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 


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?

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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


> 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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>
> 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


> 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/

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/*   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."

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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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