Same mind, different universes…the Earth as the Kim Kardashian of our solar system ….

Workout notes
6.1-6.2 mile “run” in 1:04 (hilly; two Cornstalk loops plus a mini-loop). The leg didn’t hurt until 48 minutes or so. It was cold (sub freezing) and sunny. Then I stretched for about 10-15 minutes as I slept through yoga class.

Quantum Mechanics and its relation to classical mechanics
This is a nice, somewhat non-technical but not insultingly so discussion of quantum mechanics and the role of probability.

This is a longer article but I really love the following paragraph:

It’s even easier to understand why humans don’t “get” QM. Our brains evolved according to selection pressures that involved only macroscopic objects like fruit, tigers and trees. We didn’t have to develop neural circuitry that had an intuitive feel for quantum interference phenomena, because there was no evolutionary advantage to doing so. Freeman Dyson once said that the book of the world might be written in Jabberwocky, a language that human beings were incapable of understanding. QM is not as bad as that. We CAN understand the language if we’re willing to do the math, and if we’re willing to put aside our intuitions about how the world must be, in the same way that we understand that our intuitions about how velocities add are only an approximation to the correct rules given by the Lorentz group. QM is worse, I think, because it says that logic, which our minds grasp as the basic, correct formulation of rules of thought, is wrong. This is why I’ve emphasized that once you formulate logic mathematically, QM is an obvious and inevitable consequence. Systems that obey the rules of ordinary logic are special QM systems where a particular choice among the infinite number of complementary QM observables remains sharp for all times, and we insist that those are the only variables we can measure. Viewed in this way, classical physics looks like a sleazy way of dodging the general rules. It achieves a more profound status only because it also emerges as an exponentially good approximation to the behavior of systems with a large number of constituents.

Emphasis mine. Note: our poor underpowered minds don’t come naturally to this; I’ve read that our minds didn’t evolve to do mathematics. They evolved to tell us to come in out of the rain and to tell us how to find berries and how to avoid getting eaten by tigers.

Speaking of mathematics, this is a very interesting article about the volumes of n-balls (the region in n-space bounded by the traditional n-1 sphere which would have coordinate equations .

The upshot: as the dimension increases, the volume (hypervolumes) actually decreases with after .

There is this graph which shows this:

Astronomy
Here is a chart of the various moons:

Note that the moon to planet ratio of the earth and its moon is quite large; remember how big Jupiter and Saturn are. You might say that the earth is the Kim Kardashian of our solar system (large “moon” to “overall size” ratio):

Of course this photo reminds me of this recent Onion article: call it a “Safe FAP” alarm (via the Onion)

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