According to Nature, this is the "first true three-dimensional representations of the Mandelbrot set." It was created by computer programmer Daniel White from Bedford, UK. See more of his work, and get a full explanation of the Mandelbulb, on his site.

via Nature

Patrick J. Kiger, a journalist and blogger for the Science Channel, has been criticized for focusing on technologies in his column Is This a Good Idea? that currently exist only in the realm of speculative fiction. To answer those critics, Kiger looks at the recent study by mathematicians in Ottawa as to the best response to a zombie outbreak. What good, Kiger asks, is it to study a phenomenon that we know does not actually exist?

Kiger spends some time contemplating whether or not we might actually have to fear attacks from the flesh-eating undead, but ultimately, his point is that the possibility of a literal zombie attack is irrelevant to the value of such studies. Studying zombie attacks is valuable, he argues, precisely because they represent a level of crisis that we do not have any experience with, and our ability to logically respond to such a crisis:

But whether real or imagined, a zombie attack is a potent metaphor. Think of the undead not as klutzy cannibals but as the X factor, the Rumsfeldian "unknown unknown," the totally unexpected menace that suddenly confronts us. (The Canadian researchers' mathematical modeling of zombie attacks maybe seem like an elaborate joke, but in actuality it was led by a mathematician whose expertise is in studying the spread of actual epidemics such as malaria and West Nile Virus, and its underlying purpose was to demonstrate the progression of a rapidly spreading, unfamiliar public health threat.) In recent experience we've been confronted increasingly with such X factors, ranging from AIDS to terrorism to climate change. And time and again, we've been exposed as dangerously unprepared to deal with such paradigm-shattering threats. I'm not talking about stocking up on bottled water and Spam, having a battery-powered radio, a shotgun and the ingredients for Molotov cocktails. I'm talking about our societal tendency to do exactly what most of the characters in the Romero movies do when confronted with a zombie attack - i.e., to become hysterical and fight among themselves for control of the group, which ultimately leads to them squandering resources and opportunities for survival, and undermining each others' efforts. I think we need to find a way to tone down the cable TV news-induced histrionics and learn to cooperate towards a common objective, before some real menace arrives to do us in.

Is This A Good Idea? Preparedness for Zombie Attacks? [Discovery Blogs]

"In Case of Zombies" image from Threadless.

In a paper published in Infectious Disease Modelling Research Progress, a team of mathematicians from Carleton University and the University of Ottawa have created a series of mathematical models to explore the effects of a zombie outbreak and determine the best course for human survival. For the purpose of the paper, the team limited their models to the George Romero slow-moving zombies, and created separate models for zombie infections that cause the infected to resurrect immediately after contact with a zombie and for zombie infections with a 24-hour incubation period.

The paper examines three possible methods of dealing with a zombie outbreak: quarantine of the zombies, treatment of zombies so that they once again become human, and impulsive eradication of the zombies whenever possible. The models found that quarantine could work, but the end result would be either the eradication of all zombies or the eradication of all humans; if a cure for being a zombie were found, humans would coexist with zombies, but only in low numbers; but eradication, if properly coordinated, could wipe out the entire zombie population in a mere ten days.

Science has proved it: aim for the head, and kill without mercy.

When Zombies Attack!: Mathematical Modelling of an Outbreak of Zombie Infection [University of Ottawa]

If you've ever read Salem's Lot (or seen the lame Starsky and Hutch-era miniseries adaptation starring David Soul), then you know that after a vampire decides to settle in your town, the undead begin to multiply at an alarming rate (he bites two friends, who bite two friends, and so on, and so on…).

Putting aside for a moment the issue of how that would impact neighborhood property values, this phenomenon raises an even more pressing question: If vampires are indeed living (unliving?) among us, then shouldn't we have seen an undead population explosion by now?

Fortunately, our best minds are on the case. Physicists Costas Efthimiou and Sohang Gandhi's paper "Cinema Fiction vs. Physics Reality" offers a full explanation.

Efthimiou and Gandhi conduct a thought experiment: Assume that the first vampire appeared on January 1, 1600. At that time, according to data available at the U.S. Census website, the global population was 536,870,911. Efthimiou and Gandhi calculate that, once the Nosferatu feeding frenzy began, the entire human race would have been wiped out by June 1602 (thus forever changing the course of history by preventing the invention of the slide rule eighteen years later).

The physicists note:

Another philosophical principal related to our argument is the truism given the elaborate title, the anthropic principle. This states that if something is necessary for human existence, then it must be true since we do exist. In the present case, the nonexistence of vampires is necessary for human existence. Apparently, whomever devised the vampire legend had failed his college algebra and philosophy courses.

Oooh, snap! But, this gauntlet had been barely thrown down before it invited a rebuttal from mathematician Dino Sejdinovic. In his article, "Mathematics of the Human Vampire Conflict" (Math Horizons, November 2008) Sejdinovic faults Efthimiou and Gandhi's logic, since they have not "accounted for the birth-rate of non-vampires and death-rate of vampires (actually the death-death-rate since they are already dead, but when they die again they should stay dead but stop being living) due to close encounters with stakes, garlic and holy water." Moreover, "vampires are presented exclusively as greedy consumers: a rational strategy of managing their human resources is not considered."

