> square of rational numbers is countable, the number of points in the unit square
> of irrational numbers is not.

  Is the set of irrational numbers in a unit square larger or equal to
the set of irrational numbers in a unit line?

-- 
                                                          - Warp

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Warp wrote:
>> 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?
> 
>   There's no other possibility (in GR). A black hole can only grow (if
> more matter is fed to it), not shrink.

Warp is right. But what happens in QM is, essentally, particles of negative 
and positive mass spontaneously spring into existence close to the edge of 
the black hole, and the particle of negative mass falls into the hole while 
the particle of positive mass escapes. Hence, it looks like it's leaking mass.

According to the math, the likelihood of this asymptotically approaches zero 
at the size of the hole approaches how big it has to be to turn into a black 
hole anyway. In other words, if a sun of 4.9 solar masses doesn't turn into 
a black hole, and a sun of 5.1 solar masses does, the likelihood of a 
positive/negative pair splitting and having half escape approaches zero as 
the size of the black hole approaches 5 solar masses.

-- 
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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Warp wrote:
>   I'm not sure how that would work. All the mass in those particles would
> need to be compressed into a volume smaller than the Schwarzschild radius
> of those masses, which is really, really small. Could we be hitting the
> limits of planck volumes?

Wikipedia implies a mass the hole of the moon would be about 1/10th a 
milimeter in diameter. (Altho, technically, you'd have to measure the 
circumference, as the diameter would actually be infinite.)


>   Perhaps if you get enough particles close enough to each other by
> colliding them all at the same time, you could get a mass that is so
> dense that it's smaller than its own Schwarzschild radius.

That's basically what you have to do.

http://en.wikipedia.org/wiki/Black_hole#Evaporation

Given that, I'm pretty sure this is exactly the kind of situation where QM 
and GR conflict, so I'm not sure any of this is other than speculation.

-- 
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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