How Math Explains the World.pdf

(Marcin) #1
that a doughnut is topologically equivalent to a coffee mug, because each has
precisely one hole (you know where it is in the doughnut; the hole in the coffee
mug is where you put your finger through when you hold the mug). If you had a
piece of clay, and poked a hole in it, you could shape it like a doughnut (easy) or
a coffee mug (not so easy) by stretching and bending the clay without any fur-
ther tearing.


  1. See http://en.wikipedia.org/ wiki/Standard_Model. This is an excellent short ex-
    position of the Standard Model, along with a beautiful chart that puts the peri-
    odic table to shame. You have to click several times on the chart before you get to
    a readable resolution, but it’s worth it.

  2. See http://en.wikipedia.org/ wiki/ Electroweak. The first two paragraphs give you
    all you need, but if you like staring at equations, there’s a nice little window that
    has the basic equations of the theory—if Emc^2 is the most impressive equation
    you’ve ever seen, take a look. Because Wikipedia is user composed, the depth of
    treatment in different sections varies wildly. I’m not a physicist, but I can recog-
    nize the symbols and what the equations are saying, but I have no idea where
    they come from and how they might be used.

  3. See http://en.wikipedia.org/ wiki/ Big_Bang. If explanatory Web sites were rated
    on a 1 to 10 scale, this one would be a 10 —it’s as good as it gets. Good graphics,
    understandable explanations, excellent hyperlinking—this site is so good if it
    had pop-up ads, you wouldn’t mind it.

  4. See http:// en .wikipedia .org/ wiki/ Steady _State _theory. This site is nowhere near
    as impressive as the one for the big bang theory. No graphics, a rather perfunc-
    tory explanation, but that’s not really surprising, because the steady state theory
    is dead, dead, dead. I imagine that sighs of relief were heard throughout the
    astrophysical community when this theory bit the dust, because matter-energy
    conservation is so fundamental a principle you’d hate to abandon it.


40 How Math Explains the World

Free download pdf