It's a lot less mathematically tractable than the "homogeneous population" model, so you can't just throw calculus at it. AFAIK there haven't been any good empirical studies, but I don't follow the literature so I could be off-base. I would naïvely expect that someone's tried Monte Carlo or other computer simulation methods? Again, not familiar with the literature so I'm unqualified to comment further.

Yes. The measles herd immunity threshold for the MMR vaccine is 92-94%. If more than 6% of the idiots around you go unvaccinated, measles becomes likely to spread among people who have already taken the vaccine or otherwise acquired immunity.

The reason is simple: the immune system is random. The B cells in each vaccinated individual produce different antibodies in response to the same antigen. Since an antibody's response to antigen X1 doesn't correlate much with its response to antigen X2, and different lines of a disease have different antigens, no vaccine can be 100% effective. Any one person might have total immunity to some given line of the disease (called a "quasispecies"), yet be totally vulnerable to some other quasispecies whose antigens are invisible to the existing antibodies. Different people are vulnerable to different quasispecies, and there are thousands of quasispecies (grouped into 21 strains in the case of measles), so we usually just throw our hands up in the air and pretend that infection vulnerability is a wholly non-deterministic thing.

Herd immunity is the threshold where each infection produces, on average, one new infection. If the vaccination rate is above herd immunity, each infection produces less than one new infection (exponential decay). The outbreak reaches its peak quickly, then vanishes as the existing victims fight off the disease (or die). If the vaccination rate is below herd immunity, then each infection leads to more than one new infection (exponential growth). The outbreak then grows rapidly until so many people are already carrying the disease that the disease runs out of new hosts, reaching a new steady-state of one new infection per infection... at which point we say it has transformed from epidemic (an outbreak) to endemic (never going away on its own).

If vaccines were 100% effective, falling below the herd immunity threshold wouldn't be so worrisome for people who are vaccinated. True, among vaccine-refusing populations (and those who can't benefit from vaccines, e.g. babies, the very elderly, AIDS patients, and organ transplant recipients) the disease would perpetually rage, as there would be enough contact between vulnerable islands that the disease never quite burns out. But in reality (a) each person who is immunized has a small-but-nonzero chance of catching the infection (and passing it on), so everyone is potential virus-habitat regardless of vaccination status, and (b) more victims means larger viral population means more viral reproduction means creation of more quasispecies. More quasispecies means that, if there is some way that the antigens can change that will give the disease access to new victims without compromising the disease's ability to spread, evolution will find and exploit it sooner rather than later, so the virus can get its grubby little capsid proteins on fresh meat that other strains can't touch (i.e. you).

What we're seeing in Texas is an outbreak in an overall US population where vaccination rates are falling, but still above the herd immunity threshold... for now. If rates continue to fall, we can expect these outbreaks to become larger and more frequent, until they eventually reach criticality and the end of one outbreak always overlaps the beginning of the next, i.e. the disease becomes endemic again.

(Pertussis is also stupid contagious and thus has a high threshold for herd immunity, but pertussis is about 10 times more likely to kill a baby than measles is. Like measles, pertussis is also seeing big ugly outbreaks these days: the Denver metro area, Northern California around Marin, Washington state, i.e. basically the places where the cultish and vaccine-refusing Waldorf School has a notable presence. Annoyingly enough, the DPT and TDaP vaccines was never even implicated in the original Wakefield autism-vaccine nonsense, yet the vaccination rates have been falling about as dramatically as those of MMR, probably because Wakefield's "MMR is bad (and here's a patented replacement vaccine, no payola I promise!)" got simplified into "vaccines are bad" in the US's celebrity-worshipping mass media echo chamber.)

Back when I was living in Wichita, Kansas, one of the few nice things about the area was the Cosmosphere, a shockingly out of place top-notch aerospace museum in nearby retirement town Hutchinson. It has a decommissioned SR-71 hanging from the ceiling in the lobby. I'm not by any means an aircraft geek, but even I have to stop and mumble "that is a gorgeous plane".

The LZW patents were the impetus for PNG, but PNG is superior in every possible way... except that PNG skipped animation, because animated GIFs didn't seem like an important use case to support. (As I recall, their primary use at the time was badly pixelated spinning red alarm lights on Geocities pages.)

