>> Well, with no actual data to estimate with, it's kinda hard. :-P
> 
> The point is you are meant to have a rough understanding of density of 
> gases.
> 
>> Heh. Well, I have no idea what the volume of this room is.
> 
> Usually best to simplify it to a shape that it is easy to calculate the 
> volume of, ie a cuboid.

This room *is* a cuboid! ;-)

>> I don't even "really" know how big a meter is. It used to be the 
>> length of my arms, but they're a tad bigger now. ;-)
> 
> You can estimate though, I suspect you can tell if your room is 2 metres 
> long or 10 metres long, or 50 metres long.  Remember you are about 2 
> metres tall...

If I had to guess, I'd say this room is 3 m by 3 m by 3 m.

>> (E.g., off the top of my head Oxygen is supposed to be something silly 
>> like 0.000004 g per cubic meter or something.)
> 
> Wikipedia tells me it's 1.429 kg per cubic metre...

Really? Wow, that's pretty crazy... I'm *sure* when I looked it up it 
was way less than that.

Ah, here we go: H2 is "0.08988 g/L". Apparently air itself is heavier 
than that.

(You would, of course, *expect* air to be heavier than the lightest gas 
in the universe. But not thousands of times heavier...)

>> Now, see, I was under the impression that lagging traps air, and hence 
>> the "effective" surface area would still be the same.
> 
> No, because the lagging has thickness, and the outer surface of the 
> lagging is the effective surface area for radiating the heat.  Even 
> though the surface temperature will be less with the lagging, for small 
> radii the surface area increase is enough to overcome the effectiveness 
> of the lagging.  Obviously the exact radius depends on the situation, 
> but there will always be a minimum value where lagging works (below that 
> it has the opposite effect than you probably imagined).

Heh. So does it matter which bird then? A hummingbird has different size 
legs to an ostrich. ;-)

>> Aww, c'mon! I thought that was a really neat drawing! :-D
> 
> Yes I have to admit it was pretty cool.

WIN! :-D

>> ...OK, I am now completely bemused. Apparently e^3 is roughly 20. I 
>> cannot work out how that can possibly be. 2^3 is clearly 8. My head 
>> hurts just thinking about it.
> 
> Think about 2^3 and 3^3, then e^3 doesn't seem so bad.

If I could actually compute 3^3 mentally I'd probably agree with you. ;-)

>> As an aside, I notice the difference turns out to be especially tiny. :-P
> 
> Would have been cool if e^pi = pi^e

I can't find it now, but I'm pretty damned certain there's a quote on 
Bash.org where somebody claimed this was true, and some poor sap spent 
hours trying to figure out why their math implementation was wrong...

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