Why is it that women generally get more cold than men?

MacWagon · 27 days

Yes this is correct, the assumption that there is only one length scale for a human is not quite right. It's the same as assuming that everyone is the same shape as everyone else, just a different size, so the dimensional analysis is at best approximate. I always wonder though how close to "true" the square-cube law is for this, and how much the other stuff matters. Its hard to say which is the most dominant effect, and even harder to quantify by how much.

MacWagon · 27 days

I'm not an expert on this, but this is related to a really cool math/physics problem that I love, so I thought I'd share (I am a mathematician!) I will add a disclaimer that the mathematical analysis here idealizes the situation greatly, so it may not be the most relevant factor in this issue and other biological issues may be the dominant effect. However, its awesome so here goes:

The problem is about dimensional analysis. Let's call the height of a person "L" which is a length (measured in meters or feet). The volume V of a person is a [length]^3, i.e measured in cubic meters or cubic feet. It's a mathematical fact that if there are no other length scales floating around, that it must be the case that V is proportional to L^3. (This fact is the content of the Buckingham Pi theorem ) Similarly, the surface area of a person must be proportional to L^2, as long as there are no other length scales around.

What's the upshot of all this? Well, people generate warmth proportional to their volume (this is a spherical cow type argument...very idealized) and lose it proportional to the surface area. Since volume goes like L³ and area goes like L^2, taller people will stay warmer than shorter people (they generate L³ heat, but then only lose L² heat). Since woman are on average shorter than men, they will have a harder time keeping warm. If your girlfriend is shorter than you, this may be a contributing factor to this phenomenon.

ViperRobK · 1 month

Came here to say this. The Hilbert Hotel was the coolest thing ever when I was a kid!

Coolguy_McAwesome · 1 month

If I recall correctly the exemptions are attached to the house....so if your neighbors don't mind/don't know you can register under their house to get more exemptions.

cc_1988 · 2 months

This is a great solution! I think I get what you're doing here. I think the matrix multiplication should be:

                                100
                /1 0 0 0 0 0\      
                |p 0 0 0 0 p|  
                |0 p 0 0 0 p|  
[0,0,0,0,0,1] * |0 0 p 0 0 p|     =  [v, *, * ,*, *, *]
                |0 0 0 p 0 p|      
                \0 0 0 0 p p/

ozzy88 · 2 months

I really like you exposition here. It's clear and concise. Well done.

One thing that I think is worth mentioning explicitly is that the fact that its a "2D universe" doesn't make any difference because conservation of angular momentum restricts the orbit to a plane. This is true even in 3D.

ozzy88 · 2 months

It's highly dependent on which numerical method is being used. Some will conserve energy for this problem, while others don't. It's really hard to say what's a numerical artifact and what's not if you don't what method. It's especially hard to conclude if the orbit is stable or not numerically....you are much better off doing some analysis.

ozzy88 · 2 months

What numerical method is this using? You have to be careful when drawing conclusions about things like the closed-ness of orbits from this because its hard to be sure what is a numerical error, and what isn't. Numerical simulations are always approximate and every numerical method will have some features which it distorts.

mcnica · 3 months

Amazing! Thanks so much. It reminds me of a car engine or something similar.

mcnica · 3 months

That's why I'm looking for a good explanation. I didn't say it was easy!

PowerDowner · 3 months

Is it a countable number of mathematicians? Otherwise how could we find "the first one"?

siriusgrey · 3 months

Mine's the opposite: Leave a mark that'll be remembered 100 years from now.

jayjaym · 3 months

Once I ordered a cheesecake from a restaurant. It had a red sauce on it which looked delicious. Turns they mixed up the ketchup and the raspberry coulis that night.

PSFalcon · 4 months

Where is he located if you don't mind my asking?

ProfessorLex · 4 months

I really liked Bak and Newman...it was exactly the right balance for me between rigor and examples. Alfors was too hard and Needham was too elementary, but Bak and Newman was just right.

TrampolineTales · 4 months

I love sharing! Here's mine: http://i.imgur.com/Gwblo.png

Part of the mechanic of my game is the feeling of not being able to see around looking around corners and hidden monsters, so I tried to make it a bit more maze-y than a traditional rouge like, but still having lots or nice big rooms to mess around in.

cmalkus · 5 months

Looks awesome! One thing that would be great is if it could include the details for how combat works more specifically.

Veggie · 5 months

Nice! I've never seen this proof done explicitly like this before. There is a really slick way using calculus of variations that is actually pretty elementary; its like the very first example of a calculus of variations problem you see.

Can anyone find a link? If not I can reproduce it if there is interest.

kickaguard · 5 months

The first half the way is 0.5, but then after the second half the way your at 0.5 + 0.25 = 0.75, not 0.55 as you suggest. Your argument is an expression of the fact that 0.5 + 0.25 + 0.125 + ... = 1

kickaguard · 5 months

The point is that 0.99.. should be thought of as the limit of the series 0.9 + 0.09 + 0.009 + ... . This is the definition of 0.9999..., there is no other way to precisely say what 0.99.. means.

Now, the definition of a limit is that it is by definition equal to whatever it gets "infinitely close to". (see http://en.wikipedia.org/wiki/Limit_of_a_sequence). So the fact that its "literally infinitely close to being equal 1" is precisely the statement that the limit IS 1.

This can be confusing if you aren't familiar with limits....and it might seem just made up. Who said that that's the definition of a limit anyways??!?! If you start doing lots more higher level math though, you realize that this is the only sensible definition and it actually makes a lot of sense and is a really cool idea. For now though you just have to trust us :)

imfromthepast · 5 months

This is great! You should write it up really nice and try getting it published.

It reminds me a little bit of a short story called "Vengeance Fleet" I read once. I'm slightly embarrassed because I can't remember the author, but it's in the anthology: "The Young Oxford Book of Timewarp Stories" if I'm not mistaken. It's actually a really good collection if you like time travel IMO.

http://www.amazon.com/Young-Oxford-Timewarp-Stories-Books/dp/0192781677

EDIT: The author is possibly Fredric Brown

mcnica

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