FASCIA is actually a real word: the name for the thin sheets of connective tissue that bundle other tissues into tubes. It's not uncommon for someone with arch support problems to pull or tear a muscle fascia in their foot. More ominously, fasciae have previously made it into the news by way of "flesh-eating disease" (necrotizing fasciitis), which is where a bacterial infection (esp. strep or staph) breaches the superficial fascia and uses it to spread quickly under the skin, faster than the immune system can pin it down and mount a credible threat.

The Periodic Table isn't a model, or at least not a functional model. It's a chart - a way to represent data.

It's more than a chart. A table is not just a way to represent data; a simple list of all items in random order can represent the data just as well as a table can. A table is a way to organize data -- by spotting patterns, identifying which patterns are most important, then arranging the items to highlight those patterns. By choosing which patterns are important, you are implicitly constructing a model of what the items in the table are.

The Mendeleev-derived periodic table has done quite nicely for us: it predicted the properties of many elements long before we actually isolated them, and it was doing so well before we understood that the patterns highlighted by the table (the table's implicit model) were ultimately caused by the arrangement of electrons into quantum-mechanical energy-level shells by way of Pauli exclusion, with the arrangement of elements in each row directly dependent on the quantized degrees of freedom in each shell's energy level (hence the 2*[1], 2*[1+3], 2*[1+3+5], 2*[1+3+5+7] pattern in the table's row widths). Think of the table as a quick first-order approximation to the deeper equations needed to compute the true physics, such as the energy of a filled d-orbital in the third electron shell. A more complex table with an extra dimension or two of symmetry might be able to capture more patterns, giving us a more detailed model that produces better, more subtle approximations than the Mendeleev-derived model can yield; yet that new model would still bypass the tough work of calculating how electrons actually behave when packed around a single nucleus. (Or perhaps we could capture some symmetry affecting how an atom forms molecular bonds, or a nucleon symmetry that gives better predictions of stability and half-life or that better captures why the stable proton:neutron ratio isn't a perfectly smooth curve.)

... and, uh, "praise" is not the word to describe what my co-workers are saying about the movie.

Go read "What Colour are your bits?".

This is, of course, why XCB has taken the Linux universe by storm and everyone has abandoned toolkits like GTK in favor of the unicorns and puppies that XCB brings us. Everyone loves atoms, pixmaps, and server-side bitmap fonts.

What's holding up the plane in the first place, giving the chair the potential energy to shatter on the ground below? Oh, right, the electrostatic repulsion of the electrons in the air pushing against the electrons in the plane's wing.

Seriously, though: gravity is 10,000,000,000,000,000,000,000,000,000,000,000,000 times weaker than the electromagnetic force.

Both decay 1/d^2, but the chair is electrically neutral (or very close to it), while the Earth is pulling against you with the full might of 10^24 kg of gravitational charge. Because the chair is neutral, it can only hold you up with the residual electromagnetic force, i.e. the fact that electrons and protons aren't evenly smeared throughout the atom's interior, and that's an incredibly weak effect compared to the actual electromagnetic force.

(This, by the way, is why the Electric Universe cranks inhabiting Slashdot are so off-base. Do they really think nobody would notice the un-subtle effects of a force 10^37 times more powerful than gravity?)

I was simplifying things for the audience, and wasn't even remotely about to bring up frame dragging. That said, I'm an interested layman who's never taken a physics class touching GR so correct me if I'm totally off-base, but I'm pretty sure that Hawking's conclusion was initially solved for Schwarzschild black holes, and if so the ergosphere around Kerr black holes clearly doesn't come into it. The region between the photon sphere and the event horizon has no stable orbits, but wouldn't there still be some trajectories that would send a particle out past the photon sphere? (On a more circuitous path than a straight line, I mean.) And the Wikipedia article for the photon sphere says that "[a]ny orbit that crosses [the photon sphere] from the inside escapes to infinity".

I will admit to never having plugged numbers into a tensor equation in my life, so I could be totally bullshitting here.

Both the particle and the antiparticle are affected equally by gravity, but gravity is the weakest force in nature. Think about it: a simple chair, held together by the electromagnetic force, supports you above the ground by counteracting the gravitational attraction of the entire Earth pulling you down.

