Archive for July, 2010

Our Flat Solar System

July 31, 2010

How come the planets aren’t arranged spherically around the sun?

the solar system

Instead of being spherical, as seems to be the default shape of things in the universe, the planets are arranged in a more-or-less flat disk — a series of concentric ellipses.

planets and planetessimals

What’s up with that?

Answer: angular momentum + gravity.

The nascent planets (or planetesimals) may have started out spherically arranged around the sun.

But then the spinning sun (or proto-sun) flung its satellites—including Earth—further out into space, like how a merry-go-round flings you off when it spins fast.  So the shape would have become an oblate spheroid, with the major axis being the direction of the sun’s spin.

[an oblate spheroid]

At the same time as centrifugal force pushed out in just one circle, gravity pulled in on the entire sphere.

So the minor axis of the oblate spheroid had nothing pushing it out, only something pulling in, while the major axis was being pushed and pulled.  Eventually the minor axis mostly collapsed and now we humans observe the “flat disk” shape.

SOURCE: Essentials of Geophysics, Part One

Advertisements

weight loss

July 29, 2010

Here is a low-effort way to lose weight:

toothbrush

When your mouth gets the taste for food, brush your teeth first.  I’ve noticed that removing all the food tastes from my mouth reduces cravings.

gallon of water

Also, you can keep yourself full by drinking water.  It looks weird but I often carry a gallon of water around with me.  Just rinse out a milk jug and use that.  Simply having the gallon of water near you, redirects your snack impulses to something that’s calorie-free.  Also, aren’t most Americans chronically dehydrated anyway?  You’re supposed to drink some ridiculous amount of water per day—like 8 cups, and nobody I know does that daily.

This works best if you have some really good-tasting water.

Quantum Probability, Quantum Logic

July 27, 2010

F && F    =    T,     T && T     =    F

To those who have studied formal Logic, the above statements should provoke hysteria—and not just because I’m using whitespace instead of parentheses.

Normally in Propositional Calculus, one considers statements like “I’m shopping and I don’t have time to talk about this right now.”  If either (A) the speaker isn’t shopping, or if (B) the speaker does have time to talk about this right now, then the statement is considered false.  The statement is abbreviated A and B, or A ^ B, and considered formalistically.  True and False can also be thought of as 1 and 0, with AND ^ working like multiplication •.  That is, a legal functor maps ({1,0}, •) to ({T,F}, AND).

T^T=T;   T^F=F, F^T=F, F^F=F

Nothing could be more obvious than this interpretation of the word “and”.  However, obvious doesn’t cut it in quantum mechanics.

Not only does False AND False = True in QM, but negative probabilities abound, too!  Yipes!  Well it’s not that surprising coming from the field that brought us quantum tunneling.

Pitowsky represents probabilities as convex hulls which live inside the [0,1] boundary.  Logic inhabits only the boundary; probability lives in the interior.  Oh, just go get yourself a copy!  I don’t want to write for too long about the technicalities.

Quantum Probability, Quantum Logic by Itamar Pitowsky.

July 26, 2010

cool corporate art

from the North American Derivatives Exchange (NADEX aka HedgeStreet)

Oil Wells

July 25, 2010

Let’s say you are standing on the outside of a hollow sphere, about the size of the Earth.  There is a single rod underneath where you’re standing which varies in density d(x) along its entire length.  Its mass pulls on you.  You have tools which can measure precisely the gravitational pull wherever you’re standing.  How many different measurements do you need to take—and where—in order to figure out where the rod is heavy and where it’s light?

The real problem of finding stuff in the ground has to be much much harder, but I just want to know the answer to this “simple” question for starters.

My first intuition would be to measure right on top of the rod, then move to two other spots so you have formed an equiangular triangle on the sphere.  But still leaves ∞ degrees of freedom if you started out with an entire function’s worth of freedom, right?

July 24, 2010

This is bad science fiction.

It extrapolates certain stereotypes from the present — the ability to look things up makes people lazy; kids are inarticulate; stores convince you what to buy, even taking away your power to think for yourself; teenagers’ fashion becomes ever more disgusting (teenagers lacerate themselves in Feed); consumerism and the internet are bosom buddies.  Nevermind that an encyclopedia is one of the most popular sites, along with newspapers — people sure are stupid and inarticulate.

The text is also crippled by a tasteless dialect.  Dialogue is peppered with kids calling each other “Unit” — whereas the parents still use the future-outdated “dude”.

Not recommended!

July 23, 2010

tesseract, hypercube, 4-cube (via divergencetheorem)

Mortgages

July 21, 2010

Americans owe $11 trillion on their mortgages.

SOURCE: Wired 2/23/09