Pauli Giveth and Pauli Taketh Away

Ask Ethan #36: The Amazing Spinning Electron

Nice illustration of symmetric vs antisymmetric states and why one forms bonds while the other does not.

Even though we have no way of distinguishing one electron from another (because they’re identical), each atomic system is unique. In other words, if I have four different hydrogen atoms in the ground state, they’re not going to be required to occupy different energy states.


A Million Prescient Monkeys

A History of Books that Forecast the Future

As interesting as this is, it’s also an example of selection bias. Also: 2013 is the year for government spying on individuals, like this wasn’t happening earlier? really? But I digress…

Lots of stories appear to make predictions of the future, but are they really predictions or just fanciful things thought up by the author? What sci-fi devices haven’t come to pass? (How many have flying cars or superluminal travel of some sort, etc.?) That’s context that’s missing, because looking only at successful predictions (more on that in a moment) is the wrong way to look at it. If the author is truly a visionary maker of predictions, s/he has to be right more often than chance. It’s tough to measure that in an open-ended medium like storytelling, but one could at least do a systematic measure of it. Regardless, with myriad predictions, some are bound to be right. So what’s the success rate?

Also, how do you define success? For predictions that are vague it’s much easier to argue that it was successful, but of course vague predictions are next to useless precisely because they are vague. This is one element of how so-called psychics and their ilk make their livings – be vague enough that you can throw up your hands and declare success no matter what happens. I’m not familiar enough with the stories to know how much leeway the authors are being given.

The next step and the real trick — much harder IMO — is if the author was able to capture how society exploited the technology.

Spherical Tygers, Burning Bright

The Sacred, Spherical Cows of Physics

Oh, that fearful symmetry

Early in their training, many physics students come across the idea of spherical cows. Cows in the real world—even at their most plump and well-fed—are hardly spherical, and this makes it tricky to calculate things like, say, how their volume or surface area scales with their height. But students learn that these numbers are easy to calculate if they assume the cow is a perfect sphere, or in other words, that it has spherical symmetry. The lesson: Hard problems become easier when certain underlying (though approximate) symmetries are enforced.

It’s a very informative post, but it seems to me this introduction has little to do with the symmetry discussions that follow. A spherical cow approximation is less about applying symmetry than about physicists using approximations in an attempt at getting an answer that’s actually solvable and (one hopes) close enough to what nature says it is. An equation describing an actual cow shape would likely be exceedingly difficult to manipulate, for whatever problem you were trying to solve. So you approximate, and hope that whatever information is lost is negligible. That the shape is symmetrical incidental; the important point is that it’s simple — it’s also why we employ frictionless surfaces, perfectly elastic collisions and ignore numbers that are small compared to other numbers in a problem. I think the rest of the piece stands on its own without the spherical cow reference.