Since virtual particle pairs start from vacuum, they are always created with equal but opposite momentum. This momentum can't be very big because the attraction between the pair (usually electromagnetic) has to be strong enough to quickly counteract that initial momentum (and bring the particles back together fast enough for them to still count as "virtual"). But just because the momentum can't be very big doesn't mean it can't be big enough for one particle to escape a black hole, if the particles happen to pop into existence with one of them pointing in just the right direction to escape. Hawking predicts that the odds are 50/50 on whether it's the matter particle or the antimatter particle that does the escaping; it has nothing to do with the particles responding differently to gravity.

(Keep in mind that the escaping particle doesn't have to rocket out in a straight line at escape velocity. Instead, it can take a few swings around the black hole in a rapidly decaying orbit, until it slingshots out on a hyperbolic path. The smaller the black hole gets, the more definite the position is for every matter/antimatter particle pair, and by Heisenberg's uncertainty principle applied to position-momentum, this makes it easier for one of the two particles to escape. A smaller black hole also has the bonus that, looking out from just above the event horizon, more directions point away from the black hole, giving more chances to escape.)

You could actually make a black hole that radiates away Hawking radiation with a bias toward antimatter over matter, or vice versa. It's easy: black holes can have an electric charge, so just electrically charge the black hole! Like charges repel, so if the black hole is positively charged, it will preferentially eject positrons instead of electrons. However, the absorbed electrons neutralize the black hole's electric charge, bringing it back to neutral and making the Hawking radiation return to a 50/50 ratio between matter and antimatter.

(We suspect that the universe has a small preference for matter over antimatter, and this is why the universe is made of matter. But this mostly happens for some heavy uncharged mesons, not for lightweight simple particles like electrons. Here, "heavy" means "high energy" means "unlikely to appear in Hawking radiation". So the radiation may not strictly be 50/50, but it should be very close.)

I grew up in the Wichita, Kansas area with Tibicen pruinosa. Here's a YouTube video of one singing.

One year (summer of '98?) the cicadas emerged in such numbers that they refused to stop singing at night. A wall of sound, blaring like a siren 24 hours a day, so loud you couldn't escape it indoors. After the first 50 kills on the front porch, my cats didn't know what to do with themselves. Tibicen is an annual genus, so I can only assume that the previous year's generation had simply been... busy.

What does "genetically male" mean? 46,XY? Congratulations, you just excluded men with 47,XXY (Klinefelter syndrome) and 47,XYY (XYY syndrome) as "not male". Presence of a Y chromosome? Congratulations, women with 46,XY who lack the SRY gene (Swyer syndrome) are now "male". Presence of the SRY gene? Congratulations, 46,XY women with SRY but non-functional testosterone receptors (CAIS, complete androgen insensitivity syndrome) are now "male". And those are merely some of the conditions that are diagnosed by hormones and genitalia, without even looking at the giant ball of complexity that is the brain.

Self-identification of gender isn't bullshit 70's pop psychology. It's a practical consideration: science doesn't currently know what triggers male versus female identity in the brain. We know there's a surge of prenatal testosterone in the male fetus, followed by another testosterone surge a few weeks after birth, and that these two surges seem to trigger changes in the brain, but beyond that... hell if we know. We don't even know to what degree male identity is controlled by those testosterone surges versus direct action of SRY, or how many specific biological components there are in the brain that need to be affected. We don't know which circuits in the brain control self-identity ("I am a man/woman") versus proprioception ("my mental body map expects to receive sense data from male/female genitals") versus presentation ("other people see my behavior as feminine/masculine") versus orientation ("I am attracted to women/men"), if there are other categories than the ones I listed, where the lines are between these categories, or how blurry those lines are. Given how stable they are, we can infer that they're hardwired, which means that they must be phenotypes set during development; yet, the easiest way for a doctor to find out how genotype became phenotype in any particular patient is for the doctor to ask that patient to say their own gender identity.

Is it really "privacy" I'm guarding if I try to keep secrets from (a) a non-sentient computer program that (b) will never pass those secrets along to another human being (or even another non-sentient computer program at another company)?