Here, Sejdinovic cites the pioneering research conducted by Austrian mathematicians Richard Hartl and Alexander Mehlmann, who published the landmark 1982 paper, "The Transylvanian Problem of Renewable Resources," later followed up by "Cycles of Fear: Periodic Bloodsucking Rates for Vampires" (Journal of Optimization Theory and Application, December 1992). Hartl and Mehlmann argue that vampires would never be stupid enough to deplete their entire food supply, and by applying the Hopf-Bifurcation Theorem (don't ask), they demonstrate how vampires can adopt an optimal "cyclical bloodsucking strategy."

However, there is a serious flaw in the Hartl and Mehlmann model: The assumption that human beings would be docile prey. Their research provoked an outraged response from economist Dennis Snower, who in his article "Macroeconomic Policy and the Optimal Destruction of Vampires" (The Journal of Political Economy, June 1982), declared:

One wonders what conceivable interest the authors could have had in helping vampires solve their intertemporal consumption problem. The implicit assumption of the Invisible Hand (or Fang)-whereby vampires, in pursuing their own interests, pursue those of human beings as well-is of questionable validity. The study by Hartl and Mehlmann is not concerned with the macroeconomic implications of blood-sucking behavior modes. Nor does it consider the policy instruments whereby human beings can protect themselves from vampires. Instead, humans are modeled as passive receptacles of blood whose cultivation and harvest are left to vampire discretion.

Hooyah! Snower argues that the mortal world can manage its resources in a manner that keeps the undead population in check, while simultaneously promoting long-term economic growth:

A transfer of labor services from the widget sector to the stake sector reduces human welfare at present but may raise welfare in the future (since an increase in stake production reduces the vampire population and thereby increases the future labor force whereby future widgets may be produced).

Still, I'm not entirely confident in Snower's conclusions-not least because his complex mathematical proof indicates that the complete destruction of vampires would not be "socially optimal." (And you wonder why economics is known as the dismal science?)

In fact, all of these models rest upon the assumption that vampires are at the top of the undead food chain. Who says that the blood-sucking population is not kept in check by something that preys on vampires? Time to consult the zoology journals.

Mark Strauss is a senior editor at Smithsonian magazine.

• Babbage had a life-threatening fever when he was 8 years old, and the parents ordered that his "brain was not to be taxed too much." Babbage later thought that this left him free to daydream, which led to his computers.
• Babbage was later schooled at the Holmwood Academy, which only had 30 students. They also had a massive library, with many books focused on mathematics, which he fell in love with.
• He worked on calculating machine designs from other inventor/mathematicians like Blaise Pascal, Wilhelm Schickard, and Gottfried Leibniz. All of these men had designed working calculators from the 1500s on. In Shickard's case, he had invented a calculating machine called "The Speeding Clock" that could work with six-digit numbers and would ring a bell to indicate memory overflow. It was later destroyed in a fire, but a working replica was constructed in 1960.
• Babbage himself first proposed building a "calculating engine" with much more capacity in 1822, and he went on to design several machines which he called "Difference Engines." Sadly, they were never built because of their enormous size, cost, and also because Babbage's personality frequently clashed with investors. Also, in 1827, Babbage's father, wife, and two of his sons died... all in the same year. He had a resulting mental breakdown which further delayed any construction or design.
• The first Difference Engine design had over 25,000 parts, would have been eight feet high, and would have weighed 15 tons. It was never fully completed during his lifetime, although different sections were later assembled and shown to work by his son, Henry Provost Babbage, after he inherited them.
• Babbage revised his designs for the Difference Engine No. 2, although this was never built during his lifetime either. In 1989, the London Science Museum began constructing one from his designs, and it was completed in 1991. It has 8,000 parts of bronze, cast iron and steel, weighs five tons and measures eleven feet long and seven feet high.
• Only two versions of this Engine exist: the one built for the London Science Museum, and a second one that was built by the museum on special commission for millionaire Nathan Myhrvold.
• The first completed Difference Engine No. 2 performed its first calculation in 1991, and returned results to more than 31 digits. That's more than your souped-up pocket calculator.
• A separate printing unit that Babbage designed was constructed for the Engine in 2000 and didn't need USB a to b cables or a serial interface. Pretty fancy stuff for the 19th Century.
• Babbage improved on his Difference Engine ideas again by working on plans for an Analytical Engine that could be reprogrammed by inserting programs on punch cards into the machine. This was the first programmable computer, which later led to other scientists improving on these ideas and eventually to the modern computer.
• Besides working on engines and calculating machines, Babbage also served as a mathematics professor at Cambridge for many years, won a Gold Medal from the Royal Astronomical Society, working on railroad rail gauges, invented uniform postal rates, ran for Parliament, worked in cryptography, and also invented the "pilot" (better known as a cow-catcher) that was mounted on the front of locomotives to "push" cows off the tracks to help prevent derailings.
• Babbage also didn't suffer from what he called public nuisance very well, either. He published "Observations of Street Nuisances" in 1864, which was a summary of 165 nuisances that he observed over 80 days. He also wrote "Table of the Relative Frequency of the Causes of Breakage of Plate Glass Windows" after counting the broken windows on a nearby factory.
• On a side note, growing up in Dallas, Texas, I used to beg my parents to take me to a little software shop to buy computer games. It was called Babbage's. Today it's better known as GameStop, but I still have a soft spot for that geeky little store.
• To this date, Charles Babbage's brain is preserved in a glass jar at the London Science Museum, just awaiting the perfect moment for reanimation.