>> 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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